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"forward" + }, + { + "time": 69, + "stage": 7, + "replica": 7, + "provider": "jp8", + "orientation": "backward" + }, + { + "time": 70, + "stage": 8, + "replica": 6, + "provider": "jp8", + "orientation": "forward" + }, + { + "time": 71, + "stage": 8, + "replica": 7, + "provider": "jp8", + "orientation": "forward" + } + ], + "profile": { + "1": 181864, + "2": 28660, + "3": 32256, + "4": 12092, + "5": 4612, + "6": 288, + "8": 576, + "44": 1, + "48": 2228 + }, + "live": 7168, + "rank_mass": 520704, + "deficit": 2560 +} diff --git a/research/kappa-packing-pr643-20261013/README.md b/research/kappa-packing-pr643-20261013/README.md new file mode 100644 index 0000000000..6541aa8cf0 --- /dev/null +++ b/research/kappa-packing-pr643-20261013/README.md @@ -0,0 +1,21 @@ +# Literal owner packing after PR643 + +Chi Zhao, with substantial OpenAI Codex assistance. Apache-2.0. + +This supplement starts from Jeremy Kothe's PR643 at `bbfa9fe1d84d5572f4d144c2ee56a3eddc7a83f5` and changes only owner assignments. The idle profile improves from `{12:1,32:1,48:2228}` to `{44:1,48:2228}`. Suppliers, widths, schedule, and dispatch remain unchanged: 71 JP8 calls and one JP8b call. These are the two verified versions used by the upstream twin-supplier package. + +A bounded integer CP-SAT model reassigns roles among 123 owners, permitting capacity48 owners to exchange which ones are empty. It leaves one gap of rank 44 and fills the previous empty capacity32 owner. The retained nomination changes 36 literal rows, including compaction offsets. All 35,424 roles pass the independent integer structural validator: complete role inventory, provider width, window eligibility, physical-family exclusions, interval capacity/nonoverlap, compact offsets, paid profile, rank mass 520704, and deficit 2560. + +The reproducible admission path needs only the Python standard library: + +```sh +python3 -I -O -B replay_owner_map.py --base-data /path/to/PR643/data --out /tmp/pr643-owner-export --negative-controls +``` + +The exporter checks pinned source bytes, applies the 36 recorded rows, verifies the entire map and canonical decompressed payload, and rejects duplicate-role, width, offset, and family corruptions. Regenerated gzip containers may differ across zlib versions; the decompressed canonical payload is the portability check. The enclosing witness independently rebuilds native suppliers and certifies the global moment and assembly. This supplement alone certifies ownership and the resulting paid profile. + +`search_neighborhood.py` is optional nomination provenance, requiring OR-Tools 9.15. The retained solve is trial 11 with 123 owners, seed 123, four workers, and a three-second limit per trial. Its OPTIMAL status certifies feasibility of its constraints. A rerun may find a different map; the recorded changes provide deterministic reproduction. + +For these fixed supplier profiles, widths, dispatch and capacity cap48, total idle rank is 106988 = 2228×48 + 44. For every 0 < q < 1, concavity of `r**(1-q)` implies the smallest idle moment under this cap is attained by this maximally concentrated profile. Our literal map attains that relaxed bound and therefore the constrained packing optimum for this fixed setup. This does not bound different suppliers, dispatch or geometry. + +PR643's supplier words, twin dispatch, and starting map are credited to Jeremy Kothe (`jeremykothe2`). Inherited constructions include Jeremy Diviney's PR627 and Jeremy Kothe's PR629. This supplement claims the ownership change, by Chi Zhao with substantial OpenAI Codex assistance. diff --git a/research/kappa-packing-pr643-20261013/SEARCH.json b/research/kappa-packing-pr643-20261013/SEARCH.json new file mode 100644 index 0000000000..8ffd92acdb --- /dev/null +++ b/research/kappa-packing-pr643-20261013/SEARCH.json @@ -0,0 +1,16 @@ +{ + "schema": 1, + "method": "exact integer CP-SAT owner reassignment with exchangeable empty capacity48 owners", + "base_pr": 643, + "seed": 123, + "trial": 11, + "owners_in_winning_neighborhood": 123, + "workers": 4, + "seconds_per_trial": 3, + "status": "OPTIMAL feasibility", + "target_idle": { + "44": 1, + "48": 2228 + }, + "scope": "Search may nominate different literal maps on rerun. Deterministic acceptance uses recorded row changes and exact structural validation." +} diff --git a/research/kappa-packing-pr643-20261013/SOURCE.json b/research/kappa-packing-pr643-20261013/SOURCE.json new file mode 100644 index 0000000000..58d3fad0dd --- /dev/null +++ b/research/kappa-packing-pr643-20261013/SOURCE.json @@ -0,0 +1,21 @@ +{ + "schema": 1, + "author": "Chi Zhao", + "assistance": "Substantial OpenAI Codex assistance", + "license": "Apache-2.0", + "base": { + "repository": "jeremykothe2/integer-mult-bounds", + "pr": 643, + "commit": "bbfa9fe1d84d5572f4d144c2ee56a3eddc7a83f5", + "package": "research/complex-571-cold14-twin", + "plan_sha256": "ad36aaa7347dba4a28cf42efdcc6db14b3fca94f1d5c008af1dd3db040951af2", + "owners_sha256": "eeecd3a817965f342400aa40e85cb2695c04495f81abb047cea500953af1d81e" + }, + "target_owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", + "target_owners_content_sha256": "1351a8a87e83dd67fec90bc27566d6ec9278585d2435535e367aeea42a0688ef", + "moves_sha256": "2a4ec3d939039518b51904a35356e7b48bb6beb4f5cbb9a584c72ad868323a17", + "template_sha256": "6763d6fb8c2c9bffe8d64f899f97fb8907963f4b71f8d61304d924343dd99536", + "changed_literal_rows": 36, + "roles": 35424, + "scope": "Owner reconstruction only; native provider rebinding and full conditional exponent require the enclosing supplier replay." +} diff --git a/research/kappa-packing-pr643-20261013/STRUCTURAL.json b/research/kappa-packing-pr643-20261013/STRUCTURAL.json new file mode 100644 index 0000000000..0c6a121550 --- /dev/null +++ b/research/kappa-packing-pr643-20261013/STRUCTURAL.json @@ -0,0 +1,30 @@ +{ + "roles": 35424, + "idle_profile": { + "44": 1, + "48": 2228 + }, + "profile": { + "1": 181864, + "2": 28660, + "3": 32256, + "4": 12092, + "5": 4612, + "6": 288, + "8": 576, + "44": 1, + "48": 2228 + }, + "rank_mass": 520704, + "dispatch": { + "jp8": 71, + "jp8b": 1 + }, + "owners_content_sha256": "1351a8a87e83dd67fec90bc27566d6ec9278585d2435535e367aeea42a0688ef", + "negative_controls": [ + "duplicate", + "width", + "offset", + "family" + ] +} diff --git a/research/kappa-packing-pr643-20261013/replay_owner_map.py b/research/kappa-packing-pr643-20261013/replay_owner_map.py new file mode 100644 index 0000000000..228ec06a57 --- /dev/null +++ b/research/kappa-packing-pr643-20261013/replay_owner_map.py @@ -0,0 +1,149 @@ +#!/usr/bin/env python3 +"""Reconstruct the literal owner map from pinned PR643 and recorded changes. +Chi Zhao, with substantial OpenAI Codex assistance. Apache-2.0. +No solver, floating objective, or Python assertions are used for admission. +""" +import argparse +from collections import Counter, defaultdict +import copy +import gzip +import hashlib +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def sha(data): + return hashlib.sha256(data).hexdigest() + + +def key(row): + return row['time'], row['helper'] + + +def validate(rows, template): + roles = set() + families = defaultdict(set) + occupied = defaultdict(set) + registry = template['provider_registry'] + calls = template['provider_calls'] + for row in rows: + t, helper = key(row) + require(isinstance(t, int) and 0 <= t < len(calls), 'invalid time') + call = calls[t] + require(call['time'] == t, 'call order mismatch') + widths = registry[call['provider']]['widths'] + require(isinstance(helper, int) and 0 <= helper < len(widths), 'invalid helper') + require((t, helper) not in roles, 'duplicate role') + roles.add((t, helper)) + stage, replica = template['order'][t] + require((row['stage'], row['replica']) == (stage, replica), 'role chronology mismatch') + require((call['stage'], call['replica']) == (stage, replica), 'call chronology mismatch') + owner, child, port = row['owner_replica'], row['child'], row['port'] + require(isinstance(port, int) and 0 <= port < 112, 'invalid port') + win_key = f'{owner},{child}' + require(win_key in template['windows'], 'invalid owner window') + cap, eligible = template['windows'][win_key] + require(t in eligible, 'time outside owner window') + require(row['width'] == widths[helper], 'helper width mismatch') + family = owner * 896 + (2 * template['pairs'][str(child)] + template['sides'][str(child)]) * 112 + port + require(row['family'] == family and row['copy'] == owner * 112 + port, 'owner identity mismatch') + require(family not in families[t], 'physical family reused in call') + families[t].add(family) + off, width = row['offset'], row['width'] + require(isinstance(off, int) and off >= 0 and off + width <= cap, 'interval exceeds owner') + cells = set(range(off, off + width)) + index = (owner, child, port) + require(not occupied[index] & cells, 'overlapping intervals') + occupied[index].update(cells) + expected = {(t, h) for t, call in enumerate(calls) + for h in range(len(registry[call['provider']]['widths']))} + require(roles == expected, 'missing or extra role') + idle = Counter() + for win_key, (cap, _) in template['windows'].items(): + owner, child = map(int, win_key.split(',')) + for port in range(112): + cells = occupied[owner, child, port] + require(cells == set(range(len(cells))), 'owner intervals are not compacted') + if len(cells) < cap: + idle[cap - len(cells)] += 1 + profile = Counter() + for call in calls: + profile.update({int(r): n for r, n in registry[call['provider']]['actual_paid_profile'].items()}) + profile.update(idle) + require(dict(profile) == {int(r): n for r, n in template['profile'].items()}, 'paid profile mismatch') + require(sum(r * n for r, n in profile.items()) == template['rank_mass'] == 520704, 'rank mass mismatch') + require(73 * template['live'] - template['rank_mass'] == template['deficit'] == 2560, 'deficit mismatch') + return dict(roles=len(roles), idle_profile=dict(sorted(idle.items())), + profile=dict(sorted(profile.items())), rank_mass=520704, + dispatch=dict(Counter(c['provider'] for c in calls))) + + +def negative_controls(rows, template): + mutations = [('duplicate', lambda r: r.append(copy.deepcopy(r[0]))), + ('width', lambda r: r[0].update(width=r[0]['width'] + 1)), + ('offset', lambda r: r[0].update(offset=1000)), + ('family', lambda r: r[0].update(family=-1))] + for name, mutate in mutations: + bad = copy.deepcopy(rows) + mutate(bad) + try: + validate(bad, template) + except ValueError: + continue + raise ValueError(f'negative control unexpectedly accepted: {name}') + return [name for name, _ in mutations] + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--base-data', type=Path, required=True, + help='data directory of exact pinned PR643 package') + parser.add_argument('--out', type=Path, required=True) + parser.add_argument('--negative-controls', action='store_true') + args = parser.parse_args() + source = json.loads((HERE / 'SOURCE.json').read_text()) + base_plan = (args.base_data / 'PLAN.json').read_bytes() + base_owners = (args.base_data / 'OWNERS.json.gz').read_bytes() + require(sha(base_plan) == source['base']['plan_sha256'], 'base plan pin mismatch') + require(sha(base_owners) == source['base']['owners_sha256'], 'base owners pin mismatch') + moves_data = (HERE / 'OWNER-MOVES.json.gz').read_bytes() + template_data = (HERE / 'OWNER-TEMPLATE.json').read_bytes() + require(sha(moves_data) == source['moves_sha256'], 'moves pin mismatch') + require(sha(template_data) == source['template_sha256'], 'template pin mismatch') + original = json.loads(gzip.decompress(base_owners)) + rows = {key(row): row for row in original} + require(len(rows) == len(original) == source['roles'], 'base role inventory mismatch') + moves = json.loads(gzip.decompress(moves_data)) + require(len(moves) == source['changed_literal_rows'], 'move count mismatch') + require(len({key(row) for row in moves}) == len(moves), 'duplicate recorded move') + for row in moves: + require(key(row) in rows, 'move refers to absent base role') + rows[key(row)] = row + rows = [rows[k] for k in sorted(rows)] + template = json.loads(template_data) + receipt = validate(rows, template) + if args.negative_controls: + receipt['rejected_controls'] = negative_controls(rows, template) + payload = json.dumps(rows, sort_keys=True, separators=(',', ':')).encode() + require(sha(payload) == source['target_owners_content_sha256'], 'reconstructed payload mismatch') + data = gzip.compress(payload, compresslevel=9, mtime=0) + data = data[:9] + b'\xff' + data[10:] + args.out.mkdir(parents=True, exist_ok=True) + (args.out / 'OWNERS.json.gz').write_bytes(data) + receipt.update(status='PASS_LITERAL_OWNER_EXPORT', owners_sha256=sha(data), + owners_content_sha256=sha(payload), + published_owners_sha256=source['target_owners_sha256'], + scope='Owner structure only; full native supplier and exact assembly replay remain required.') + (args.out / 'EXPORT.json').write_text(json.dumps(receipt, indent=2) + '\n') + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/kappa-packing-pr643-20261013/search_neighborhood.py b/research/kappa-packing-pr643-20261013/search_neighborhood.py new file mode 100644 index 0000000000..be61df67b1 --- /dev/null +++ b/research/kappa-packing-pr643-20261013/search_neighborhood.py @@ -0,0 +1,62 @@ +"""Bounded CP-SAT owner search. Chi Zhao with substantial OpenAI Codex assistance. Apache-2.0.""" +from ortools.sat.python import cp_model +from pathlib import Path +from collections import defaultdict,Counter +import json,gzip,random,time,hashlib,math +import argparse +ap=argparse.ArgumentParser();ap.add_argument('--base-data',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);args=ap.parse_args() +p=json.loads((args.base_data/'PLAN.json').read_text());rows=json.loads(gzip.decompress((args.base_data/'OWNERS.json.gz').read_bytes()));bins=defaultdict(list) +for i,r in enumerate(rows):bins[r['owner_replica'],r['child'],r['port']].append(i) +cap=lambda b:p['windows'][f'{b[0]},{b[1]}'][0] +allow=lambda b:set(p['windows'][f'{b[0]},{b[1]}'][1]) +gap=lambda b:cap(b)-sum(rows[i]['width']for i in bins[b]) + +for key in p['windows']: + r,ch=map(int,key.split(',')) + for port in range(112):bins[r,ch,port] +partial=[b for b in bins if 0 1. The positive root therefore lies in +(0,1), and the κ conversion q/(1+q) is monotone. This packing maximizes the +moment-limited exponent ceiling for these fixed inputs; other admission +conditions remain separate. The decimal κ is an exactly certified lower +bound, not the exact root. + +There are 16,128 owner segments of total capacity 387,072 and 280,084 required +helper-width units. This proof does not bound different suppliers, widths, +dispatch, scheduling geometry, or invoice conventions. diff --git a/research/pr643-improvement-20261013/README.md b/research/pr643-improvement-20261013/README.md new file mode 100644 index 0000000000..0e0f0d8921 --- /dev/null +++ b/research/pr643-improvement-20261013/README.md @@ -0,0 +1,38 @@ +# Fixed-dispatch packing improvement on PR643 + +Conditional **κ = 0.001636569158555067**, exceeding +[PR643](https://github.com/CrocSwap/integer-mult-bounds/pull/643) by +**0.000000026935112958**. The conservative bound is +**κ = 0.001636569155685695**. + +A 36-row owner reassignment combines idle gaps 12 and 32 into one gap of +44, retaining 2228 gaps of 48. Both native suppliers, helper widths, the +71-JP8/1-JP8b dispatch, call order, geometry and admission code are unchanged. +The [packing proof](FIXED-DISPATCH-PACKING-BOUND.md) shows this minimizes the +idle moment for these fixed inputs. Different suppliers and dispatch remain +possible avenues for improvement. + +The [portable witness](witness/README.md) contains all pinned dependencies. +The [owner supplement](../kappa-packing-pr643-20261013/README.md) reconstructs +the literal assignment from pinned PR643 inputs. Upstream is fixed at +`bbfa9fe1d84d5572f4d144c2ee56a3eddc7a83f5`. + +Exact binding, owner admission and its mutation controls, the finite invoice, +and both upstream moment engines passed. A separate checker recomputed both +actual native supplier profiles and widths, all 35,424 helper intervals, +and the strict rational moment inequality. The source and packing review +is retained in [validation/independent-review/](validation/independent-review/). +The final fresh candidate replay passed **58/58 stages** without reuse in 327.44 seconds, followed by all supplemental checks: independent native/owner/moment verification and five mutations, declarative reconstruction, exact owner reproduction and four mutations, and six U4 mutations. All 46 receipt artifacts and 58 stage logs were independently hash-checked. Full candidate and source replay archives are retained in validation. Execution was on macOS; no Linux replay is claimed. + +```sh +PYTHON=python3 sh research/pr643-improvement-20261013/witness/verify.sh /tmp/pr643-improved-fresh +``` + +Use Python 3.10+, a C++ compiler, Boost headers, and a new output directory. +The inherited all-size, compiler, common-label/mutable-source realization, +whole-call hosting, precision/tape/exact-recovery, analytic-transfer and bit +H1–H5 assumptions remain. This is finite conditional evidence. Prepared by +Chi Zhao with substantial OpenAI Codex assistance; upstream construction +and contributor credits are preserved in the witness. + +The replay used commit `15595d482fd0f2fe6baf4d623e0f8e8a6b8047ef`. Only the witness README and its manifest entry changed afterward; [DOCUMENTATION-UPDATE.json](DOCUMENTATION-UPDATE.json) records that all 313 other manifested inputs are unchanged. diff --git a/research/pr643-improvement-20261013/validation/EXECUTED-MANIFEST.json b/research/pr643-improvement-20261013/validation/EXECUTED-MANIFEST.json new file mode 100644 index 0000000000..9548914824 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/EXECUTED-MANIFEST.json @@ -0,0 +1,316 @@ +{ + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE.md": "3548f7ca53b2b5c80b1c593595b7f43c1ac7e6cc785a407451d39137c5008796", + "PROOF-COMMUTING-PREFIX.md": "59899b2a1a76d88275e57f983c0aea391dc2c7f1d2d66c33b92429be0a1cf5e1", + "PROOF-NOTE-R.md": "22312bb347bdf159e6a01a45c47675e6170d33b258e2fd9ed52aee88fb92c0ed", + "PROOF-NOTE.md": "f5737f0ab23dbf8f017d405dfe940a5ce6d423de175da5eb06b83903f91c1705", + "README.md": 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"1a0e92f610f96a5e642310a2823b152cf573c0d1630b9c174fcc8388d1ffd2a2", + "vendor/structural_gain/MANIFEST.json": "eb0499a927665a48a25355075dcb7dc76d0fc43c67ea6d311d9e0242b6d4a25d", + "vendor/structural_gain/README.md": "b9132c6bfa65a6a1187ace1f42b938dfeb1d1c7544bdb4c56b0a47409e2822d2", + "vendor/structural_gain/frontier-composition/combined-prefix-word/FULL-WORD.json.gz": "a6cd88224427bad6d00b6fbe1d201a2c09e496c90e2cecdc04d7f2ff11a4ba42", + "verify.py": "4c8dea601fe9255bd9fbbf7840d3bfacc3dcf0b1deaf7ffab467e3c10648a3b7", + "verify.sh": "e472bbca5d3f7398e1164271d55b7adc46cc2c557d7a9dff2b5a011a281a441b" +} diff --git a/research/pr643-improvement-20261013/validation/EXECUTED-README.md b/research/pr643-improvement-20261013/validation/EXECUTED-README.md new file mode 100644 index 0000000000..d6941ddb55 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/EXECUTED-README.md @@ -0,0 +1,23 @@ +# PR643 twin-supplier owner packing improvement + +This witness retains Jeremy Kothe's PR643 suppliers and changes the literal owner map: idle ranks 12+32 become 44. The exact admitted bound is κ = 1636569158555067/1000000000000000000 = **0.001636569158555067**, above pinned PR643's 0.001636542223442109. Dispatch remains 71 PR637 JP8 calls and one PR635 JP8 call (named jp8b); all 35,424 literal roles retain their window, family, width and disjoint-interval constraints. This does not claim an unrestricted optimum. + +Pinned predecessor: `jeremykothe2/integer-mult-bounds` commit `bbfa9fe1d84d5572f4d144c2ee56a3eddc7a83f5`, package `research/complex-571-cold14-twin`. Every Python file in `code/` and `verify.py` is byte-identical to that source. Six pinned dependencies are vendored unchanged. Source preservation is recorded in SOURCE-COMPARISON.json. + +## Reproduce + +Use Python >=3.10 with assertions enabled, a C++ compiler and Boost headers for the frozen baseline. Python admission uses the standard library. Choose a new output directory: + +```sh +PYTHON=python3 sh verify.sh /tmp/pr643-owner-replay +``` + +The wrapper rebuilds both suppliers and the baseline without reuse, then runs independent native-width/owner/rational checks and five mutations, declaration reconstruction, a portable owner exporter with four mutations, and six independent U4 mutations. Owner reproduction compares decompressed payloads. The full fresh candidate replay is pending at publication; its terminal evidence will be retained in the enclosing validation directory. Prepublication exact assembly and 114 admission controls passed using actual supplier outputs from an independently completed fresh PR643 replay. That baseline source replay passed all 58 stages without reuse; it is distinct from the candidate's fresh replay. + +`owner-search/README.md` documents the recorded export from pinned PR643 data. Solver output is nomination only. Inherited proof notes describe the unchanged supplier construction. Both orientations, arbitrary-dirt native scalar/frame behavior, exact phase edges and whole-provider identity bindings remain checked by the complete core replay. + +## Attribution and scope + +Chi Zhao prepared the owner repair, independent audit and portable package with substantial OpenAI Codex assistance. Jeremy Kothe (CarrierBypass) supplied PR643's twin dispatch and the PR635/637 suppliers, building on Jeremy Diviney's factored ends and earlier contributors retained in NOTICE.md. The separate interval checker retains Chafik Boukhalfa's PR626 exact interval engine. + +This is a conditional native exact-complex witness, not formal verification of the multiplication theorem or a measured implementation speedup. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape recovery, analytic transfer and bit H1–H5 premises remain. The inherited PR543 bit supplier is repriced rather than rebuilt. Publication does not assert that this is the latest unreviewed frontier. diff --git a/research/pr643-improvement-20261013/validation/EXECUTION-ENVIRONMENT.json b/research/pr643-improvement-20261013/validation/EXECUTION-ENVIRONMENT.json new file mode 100644 index 0000000000..fbcf1de790 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/EXECUTION-ENVIRONMENT.json @@ -0,0 +1,7 @@ +{ + "executed_commit": "15595d482fd0f2fe6baf4d623e0f8e8a6b8047ef", + "python": "3.14.8 (main, Sep 30 2026, 17:55:09) [Clang 21.0.0 (clang-2100.3.34.2)]", + "platform": "macOS-27.0.1-arm64-arm-64bit-Mach-O", + "wrapper_command": "PYTHON=/opt/homebrew/bin/python3 sh research/pr643-improvement-20261013/witness/verify.sh /tmp/pr643/owner-fresh", + "fresh_output": "/tmp/pr643/owner-fresh" +} diff --git a/research/pr643-improvement-20261013/validation/FRESH-REPLAY.tar.gz b/research/pr643-improvement-20261013/validation/FRESH-REPLAY.tar.gz new file mode 100644 index 0000000000..49dbd92ac1 Binary files /dev/null and b/research/pr643-improvement-20261013/validation/FRESH-REPLAY.tar.gz differ diff --git a/research/pr643-improvement-20261013/validation/FRESH-WRAPPER.log b/research/pr643-improvement-20261013/validation/FRESH-WRAPPER.log new file mode 100644 index 0000000000..ba17828323 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/FRESH-WRAPPER.log @@ -0,0 +1,156 @@ +RUN frozen558-full-replay +PASS frozen558-full-replay +RUN jp8_504-step0-cold_kernel-construction +PASS jp8_504-step0-cold_kernel-construction +RUN jp8_504-step0-cold_kernel-omissions +PASS jp8_504-step0-cold_kernel-omissions +RUN jp8_504-step1-multicut-construction +PASS jp8_504-step1-multicut-construction +RUN jp8_504-step1-multicut-omissions +PASS jp8_504-step1-multicut-omissions +RUN jp8_504-step2-frozen558_scalar_audits-static44 +PASS jp8_504-step2-frozen558_scalar_audits-static44 +RUN jp8_504-step2-frozen558_scalar_audits-rank5 +PASS jp8_504-step2-frozen558_scalar_audits-rank5 +RUN jp8_504-step3-joint_prefix-construction +PASS jp8_504-step3-joint_prefix-construction +RUN jp8_504-step3-joint_prefix-all-kernel-omissions +PASS jp8_504-step3-joint_prefix-all-kernel-omissions +RUN jp8_504-step3-joint_prefix-rank5-omissions +PASS jp8_504-step3-joint_prefix-rank5-omissions +RUN jp8_504-step3-joint_prefix-independent-joint-prefix-and-coverage +PASS jp8_504-step3-joint_prefix-independent-joint-prefix-and-coverage +RUN k-triangle-control-pr531-construct504 +PASS k-triangle-control-pr531-construct504 +RUN k-triangle-control-empty-schedule +PASS k-triangle-control-empty-schedule +RUN jp8-base-k_triangle-construction +PASS jp8-base-k_triangle-construction +RUN jp8b-step0-port_stage-construction +RUN jp8-step0-port_stage-construction +PASS jp8b-step0-port_stage-construction +RUN jp8b-step0-port_stage-native-audit +PASS jp8-step0-port_stage-construction +RUN jp8-step0-port_stage-native-audit +PASS jp8-step0-port_stage-native-audit +PASS jp8b-step0-port_stage-native-audit +RUN jp8-step1-port_stage-construction +RUN jp8b-step1-port_stage-construction +PASS jp8-step1-port_stage-construction +RUN jp8-step1-port_stage-native-audit +PASS jp8b-step1-port_stage-construction +RUN jp8b-step1-port_stage-native-audit +PASS jp8b-step1-port_stage-native-audit +PASS jp8-step1-port_stage-native-audit +RUN jp8b-step2-port_stage-construction +RUN jp8-step2-port_stage-construction +PASS jp8-step2-port_stage-construction +RUN jp8-step2-port_stage-native-audit +PASS jp8b-step2-port_stage-construction +RUN jp8b-step2-port_stage-native-audit +PASS jp8b-step2-port_stage-native-audit +PASS jp8-step2-port_stage-native-audit +RUN jp8b-step3-port_stage-construction +RUN jp8-step3-port_stage-construction +PASS jp8b-step3-port_stage-construction +RUN jp8b-step3-port_stage-native-audit +PASS jp8-step3-port_stage-construction +RUN jp8-step3-port_stage-native-audit +PASS jp8b-step3-port_stage-native-audit +PASS jp8-step3-port_stage-native-audit +RUN jp8b-step4-frame_regroup-construction +RUN jp8-step4-frame_regroup-construction +PASS jp8-step4-frame_regroup-construction +RUN jp8-step5-hyperplane_end-construction +PASS jp8b-step4-frame_regroup-construction +RUN jp8b-step5-hyperplane_end-construction +PASS jp8-step5-hyperplane_end-construction +RUN jp8-step5-hyperplane_end-controls +PASS jp8b-step5-hyperplane_end-construction +RUN jp8b-step5-hyperplane_end-controls +PASS jp8-step5-hyperplane_end-controls +PASS jp8b-step5-hyperplane_end-controls +RUN jp8-step6-cold_end-construction +RUN jp8b-step6-cold_end-construction +PASS jp8-step6-cold_end-construction +RUN jp8-step6-cold_end-controls +PASS jp8b-step6-cold_end-construction +RUN jp8b-step6-cold_end-controls +PASS jp8-step6-cold_end-controls +RUN jp8-all-columns-native-frames +PASS jp8-all-columns-native-frames +RUN jp8-both-reflected-ledgers +PASS jp8-both-reflected-ledgers +RUN jp8-independent-local-controls +PASS jp8-independent-local-controls +RUN jp8-normalized-wrappers +PASS jp8-normalized-wrappers +RUN jp8-all-phase-edges +PASS jp8b-step6-cold_end-controls +RUN jp8b-all-columns-native-frames +PASS jp8b-all-columns-native-frames +RUN jp8b-both-reflected-ledgers +PASS jp8b-both-reflected-ledgers +RUN jp8b-independent-local-controls +PASS jp8b-independent-local-controls +RUN jp8b-normalized-wrappers +PASS jp8b-normalized-wrappers +RUN jp8b-all-phase-edges +PASS jp8-all-phase-edges +PASS jp8b-all-phase-edges +RUN bind-providers +PASS bind-providers +RUN emit-controller +PASS emit-controller +RUN independent-controller-and-controls +PASS independent-controller-and-controls +RUN fresh-invoice +PASS fresh-invoice +RUN conservative-and-native-exact-assembly +PASS conservative-and-native-exact-assembly +RUN admission-controls +PASS admission-controls +RUN phase-timing-portability-controls +PASS phase-timing-portability-controls +RUN actual-recompression-and-rebound-controls +PASS actual-recompression-and-rebound-controls +{ + "status": "PASS_COLD14_NATIVE_COMPLEX_AND_CITED_BIT", + "kappa": "1636569158555067/1000000000000000000", + "kappa_decimal": "0.001636569158555067", + "complex_lower": "4098129769175658129/2500000000000000000000", + "bit_lower": "413456747036699736067/250000000000000000000000", + "conservative_kappa_decimal": "0.001636569155685695", + "conservative_complex_lower": "327850380958295199433/200000000000000000000000", + "global_profile": { + "1": 181864, + "2": 28660, + "3": 32256, + "4": 12092, + "5": 4612, + "6": 288, + "8": 576, + "44": 1, + "48": 2228 + }, + "provider_counts": { + "jp8": 71, + "jp8b": 1 + }, + "surcharge_model": { + "complex": false, + "bit": true + }, + "seconds": 327.43738016701536, + "reused": { + "baseline": false, + "locals": [] + }, + "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The frozen PR582 plain-joint-prefix, added-kernel and entrance-promoted provider dispatch with the new frame coalescences composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification." +} +PASS_INDEPENDENT_NATIVE_OWNERS_AND_MOMENT +PASS independent positive and five rejection controls +PASS declarative inputs and outputs reconstruct SPEC +{"dispatch": {"jp8": 71, "jp8b": 1}, "idle_profile": {"44": 1, "48": 2228}, "owners_content_sha256": "1351a8a87e83dd67fec90bc27566d6ec9278585d2435535e367aeea42a0688ef", "owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", "profile": {"1": 181864, "2": 28660, "3": 32256, "4": 12092, "5": 4612, "6": 288, "8": 576, "44": 1, "48": 2228}, "published_owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", "rank_mass": 520704, "rejected_controls": ["duplicate", "width", "offset", "family"], "roles": 35424, "scope": "Owner structure only; full native supplier and exact assembly replay remain required.", "status": "PASS_LITERAL_OWNER_EXPORT"} +PASS exact owner nomination payload +PASS_INDEPENDENT_U4_ISOLATION_FRAMES_AND_RESTORATION jp8 6 mutations rejected diff --git a/research/pr643-improvement-20261013/validation/INDEPENDENT-NATIVE-OWNERS.json b/research/pr643-improvement-20261013/validation/INDEPENDENT-NATIVE-OWNERS.json new file mode 100644 index 0000000000..820d764b84 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/INDEPENDENT-NATIVE-OWNERS.json @@ -0,0 +1,50 @@ +{ + "status": "PASS_INDEPENDENT_NATIVE_OWNERS_AND_MOMENT", + "roles": 35424, + "calls": 72, + "native_profiles": { + "jp8": { + "1": 2526, + "4": 168, + "8": 8, + "3": 448, + "2": 398, + "5": 64, + "6": 4 + }, + "jp8b": { + "1": 2518, + "4": 164, + "8": 8, + "3": 448, + "2": 402, + "5": 68, + "6": 4 + } + }, + "idle": { + "48": 2228, + "44": 1 + }, + "global_profile": { + "1": 181864, + "4": 12092, + "8": 576, + "3": 32256, + "2": 28660, + "5": 4612, + "6": 288, + "48": 2228, + "44": 1 + }, + "complex_lower": "4098129769175658129/2500000000000000000000", + "moment_lower": "105106603598892035942648398441366566653685356332048995262888980245/105106603598892035942648656535850763505772253417344913771392401408", + "moment_upper": "210213207197784071885296796882733133307370712664098043342945634785/210213207197784071885297313071701527011544506834689827542784802816", + "strict_margin_lower": "516188968393704173794170591784199839168031/210213207197784071885297313071701527011544506834689827542784802816", + "kappa": "1636569158555067/1000000000000000000", + "reference643_kappa": "1636542223442109/1000000000000000000", + "absolute_kappa_gain": "13467556479/500000000000000000", + "relative_kappa_gain": "8978370986/545514074480703", + "interval_engine_sha256": "aa3c2327c5d3742248b720a87b2de0bbe2e34ed2af89a578e3c8d5bd2656a9cf", + "scope": "Literal finite native profile and width/owner interval accounting with a separate rational moment engine; strict supplier/physical/phase/outer admission is checked by the separate full replay." +} diff --git a/research/pr643-improvement-20261013/validation/INDEPENDENT-OWNER-CONTROLS.json b/research/pr643-improvement-20261013/validation/INDEPENDENT-OWNER-CONTROLS.json new file mode 100644 index 0000000000..858c249962 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/INDEPENDENT-OWNER-CONTROLS.json @@ -0,0 +1,36 @@ +{ + "status": "PASS_INDEPENDENT_OWNER_CONTROLS", + "isolated_optimized": true, + "cases": [ + { + "name": "positive", + "status": "PASS", + "expected_reason": null + }, + { + "name": "wrong_width", + "status": "REJECTED", + "expected_reason": "actual width" + }, + { + "name": "duplicate_helper", + "status": "REJECTED", + "expected_reason": "helper uniqueness" + }, + { + "name": "wrong_family", + "status": "REJECTED", + "expected_reason": "physical family" + }, + { + "name": "wrong_profile", + "status": "REJECTED", + "expected_reason": "native plus idle profile" + }, + { + "name": "false_moment", + "status": "REJECTED", + "expected_reason": "strict exact moment" + } + ] +} diff --git a/research/pr643-improvement-20261013/validation/INDEPENDENT-RECEIPT-AUDIT.json b/research/pr643-improvement-20261013/validation/INDEPENDENT-RECEIPT-AUDIT.json new file mode 100644 index 0000000000..27074a8bf2 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/INDEPENDENT-RECEIPT-AUDIT.json @@ -0,0 +1,11 @@ +{ + "status": "PASS_INDEPENDENT_RECEIPT_AUDIT", + "wrapper_exit_code": 0, + "artifacts_verified": 46, + "stage_logs_verified": 58, + "all_exit_codes_zero": true, + "no_reuse": true, + "kappa": "1636569158555067/1000000000000000000", + "seconds": 327.43738016701536, + "manifest_sha256": "02cb97a60998646dcaa65920a25091a74c317b21490feed1abcb27e6e9b90084" +} diff --git a/research/pr643-improvement-20261013/validation/INDEPENDENT-U4-CONTROLS.json b/research/pr643-improvement-20261013/validation/INDEPENDENT-U4-CONTROLS.json new file mode 100644 index 0000000000..e7a983d513 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/INDEPENDENT-U4-CONTROLS.json @@ -0,0 +1,48 @@ +{ + "status": "PASS_INDEPENDENT_U4_ISOLATION_FRAMES_AND_RESTORATION", + "provider": "jp8", + "word_content_sha256": "b82c7888e7fad97b752cec3fd5be459df2ad35fdcdf15434beb04f4bf0c05922", + "ended_rows_columns": 68, + "new_ends": [ + 233, + 265, + 425, + 441 + ], + "new_terminal_rank": 8, + "climb_profile": { + "1": 2526, + "2": 398, + "3": 448, + "4": 168, + "5": 64, + "6": 4 + }, + "rejected_controls": [ + { + "name": "omit_transferred_premix", + "reason": "ended row isolation" + }, + { + "name": "flip_transferred_premix", + "reason": "ended row isolation" + }, + { + "name": "omit_new_accumulator", + "reason": "ended row isolation" + }, + { + "name": "double_new_accumulator", + "reason": "ended row isolation" + }, + { + "name": "duplicate_new_accumulator", + "reason": "ended row isolation" + }, + { + "name": "wrong_dim8_terminal", + "reason": "declared new terminal frame" + } + ], + "scope": "Separate Fraction replay of all ended row/column isolation and remaining non-target cleanup; GF2 monotone frames and paid climbs. Native compensation, wrappers, phases and global admission are separate." +} diff --git a/research/pr643-improvement-20261013/validation/OWNER-REPRODUCTION.json b/research/pr643-improvement-20261013/validation/OWNER-REPRODUCTION.json new file mode 100644 index 0000000000..6954d046e8 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/OWNER-REPRODUCTION.json @@ -0,0 +1,34 @@ +{ + "roles": 35424, + "idle_profile": { + "44": 1, + "48": 2228 + }, + "profile": { + "1": 181864, + "2": 28660, + "3": 32256, + "4": 12092, + "5": 4612, + "6": 288, + "8": 576, + "44": 1, + "48": 2228 + }, + "rank_mass": 520704, + "dispatch": { + "jp8": 71, + "jp8b": 1 + }, + "rejected_controls": [ + "duplicate", + "width", + "offset", + "family" + ], + "status": "PASS_LITERAL_OWNER_EXPORT", + "owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", + "owners_content_sha256": "1351a8a87e83dd67fec90bc27566d6ec9278585d2435535e367aeea42a0688ef", + "published_owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", + "scope": "Owner structure only; full native supplier and exact assembly replay remain required." +} diff --git a/research/pr643-improvement-20261013/validation/PINNED643-FRESH-AUDIT.json b/research/pr643-improvement-20261013/validation/PINNED643-FRESH-AUDIT.json new file mode 100644 index 0000000000..cf758dab82 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/PINNED643-FRESH-AUDIT.json @@ -0,0 +1,15 @@ +{ + "status": "PASS_FULL_FRESH_PINNED_PR643", + "commit": "bbfa9fe1d84d5572f4d144c2ee56a3eddc7a83f5", + "wrapper_exit_code": 0, + "stages": 58, + "artifact_hashes_checked": 46, + "log_hashes_checked": 58, + "seconds": 374.59400120799546, + "kappa": "0.001636542223442109", + "reused": { + "baseline": false, + "locals": [] + }, + "manifest_sha256": "22b6a169b52232164bee03c71d7832c493a158f245824652bd8c2dbcf9c1f6f2" +} diff --git a/research/pr643-improvement-20261013/validation/PINNED643-FRESH-REPLAY.tar.gz b/research/pr643-improvement-20261013/validation/PINNED643-FRESH-REPLAY.tar.gz new file mode 100644 index 0000000000..09d1959640 Binary files /dev/null and b/research/pr643-improvement-20261013/validation/PINNED643-FRESH-REPLAY.tar.gz differ diff --git a/research/pr643-improvement-20261013/validation/PINNED643-INDEPENDENT-FRESH-AUDIT.json b/research/pr643-improvement-20261013/validation/PINNED643-INDEPENDENT-FRESH-AUDIT.json new file mode 100644 index 0000000000..f64cbb0fd3 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/PINNED643-INDEPENDENT-FRESH-AUDIT.json @@ -0,0 +1,15 @@ +{ + "status": "PASS_INDEPENDENT_PR643_BASELINE_RECEIPT_AUDIT", + "receipt_sha256": "afb2c3ba814243633afb92a41ac5ae3fffa6389a5debf6718bfe2c1ef52d8bdc", + "result_sha256": "f1cc43fbb82bc7d683d0ab543f211dd7873f479f2d314872fca76a2105fff726", + "stages": 58, + "verified_stage_logs": 58, + "verified_artifacts": 46, + "kappa_decimal": "0.001636542223442109", + "seconds": 374.59400120799546, + "reused": { + "baseline": false, + "locals": [] + }, + "scope": "Baseline upstream643 freshcore receipt audit; owner44 improvement and final wrapper are separate." +} diff --git a/research/pr643-improvement-20261013/validation/PREPUBLICATION-ASSEMBLY-CONTROLS.json b/research/pr643-improvement-20261013/validation/PREPUBLICATION-ASSEMBLY-CONTROLS.json new file mode 100644 index 0000000000..95ee5f0de3 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/PREPUBLICATION-ASSEMBLY-CONTROLS.json @@ -0,0 +1,147 @@ +{ + "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS", + "valid_receipt_kappa": "1636569158555067/1000000000000000000", + "input_sha256": { + "owner_audit": "6386acc000c57299e67e6f7f9045df531d198734bfb2ac9be18e16341651147c", + "fresh_invoice": "861756e2faead9db3b86e0079fc3d2f5265c959282345ef6d97192ea1a14453e", + "inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d", + "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482", + "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098", + "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c" + }, + "assembler_sha256": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd", + "rejected_controls": [ + "empty_certification_maps", + "failed_invoice_status", + "nonboolean_precision_check", + "wrong_owner_role_count", + "understated_physical_stock", + "changed_profile_same_rank_mass", + "insufficient_finite_C0", + "missing_finite_check", + "wrong_reflected_orientation_selfconsistent_totals", + "missing_selected_call", + "wrong_selected_primitive_sum", + "wrong_selected_coefficient_work_sum", + "unpaid_wrapper_factors", + "wrong_global_compiler", + "wrong_global_adapter_maximum", + "understated_exact_prefix_and_global_sum", + "wrong_global_prefix_sum", + "wrong_row_prefix_reserve", + "wrong_parent_geometry_charge", + "wrong_rebased_geometry_charge", + "wrong_complete_pervertex_envelope", + "wrong_prior_added_complete_invoice", + "wrong_finite_router_bits", + "wrong_finite_literal_bits", + "wrong_finite_physical_stock_bits", + "wrong_finite_row_coefficient", + "reordered_complete_calls", + "understated_explicit_idle_remainders", + "understated_actual_chart_types", + "wrong_cross_replica_role_count", + "old_no_cold_wrapper_counts_selfconsistent", + "jp8:missing_provider", + "jp8:missing_backward_orientation", + "jp8:unpaid_scalar_primitive", + "jp8:wrong_local_artifact_binding", + "jp8:false_dirty_restoration", + "jp8:wrong_declared_provider_count", + "jp8:wrong_local_compiler", + "jp8:wrong_local_adapter_charge", + "jp8:wrong_local_primitive_bound", + "jp8:forged_provider_and_call_program_hash", + "jp8:provider_at_wrong_call", + "jp8:stale_partner_program_consistent_call_hashes", + "jp8:stale_partner_profile_consistent_child_total", + "jp8:relocated_against_partner_same_counts", + "jp8:compensating_false_profiles_with_jp8b", + "jp8:synchronized_forged_source_recipe_hash", + "jp8:synchronized_forged_phase_review_semantics", + "jp8:width_order_swap_4_5", + "jp8:width_inventory_shift_4_5", + "jp8:width_order_swap_4_7", + "jp8:width_inventory_shift_4_7", + "jp8:width_order_swap_4_8", + "jp8:width_inventory_shift_4_8", + "jp8:width_order_swap_4_9", + "jp8:width_inventory_shift_4_9", + "jp8:width_order_swap_5_7", + "jp8:width_inventory_shift_5_7", + "jp8:width_order_swap_5_8", + "jp8:width_inventory_shift_5_8", + "jp8:width_order_swap_5_9", + "jp8:width_inventory_shift_5_9", + "jp8:width_order_swap_7_8", + "jp8:width_inventory_shift_7_8", + "jp8:width_order_swap_7_9", + "jp8:width_inventory_shift_7_9", + "jp8:width_order_swap_8_9", + "jp8:width_inventory_shift_8_9", + "jp8:cold_helper_width_swap_264", + "jp8:cold_helper_width_swap_276", + "jp8:cold_helper_width_swap_288", + "jp8:cold_helper_width_swap_300", + "jp8b:missing_provider", + "jp8b:missing_backward_orientation", + "jp8b:unpaid_scalar_primitive", + "jp8b:wrong_local_artifact_binding", + "jp8b:false_dirty_restoration", + "jp8b:wrong_declared_provider_count", + "jp8b:wrong_local_compiler", + "jp8b:wrong_local_adapter_charge", + "jp8b:wrong_local_primitive_bound", + "jp8b:forged_provider_and_call_program_hash", + "jp8b:provider_at_wrong_call", + "jp8b:stale_partner_program_consistent_call_hashes", + "jp8b:stale_partner_profile_consistent_child_total", + "jp8b:relocated_against_partner_same_counts", + "jp8b:compensating_false_profiles_with_jp8", + "jp8b:synchronized_forged_source_recipe_hash", + "jp8b:synchronized_forged_phase_review_semantics", + "jp8b:width_order_swap_4_5", + "jp8b:width_inventory_shift_4_5", + "jp8b:width_order_swap_4_7", + "jp8b:width_inventory_shift_4_7", + "jp8b:width_order_swap_4_8", + "jp8b:width_inventory_shift_4_8", + "jp8b:width_order_swap_4_9", + "jp8b:width_inventory_shift_4_9", + "jp8b:width_order_swap_5_7", + "jp8b:width_inventory_shift_5_7", + "jp8b:width_order_swap_5_8", + "jp8b:width_inventory_shift_5_8", + "jp8b:width_order_swap_5_9", + "jp8b:width_inventory_shift_5_9", + "jp8b:width_order_swap_7_8", + "jp8b:width_inventory_shift_7_8", + "jp8b:width_order_swap_7_9", + "jp8b:width_inventory_shift_7_9", + "jp8b:width_order_swap_8_9", + "jp8b:width_inventory_shift_8_9", + "jp8b:cold_helper_width_swap_264", + "jp8b:cold_helper_width_swap_276", + "jp8b:cold_helper_width_swap_288", + "jp8b:cold_helper_width_swap_300", + "wrong_owner_receipt_hash" + ], + "discovery_accepted_controls": [], + "exact_outer_controls": [ + "next_grid", + "zero_eta", + "zero_beta", + "unit_beta" + ], + "conservative_outer_controls": [ + "next_grid", + "zero_eta", + "zero_beta", + "unit_beta" + ], + "recurrence_model_controls": [ + "native_complex_endpoint_rejected_with_old_surcharge", + "omitting_bit_surcharge_would_fail_next_endpoint_rejection" + ], + "scope": "Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay." +} diff --git a/research/pr643-improvement-20261013/validation/PREPUBLICATION-ASSEMBLY.json b/research/pr643-improvement-20261013/validation/PREPUBLICATION-ASSEMBLY.json new file mode 100644 index 0000000000..9c4a900d74 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/PREPUBLICATION-ASSEMBLY.json @@ -0,0 +1,329 @@ +{ + "status": "PASS_FRESH_MIXED_048_ALLCOLD_NATIVE_EXACT_ASSEMBLY", + "kappa": "1636569158555067/1000000000000000000", + "kappa_decimal": "0.001636569158555067", + "complex_lower": "4098129769175658129/2500000000000000000000", + "complex_decimal": "0.0016392519076702632516", + "bit_lower": "413456747036699736067/250000000000000000000000", + "bit_decimal": "0.001653826988146798944268", + "binding": "complex", + "gain_over_pinned569_percent": "2.205075054542788166186502379460439220991927019520557204612728552015288", + "complex_profile": { + "1": 181864, + "2": 28660, + "3": 32256, + "4": 12092, + "5": 4612, + "6": 288, + "8": 576, + "44": 1, + "48": 2228 + }, + "provider_counts": { + "jp8": 71, + "jp8b": 1 + }, + "surcharge_model": { + "complex": false, + "bit": true + }, + "conservative_complex_lower": "327850380958295199433/200000000000000000000000", + "conservative_complex_decimal": "0.001639251904791475997165", + "conservative_kappa": "327313831137139/200000000000000000", + "conservative_kappa_decimal": "0.001636569155685695", + "conservative_moments": [ + { + "side": "conservative_complex", + "surcharge": true, + "endpoint": "327850380958295199433/200000000000000000000000", + "accept": true, + "mercator": [ + "-68661391756201967950625890878045959884286545/26959946667150639794667015087019630673637144422540572481103610249216", + "-68661391756201967950625890878045959884286543/26959946667150639794667015087019630673637144422540572481103610249216" + ], + "base_two": [ + "-12733965387276165064659/5000000000000000000000000000000000000000000000", + "-3183490096819041266147/1250000000000000000000000000000000000000000000" + ] + }, + { + "side": "conservative_complex", + "surcharge": true, + "endpoint": "819625952395737998583/500000000000000000000000", + "accept": false, + "mercator": [ + "12042678189472335146110157516423336700055169/26959946667150639794667015087019630673637144422540572481103610249216", + "12042678189472335146110157516423336700055171/26959946667150639794667015087019630673637144422540572481103610249216" + ], + "base_two": [ + "4466869225817404203563/10000000000000000000000000000000000000000000000", + "2233439612908702101853/5000000000000000000000000000000000000000000000" + ] + } + ], + "conservative_bootstrap": [ + { + "exponent": "65465112137937864182617130060979157496431699646863790706641809225606735900641663666756478511/40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "gap": 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outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The frozen PR582 plain-joint-prefix, added-kernel and entrance-promoted provider dispatch with the new frame coalescences composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification." +} diff --git a/research/pr643-improvement-20261013/validation/PREPUBLICATION-INDEPENDENT-NATIVE-OWNERS.json b/research/pr643-improvement-20261013/validation/PREPUBLICATION-INDEPENDENT-NATIVE-OWNERS.json new file mode 100644 index 0000000000..820d764b84 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/PREPUBLICATION-INDEPENDENT-NATIVE-OWNERS.json @@ -0,0 +1,50 @@ +{ + "status": "PASS_INDEPENDENT_NATIVE_OWNERS_AND_MOMENT", + "roles": 35424, + "calls": 72, + "native_profiles": { + "jp8": { + "1": 2526, + "4": 168, + "8": 8, + "3": 448, + "2": 398, + "5": 64, + "6": 4 + }, + "jp8b": { + "1": 2518, + "4": 164, + "8": 8, + "3": 448, + "2": 402, + "5": 68, + "6": 4 + } + }, + "idle": { + "48": 2228, + "44": 1 + }, + "global_profile": { + "1": 181864, + "4": 12092, + "8": 576, + "3": 32256, + "2": 28660, + "5": 4612, + "6": 288, + "48": 2228, + "44": 1 + }, + "complex_lower": "4098129769175658129/2500000000000000000000", 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a/research/pr643-improvement-20261013/validation/PREPUBLICATION-INDEPENDENT-OWNER-CONTROLS.json b/research/pr643-improvement-20261013/validation/PREPUBLICATION-INDEPENDENT-OWNER-CONTROLS.json new file mode 100644 index 0000000000..858c249962 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/PREPUBLICATION-INDEPENDENT-OWNER-CONTROLS.json @@ -0,0 +1,36 @@ +{ + "status": "PASS_INDEPENDENT_OWNER_CONTROLS", + "isolated_optimized": true, + "cases": [ + { + "name": "positive", + "status": "PASS", + "expected_reason": null + }, + { + "name": "wrong_width", + "status": "REJECTED", + "expected_reason": "actual width" + }, + { + "name": "duplicate_helper", + "status": "REJECTED", + "expected_reason": "helper uniqueness" + }, + { + "name": "wrong_family", + "status": "REJECTED", + "expected_reason": "physical family" + }, + { + "name": "wrong_profile", + "status": "REJECTED", + "expected_reason": "native plus idle profile" + }, + { + "name": "false_moment", + "status": "REJECTED", 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"complex": false, + "bit": true + }, + "seconds": 327.43738016701536, + "reused": { + "baseline": false, + "locals": [] + }, + "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The frozen PR582 plain-joint-prefix, added-kernel and entrance-promoted provider dispatch with the new frame coalescences composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification." +} diff --git a/research/pr643-improvement-20261013/validation/SHA256SUMS b/research/pr643-improvement-20261013/validation/SHA256SUMS new file mode 100644 index 0000000000..4fdf235c04 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/SHA256SUMS @@ -0,0 +1,27 @@ +02cb97a60998646dcaa65920a25091a74c317b21490feed1abcb27e6e9b90084 EXECUTED-MANIFEST.json +5405dda4e7beb2936d062f53adfef832c96ffdb173f6c7e113abcab81ef7c6ca EXECUTED-README.md +7944d6c2f73a1ccb8a24bdc58297d3659e8e38f7549f5e834b93894cae1de927 EXECUTION-ENVIRONMENT.json +d9f9f000b8523e4e480a8d9f5bfdb7e2bbcb04c9369f4b08133e127a5e1cbd12 FRESH-REPLAY.tar.gz +8bf84ea9e0f31e5b4fe6af21ce049f6e886329ea28cd05602b477a5f9f4340b2 FRESH-WRAPPER.log +659a5805f90a28168f2060145d061fae86c6186ef8dd215f7de35570aed2317c INDEPENDENT-NATIVE-OWNERS.json +2226951b6d768e262c59727ea344081234dc0fc2f982394fd6003fac6d889e79 INDEPENDENT-OWNER-CONTROLS.json 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"1927269155106a90450f9a036445c6b29bf44598dc3ca49e46408e1bf8b0efa0" + }, + { + "name": "jp8b-step6-cold_end-construction", + "exit_code": 0, + "seconds": 0.298, + "log_sha256": "b460d726c39d59d7765b12e73a48e0607fb5642c79b3823a6a5e242a2902eef9" + }, + { + "name": "jp8-step6-cold_end-controls", + "exit_code": 0, + "seconds": 26.551, + "log_sha256": "ebad226e41ec21ce1ab949afc7a0b5e804111c05dfc08e4861a7d77a934b2ba8" + }, + { + "name": "jp8-all-columns-native-frames", + "exit_code": 0, + "seconds": 0.985, + "log_sha256": "de9c64c0945a17f0abd875fadef0006b1cada2cd19b97608026b402f61f8f820" + }, + { + "name": "jp8-both-reflected-ledgers", + "exit_code": 0, + "seconds": 0.711, + "log_sha256": "1afc39962063647fa681aeeb771f82123acdc9622802545b237f4373bdd4fb07" + }, + { + "name": "jp8-independent-local-controls", + "exit_code": 0, + "seconds": 3.793, + "log_sha256": "dd643a58258431c3b07d3b06d9060c49677fa23b4fafc9f10988ed1f6867bd9a" + }, + { + "name": "jp8-normalized-wrappers", + "exit_code": 0, + "seconds": 1.317, + "log_sha256": "74b13cf8570ca2f32ce0018575b1b73e95af77a28e59d09556fec59260bdbba5" + }, + { + "name": "jp8b-step6-cold_end-controls", + "exit_code": 0, + "seconds": 72.961, + "log_sha256": "1bf741cf6db299148c7c4673b1e322558250beb59566c32bde578091e0a16810" + }, + { + "name": "jp8b-all-columns-native-frames", + "exit_code": 0, + "seconds": 2.718, + "log_sha256": "b5c24662a18b4594c68e7c262e7e1d4c4b5ff724a23e3d2fd18cb554de006d6c" + }, + { + "name": "jp8b-both-reflected-ledgers", + "exit_code": 0, + "seconds": 2.152, + "log_sha256": "0aa53392bf50c4096c267f0f69c561fa9b9139f4c8299e3449bf9a8f1cb61e87" + }, + { + "name": "jp8b-independent-local-controls", + "exit_code": 0, + "seconds": 10.234, + "log_sha256": "dd643a58258431c3b07d3b06d9060c49677fa23b4fafc9f10988ed1f6867bd9a" + }, + { + "name": "jp8b-normalized-wrappers", + "exit_code": 0, + "seconds": 1.284, + "log_sha256": "74b13cf8570ca2f32ce0018575b1b73e95af77a28e59d09556fec59260bdbba5" + }, + { + "name": "jp8-all-phase-edges", + "exit_code": 0, + "seconds": 80.845, + "log_sha256": "dcc6261db7171bf91709cbb135b3e85c16d1ea23be31e13a8a9183db7df0ce9a" + }, + { + "name": "jp8b-all-phase-edges", + "exit_code": 0, + "seconds": 77.415, + "log_sha256": "accfc930145ba531051ba38e07fec200e7461043bdba00187f862b9e307f7483" + }, + { + "name": "bind-providers", + "exit_code": 0, + "seconds": 0.4, + "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a" + }, + { + "name": "emit-controller", + "exit_code": 0, + "seconds": 2.063, + "log_sha256": "8456359b900ce192f2f635351c4e2794dd09b2660000889a0da507ee5f5b71d7" + }, + { + "name": "independent-controller-and-controls", + "exit_code": 0, + "seconds": 13.63, + "log_sha256": "95b17780a7488f16812b1e44679c3dada12ffd3d5c5d8a0aa3fed4248e84b3b3" + }, + { + "name": "fresh-invoice", + "exit_code": 0, + "seconds": 1.226, + "log_sha256": "ad9609b60c8ad79bf2499c6a7b7607db8e8d1c3e0de8b5dc7cc09c225853c6e9" + }, + { + "name": "conservative-and-native-exact-assembly", + "exit_code": 0, + "seconds": 0.223, + "log_sha256": "ee57aae13cf28fe30b788838f9753eb8e0b564eee8af89d00b39d9f4c89cc358" + }, + { + "name": "admission-controls", + "exit_code": 0, + "seconds": 0.297, + "log_sha256": "40f0c35552fb10f02288ae8d2c6b9f902050fb370c0a19b7b88c977d0d44dab1" + }, + { + "name": "phase-timing-portability-controls", + "exit_code": 0, + "seconds": 0.578, + "log_sha256": "d4300a182a615922dd73ff2b945ff671086b86d5b80dbc009539e96d9b4dfe82" + }, + { + "name": "actual-recompression-and-rebound-controls", + "exit_code": 0, + "seconds": 2.389, + "log_sha256": "9c20730203542b9a5ed97e1ce2e2c51526e88de0b2983d4f15d7e550b8ed02ea" + } +] diff --git a/research/pr643-improvement-20261013/validation/independent-review/EXPORT-NORMAL.json b/research/pr643-improvement-20261013/validation/independent-review/EXPORT-NORMAL.json new file mode 100644 index 0000000000..6954d046e8 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/independent-review/EXPORT-NORMAL.json @@ -0,0 +1,34 @@ +{ + "roles": 35424, + "idle_profile": { + "44": 1, + "48": 2228 + }, + "profile": { + "1": 181864, + "2": 28660, + "3": 32256, + "4": 12092, + "5": 4612, + "6": 288, + "8": 576, + "44": 1, + "48": 2228 + }, + "rank_mass": 520704, + "dispatch": { + "jp8": 71, + "jp8b": 1 + }, + "rejected_controls": [ + "duplicate", + "width", + "offset", + "family" + ], + "status": "PASS_LITERAL_OWNER_EXPORT", + "owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", + "owners_content_sha256": "1351a8a87e83dd67fec90bc27566d6ec9278585d2435535e367aeea42a0688ef", + "published_owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", + "scope": "Owner structure only; full native supplier and exact assembly replay remain required." +} diff --git a/research/pr643-improvement-20261013/validation/independent-review/EXPORT-OPTIMIZED.json b/research/pr643-improvement-20261013/validation/independent-review/EXPORT-OPTIMIZED.json new file mode 100644 index 0000000000..6954d046e8 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/independent-review/EXPORT-OPTIMIZED.json @@ -0,0 +1,34 @@ +{ + "roles": 35424, + "idle_profile": { + "44": 1, + "48": 2228 + }, + "profile": { + "1": 181864, + "2": 28660, + "3": 32256, + "4": 12092, + "5": 4612, + "6": 288, + "8": 576, + "44": 1, + "48": 2228 + }, + "rank_mass": 520704, + "dispatch": { + "jp8": 71, + "jp8b": 1 + }, + "rejected_controls": [ + "duplicate", + "width", + "offset", + "family" + ], + "status": "PASS_LITERAL_OWNER_EXPORT", + "owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", + "owners_content_sha256": "1351a8a87e83dd67fec90bc27566d6ec9278585d2435535e367aeea42a0688ef", + "published_owners_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", + "scope": "Owner structure only; full native supplier and exact assembly replay remain required." +} diff --git a/research/pr643-improvement-20261013/validation/independent-review/OWNER44-STRUCTURAL.json b/research/pr643-improvement-20261013/validation/independent-review/OWNER44-STRUCTURAL.json new file mode 100644 index 0000000000..f1bd444530 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/independent-review/OWNER44-STRUCTURAL.json @@ -0,0 +1,29 @@ +{ + "roles": 35424, + "idle_profile": { + "44": 1, + "48": 2228 + }, + "profile": { + "1": 181864, + "2": 28660, + "3": 32256, + "4": 12092, + "5": 4612, + "6": 288, + "8": 576, + "44": 1, + "48": 2228 + }, + "rank_mass": 520704, + "dispatch": { + "jp8": 71, + "jp8b": 1 + }, + "scope": "Literal owner structure and pinned-provider registry comparison; exact moment and admission are separate.", + "provider_registry_matches643": true, + "owners_gzip_sha256": "de62f3092f8283d4e484c7f927e0176cf796e67a0d056e84cb0ccc5ce22eb4b4", + "owners_payload_sha256": "1351a8a87e83dd67fec90bc27566d6ec9278585d2435535e367aeea42a0688ef", + "provisional_plan_sha256": "2457566617f1a320e1b790a388b45e7180333b496ff39383159e659a4eb5059b", + "status": "PASS_INDEPENDENT_OWNER44_LITERAL_STRUCTURE" +} diff --git a/research/pr643-improvement-20261013/validation/independent-review/PACKING-BOUND-REVIEW.json b/research/pr643-improvement-20261013/validation/independent-review/PACKING-BOUND-REVIEW.json new file mode 100644 index 0000000000..bc5d409503 --- /dev/null +++ b/research/pr643-improvement-20261013/validation/independent-review/PACKING-BOUND-REVIEW.json @@ -0,0 +1,22 @@ +{ + "status": "PASS_FIXED_DISPATCH_PACKING_BOUND_REVIEW", + "provider_counts": { + "jp8": 71, + "jp8b": 1 + }, + "owner_segments": 16128, + "owner_capacity": 387072, + "max_segment_capacity": 48, + "required_width": 280084, + "unused_capacity": 106988, + "optimal_relaxed_idle": { + "44": 1, + "48": 2228 + }, + "supplier_atoms": 260348, + "supplier_rank_mass": 413716, + "full_rank_mass": 520704, + "normalization_rank_mass": 523264, + "proof": "Strict concavity of g^(1-q) for 04 x14, 8->7 x2. LP screen (kscreen, #610 dispatch +jp8x71+ck): v2 0.0016345792 = +0.553% over the like-for-like screen base 0.0016255869 (the #610 literal is +0.0016253652); v3 0.0016347434; free dispatch 0.0016353016. + +## What changes +#604's `cold_end` step allowed exactly one change to section A: a rank-0 premix on cold helpers at the head of A +(`y['A'] == premix + x['A']`, every premix register a helper at its start frame). This package widens that allowlist +(`code/build_cold_end.py::apply`, and independently `verify.py::cold_end`) by two primitives. No audit is weakened; +every downstream check runs unchanged on the resulting word. + +1. **Premix target writes.** `['add', t, k, p, q, []]`, with `t` a target, `k` a cold helper, and frame `[]`. These are + placed in the premix, so they run after the entry adapters and paid wrappers. +2. **Forward absorptions.** `[[i, ['add', q, g, p, s, F]]]`, inserted into A right after input-A gate `i`, with three + conditions: + - **(a)** neither register is a target; + - **(b)** `q` is dead from then on: no later A, cut or B gate touches it; + - **(c)** after gate `i`, both `q` and `g` already sit at frame `F`. + +## Why the forward computation is unchanged +- **Absorption.** The gate changes only `q`'s value, and `q` is never read again in A, cut or B (condition b). So every + register that is ever read afterwards has its old forward value. That covers targets, centres, live helpers and + live ports. Only `q`'s end-of-B value changes, and `q` is a non-target, so the cleanup is responsible for it. + - Condition (c) makes the gate frame equal both registers' current frame, so no climb happens. + - The paid profile and all frame chains are therefore identical to the input's. `chain_profile` recomputes them, + and the transport's `climb` re-asserts monotonicity. +- **Target write.** The gate reads a cold helper and writes a target. The transport assertion "no non-target register + reads a target in A/B" still holds. + - Targets start at level 0, which is frame `[]`, so the gate is rank 0. The transport still asserts at the start + of B that every target sits at its level. + - Its scalar content is the same kind of operation as a zero-frame compensation gate, `target += d·helper`. + - The only difference is placement: it runs after the cold wrappers and the helper premix. So it can cancel, + inside main, the dirt that an ended helper's premix column `c_h` delivers to targets. The carrier `k` has unit + weight on `h` and zero weight on every other ended helper. + - The verifier's own zero-frame compensation, recomputed from main, then contains no term on an ended helper. The + transport asserts this: no precondition or compensation gate touches a cold-ended helper + (`hpe_audit_and_transport.py:157`). + - **That assertion is THE guard for target writes.** A doubled, dropped or retargeted target write leaves the scalar + program exact (the compensation simply absorbs the difference), so exactness alone would accept it. It is rejected + only because the recomputed compensation must then read the ended helper, which :157 forbids. Every target-write + mutant below is rejected by :157 (the entering-helper one by the frame climb). + +## What is re-verified on the resulting word (unchanged code) +- **Scalar replay.** `hpe_audit_and_transport.py` runs the exact arbitrary-dirt endpoint replay of precondition + + compensation + main + tail + refactored cleanup in both orientations. It also checks dyadic primitives, the frame + chains, the end-of-B row/column cone pre-check for every low-frame end, and the paid profile. +- **Local replay.** `hpe_emit_local.py` and `hpe_audit_local.py` run the event-level independent replay and the + wrapper-order check: every scalar on a wrapped helper lies between its pre and post adapters. +- **Wrappers.** `hpe_adapters_local.py` checks Lemma A wrappers for `(0, U)`. +- **Phases.** `phases_full.py` checks all phase edges. +- **Global stages.** Binding, the owner audit, the invoice, both moment engines and the assembly controls all run. + +## Lean coverage +Both primitives are ordinary section-A gates of the native word: frame-`[]` adds and an add at its registers' common +frame. The HPE / cold-end Lean statements (PR593, PR599) are about the helper labels, tails and terminal frames, and +none of those change. The ended helpers end at `U_b` (dim 4) with `(0, U)` wrappers exactly as in #604. No new Lean +rule is needed. The change is to the build-step allowlist only. + +## Negative controls (`code/cold_end_controls.py`; all must be rejected by the transport) +#604's 14 controls, ColdSupply's 6 entering-end controls (E1), plus these 12 (32 in total): +- target writes moved into the zero-frame precondition (before the wrappers); +- one target write dropped; +- a target-write coefficient doubled; +- a target write reading an entering helper; +- a target write reading the same factory slot of another block, which carries none of the ended helper's dirt; + - (Reading another register with the same weight on `h` is a valid variant: it is accepted, which is why this mutant + was chosen instead.) +- absorption dropped; +- absorption coefficient doubled; +- absorption placed before the absorbed register's last kernel write; +- absorption placed while the absorbing register is still live; +- absorption into a centre (a live register read by the cut); +- absorption at a lower frame; +- absorption at a higher frame (FULL). + +In addition, `verify.py::cold_end` independently checks the allowlist conditions: +- target writes are frame-`[]` adds from a cold, non-entering helper; +- each absorption satisfies conditions (a)–(c): unique, in-range insertion indices; frames compared as spans and + seeded from the port / start_extra frame when the register has no earlier A gate; +- `y['A'] == premix + (x['A'] with the absorptions inserted)`. + +## K-triangle provider words (complex-571-cold14-k492) + +The provider words are produced by search-side constructors. None of them is trusted. What is trusted is the exact audits that certify every word. Every intermediate word also has its content hash pinned in `data/SPEC.json`. This note says what each constructor does, and which independent check certifies its output. + +### 1. `k_triangle`: `code/construct_k_triangle.py` + +**Origin.** This is PR531's `code/construct_504.py` (pinned source `direct_delivery`, file hash pinned), extended with AtomScout's leaver-read K-triangle atom. Every assertion of PR531's constructor is kept, with 504 replaced by NH = 504 − 3·|triangles|. + +**The atom.** A coordinate pair p is *full* when the selected partition contains p in all three blocks containing p. Then both triangles (p, ±1) are consumed only by K-coordinates. For a scheduled triangle: +- the three face packets are never formed and never copied; +- each K-coordinate target t first reads the leaver that is its K-basis own token, `own_rows[t]`. The constructor checks this is the same register and coefficient as in the 504 word; +- t then reads the four unformed leavers (butterfly outputs) of the other two faces. Each is read with coefficient `coef·alpha`, from the 504 word's face-packet request. + +The read order (`data/TRI-SCHEDULE.json`) keeps every target frame inside hyper(P_t); the constructor asserts this for each read. + +**Exactness.** The constructor asserts the following, exactly as PR531 does: +- the side identity `rows[v+t] == {s: −G[t][s]/2}` for every target t; +- the clean-column replay `A + cut + B + cleanup = identity` on the 2v + NH columns; +- the rank-mass identity Σ r·H_r = 9·NH + 240·8 + 72. + +**Helper map.** Each allocation advances the 504 numbering. A packet copy that the schedule never forms advances it without allocating. `HELPER-MAP.json` is therefore the 504 → NH register map: registers below 448 keep their ids, and the 12 removed packet copies [448, 458, 460, 470, 472, 482, 580, 590, 592, 602, 604, 614] have no image. + +**Controls in `verify.py`.** +- PR531's unchanged constructor reproduces PR552's `RAW504.json.gz` byte for byte in content. +- This constructor with an empty schedule also reproduces it, and gives the identity map. +- With the package schedule it gives R = 492 = 504 − 3·4 and a 12-entry removed set, and the map's hash is pinned. +- Independently (AtomReviewer), the 492 raw word passes vendor531's and the generalised `audit_and_transport` (exact forward and inverse-transpose replay of every column, native frames), and an independent mod-p replay. + +### 2. `port_stage`: `code/build_port_stage.py` + +**What it replays.** A stage I4 → O4 of a 504-helper chain is one of: +- PR558's reconstruction raw504 → promoted; +- PR571's prefix word; +- PR568 `cold_kernel` / `multicut`; +- PR575 `joint_prefix`; +- PR569 `promote`, PR568 `greedy_kernels`, PR583 `frame_coalesce`, and this lineage's `gate_move_coalesce`. + +Each stage is rebuilt in the same run from pinned sources, with its own constructor, omission controls and content pins (`build.shadows`). + +**How it is replayed.** The stage is replayed onto the K-triangle word I8 at the matching chain point: +- I4 and O4 are renumbered through the helper map, dropping gates on removed registers; +- gates are aligned by scalar operation (gate without frame); +- in O4 order, matched gates come from I8, with O4's frame where the stage changed it; +- stage-introduced gates come from O4; +- the K-triangle reads, which have no 504 counterpart, stay after their I8 predecessor's image; +- start_extra and target_levels changes are replayed; +- the cleanup is rebuilt with the inherited inverse rule. + +**What certifies the output.** The port is a transfer heuristic and claims nothing by itself. `verify.py` certifies every ported word in four ways: +1. It runs the generalised native audit `code/hpe_audit_and_transport.py`: status PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES, exact forward and inverse-transpose replay of all 2v+R columns with arbitrary dirt, native monotone frame chains, and the entrance and paid-profile census. +2. It checks that only A, B, cleanup, start_extra, target_levels and the report changed, and that R is unchanged. +3. It pins input, shadow input, shadow output and output by content hash. +4. Localization later re-derives everything again: native chain, independent local replay with its negative controls, wrappers, and all phase edges. + +So a wrong transfer can only fail closed. + +### 3. `frame_regroup`: `code/build_frame_regroup.py` + +This is PR583's `build_frames.py`, with the required per-change profile delta read from the recipe instead of fixed at {1:−2, 2:+1}. The constructor checks the following: +- scalar operations, every field outside A/B/report, helper widths and all initial helper responses are unchanged; +- entering helper responses are zero; +- the cleanup already follows the inherited inverse rule, which uses only FULL frames; +- every change has the recipe's exact sequential delta, and the profile matches the recipe before and after; +- frame-chain monotonicity holds (gk_word.profile asserts it); +- the controls reject every omission and every FULL over-promotion (48 controls for 24 changes). + +`verify.py` then repeats `frame_coalesce`'s independent comparison: only the recipe gates' frames change. + +The recipe's 24 changes coalesce the K-read gates of the eight K-coordinate targets, each with delta {1:−3, 2:+3, 3:−1}. Port480's `frameopt.py` found them by maximising Σ d·ln d. + +### 4. `hyperplane_end` and `cold_end` + +These steps run the package's unchanged B3 constructors, controls and independent comparisons: +- `build_hpe.py` / `hpe_controls_atc.py`: 34 candidates, all admissible; +- `build_cold_end.py` / `cold_end_controls.py`. + +The cold_end recipes come from ColdBeyond's `construct2` with single-unit blocks (Port480 `construct2b.py`). Each recipe has: +- S b.10 cold ends in all 14 blocks; +- S b.9 second cold ends with dead-port absorption in blocks 3–10 only. In blocks 0–2 and 11–13 the K-triangle words do not admit them; +- the E1 entering pair. + +The allowlist and its proof are B3's `PROOF-NOTE.md`, unchanged. + +### Reproduction +Every intermediate word was rebuilt outside `verify.py` (scratch `Stack492/rebuild.py`) and inside the strict run. Each one equals Port480's search word in content, for every stage of ck, jp8 and atm3. + +## ColdThird (h4a): dim-8 cold ends and the widened forward-absorption allowlist + +This section supersedes the earlier sections wherever they describe the `cold_end` allowlist. On top of the #622/#626 +construction, each provider word (jp8, ck) gains 4 cold ends at the dim-8 frame U8a = [256,128,65,33,17,9,4,2] +(helpers S1.3, S3.3, S5.3, S7.3), each with 2 lifted partners, plus dead-port absorptions. Per word the paid profile +changes by {1:+4, 4:+4, 6:-4} against #622 v3, and 4 helpers go from width 9 to width 8. + +### What soundness rests on +Soundness does **not** rest on the deadness condition of the allowlist. It rests on checks that re-run unchanged on +the spliced word: +- the transport's exact arbitrary-dirt **endpoint replay** in both orientations (`code/hpe_audit_and_transport.py`), + which re-verifies the exact refactored cleanup, so every port and helper is restored exactly; +- the **`:157` guard** in `code/hpe_audit_and_transport.py`: no precondition or compensation gate touches a + cold-ended helper; +- the frame chains / paid-profile pin and the cone pre-check, recomputed from the word. + +The deadness rule ("`q` untouched by every later *input* A, cut or B gate") is an allowlist restriction on recipes, +not a load-bearing hypothesis: the independent review moved a dirt release before its port's last kernel write, the +transport replay still accepted it (the two additions commute), and only the allowlist rejected it. + +### What changes +ColdBeyond allowed forward absorptions `q += a·g` in section A of the `cold_end` step, each inserted right after a distinct +input-A gate `t`. It required: +- (a) neither register is a target; +- (b) `q` is untouched by every later A, cut or B gate; +- (c) `q` and `g` both already sit at the gate frame. + +ColdThird changes the allowlist in exactly two places, `code/build_cold_end.py::apply` and `verify.py::cold_end`: +1. **Several absorptions after the same input gate.** The recipe list is sorted by `t`, and gates that share a `t` run in + recipe order. +2. **Deadness is judged against the input word.** `q` must be untouched by every later *input* A, cut or B gate. A later + absorption may write `q` or read it. + +Section B and the cut are still never modified. + +Old recipes keep their meaning: all three `#622` v3 recipes rebuild to byte-identical words under the widened builder. + +### Why the forward computation is unchanged +**Induction over the spliced A.** Let D be the set of registers that some absorption has already written. +- Every input gate sees exactly the operands it had before. An input gate never touches a register of D after that + register's absorption point, by (b) against input gates. +- An absorption writes only its own `q`, which joins D. +- An absorption may read a register of D. That only changes the value of another register of D. +- Hence every register outside D has its old value at every input gate, and so do targets, centres, live helpers and + live ports. + +**What changes, and who handles it.** Only the end-of-B values of D-registers change. These are non-target ports and +helpers, whose cleanup is part of the exact refactored cleanup. That cleanup is re-verified by the transport's +arbitrary-dirt endpoint replay in both orientations. + +**Frames and profile.** By (c), absorptions are at their registers' current frame. So every frame chain, and therefore +the paid profile, equals the input's. `chain_profile` recomputes the profile, and the transport's climb re-asserts +monotonicity. + +### What the new absorptions do +Two kinds of absorption are new: dirt releases (K side) and L-side gates. Together they let a cold end sit at a dim-8 +frame U8 = [256,128,65,33,17,9,4,2] with only 2 lifted partners per end. + +- **Dirt releases (K side).** For example `p15 += -1/4·S3.3` after `p15`'s last kernel gate. A dead U_b port takes a + live helper's value, so the new end's premix column leaves no dirt on that port. Without this, the port would have to + be lifted to U8. +- **L-side gates.** For example `p12 += -p15; p12 += -S3.3` at one anchor. These make the row of the lifted partner + `p12` data-free on the cold group, so the row fix needs no further partners. + +Each per-word package has these parts: +- 4 new ends: S1.3, S3.3, S5.3 and S7.3, all at U8. +- Lifted partners: the dim-4 port at offset 4 and S.13 of blocks 3, 5, 7 and 9. +- 16 new absorptions: 8 releases and 8 L-side gates. + +The premix is now one rank-0 factorisation over all cold units: the block units at U_b plus the U8 units. It is jointly +biorthogonal: the block rows are re-solved against the U8 columns, using block 3/5/7/9's third row dimension created by +the L-side gates. + +Target writes may now combine several carriers, `t += Σ β_k y_k` with `Σ β_k M[k,·]` = e_h on the ended columns. This +is the same primitive: frame-[] target writes from cold, non-entering helpers. + +### Re-verified downstream (code unchanged) +- `hpe_audit_and_transport.py`: + - exact replay; + - the cone pre-check for all 26 low-frame ends; + - the paid-profile pin; + - the `:157` guard (no precondition or compensation gate touches an ended helper). +- The local emit/replay, wrapper and phase stages, and all global stages. +- No new Lean rule is needed: both primitives are ordinary section-A gates of the native word, and the U8 ends are + `(0, U)` cold ends of the PR599 kind. + +### Negative controls +See `code/cold_end_controls.py`, COLD-THIRD block. Each control must be rejected at a pinned assertion: +- second absorption sharing an anchor dropped; +- shared-anchor coefficient changed; +- dirt-release absorption dropped; +- dirt-release coefficient changed; +- dirt-release absorption moved before the port's last kernel write (port still live); +- dim-8 end at another dim-8 frame; +- dim-8 end lower-frame gate dropped; +- dim-8 end profile pin. + +These come on top of the 38 inherited controls. + +### Inherited control re-pin: `ab_centre` +`code/cold_end_controls.py` changes one inherited control. When the word has dim-8 cold ends +(`any(len(helper_final[h]) == 8 for h in cold)`), the `ab_centre` mutant (the ColdBeyond U_b absorption retargeted +into a centre, a live register read by the cut) is expected to be rejected by COLDPRE ("touches a cold +hyperplane-ended helper") instead of by the arbitrary-dirt ENDPOINT replay: the retargeted absorption first leaks an +ended helper's dirt into the cut's targets, which the `:157` guard catches before the replay runs. The retarget +centre is now also chosen outside the cold set (`c not in cold`), so the mutant always targets a live centre. The +mutant is still rejected; this is a change of the pinned rejection site, not a weakening. With the 8 ColdThird +controls the `cold_end` step pins 46 rejected controls per word. + +## st2: PR627's two factored jp8 ends stacked on h4a (complex-571-cold14-st2) + +This section adds to the ColdThird section above; the code is h4a's reviewed code, unchanged. Only the jp8 `cold_end` +recipe changes (`data/recipes/k492-jp8-cold_end.json.gz`); ck is h4a's. H4aReviewer, Addendum 2: SOUND for the local +stages. + +### What is stacked +PR627 (jeremydiviney, `complex-571-cold14-k492b`, `data/FACTORED-END.json`) ends two jp8 cold helpers, 590 and 581, at +dim-7 frames, using factored lower-frame tails. Their input HPE word is the same as h4a's. On top of h4a's jp8 recipe, +the stacked recipe adds: +- the new cold ends 590 and 581 at dim-7 frames, each with its lower-frame tail (PR627's extra tail); +- 12 rank-0 premix gates on cold, non-ended helpers at frame `[]`; +- 3 forward absorptions: P95 += −H405 and P92 += ¼·H403 after input-A gate 1665, and P87 += ½·H419 after gate 1800. +All of h4a's absorptions and cold ends are kept. Where PR627's absorptions share an anchor with h4a's, they run after +h4a's in recipe order. + +### Premix re-derivation +PR627's premix was derived in PR627's basis, so it is re-derived in h4a's basis (H4aFinish `solve627.py`). The word +used is h4a's premix, followed by input A with h4a's and PR627's absorptions, then the cut, B, h4a's early tail and +PR627's extra tail. On that word the premix is solved exactly: row gates (h += x_l·l) followed by column gates +(k += y_k·h), with l and k cold non-ended helpers at frame `[]`. It is chosen so that, in the total state map, row h is +e_h and column h is e_h on every non-target row, for h = 590 and 581. + +### The q92 absorption +h4a has a dirt release at anchor 1665 (q95 += −¼·S403). Stacked, that release leaks into end 581's accumulator through +port 92, which is read by 88 += 92. H4aFinish `fix581.py` searches the dead-port absorptions at that anchor by an exact +linear solve and finds a single gate, `[1665, ['add', 92, 403, 1, 4, [265, 137, 96, 6]]]`, i.e. q92 += ¼·S403. Port 92 +is dead after gate 1665, and both registers are already at the gate frame, so the gate is admitted by the +ColdThird allowlist. With it the residual is empty and the solve above succeeds for 581. + +### What is re-verified (unchanged code) +- The reviewed `build_cold_end.apply`, applied to the Port480 input word, rebuilds the st2 jp8 word (content 7f4c71dd…). +- The transport's exact endpoint replay is exact in all three orientations, the refactored cleanup is dyadic, and + `:157` holds: the compensation reads no ended helper. +- The (N) wrappers for the new (0, U7) pairs pass in `hpe_adapters_local.py` (17 cold pairs in the reviewed D4 WRAPPER-CHECKS). +- The 46 `cold_end` controls are rejected. +- The paid profile changes against h4a by {1:+2, 2:+2, 5:−2} per jp8 word (rank mass −4). Ends 581 and 590 move from + (6,9) to (6,7), and ports 80 and 88 from (4,9) to (4,7)+(7,9). The recomputed profile equals the reported one. + +### Credits +PR627 (jeremydiviney) for the two factored jp8 ends and their tails. The re-derivation, the q92 fix and the stacking +are H4aFinish's. +## st2u4: CarrierBypass's premix-only dim-8 cold ends with factored row partners (complex-571-cold14-st2u4) + +This section adds to the st2 section above. It reproduces CarrierBypass's proof note (`CarrierBypass/PROOF-NOTE.md`, "u4"). The code is h4a's reviewed code, except `code/cold_end_controls.py`: CarrierBypass's patched controls add an accumulator block and run the dim-8 block for every distinct cold dim-8 frame. The patched file gives 51 rejected controls on the u4 jp8 word and still 46 on h4a/st2 words, and H4aReviewer re-signed it in FINAL-REPORT.md, Addendum 3. Only the jp8 `cold_end` recipe changes against st2 (`data/recipes/k492-jp8-cold_end.json.gz`, CarrierBypass `st_u4/cold_end_recipe.json.gz`). H4aReviewer, Addendum 3: SOUND for the local stages, verified by rebuild with the reviewed `apply`, exact replay in all 3 orientations, `:157`, (N) for (0, U*), and pricing Δ = {1:+8, 2:−4, 4:+4, 5:−4} with 4 widths 9 → 8. + +### Change +The build stacks on st2, which is h4a (#629) plus #627 on jp8. Four extra **cold** helpers, **233, 265, 425 and 441**, end at the dim-8 HPE hyperplane U* = [256,128,64,32,16,8,6,1] instead of at FULL. ck is unchanged. + +There are no new forward gates and no new absorptions. The recipe differs from st2's in three places only: +1. **Rank-0 premix.** 16 gates with frame [] act on free cold helpers still at their start frame. They are prefixed to st2's premix, after the entry wrappers. +2. **Frame-[] target writes.** These are 40 premix target writes (ColdBeyond primitive). They cancel each new end's dirt on the targets. Each one reads a cold carrier that has unit weight on its end and zero weight on every other ended helper. +3. **The refactored cleanup.** + - The tail is st2's tail, followed by the new lower-frame gates for each end. + - The remainder is an exact dyadic Gauss–Jordan factorisation at FULL. + +The word is `build_cold_end.apply(hpe, recipe)`. The `apply` and `hpe_audit_and_transport` code is unchanged; it is the reviewed h4a package code. **No verifier widening is needed.** The `cold_end` controls are extended (see Controls below). + +### Exactness +Definitions: +- P_t is the state after main and st2's tail. +- Q_U is the set of non-target, non-ended registers whose frame after st2's tail lies in U. + +For each new end h, with premix column c_h = M e_h and premix row r_h = e_h^T M^{-1}: +- **Column.** P_t c_h is zero outside Q_U on non-target rows. Its target rows are cancelled by the target writes; the guard at `:157` re-checks this. +- **Row.** r_h P_t^{-1} is zero outside Q_U. +- **Pairing.** r_i · c_j = δ_ij across the four ends. The premix group excludes every ended helper, so the rows and columns of the old ends (v3, E1, h4a, #627) are untouched. + +The tail gates are at frames ⊆ U*. They make row h and column h equal to e_h exactly, for every ended helper. The constructor asserts this in exact rationals before the Gauss–Jordan step. The transport replays every arbitrary input column in both orientations, re-checks the cone, frame chains and paid profile, and passes (`aud/st_u4`). + +### Factored row partners +Take end 233. Its row is supported on: +- 233 itself; +- 239, which is already lifted to U* by HPE-457's inherited tail, so reading it is free; +- ports 59 and 61. Both sit at the same dim-4 frame U_b, where the v3 block tail left them. + +The tail is: +- `59 += −61` at U_b. Both registers already sit at U_b, so there is no climb. **59 is the accumulator.** +- `233 += x·59` at U*. Only 59 climbs, 4 → 8. +- Then 233's other row and column gates at U*. + +The same pattern holds for the other three ends, with accumulators **19** (`19 += −21`), **83** (`83 += −85`) and **51** (`51 += −53`). + +This is exact because: +- no later tail gate touches the accumulator; +- the Gauss–Jordan remainder is recomputed from the resulting state, so it restores the accumulator and its partner at FULL. + +Delta per end: {1:+2, 2:−1, 4:+1, 5:−1}, width 9→8. The helper climbs 7→8 instead of 7→9, and one port climbs 4→8→9 instead of 4→9. Without factoring, two ports split their 5-climbs, and the end is LP-negative. + +### Numbers +| | jp8 delta | LP (ColdThird lp, free dispatch) | +|---|---|---| +| st2 | — | 0.0016363477 | +| st2 + u4 | {1:+8, 2:−4, 4:+4, 5:−4}, widths 9→8 ×4 | 0.0016366171 (+2.69e-7) | + +### Controls (`ctl/cold_end_controls.py`, patched from h4a's reviewed file) +- **Dim-8 controls per distinct terminal frame.** The three controls (another dim-8 frame, lower-frame gate dropped, profile pin) now run once for each distinct dim-8 terminal frame: U8a for h4a and U* for u4. This means h4a's family keeps its own controls in the stack. +- **New: factored accumulator gate.** + - Zeroed → rejected at ENDPOINT. + - Coefficient doubled → rejected at ENDPOINT. + +Nothing else is changed. + +### Further ends (not shipped) +The joint pairing analysis finds about 23 more dim-8 ends over 7 frames. On top of u4, every one tested lowers the LP: +- 249: 0.0016364415; +- 412: 0.0016365104; +- 428: 0.0016365104. + +The reason is that h4a's absorptions into ports 29 and 93 force dim-7 partners for 249 and 409, and the remaining candidates carry dim-6 partners. + +### HPE helpers at dim 7: why the carrier cannot be bypassed +Row h at end of B is e_h − e_p. Only a gate that writes h or p can change it: +- before p's last read, such a gate changes values that the targets read; +- after that read, p sits on the s-chain frames, which contain the vector 8 ∉ F_h7. + +A bypass therefore needs a copy of p's value for each of the two chains, and so a third register that is dead or unborn at a frame ⊆ F_h7 ∩ F_p6 and whose value is cancellable helper dirt. `hpe3rd.py` lists every such candidate for all 34 HPE helpers on jp8, ck and atm3. Each candidate is either a dead port or a helper carrying port data (297, 329, 361, 393), so no copy is possible. diff --git a/research/pr643-improvement-20261013/witness/README.md b/research/pr643-improvement-20261013/witness/README.md new file mode 100644 index 0000000000..c1106e23d4 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/README.md @@ -0,0 +1,23 @@ +# PR643 twin-supplier owner packing improvement + +This witness retains Jeremy Kothe's PR643 suppliers and changes the literal owner map: idle ranks 12+32 become 44. The exact admitted bound is κ = 1636569158555067/1000000000000000000 = **0.001636569158555067**, above pinned PR643's 0.001636542223442109. Dispatch remains 71 PR637 JP8 calls and one PR635 JP8 call (named jp8b); all 35,424 literal roles retain their window, family, width and disjoint-interval constraints. This does not claim an unrestricted optimum. + +Pinned predecessor: `jeremykothe2/integer-mult-bounds` commit `bbfa9fe1d84d5572f4d144c2ee56a3eddc7a83f5`, package `research/complex-571-cold14-twin`. Every Python file in `code/` and `verify.py` is byte-identical to that source. Six pinned dependencies are vendored unchanged. Source preservation is recorded in SOURCE-COMPARISON.json. + +## Reproduce + +Use Python >=3.10 with assertions enabled, a C++ compiler and Boost headers for the frozen baseline. Python admission uses the standard library. Choose a new output directory: + +```sh +PYTHON=python3 sh verify.sh /tmp/pr643-owner-replay +``` + +The wrapper rebuilds both suppliers and the baseline without reuse, then runs independent native-width/owner/rational checks and five mutations, declaration reconstruction, a portable owner exporter with four mutations, and six independent U4 mutations. Owner reproduction compares decompressed payloads. The full fresh candidate replay passed all 58 core stages without reuse in 327.44 seconds, followed by every supplemental wrapper check. All 46 receipt artifacts and 58 stage logs were independently hash-checked. The enclosing validation directory retains full replay archives, receipts and executed input snapshots. Execution was on macOS; no Linux replay or GitHub CI success is claimed. Prepublication exact assembly and 114 admission controls passed using actual supplier outputs from an independently completed fresh PR643 replay. That baseline source replay passed all 58 stages without reuse; it is distinct from the candidate's fresh replay. + +`owner-search/README.md` documents the recorded export from pinned PR643 data. Solver output is nomination only. Inherited proof notes describe the unchanged supplier construction. Both orientations, arbitrary-dirt native scalar/frame behavior, exact phase edges and whole-provider identity bindings remain checked by the complete core replay. + +## Attribution and scope + +Chi Zhao prepared the owner repair, independent audit and portable package with substantial OpenAI Codex assistance. Jeremy Kothe (CarrierBypass) supplied PR643's twin dispatch and the PR635/637 suppliers, building on Jeremy Diviney's factored ends and earlier contributors retained in NOTICE.md. The separate interval checker retains Chafik Boukhalfa's PR626 exact interval engine. + +This is a conditional native exact-complex witness, not formal verification of the multiplication theorem or a measured implementation speedup. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape recovery, analytic transfer and bit H1–H5 premises remain. The inherited PR543 bit supplier is repriced rather than rebuilt. Publication does not assert that this is the latest unreviewed frontier. diff --git a/research/pr643-improvement-20261013/witness/SOURCE-COMPARISON.json b/research/pr643-improvement-20261013/witness/SOURCE-COMPARISON.json new file mode 100644 index 0000000000..f253e0e6f8 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/SOURCE-COMPARISON.json @@ -0,0 +1,30 @@ +{ + "predecessor_pr": 643, + "commit": "bbfa9fe1d84d5572f4d144c2ee56a3eddc7a83f5", + "unchanged_core_files": { + "code/build_port_stage.py": "beb0d30fde1b9a30db091880b38c4a8ec906da3f715c43de7db8bf7932526e72", + "code/hpe_emit_local.py": "7e4a6fbc38c8228157b6311457d1496bf460291393043932d2c365f004f77805", + "code/generated_identity.py": "c8af22719c0f3097a991a3f6ccac8f090afd2faba554745733d9ea88f2c25708", + "code/hpe_audit_local.py": "6bd9a1e279c9c9e4f3767d9f82e537b559292906feb2ddab02f380fb6523a810", + "code/phase_timing_controls.py": "1692ccee3da4b1781408d126ee4999f3e31a505cd83c64823a404033da3a6339", + "code/witness.py": "00789c911a8f32cfe9d52207c7aa78305dc3fce4a8b6305ba402b7e74117103d", + "code/build_gate_moves.py": "08bf1c2652307aeefbab089fdaf02f82e2c396ca23a1eb68e294a67e74c44252", + "code/hpe_audit_and_transport.py": "c9a05ff291016b870b4fc925b317abd9c3a604c73ffc8920dfdbbeb475e20aa3", + "code/build_hpe.py": "ba2001695d8c7547a82260c3b016e01dac686e95a61757ca124eb9879078ea8e", + "code/assemble.py": "1b1a9024ac910dc9b9d9e30150684e1fa9cb228a4c1c275b75ab04b57fdef1dd", + "code/hpe_adapters_local.py": "eb0b5c6c7161e18dc22168da3211448d321586edd15bcfb4b4741174d36993cf", + "code/assembly_controls.py": "8a365b95c412d75d10db5bb59309d47cd56c5f8a77566f940a05977795130ce8", + "code/generated_identity_controls.py": "a7b93207a673575d1fddc3e579153349c145c8f08d4575ae0a5d1e3cffec01de", + "code/build_cold_end.py": "864b4701dd73afd0c9d99761b7a749f3354c48985730f17054e18c052996a668", + "code/hpe_controls_atc.py": "63aa3909b5bfd3bf270c313bebb5c46e7789c67a8f2439f568bc4b2b4a35d17b", + "code/audit_allcold.py": "cea021ae79658ca7ca4d07f1e1a70bdb4947afaf95b362114c11032c0fef889a", + "code/bind_providers_portable.py": "2eb5c262bf481b3bec9ceaec654fa46ff6fc3a89b13d4906a29a55a89e35feea", + "code/invoice_allcold.py": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec", + "code/emit_allcold.py": "fe26f10fe5d30ed407a37540a45ef94f44576dd241d09e19aef5db1efb072746", + "code/cold_end_controls.py": "68dbfb291115132d79b4ab7304b3e03d540b977a912ff17d709cabdd2a0b52c4", + "code/construct_k_triangle.py": "66fc460df8eb8067efe3d8a3f9e97a7244aacd7bf11650a6ce656e868ce053da", + "code/build_frame_regroup.py": "e2549ccc7a90008831be3b59aeb37b47db696640f5f5c2b72dd888b2f1e7e5c9", + "verify.py": "4c8dea601fe9255bd9fbbf7840d3bfacc3dcf0b1deaf7ffab467e3c10648a3b7" + }, + "source_manifest_sha256": "e9e38dd802b385ac16df8add86a8a59f98ac6956f85819d19f7a5c26689882ab" +} diff --git a/research/pr643-improvement-20261013/witness/code/assemble.py b/research/pr643-improvement-20261013/witness/code/assemble.py new file mode 100644 index 0000000000..d1674e657f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/assemble.py @@ -0,0 +1,216 @@ +"""Hardened 63 width-seven (#571 prefix word) and 9 plain eight-cold (#568 E8) provider assembly with the native exact-complex moment. + +Prepared with OpenAI Codex assistance. The rational engines and outer +constraints are retained from PR547/PR548 and their preserved ancestry. +The bit operator is the cited unchanged PR543 supplier. The complex owner +and invoice inputs must be freshly emitted by the packaged physical replay. +All conservative admission guards and conservative moment/outer witnesses run +before the PR559 native-complex correction. The bit surcharge is retained. +""" +from pathlib import Path +from fractions import Fraction as Q +from decimal import Decimal, localcontext +import argparse,json,hashlib,importlib.util,os,sys +from collections import Counter +assert __debug__, 'Assertions required' +P=Path(sys.argv[1] if __name__=='__main__' else os.environ['GAIN_PR564_SOURCE']).resolve() +read=lambda p:json.loads(p.read_text()) +sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +hash_ok=lambda x:isinstance(x,str) and len(x)==64 and all(t in '0123456789abcdef'for t in x) +digest=lambda x:hashlib.sha256(json.dumps(x,separators=(',',':')).encode()).hexdigest() +def load(n): + s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +M,B,A=[load(n)for n in ('moment','base_two_moment','outer')] +def dec(x): + with localcontext()as ctx:ctx.prec=70;return str(Decimal(x.numerator)/Decimal(x.denominator)) +from witness import DISPATCH,CALL_ORDER,COUNTS,PIDS,X,DISCOVER,pin,SPOT + + +def assemble(owner,invoice,owner_sha,invoice_sha): + # These are admission receipts, not optional collections of successful rows. + # Require both orientations and every finite check before pricing anything. + assert owner['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE' + assert invoice['status']=='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE' + assert all(hash_ok(x)for x in (owner_sha,invoice_sha,owner['template_sha256'],owner['controller_audit_sha256'],invoice['parent_template_sha256'])) + checks={'local_primitive_bound','logical','router','literal','mass','precision','tape','row','halving'} + assert set(invoice['strict_checks'])==checks + assert all(invoice['strict_checks'][name] is True for name in checks) + assert set(invoice['providers'])==set(PIDS) + assert invoice['provider_counts']==COUNTS + assert owner['all_live_owners_per_call_distinct'] is True + # R (helpers per provider word) is read from the invoice and must be shared by every provider; n=2v+R. + R=invoice['helpers'];assert type(R) is int and R>0 and all(p['helpers']==R for p in invoice['providers'].values()) + assert owner['owners_per_call']==2*112+R and owner['actual_helper_owner_charts']==owner['hosted_residuals']==72*R==pin('expected.hosted_residuals',owner['hosted_residuals']) + pin('expected.rank_mass',owner['rank_mass']) + pin('expected.actual_73column_sigmas',owner['actual_73column_sigmas']);pin('expected.cross_replica_helper_roles',owner['cross_replica_helper_roles']) + pin('expected.idle_remainders',owner['explicit_idle_remainder_children']) + assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==72 + assert invoice['live']==owner['live'] and invoice['physical']==owner['physical'] + assert invoice['centres']==8 + assert invoice['physical_stock_identity']==dict(data_and_owner_families=7168,local_helpers=R,private_centres=8,coefficient_work=2) + assert sum(invoice['physical_stock_identity'].values())==invoice['physical'] + assert invoice['controller_audit_sha256']==owner['controller_audit_sha256'] + for pid,p in invoice['providers'].items(): + assert set(p['local'])=={'forward','backward'} + assert p['helpers']==R and p['centres']==8 and p['n']==2*112+R and p['v']==112 and p['h']==9 + K='providers.'+pid+'.';pin(K+'entering',p['entering_helpers']);pin(K+'entrance',p['entrance_rank']) + pin(K+'inventory',p['width_inventory']) + assert all(type(w) is int and 0=0 for n in idle.values()) + idle=+idle;assert sum(idle.values())==owner['explicit_idle_remainder_children'] + pin('expected.idle_remainder_profile',{str(r):n for r,n in sorted(idle.items())}) + paid.update(idle) + assert dict(paid)=={int(r):n for r,n in owner['paid_profile'].items()} + assert invoice['compiler']==64*74**3 + assert invoice['local_adapters']==max(p['local_adapters']for p in invoice['providers'].values()) + assert invoice['local_primitive_bound']==max(p['local_primitive_bound']for p in invoice['providers'].values()) + # Recount the retained dedicated-bank envelope independently. Its geometry + # stays fixed, while every local primitive and wrapper comes from the actual + # selected provider/orientation sums above. + parent_live,parent_physical,parent_idle=11704,12218,16128 + parent_banks,rem=divmod(parent_live-2*112*4*8,9);assert rem==0 and parent_physical==parent_live+parent_banks+8+2 # parent R0=504 dedicated helpers per stage bank + assert owner['source_idle_children_charged']==parent_idle + bridges,shifts=2*112*72,4*112*8;moves=2*shifts + nonlocal_items=(4*112*8*9+2*112*8*9+2*72*R+parent_idle+9*parent_banks+bridges+shifts+moves+parent_live+parent_physical+invoice['wrapper_elementary_factors_charged']) + outside=8*nonlocal_items+64*73 + pervertex=(invoice['selected_real_component_primitives']+bridges+shifts+moves+parent_live+(72*invoice['local_adapters']+outside)*invoice['compiler']+64*parent_physical) + rebased=pervertex+65*(invoice['physical']-parent_physical)+(invoice['live']-parent_live) + assert invoice['unhosted_pervertex']==pervertex and invoice['hosted_rebased_pervertex']==rebased + used=max(pervertex,rebased) + prior=invoice['retained_prior_overcharge'] + if prior is not None: + assert hash_ok(prior['sha256']) and type(prior['previous_pervertex_allowance']) is int and prior['previous_pervertex_allowance']>0 + assert prior['added_complete_new_pervertex']==pervertex + assert prior['policy']=='Retain old allowance and add entire fresh mixed recount.' + used=max(used,prior['previous_pervertex_allowance']+pervertex) + assert invoice['conservative_pervertex_used']==used + finite=invoice['finite'] + assert 02*48*48) + assert actual_checks==invoice['strict_checks'] and all(actual_checks.values()) + bit_path=P/'inputs/PR543-EXPECTED.json';bit_data=bit_path.read_bytes() + assert hashlib.sha1(b'blob '+str(len(bit_data)).encode()+b'\0'+bit_data).hexdigest()=='b61d859826246e0c3dabbe096e57ad7015eadfd5' + bit=json.loads(bit_data)['nine'] + c=Q(bit['bit_lower']) + H={int(r):n for r,n in owner['paid_profile'].items()};pin('expected.global_profile',owner['paid_profile']) + # Claimed lower endpoints come from the spec; discovery derives them with the same certified moment engine. + # Either way they are verified below (accepted at b, rejected at b+1e-24). + if DISCOVER:b=Q(M.certify(H,73,owner['live'],False)['lower']);conservative_b=Q(M.certify(H,73,owner['live'],True)['lower']) + else:b=Q(X['complex_lower']);conservative_b=Q(X['conservative_complex_lower']) + assert owner['template_sha256']==invoice['template_sha256'] and owner_sha==invoice['owner_audit_sha256'] + pin('expected.live',owner['live']);pin('expected.physical',owner['physical']);assert owner['deficit']==2560 + assert owner['banked_residuals']==0 + def check_moment(side,h,m,W,lower,deficit,bad): + assert m*W-sum(r*n for r,n in h.items())==deficit and m*m>2*max(h)**2 + rows=[] + for z,accept in [(lower,True),(lower+Q(1,10**24),False)]: + l,u=M.moment(h,m,W,z,bad);ll,uu=B.moment(m,W,list(h.items()),z) + if bad: + fl,fu=B.moment(m,W,[(1,32*m*m*sum(h.values()))],z);ll+=fl/10**16;uu+=fu/10**16 + assert (u<1 and uu<1)if accept else(l>1 and ll>1) + rows.append(dict(side=side,surcharge=bad,endpoint=str(z),accept=accept,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)])) + return rows + bitH={int(r):n for r,n in bit['profile'].items()} + bit_moments=check_moment('bit',bitH,64,bit['bit']['live'],c,9984,True) + conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,2560,True) + assert bit['bit']['two_level_coefficient_bits']0 + ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512) + cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a) + q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18) + bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}} + outer=A.assembly(chain[-1],bb,bridge,k,eta=eta,beta=beta);assert len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values()) + controls=[] + for name,kk,ee,be in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]: + try:A.assembly(chain[-1],bb,bridge,kk,eta=ee,beta=be) + except AssertionError:controls.append(name) + else:raise AssertionError(name) + return k,cuts,outer,controls + conservative_k,conservative_cuts,conservative_outer,conservative_controls=outer_witness(conservative_b) + pin('expected.conservative_kappa_decimal',dec(conservative_k)) + # Only after every conservative supplier/admission/outer check succeeds is + # the reviewed native exact-complex recurrence selected. Bit charge stays. + native_moments=check_moment('complex',H,73,owner['live'],b,2560,False) + k,cuts,outer,controls=outer_witness(b) + pin('expected.kappa_decimal',dec(k)) + assert M.moment(H,73,owner['live'],b,True)[0]>1 + assert M.moment(bitH,64,bit['bit']['live'],c+Q(1,10**24),False)[1]<1 + model_controls=['native_complex_endpoint_rejected_with_old_surcharge','omitting_bit_surcharge_would_fail_next_endpoint_rejection'] + moments=bit_moments+native_moments + input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'inputs/PR543-EXPECTED.json':sha(bit_path)} + input_hashes.update({'engines/'+name+'.py':sha(P/'engines'/(name+'.py'))for name in ('moment','base_two_moment','outer')}) + return dict(status='PASS_FRESH_MIXED_048_ALLCOLD_NATIVE_EXACT_ASSEMBLY',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex',gain_over_pinned569_percent=dec(100*(k/Q(X['gain_baseline_kappa'])-1)),complex_profile=H,provider_counts=invoice['provider_counts'],surcharge_model={'complex':False,'bit':True},conservative_complex_lower=str(conservative_b),conservative_complex_decimal=dec(conservative_b),conservative_kappa=str(conservative_k),conservative_kappa_decimal=dec(conservative_k),conservative_moments=conservative_moments,conservative_bootstrap=conservative_cuts,conservative_outer={n:str(v)for n,v in conservative_outer['strict_constraints'].items()},conservative_controls=conservative_controls,model_controls=model_controls,native_correction_gain=dec(k-conservative_k),template_sha256=owner['template_sha256'],input_sha256=input_hashes,bit_supplier=dict(pr=543,repository='eumemic/integer-mult-bounds',commit='2065fe4f72a914d907f1046603f5a36f17018535',path='research/e8-bit-r420/EXPECTED.json',git_blob_sha1='b61d859826246e0c3dabbe096e57ad7015eadfd5',replay_scope='Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit.'),moments=moments,bootstrap=cuts,outer={n:str(v)for n,v in outer['strict_constraints'].items()},controls=controls,scope='Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The frozen PR582 plain-joint-prefix, added-kernel and entrance-promoted provider dispatch with the new frame coalescences composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.') +if __name__=='__main__': + import sys + package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists() + owner_path=C/'audit/OWNERS-AND-PROFILE.json';invoice_path=C/'audit/PREFIX-AND-INVOICE.json' + owner,invoice=read(owner_path),read(invoice_path) + assert owner['template_sha256']==read(C/'hosted/HOSTED.json')['template_sha256'] + r=assemble(owner,invoice,sha(owner_path),sha(invoice_path));out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],r['kappa_decimal']) diff --git a/research/pr643-improvement-20261013/witness/code/assembly_controls.py b/research/pr643-improvement-20261013/witness/code/assembly_controls.py new file mode 100644 index 0000000000..d3f0e8c03e --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/assembly_controls.py @@ -0,0 +1,251 @@ +"""Independent admission controls for the N-provider native-complex assembly (per-provider controls). + +Prepared with OpenAI Codex assistance; Apache-2.0. Mutation receipts are +rebound to their new owner digest, so unrelated stale hashes cannot conceal +an incomplete width, provider, orientation, paid-profile or finite check. +The fresh physical replay remains a separate prerequisite. +""" +import argparse +import copy +import itertools +import math +import hashlib +import json +import os +from pathlib import Path +import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent)) +from witness import * + +assert __debug__, 'Assertions required' +P = Path(__file__).resolve().parent +sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest() +digest = lambda x: hashlib.sha256(json.dumps(x, sort_keys=True, separators=(',', ':')).encode()).hexdigest() + + +def verify(owner_path, invoice_path, source_package): + os.environ['GAIN_PR564_SOURCE'] = str(source_package.resolve()) + from assemble import assemble + owner = json.loads(owner_path.read_text()) + invoice = json.loads(invoice_path.read_text()) + baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path)) + + def empty_maps(o, i): + i['strict_checks'] = {} + i['providers'] = {} + + def understated_stock(o, i): + o['physical'] -= 1 + i['physical'] -= 1 + i['physical_stock_identity']['coefficient_work'] -= 1 + + def changed_profile(o, i): + o['paid_profile']['1'] += 2 + o['paid_profile']['2'] -= 1 + + def wrong_orientation(o, i): + c = next(c for c in i['selected_calls'] if c['stage'] == 0) + c['orientation'] = 'backward' + p = i['providers'][c['provider_id']] + z = p['local']['backward'] + c['program_sha256'] = p['program_hashes']['backward'] + for name in ('events', 'macros', 'real_component_primitives', + 'coefficient_work_primitive_count', 'pre_wrappers', 'post_wrappers'): + c[name] = z[name] + i['selected_real_component_primitives'] = sum(c['real_component_primitives'] for c in i['selected_calls']) + i['selected_coefficient_work_primitive_count'] = sum(c['coefficient_work_primitive_count'] for c in i['selected_calls']) + + def understated_prefix(o, i): + for p in i['providers'].values(): + for z in p['local'].values(): + z['prefix_bits'], z['prefix_l1'] = 1, '1' + i['global_prefix_bits'] = 1 + 37 + 72 + 72 + 4 + + def reordered_calls(o, i): + i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0] + + def no_cold_wrappers(o, i): + for p in i['providers'].values(): + p['entering_helpers'] -= 4 + for z in p['local'].values():z['pre_wrappers'] = z['post_wrappers'] = p['entering_helpers'] + for c in i['selected_calls']: + c['entering_helpers'] = c['pre_wrappers'] = c['post_wrappers'] = i['providers'][c['provider_id']]['entering_helpers'] + i['wrapper_elementary_factors_charged'] = sum(2*c['pre_wrappers'] for c in i['selected_calls'])*i['factors_per_wrapper'] + + controls = [ + ('empty_certification_maps', empty_maps), + ('failed_invoice_status', lambda o, i: i.__setitem__('status', 'FAIL')), + ('nonboolean_precision_check', lambda o, i: i['strict_checks'].__setitem__('precision', 'true')), + ('wrong_owner_role_count', lambda o, i: o.__setitem__('actual_helper_owner_charts', o['actual_helper_owner_charts'] - 1)), + ('understated_physical_stock', understated_stock), + ('changed_profile_same_rank_mass', changed_profile), + ('insufficient_finite_C0', lambda o, i: i['finite'].__setitem__('required_C0_bits', 210001)), + ('missing_finite_check', lambda o, i: i['strict_checks'].pop('halving')), + ('wrong_reflected_orientation_selfconsistent_totals', wrong_orientation), + ('missing_selected_call', lambda o, i: i['selected_calls'].pop()), + ('wrong_selected_primitive_sum', lambda o, i: i.__setitem__('selected_real_component_primitives', i['selected_real_component_primitives'] - 1)), + ('wrong_selected_coefficient_work_sum', lambda o, i: i.__setitem__('selected_coefficient_work_primitive_count', i['selected_coefficient_work_primitive_count'] - 1)), + ('unpaid_wrapper_factors', lambda o, i: i.__setitem__('wrapper_elementary_factors_charged', i['wrapper_elementary_factors_charged'] - 144)), + ('wrong_global_compiler', lambda o, i: i.__setitem__('compiler', 1)), + ('wrong_global_adapter_maximum', lambda o, i: i.__setitem__('local_adapters', 1)), + ('understated_exact_prefix_and_global_sum', understated_prefix), + ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)), + ('wrong_row_prefix_reserve', lambda o, i: i.__setitem__('row_prefix_extra', 0)), + ('wrong_parent_geometry_charge', lambda o, i: i.__setitem__('unhosted_pervertex', 1)), + ('wrong_rebased_geometry_charge', lambda o, i: i.__setitem__('hosted_rebased_pervertex', 1)), + ('wrong_complete_pervertex_envelope', lambda o, i: i.__setitem__('conservative_pervertex_used', 1)), + ('wrong_prior_added_complete_invoice', lambda o, i: i['retained_prior_overcharge'].__setitem__('added_complete_new_pervertex', 1)), + ('wrong_finite_router_bits', lambda o, i: i['finite'].__setitem__('router_bits', 1)), + ('wrong_finite_literal_bits', lambda o, i: i['finite'].__setitem__('literal_bits', 1)), + ('wrong_finite_physical_stock_bits', lambda o, i: i['finite'].__setitem__('physical_stock_bits', 1)), + ('wrong_finite_row_coefficient', lambda o, i: i['finite'].__setitem__('physical_row_coefficient', 1)), + ('reordered_complete_calls', reordered_calls), + ('understated_explicit_idle_remainders', lambda o, i: o.__setitem__('explicit_idle_remainder_children', o['explicit_idle_remainder_children']-1)), + ('understated_actual_chart_types', lambda o, i: o.__setitem__('actual_73column_sigmas', o['actual_73column_sigmas']-1)), + ('wrong_cross_replica_role_count', lambda o, i: o.__setitem__('cross_replica_helper_roles', o['cross_replica_helper_roles']-1)), + ('old_no_cold_wrapper_counts_selfconsistent', no_cold_wrappers), + ] + + def resync(i, c): + p = i['providers'][c['provider_id']] + c['program_sha256'] = p['program_hashes'][c['orientation']] + c['entering_helpers'], c['entrance_rank'] = p['entering_helpers'], p['entrance_rank'] + for name in ('events','macros','real_component_primitives','coefficient_work_primitive_count','pre_wrappers','post_wrappers'): + c[name] = p['local'][c['orientation']][name] + + # Every provider gets the full per-provider control set, substituting a partner provider where needed. + for P in PIDS: + Qp = partner(P) + widths = invoice['providers'][P]['widths'] + + def forged_program_hash(o, i, P=P): + i['providers'][P]['program_hashes']['forward'] = '0' * 64 + for c in i['selected_calls']: + if c['provider_id'] == P: + c['program_sha256'] = '0' * 64 + + def wrong_selected_call(o, i, P=P): + c = next(c for c in i['selected_calls'] if c['provider_id'] == P) + d = next(d for d in i['selected_calls'] if d['provider_id'] != P and (d['stage'] - c['stage']) % 2 == 0) + c['stage'], d['stage'], c['replica'], d['replica'] = d['stage'], c['stage'], d['replica'], c['replica'] + + def stale_program(o, i, P=P, Qp=Qp): + p = i['providers'][P] + p['program_hashes'] = copy.deepcopy(i['providers'][Qp]['program_hashes']) + for c in i['selected_calls']: + if c['provider_id'] == P: + c['program_sha256'] = p['program_hashes'][c['orientation']] + + def stale_profile(o, i, P=P, Qp=Qp): + p = i['providers'][P] + p['paid_profile'] = copy.deepcopy(i['providers'][Qp]['paid_profile']) + p['children'] = sum(p['paid_profile'].values()) + + def moved(o, i, P=P): + a = next(c for c in i['selected_calls'] if c['provider_id'] == P) + b = next(c for c in i['selected_calls'] if c['provider_id'] != P and c['orientation'] == a['orientation']) + a['provider_id'], b['provider_id'] = b['provider_id'], a['provider_id'] + resync(i, a); resync(i, b) + + def compensating(o, i, P=P, Qp=Qp): + # Two dishonest profiles that cancel exactly in the dispatch-weighted aggregate. + g = math.gcd(COUNTS[P], COUNTS[Qp]); dp, dq = COUNTS[Qp] // g, COUNTS[P] // g + p, q = i['providers'][P], i['providers'][Qp] + p['paid_profile']['1'] += dp; q['paid_profile']['1'] -= dq + p['children'] += dp; q['children'] -= dq + + def forged_recipe(o, i, P=P): + name = 'CLIFFORD-RECIPES.json' + i['providers'][P]['artifacts'][name] = '0'*64 + o['source_artifacts']['providers/'+P+'/'+name] = '0'*64 + + def forged_phase(o, i, P=P): + i['providers'][P]['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] = '0'*64 + o['provider_phase_semantic_sha256'][P] = i['provider_phase_semantic_sha256'][P] = '0'*64 + + controls += [ + (P + ':missing_provider', lambda o, i, P=P: i['providers'].pop(P)), + (P + ':missing_backward_orientation', lambda o, i, P=P: i['providers'][P]['local'].pop('backward')), + (P + ':unpaid_scalar_primitive', lambda o, i, P=P: i['providers'][P]['local']['forward'].__setitem__('real_component_primitives', i['providers'][P]['local']['forward']['real_component_primitives'] - 1)), + (P + ':wrong_local_artifact_binding', lambda o, i, P=P: i['providers'][P]['artifacts'].__setitem__('LOCAL-PROGRAMS.json.gz', '0' * 64)), + (P + ':false_dirty_restoration', lambda o, i, P=P: i['providers'][P]['local']['backward'].__setitem__('all_dirty_helper_columns_restored', False)), + (P + ':wrong_declared_provider_count', lambda o, i, P=P: i['provider_counts'].__setitem__(P, i['provider_counts'][P] + 1)), + (P + ':wrong_local_compiler', lambda o, i, P=P: i['providers'][P].__setitem__('compiler', 1)), + (P + ':wrong_local_adapter_charge', lambda o, i, P=P: i['providers'][P].__setitem__('local_adapters', 1)), + (P + ':wrong_local_primitive_bound', lambda o, i, P=P: i['providers'][P].__setitem__('local_primitive_bound', 1)), + (P + ':forged_provider_and_call_program_hash', forged_program_hash), + (P + ':provider_at_wrong_call', wrong_selected_call), + (P + ':stale_partner_program_consistent_call_hashes', stale_program), + (P + ':stale_partner_profile_consistent_child_total', stale_profile), + (P + ':relocated_against_partner_same_counts', moved), + (P + ':compensating_false_profiles_with_' + Qp, compensating), + (P + ':synchronized_forged_source_recipe_hash', forged_recipe), + (P + ':synchronized_forged_phase_review_semantics', forged_phase), + ] + # Width order and inventory: swap the first helper of every pair of distinct widths (same inventory), + # and shift one unit between them (same total). + first = {} + for h, w in enumerate(widths): + first.setdefault(w, h) + for wa, wb in itertools.combinations(sorted(first), 2): + def swap(o, i, P=P, a=first[wa], b=first[wb]): + w = i['providers'][P]['widths']; w[a], w[b] = w[b], w[a] + def shift(o, i, P=P, a=first[wa], b=first[wb]): + w = i['providers'][P]['widths']; w[a] += 1; w[b] -= 1 + controls.append((P + ':width_order_swap_%d_%d' % (wa, wb), swap)) + controls.append((P + ':width_inventory_shift_%d_%d' % (wa, wb), shift)) + for h in SPOT: + def cold_swap(o, i, P=P, h=h): + w = i['providers'][P]['widths']; j = w.index(9); w[h], w[j] = w[j], w[h] + controls.append((P + ':cold_helper_width_swap_%d' % h, cold_swap)) + rejected = [] + accepted = [] + for name, mutate in controls: + o, i = copy.deepcopy(owner), copy.deepcopy(invoice) + mutate(o, i) + oh = digest(o) + i['owner_audit_sha256'] = oh + try: + assemble(o, i, oh, digest(i)) + except (AssertionError, KeyError): + rejected.append(name) + else: + # Discovery has no pinned values to reject spec-only mutations; the strict run must reject every control. + if not DISCOVER: + raise AssertionError('Invalid admission receipt accepted: ' + name) + accepted.append(name) + try: + assemble(owner, invoice, '0' * 64, sha(invoice_path)) + except AssertionError: + rejected.append('wrong_owner_receipt_hash') + else: + raise AssertionError('Wrong owner digest accepted') + pin('expected.assembly_controls_rejected', len(rejected)) + assert baseline['controls'] == ['next_grid', 'zero_eta', 'zero_beta', 'unit_beta'] + assert baseline['conservative_controls'] == baseline['controls'] + assert baseline['surcharge_model'] == {'complex': False, 'bit': True} + assert len(baseline['model_controls']) == 2 + return dict( + status='PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS', + valid_receipt_kappa=baseline['kappa'], + input_sha256=baseline['input_sha256'], + assembler_sha256=sha(Path(__file__).resolve().parent / 'assemble.py'), + rejected_controls=rejected, + discovery_accepted_controls=accepted, + exact_outer_controls=baseline['controls'], + conservative_outer_controls=baseline['conservative_controls'], + recurrence_model_controls=baseline['model_controls'], + scope='Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay.', + ) + + +if __name__ == '__main__': + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--source-package', type=Path, required=True) + ap.add_argument('--owner', type=Path, required=True) + ap.add_argument('--invoice', type=Path, required=True) + ap.add_argument('--out', type=Path, required=True) + a = ap.parse_args() + assert not a.out.exists() + result = verify(a.owner, a.invoice, a.source_package) + a.out.write_text(json.dumps(result, indent=2) + '\n') + print(result['status'], len(result['rejected_controls'])) diff --git a/research/pr643-improvement-20261013/witness/code/audit_allcold.py b/research/pr643-improvement-20261013/witness/code/audit_allcold.py new file mode 100644 index 0000000000..e29d90e89a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/audit_allcold.py @@ -0,0 +1,232 @@ +"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit. +Imports no emitter, optimizer, expander, edge-coloring, or source hosting code. +CLI: BASE HOSTED REPORT [--mutation-controls] +Each provider is independently read from BASE/providers, never from a baseline width histogram. +OpenAI Codex two-provider width-seven extension; retains all inherited independent controller checks. +The exact 63 width-seven and 9 plain calls are frozen below. +""" +import sys,json,gzip,hashlib,copy +assert __debug__, 'Assertions must remain enabled' +from pathlib import Path +from collections import Counter,defaultdict +import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent)) +from witness import * +from generated_identity import artifact_identities +BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz') +ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json') +ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json') +sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +provider_ids=PIDS +providers={};registry={};phase_semantic_hashes={};artifact_semantic_hashes={} +required_artifacts={'work/complex-nine-native/DATA-PHASES.json'} +provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json', + 'INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json') +for pid in provider_ids: + p=BASE/'providers'/pid + c=read(p/'CANONICAL-WORD.json.gz');checks=read(p/'LOCAL-CHECKS.json') + programs=read(p/'LOCAL-PROGRAMS.json.gz');replay=read(p/'INDEPENDENT-LOCAL-REPLAY.json') + phase=read(p/'CLIFFORD-REVIEW.json');adapters=read(p/'RESIDUAL-ADAPTERS.json')['recipes'] + widths=[len(c['frames'][c['final'][2*c['v']+h]])-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])] # HPE: residual width |final|-|start| + assert all(widths[h]==8 for h in SPOT);pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())}) + canonical_sha=sha(p/'CANONICAL-WORD.json.gz');programs_sha=sha(p/'LOCAL-PROGRAMS.json.gz') + assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY' + assert replay['canonical_word_sha256']==canonical_sha and replay['local_programs_sha256']==programs_sha + assert replay['v']==c['v'] and replay['helpers']==c['R'] + assert set(programs)==set(checks)==set(replay['local'])==set(replay['paid_profiles'])=={'forward','backward'} + for orientation,events in programs.items(): + ck=checks[orientation];rr=replay['local'][orientation] + assert hashlib.sha256(json.dumps(events,sort_keys=True,separators=(',',':')).encode()).hexdigest()==ck['sha256'] + assert ck['events']==len(events) and ck['all_columns']==2*c['v']+c['R'] + assert ck['private_centers_cleared'] and ck['private_coefficient_stream_cleared_after_each_macro'] + assert rr['all_exact_columns']==2*c['v']+c['R'] and rr['private_work_erased'] + literal=Counter(e[-1]for e in events if e[0]in('climb','center')) + assert dict(literal)=={int(r):n for r,n in ck['paid_profile'].items()}=={int(r):n for r,n in c['local_profile'].items()} + assert ck['paid_profile']==replay['paid_profiles'][orientation] + assert phase['canonical_word_sha256']==canonical_sha and phase['recipe_sha256']==sha(p/'CLIFFORD-RECIPES.json') + assert phase['all_child_equalities_include_global_phase'] + artifact_semantic_hashes[pid]=artifact_identities(p) + pin('providers.%s.artifact_semantic_sha256'%pid,artifact_semantic_hashes[pid]) + phase_semantic_hashes[pid]=artifact_semantic_hashes[pid]['CLIFFORD-REVIEW.json'] + for h,w in enumerate(widths): + assert 0>i)&1==0);a=q^(1<>i&1 else 0)for i in order]+[1<2*max(paid)**2 + return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72) + +r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256'] +assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items()) +controls=[] +def reject(name,mut): + if '--mutation-controls' not in sys.argv[4:]:return + q=copy.deepcopy(ct);mut(q) + try:audit(q) + except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name) + else:raise AssertionError('ACCEPTED '+name) +enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4) +reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)])) +reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0])) +reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA)) +reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1)) +reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72)) +reject('omit idle remainder',lambda q:q['idle_children'].pop()) +reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1)) +# Per-provider substitution controls: every provider is swapped against a partner provider. +for P in provider_ids: + Qp=partner(P) + at_p=lambda q,P=P:next(c for c in q['calls']if c['provider_id']==P) + diff=[h for h in range(R)if providers[P]['widths'][h]!=providers[Qp]['widths'][h]] + narrow=next(h for h in range(R)if providers[P]['widths'][h]<9) + reject(P+': wrong provider at its invocation',lambda q,P=P,Qp=Qp,at_p=at_p:at_p(q).__setitem__('provider_id',Qp)) + reject(P+': stale per-call local program hash',lambda q,Qp=Qp,at_p=at_p:at_p(q).__setitem__('local_program_sha256',registry[Qp]['local_program_checks'][at_p(q)['orientation']]['sha256'])) + reject(P+': stale serialized provider program',lambda q,P=P,Qp=Qp:q['local_providers'][P].__setitem__('local_programs',registry[Qp]['local_programs'])) + reject(P+': unbound residual adapter hash',lambda q,P=P:q['local_providers'][P].__setitem__('residual_adapter_sha256','0'*64)) + if diff:reject(P+': partner width in provider width registry',lambda q,P=P,Qp=Qp,h=diff[0]:q['local_providers'][P]['widths'].__setitem__(h,providers[Qp]['widths'][h])) + reject(P+': wrong per-call residual width',lambda q,at_p=at_p,h=narrow:at_p(q)['owners'][2*V+h][1].__setitem__(3,at_p(q)['owners'][2*V+h][1][3]-1)) + reject(P+': wrong sweep provider',lambda q,P=P,Qp=Qp:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep'and DISPATCH[e['stage'],e['replica']]==P).__setitem__('provider_id',Qp)) + reject(P+': entering helper width silently restored to nine',lambda q,P=P,h=narrow:q['local_providers'][P]['widths'].__setitem__(h,9)) +report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,widths_by_provider={pid:dict(sorted(Counter(providers[pid]['widths']).items()))for pid in provider_ids},provider_counts=dict(Counter(c['provider_id']for c in ct['calls'])),all_provider_program_phase_and_wrapper_bindings=True,scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.') +REPORT.parent.mkdir(parents=True,exist_ok=True) +REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2)) + +owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],provider_phase_semantic_sha256=phase_semantic_hashes,provider_artifact_semantic_sha256=artifact_semantic_hashes,controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest()) +(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n') + +# Literal residual frames are a compact export of the already checked offsets, +# not another global replay. Every row names its actual inherited axes. +frames=[] +for z in ct['idle_children']: + axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes'])) + tail=axes[z['pending_offset']:] + assert len(tail)==z['rank'] + frames.append(dict(z,orthogonal_axes=tail)) +frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode() +portable=bytearray(gzip.compress(frame_raw,mtime=0));portable[9]=255 +(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(bytes(portable)) +frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'], + uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames), + rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())), + source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(), + scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.') +(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n') + diff --git a/research/pr643-improvement-20261013/witness/code/bind_providers_portable.py b/research/pr643-improvement-20261013/witness/code/bind_providers_portable.py new file mode 100644 index 0000000000..e758a0679a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/bind_providers_portable.py @@ -0,0 +1,67 @@ +"""Bind freshly verified plain and width-seven four-cold providers to the frozen literal owner plan. +Prepared with OpenAI Codex assistance; Apache-2.0. All byte-stable native +files are pinned to the plan. Only validated phase-receipt timing/serialization +and directory fields are rebound; no dispatch, width or owner choice changes. +""" +import argparse,copy,gzip,hashlib,json,shutil +from collections import Counter +from pathlib import Path +import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent)) +from witness import * +from generated_identity import artifact_identities +assert __debug__, 'Assertions required' +ap=argparse.ArgumentParser(description=__doc__) +for name in ('baseline','plan','out'):ap.add_argument('--'+name,type=Path,required=True) +ap.add_argument('--provider',action='append',required=True,help='PID=DIR');a=ap.parse_args();assert not a.out.exists();a.out.mkdir(parents=True) +def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +base=a.out/'base';shutil.copytree(a.baseline/'complex-global/base',base) +ap2=dict(x.split('=',1)for x in a.provider);dirs={k:Path(v)for k,v in ap2.items()};assert set(dirs)==set(PIDS) +for pid,src in dirs.items():shutil.copytree(src,base/'providers'/pid) +pin('data.plan_sha256',sha(a.plan)) +plan=read(a.plan);original=copy.deepcopy(plan);sources={};helpers=set() # R: helper count per provider word; all providers must agree +assert set(plan['provider_registry'])==set(dirs) +assert {(c['stage'],c['replica']):c['provider']for c in plan['provider_calls']}==DISPATCH,'PLAN dispatch differs from spec dispatch' +stable=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json') +for pid,desc in plan['provider_registry'].items(): + d=base/'providers'/pid + word,program,checks,native,phase=[read(d/name)for name in('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json')] + assert (word['v'],word['h'],len(word['centers']))==(112,9,8) and type(word['R']) is int and word['R']>0;helpers.add(word['R']) + assert word['ports']==desc['ports'] and word['centers']==desc['centers'] + widths=[len(word['frames'][word['final'][r]])-len(word['frames'][word['start'][r]])for r in range(2*112,2*112+word['R'])] # HPE: residual width |final|-|start| + assert all(widths[h]==8 for h in SPOT) + assert widths==desc['widths'];pin('providers.%s.inventory'%pid,{str(k):v for k,v in sorted(Counter(widths).items())}) + assert native['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY' + pin('providers.%s.native_negative_controls'%pid,len(native['negative_controls_rejected'])) + assert native['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and native['local_programs_sha256']==sha(d/'LOCAL-PROGRAMS.json.gz') + assert phase['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES' + assert phase['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and phase['recipe_sha256']==sha(d/'CLIFFORD-RECIPES.json') + assert phase['all_child_equalities_include_global_phase'] is True and phase['endpoint_adapters']==224 + pin('providers.%s.phase_edges'%pid,phase['directed_edges']) + assert set(program)==set(checks)=={'forward','backward'} + expected={int(r):n for r,n in checks['forward']['paid_profile'].items()};pin('providers.%s.expected_profile'%pid,checks['forward']['paid_profile']) + for orientation,events in program.items(): + profile=Counter() + for e in events: + if e[0]=='climb':profile[e[5]]+=1 + elif e[0]=='center':profile[e[4]]+=1 + assert dict(profile)==expected=={int(r):n for r,n in checks[orientation]['paid_profile'].items()}=={int(r):n for r,n in native['paid_profiles'][orientation].items()} + assert hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()==checks[orientation]['sha256'] + identities=artifact_identities(d) + pin('providers.%s.artifact_semantic_sha256'%pid,identities) + assert identities==desc['artifact_semantic_sha256'] + for name in ('LOCAL-CHECKS.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json'): + assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-reference artifact') + for c in plan['provider_calls']: + if c['provider']==pid: + assert c['orientation']==('forward'if c['stage']%2==0 else'backward') + assert c['local_program_sha256']==checks[c['orientation']]['sha256'] + desc['directory']='providers/'+pid + desc['artifact_sha256']={name:sha(d/name)for name in desc['artifact_sha256']} + sources[pid]=dict(artifact_sha256=desc['artifact_sha256'],canonical_content_sha256=hashlib.sha256(json.dumps(word,sort_keys=True,separators=(',',':')).encode()).hexdigest(),all_phase_edges=phase['directed_edges']) +assert len(helpers)==1,'providers disagree on helper count R: %s'%sorted(helpers) +plan['runtime_source_plan_sha256']=sha(a.plan) +(a.out/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n') +receipt=dict(status='PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING',source_plan_sha256=sha(a.plan),runtime_plan_sha256=sha(a.out/'PLAN.json'),providers=sources,only_rebound_fields=['provider_registry.directory','provider_registry.artifact_sha256','runtime_source_plan_sha256']) +(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n') +print(receipt['status']) diff --git a/research/pr643-improvement-20261013/witness/code/build_cold_end.py b/research/pr643-improvement-20261013/witness/code/build_cold_end.py new file mode 100644 index 0000000000..b39d7a6771 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/build_cold_end.py @@ -0,0 +1,160 @@ +"""Cold low-frame-ended helpers with a refactored exact cleanup: constructor. Apache-2.0. +DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. + +usage: build_cold_end.py --input FULL-WORD.json.gz --recipe RECIPE.json.gz --out DIR + +The input is a hyperplane-ended (HPE) provider word. RECIPE (all data, no code): + premix rank-0 gates on helpers at their start frame (frame [] for cold helpers, E for entering ones); they become the + head of section A, i.e. they run after the entry + adapters and paid wrappers, so every gate on a cold-ended helper follows its wrapper R_{0,U}^-1; + cleanup the complete new cleanup gate list (an exact refactorisation of the inverse, not the literal one); + early_cleanup [[cleanup index, frame], ...]: gates run right after B at the given frame (the multi-gate tail); + cold_ends {helper: frame}: cold helpers (no entrance) that end at that frame instead of FULL; + entering_ends optional {helper: frame}: further entering helpers ending below FULL under the same refactored cleanup; + refactored_cleanup descriptive metadata copied into the word (it also switches the transport audit from the literal + cleanup assertion to exact replay of the refactored one); + output_content_sha256. +The constructor only splices. It checks the recipe's shape (premix on cold helpers at frame [], cold ends on cold +helpers, every inherited hyperplane-end gate and terminal frame kept) and recomputes the paid local profile and the +descriptive width inventory from the actual frame chains. Exactness of the scalar program, all frame chains, the cone +pre-check, the wrapper order and the profile are re-checked independently by hpe_audit_and_transport.py; the paired +raw-word mutation audit is cold_end_controls.py.""" +import argparse, gzip, hashlib, json +from collections import Counter +from pathlib import Path + + +def span(vs): + p = {} + for x in vs: + for k in sorted(p, reverse=True): + if x >> k & 1: x ^= p[k] + if x: + k = x.bit_length() - 1 + for j in p: + if p[j] >> k & 1: p[j] ^= x + p[k] = x + return tuple(p[k] for k in sorted(p, reverse=True)) + + +def regs(e): return [e[1]] + ([e[2]] if e[0] == 'add' else []) + + +def chain_profile(w): + """Paid climbs of the A, B, tail and final chains (centre descents are unchanged by this step and not counted).""" + v, R = w['report']['v'], w['report']['R']; n = 2*v + R + cur = [() for _ in range(n)] + for i, p in enumerate(w['ports']): cur[i] = span([p]) + for r, f in w.get('start_extra', {}).items(): cur[int(r)] = span(f) + prof = Counter() + + def climb(r, F): + assert span(list(cur[r]) + list(F)) == F, ('nonmonotone', r) + if len(F) > len(cur[r]): prof[len(F) - len(cur[r])] += 1 + cur[r] = F + for part in ('A', 'B'): + for e in w[part]: + for r in regs(e): climb(r, span(e[-1])) + for i, f in w.get('early_cleanup', []): + for r in regs(w['cleanup'][i]): climb(r, span(f)) + full = span([1 << i for i in range(9)]) + final = {int(r): span(f) for r, f in w.get('helper_final', {}).items()} + for r in range(n): + if v <= r < 2*v: continue # targets end at their port level; unchanged by this step (same A/B chains) + climb(r, final.get(r, full)) + return prof, cur + + +def apply(w, r): + assert 'helper_final' in w and 'early_cleanup' in w and 'refactored_cleanup' not in w, 'input must be an HPE word' + v, R = w['report']['v'], w['report']['R']; n = 2*v + R + entering = set(map(int, w['start_extra'])) + cold = {x for x in range(2*v, n) if x not in entering} + start = lambda x: span(w['start_extra'].get(str(x), [])) + for e in r['premix']: # rank 0: every register is a helper still at its start frame (cold: [], entering: E) = the gate frame + if e[0] == 'add' and v <= e[1] < 2*v: + # TARGET WRITE (explicit post-wrapper compensation): target += q * cold helper, both at frame [] (targets start at + # level 0 = frame []); it only writes the target, so no non-target register ever reads a target. + assert 2*v <= e[2] < n and e[2] in cold and span(e[-1]) == (), ('premix target write not rank-0 from a cold helper', e) + continue + assert e[0] in ('add', 'scale') and all(2*v <= x < n and start(x) == span(e[-1]) for x in regs(e)), ('premix gate not rank-0 on helpers at their start frame', e) + # FORWARD ABSORPTIONS (optional): [[t, gate], ...] = 'add' q += a*g inserted into A right after input-A gate t; gates + # sharing t run in recipe order. q must be DEAD from then on (no later INPUT forward gate + # touches it; later absorptions may write or read it, which only feeds other dead registers), so every input gate + # sees exactly its old operands and every live register's forward value is unchanged; both q and g must already sit + # at the gate frame (no climb: the frame chains and the paid profile of the input are unchanged). + absorb = [(int(t), list(e)) for t, e in r.get('forward_insertions', [])] + A = [list(e) for e in w['A']] + if absorb: + nA, nC, nB = len(w['A']), len(w['cut']), len(w['B']) + assert all(0 <= t < nA for t, _ in absorb), 'absorption point' + assert [t for t, _ in absorb] == sorted(t for t, _ in absorb), 'absorptions not in forward order' + after = {} + for t, e in absorb: + assert e[0] == 'add' and e[1] != e[2] and not (v <= e[1] < 2*v) and not (v <= e[2] < 2*v), ('absorption shape', e) + after.setdefault(t, []).append(e) + inp = [('A', e) for e in w['A']] + [('C', e) for e in w['cut']] + [('B', e) for e in w['B']] + cur = [() for _ in range(n)] + for i, p in enumerate(w['ports']): cur[i] = span([p]) + for x, f in w.get('start_extra', {}).items(): cur[int(x)] = span(f) + touched_later = [set() for _ in range(len(inp) + 1)] # registers touched by input gates after index t + for t in range(len(inp) - 1, -1, -1): + touched_later[t] = touched_later[t + 1] | set(regs(inp[t][1])) + for t, (sec, f) in enumerate(inp): + if sec != 'C': + for x in regs(f): cur[x] = span(f[-1]) + for e in after.get(t, []): + assert e[1] not in touched_later[t + 1], ('absorption into a live register', e) + assert cur[e[1]] == span(e[-1]) and cur[e[2]] == span(e[-1]), ('absorption frame is not both registers\' frame', e) + A = [] + for t, e in enumerate(w['A']): A.append(list(e)); A += after.get(t, []) + ends = {int(h): f for h, f in r['cold_ends'].items()} + assert ends and all(h in cold and str(h) not in w['helper_final'] for h in ends), 'cold ends must be new cold helpers' + eends = {int(h): f for h, f in r.get('entering_ends', {}).items()} # optional: further ENTERING helpers ending below FULL + assert all(h in entering and str(h) not in w['helper_final'] for h in eends), 'entering ends must be new entering helpers' + assert all(len(span(f)) < 9 for f in list(ends.values()) + list(eends.values())) + new_early = [(i, f) for i, f in r['early_cleanup']] + kept = {(json.dumps(r['cleanup'][i][:-1]), json.dumps(f)) for i, f in new_early} + for i, f in w['early_cleanup']: # every inherited hyperplane-end gate stays in the tail at its frame + assert (json.dumps(w['cleanup'][i][:-1]), json.dumps(f)) in kept, ('inherited HPE gate missing', i) + old_prof, _ = chain_profile(w) + out = dict(w) + out['A'] = [list(e) for e in r['premix']] + A + out['cleanup'] = r['cleanup'] + out['early_cleanup'] = [[i, f] for i, f in new_early] + out['helper_final'] = dict(w['helper_final'], **{str(h): f for h, f in sorted({**ends, **eends}.items())}) + out['refactored_cleanup'] = r['refactored_cleanup'] + new_prof, cur = chain_profile(out) + assert all(cur[h] == span(f) for h, f in {**ends, **eends}.items()), 'end frame is not the last frame of the helper' + lp = Counter({int(k): c for k, c in w['report']['local_profile'].items()}) + lp.subtract(old_prof); lp.update(new_prof) + assert min(lp.values()) >= 0 + rep = dict(w['report']) + rep['local_profile'] = {str(k): c for k, c in sorted(lp.items()) if c} + rep['local_rank_mass'] = sum(k*c for k, c in lp.items()) + inv = Counter({int(k): c for k, c in w['report']['width_inventory'].items()}) + for h, f in ends.items(): inv[9] -= 1; inv[len(span(f))] += 1 # cold: width = |U| - 0 + for h, f in eends.items(): # entering: width = |U| - |E| + e = len(span(w['start_extra'][str(h)])); inv[9 - e] -= 1; inv[len(span(f)) - e] += 1 + assert min(inv.values()) >= 0 + rep['width_inventory'] = {str(k): c for k, c in sorted(inv.items()) if c} + out['report'] = rep + return out + + +if __name__ == '__main__': + ap = argparse.ArgumentParser(); ap.add_argument('--input', type=Path, required=True); ap.add_argument('--recipe', type=Path, required=True) + ap.add_argument('--out', type=Path, required=True) + a = ap.parse_args() + rd = lambda p: json.loads(gzip.decompress(p.read_bytes()) if p.suffix == '.gz' else p.read_bytes()) + w, r = rd(a.input), rd(a.recipe) + w = apply(w, r) + raw = json.dumps(w, sort_keys=True, separators=(',', ':')).encode(); h = hashlib.sha256(raw).hexdigest() + assert h == r['output_content_sha256'], h + a.out.mkdir(parents=True, exist_ok=False) + (a.out/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw, mtime=0)) + (a.out/'COLD-END-CONSTRUCTION.json').write_text(json.dumps(dict(status='PASS_COLD_LOW_FRAME_ENDS_SPLICED', + cold_ended_helpers=sorted(int(x) for x in r['cold_ends']), terminal_dims=sorted(Counter(len(span(f)) for f in r['cold_ends'].values()).items()), + premix_gates=len(r['premix']), early_cleanup_gates=len(r['early_cleanup']), cleanup_gates=len(r['cleanup']), + local_profile=w['report']['local_profile'], width_inventory=w['report']['width_inventory']), indent=1) + '\n', newline='\n') + print('PASS', len(r['cold_ends']), 'cold low-frame-ended helpers;', len(r['premix']), 'premix gates;', len(r['cleanup']), 'cleanup gates') diff --git a/research/pr643-improvement-20261013/witness/code/build_frame_regroup.py b/research/pr643-improvement-20261013/witness/code/build_frame_regroup.py new file mode 100644 index 0000000000..c5321f5671 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/build_frame_regroup.py @@ -0,0 +1,53 @@ +"""Apply recipe-bound gate frame changes; the scalar operations stay identical. Apache-2.0. +Extends PR583's build_frames.py (chafreaky, OpenAI Codex assisted) with changes of any profile delta, prepared with +Claude Code assistance. + +Recipe: input_content_sha256, before/after profiles, and changes [{section, index, before, after, delta}]. Each change +keeps the gate's scalar operation and replaces only its frame. Its exact sequential profile delta must equal the +recipe's `delta`, and the frame chains must stay monotone (gk_word.profile asserts this). The cleanup must already +follow the inherited inverse rule, which only uses FULL frames, so frame changes on A and B leave it unchanged. +Helper widths and all initial helper responses must be unchanged. + +Negative controls: +* each omitted change must lose the recipe profile; +* each change replaced by the FULL frame must violate a chain or cut bound.""" +from pathlib import Path +from collections import Counter +import argparse, copy, gzip, hashlib, json, sys +assert __debug__, 'Assertions required' +ap = argparse.ArgumentParser() +for k in ('--input', '--recipe', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True) +a = ap.parse_args(); assert not a.out.exists() +sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C +G.V = C.V = 112; G.DATA = C.DATA = 7168 +raw = json.loads(gzip.decompress(a.input.read_bytes())); recipe = json.loads(a.recipe.read_text()) +enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest() +assert sha(enc(raw)) == recipe['input_content_sha256']; before = G.profile(raw); assert dict(before) == {int(r): n for r, n in recipe['before'].items()} +assert raw['cleanup'] == [G.inverse(e, G.FULL) for e in reversed(raw['A'] + raw['B']) if not 112 <= e[1] < 224], 'input cleanup is not the inherited inverse rule' +assert len({(c['section'], c['index']) for c in recipe['changes']}) == len(recipe['changes']) and recipe['changes'] +w = copy.deepcopy(raw); trace = [] +for c in recipe['changes']: + part, i = c['section'], c['index']; assert part in ('A', 'B') and w[part][i] == c['before'] and c['before'][:-1] == c['after'][:-1] and c['before'][-1] != c['after'][-1] + w[part][i] = c['after']; after = G.profile(w) + delta = {r: after[r] - before[r] for r in set(after) | set(before) if after[r] != before[r]} + assert delta == {int(r): n for r, n in c['delta'].items()}, ('delta', part, i, delta); trace.append(dict(section=part, index=i, delta=delta)); before = after +assert dict(G.profile(w)) == {int(r): n for r, n in recipe['after'].items()} +for k in raw: + if k not in ('A', 'B', 'report'): assert w[k] == raw[k] +for part in ('A', 'B'): assert [e[:-1] for e in w[part]] == [e[:-1] for e in raw[part]] +assert G.widths_of(w) == G.widths_of(raw); responses = G.responses(w); assert responses == G.responses(raw) +assert all(not responses[int(r) - 224] for r in w['start_extra']) +rejected = [] +for c in recipe['changes']: + z = copy.deepcopy(w); z[c['section']][c['index']] = c['before']; assert G.profile(z) != G.profile(w); rejected.append('omission-%s-%d' % (c['section'], c['index'])) + z = copy.deepcopy(w); z[c['section']][c['index']][-1] = list(G.FULL) + try: G.profile(z) + except AssertionError: rejected.append('overpromotion-%s-%d' % (c['section'], c['index'])) + else: raise AssertionError('Invalid frame accepted') +H = G.profile(w); w['report'].update(local_profile={str(k): v for k, v in sorted(H.items())}, local_rank_mass=sum(r * n for r, n in H.items())) +a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(enc(w), mtime=0)) +receipt = dict(status='PASS_EXACT_FRAME_REGROUPING', input_content_sha256=sha(enc(raw)), output_content_sha256=sha(enc(w)), profile_before=recipe['before'], + profile_after=recipe['after'], changes=trace, negative_controls_rejected=rejected, all_scalar_operations_unchanged=True, + all_initial_helper_responses_equal=True, all_entering_helper_responses_zero=True, helper_widths_unchanged=True, + scope='Construction, frame/profile and scalar response checks only; native, phase and global admission are separate.') +(a.out / 'FRAME-CONSTRUCTION.json').write_text(json.dumps(receipt, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(receipt, indent=2)) diff --git a/research/pr643-improvement-20261013/witness/code/build_gate_moves.py b/research/pr643-improvement-20261013/witness/code/build_gate_moves.py new file mode 100644 index 0000000000..03114099c6 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/build_gate_moves.py @@ -0,0 +1,61 @@ +"""Move commuting gates, then apply source-bound frame coalescences; the scalar map stays identical. +Extends PR583's build_frames.py (chafreaky, OpenAI Codex assisted, Apache-2.0) with commuting gate moves found by +Claude Code research agents. Apache-2.0. + +Recipe: input_content_sha256, before/after profiles, moves [{section, from, to}] (applied in order; every gate the +moved gate passes must commute with it), and changes [{section, index, before, after}] (indices after the moves; +each change only raises the gate frame and must save exactly {1:-2, 2:+1}). The cleanup section is rebuilt with the +inherited rule (the input word must already satisfy it), and the helper responses must be unchanged. +""" +from pathlib import Path +import argparse,copy,gzip,hashlib,json,sys +from collections import Counter +assert __debug__,'Assertions required' +ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--recipe',type=Path,required=True);ap.add_argument('--gk-dir',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert not a.out.exists() +sys.path.insert(0,str(a.gk_dir));import gk_word as G,gk_common as C +G.V=C.V=112;G.DATA=C.DATA=7168 +raw=json.loads(gzip.decompress(a.input.read_bytes()));recipe=json.loads(a.recipe.read_text());enc=lambda x:json.dumps(x,sort_keys=True,separators=(',',':')).encode();sha=lambda x:hashlib.sha256(x).hexdigest() +assert sha(enc(raw))==recipe['input_content_sha256'];before=G.profile(raw);assert dict(before)=={int(r):n for r,n in recipe['before'].items()} +def regs(e):return(e[1],e[2])if e[0]=='add'else(e[1],) +def commute(x,y): + """Two additions commute unless one writes the other's source; any other pair must touch disjoint registers.""" + if x[0]=='add'and y[0]=='add':return x[1]!=y[2]and y[1]!=x[2] + return not set(regs(x))&set(regs(y)) +cleanup=lambda w:[G.inverse(e,G.FULL)for e in reversed(w['A']+w['B'])if not 112<=e[1]<224] +assert raw['cleanup']==cleanup(raw),'input cleanup is not the inherited inverse rule' +w=copy.deepcopy(raw);moved=[] +for m in recipe['moves']: + L=w[m['section']];i,j=m['from'],m['to'];assert i!=j and 0<=ii else range(j,i);assert all(commute(L[i],L[k])for k in passed),'noncommuting move %s'%m + L.insert(j,L.pop(i));moved.append(dict(m,passed=len(passed))) +w['cleanup']=cleanup(w);responses=G.responses(w);assert responses==G.responses(raw),'scalar responses changed by the moves' +assert G.profile(w)==before,'moves alone changed the profile';trace=[] +for change in recipe['changes']: + part,i=change['section'],change['index'];assert w[part][i]==change['before'];assert change['before'][:-1]==change['after'][:-1] + w[part][i]=change['after'];after=G.profile(w);delta={r:after[r]-before[r]for r in set(after)|set(before)if after[r]!=before[r]};assert delta=={1:-2,2:1};trace.append(dict(section=part,index=i,delta=delta));before=after +w['cleanup']=cleanup(w) +assert dict(G.profile(w))=={int(r):n for r,n in recipe['after'].items()} +for key in raw: + if key not in ('A','B','cleanup','report'):assert w[key]==raw[key] +for part in ('A','B'):assert sorted(map(enc,(e[:-1]for e in w[part])))==sorted(map(enc,(e[:-1]for e in raw[part]))) +assert G.widths_of(w)==G.widths_of(raw);responses=G.responses(w);assert responses==G.responses(raw) +assert all(not responses[int(r)-224]for r in w['start_extra']) +# Fresh negative controls: every omitted coalescence loses the new profile, every full-space frame replacement violates +# a chain/cut bound, and every move reverted before its coalescence is rejected. +rejected=[] +for c in recipe['changes']: + z=copy.deepcopy(w);z[c['section']][c['index']]=c['before'];assert G.profile(z)!=G.profile(w);rejected.append('omission-%s-%d'%(c['section'],c['index'])) + z=copy.deepcopy(w);z[c['section']][c['index']][-1]=list(G.FULL) + try:G.profile(z) + except AssertionError:rejected.append('overpromotion-%s-%d'%(c['section'],c['index'])) + else:raise AssertionError('Invalid frame accepted') +for m in reversed(recipe['moves']): + z=copy.deepcopy(w);L=z[m['section']];L.insert(m['from'],L.pop(m['to'])) + try:ok=G.profile(z)==G.profile(w) + except AssertionError:ok=False + assert not ok,'unmoved coalescence accepted';rejected.append('unmoved-%s-%d'%(m['section'],m['from'])) +w['report'].update(local_profile=dict(G.profile(w)),local_rank_mass=sum(r*n for r,n in G.profile(w).items()),status='GATE_MOVE_FRAME_COALESCENCES_PENDING_NATIVE_PHASE_ADMISSION', + # descriptive inventory fields recomputed from the actual widths (as PR586's adapted PR583 constructor does) + width_inventory={str(k):v for k,v in sorted(Counter(G.widths_of(w)).items())},entering_helpers=sum(v<9 for v in G.widths_of(w)),entrance_rank=sum(9-v for v in G.widths_of(w))) +a.out.mkdir(parents=True);(a.out/'FULL-WORD.json.gz').write_bytes(G.dump(w));receipt=dict(status='PASS_EXACT_GATE_MOVE_FRAME_COALESCENCES',input_content_sha256=sha(enc(raw)),output_content_sha256=sha(enc(w)),profile_before=recipe['before'],profile_after=recipe['after'],moves=moved,changes=trace,negative_controls_rejected=rejected,all_scalar_responses_unchanged=True,all_entering_helper_responses_zero=True,helper_widths_unchanged=True,cleanup_rebuilt_by_inherited_rule=True,scope='Construction, commutation, frame/profile and scalar response checks only; native, phase and global admission are separate.') +(a.out/'FRAME-CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt,indent=2)) diff --git a/research/pr643-improvement-20261013/witness/code/build_hpe.py b/research/pr643-improvement-20261013/witness/code/build_hpe.py new file mode 100644 index 0000000000..830906acf2 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/build_hpe.py @@ -0,0 +1,123 @@ +"""Hyperplane-ended helpers (HPE) constructor. Apache-2.0. Prepared with Claude Code assistance. + +usage: build_hpe.py --input FULL-WORD.json.gz --recipe RECIPE.json --out DIR + +RECIPE: {"changes": [{"helper": h, "cleanup_index": i, "frame": [raw vectors]}, ...], "output_content_sha256": hex}. +Each change must be an admissible early-cleanup move: + * h is an entering helper (start_extra) touched by exactly one cleanup gate, cleanup[i]; + * cleanup[i] commutes with every earlier cleanup gate on its registers (commute(): neither writes a register the + other touches, or both add into one target without reading each other's target), so it commutes with the whole + skipped cleanup prefix; in practice the skipped gates only read the partner (x -= p); + * frame == join of the registers' last A/B frames and has dimension < 9. +The output word gets early_cleanup [[i, U]], helper_final {h: U} and the exact paid profile (only the two registers' +final chains change: h ends at U instead of FULL; the partner climbs through U). Exactness of the reordered program, +the frame chains and the profile are re-checked independently by hpe_audit_and_transport.py; the paired control audit +is controls_hpe_atc.py.""" +import argparse, gzip, hashlib, json +from collections import Counter +from pathlib import Path + + +def span(vs): + p = {} + for x in vs: + for k in sorted(p, reverse=True): + if x >> k & 1: x ^= p[k] + if x: + k = x.bit_length() - 1 + for j in p: + if p[j] >> k & 1: p[j] ^= x + p[k] = x + return [p[k] for k in sorted(p, reverse=True)] + + +def regs(e): return [e[1]] + ([e[2]] if e[0] == 'add' else []) + + +def commute(a, b): + """Sufficient syntactic commutation of two scalar gates (t += q*s, t *= q): neither writes a register the other + touches, or both are additions into the same target with neither reading the other's target.""" + ra, rb = set(regs(a)), set(regs(b)) + if a[1] not in rb and b[1] not in ra: return True + return a[0] == 'add' and b[0] == 'add' and a[1] == b[1] and a[2] != b[1] and b[2] != a[1] + + +def last_frames(w): + v, R = w['report']['v'], w['report']['R']; n = 2*v + R + cur = [[] for _ in range(n)] + for i, p in enumerate(w['ports']): cur[i] = [p] + for r, f in w.get('start_extra', {}).items(): cur[int(r)] = list(f) + for part in ('A', 'B'): + for e in w[part]: + for r in regs(e): cur[r] = list(e[-1]) + return cur + + +def apply(w, changes): + assert 'early_cleanup' not in w and 'helper_final' not in w, 'input already has hyperplane-ended helpers' + v, R = w['report']['v'], w['report']['R']; n = 2*v + R + cur = last_frames(w); count = Counter(); first = {}; on = {} + for i, e in enumerate(w['cleanup']): + for r in regs(e): count[r] += 1; first.setdefault(r, i); on.setdefault(r, []).append(i) + lp = Counter({int(r): c for r, c in w['report']['local_profile'].items()}) + seen = set() + for z in changes: + h, i, U = z['helper'], z['cleanup_index'], z['frame'] + assert 2*v <= h < n and str(h) in w['start_extra'], ('not an entering helper', h) + assert count[h] == 1 and first[h] == i, ('helper must have exactly this one cleanup gate', h) + e = w['cleanup'][i]; rs = regs(e) + assert all(commute(w['cleanup'][j], e) for r in rs for j in on[r] if j < i), ('cleanup gate does not commute with the skipped cleanup gates on its registers', i) + assert not seen & set(rs), 'registers shared between changes'; seen |= set(rs) + assert span([x for r in rs for x in cur[r]]) == U and len(U) < 9, ('frame is not the join of the last frames', h) + for r in rs: # old: last -> FULL; new: last -> U (-> FULL for the partner) + d0 = 9 - len(span(cur[r])) + if d0: lp[d0] -= 1 + d1 = len(U) - len(span(cur[r])) + if d1: lp[d1] += 1 + if r != h and len(U) < 9: lp[9 - len(U)] += 1 + w['early_cleanup'] = [[z['cleanup_index'], z['frame']] for z in changes] + w['helper_final'] = {str(z['helper']): z['frame'] for z in changes} + w['report']['local_profile'] = {str(r): c for r, c in sorted(lp.items()) if c} + w['report']['local_rank_mass'] = sum(r*c for r, c in lp.items()) + if 'width_inventory' in w['report']: # descriptive metadata: one width-w helper becomes width w-(9-dim U) + inv = Counter({int(k): c for k, c in w['report']['width_inventory'].items()}) + for z in changes: + e = len(w['start_extra'][str(z['helper'])]); inv[9 - e] -= 1; inv[len(z['frame']) - e] += 1 + assert min(inv.values()) >= 0 + w['report']['width_inventory'] = {str(k): c for k, c in sorted(inv.items()) if c} + assert min(lp.values()) >= 0 + return w + + +def candidates(w): + v, R = w['report']['v'], w['report']['R']; n = 2*v + R + cur = last_frames(w); count = Counter(); first = {}; on = {} + for i, e in enumerate(w['cleanup']): + for r in regs(e): count[r] += 1; first.setdefault(r, i); on.setdefault(r, []).append(i) + out = [] + for h in range(2*v, n): + if count[h] != 1 or str(h) not in w.get('start_extra', {}): continue + i = first[h]; rs = regs(w['cleanup'][i]) + if not all(commute(w['cleanup'][j], w['cleanup'][i]) for r in rs for j in on[r] if j < i): continue + U = span([x for r in rs for x in cur[r]]) + if len(U) < 9: out.append(dict(helper=h, cleanup_index=i, frame=U)) + return out + + +if __name__ == '__main__': + ap = argparse.ArgumentParser(); ap.add_argument('--input', type=Path, required=True); ap.add_argument('--recipe', type=Path) + ap.add_argument('--out', type=Path); ap.add_argument('--nominate', type=Path, help='write a recipe with every candidate') + a = ap.parse_args() + w = json.loads(gzip.decompress(a.input.read_bytes())) + if a.nominate: + a.nominate.write_text(json.dumps(dict(changes=candidates(w), output_content_sha256=''), indent=1) + '\n', newline='\n') + raise SystemExit(0) + r = json.loads(a.recipe.read_bytes()) + w = apply(w, r['changes']) + raw = json.dumps(w, sort_keys=True, separators=(',', ':')).encode(); h = hashlib.sha256(raw).hexdigest() + assert h == r['output_content_sha256'], h + a.out.mkdir(parents=True, exist_ok=False) + (a.out/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw, mtime=0)) + (a.out/'HPE-CONSTRUCTION.json').write_text(json.dumps(dict(status='PASS_HYPERPLANE_ENDED_HELPERS', helpers=[z['helper'] for z in r['changes']], + local_profile=w['report']['local_profile']), indent=1) + '\n', newline='\n') + print('PASS', len(r['changes']), 'hyperplane-ended helpers') diff --git a/research/pr643-improvement-20261013/witness/code/build_port_stage.py b/research/pr643-improvement-20261013/witness/code/build_port_stage.py new file mode 100644 index 0000000000..259fd26feb --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/build_port_stage.py @@ -0,0 +1,125 @@ +"""Port one 504-helper construction stage onto the K-triangle word. Apache-2.0. Prepared with Claude Code assistance. + +usage: build_port_stage.py --shadow-input I4 --shadow-output O4 --input I8 --map HELPER-MAP.json --gk-dir GK --out DIR + +The shadow pair (I4 -> O4) is one stage of a 504-helper chain, rebuilt in the same run from pinned sources. I8 is the +K-triangle word at the matching point of its own chain, and HELPER-MAP.json is the 504 -> R register map written by +construct_k_triangle.py. Registers below 448 keep their ids; the removed packet copies have no image. + +The port does the following: +* It renumbers I4 and O4 through the map and drops their gates that touch a removed register. +* It matches gates by scalar operation (the gate without its frame), aligning I4 with O4 and I4 with I8 separately. +* It builds O8 in O4 gate order: + * each matched gate is taken from I8, with O4's frame wherever the stage changed that frame; + * each gate the stage introduced is taken from O4; + * each I8-only gate (the K-triangle reads) stays after the O4 image of its I8 predecessor. +* It replays the stage's entrance (start_extra) and target_levels changes. +* It rebuilds the cleanup with the inherited inverse rule. + +The constructor is a search transfer only. The verifier certifies the output independently: the generalised native +audit (exact forward and inverse replay of every column, native frame chains) runs on every ported word, and every +input and output is pinned by content hash.""" +import argparse, copy, difflib, gzip, hashlib, json, sys +from collections import Counter +from pathlib import Path + +assert __debug__, 'Assertions required' +FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1] + + +def regs(g): return (g[1], g[2]) if g[0] == 'add' else (g[1],) + + +def key(g): return json.dumps(g[:-1]) + + +def inverse(e): + e = copy.deepcopy(e) + if e[0] == 'add': e[3] *= -1 + else: e[2], e[3] = e[3], e[2] + e[-1] = list(FULL); return e + + +def align(xs, ys): + """index map xs -> ys over runs of equal scalar operations""" + sm = difflib.SequenceMatcher(None, [key(g) for g in xs], [key(g) for g in ys], autojunk=False) + return {i1 + k: j1 + k for tag, i1, i2, j1, j2 in sm.get_opcodes() if tag == 'equal' for k in range(i2 - i1)} + + +def transfer_section(I4, O4, I8, stats): + a, b = align(I4, O4), align(I4, I8) + o2i = {j: i for i, j in a.items()}; i8from4 = {j: i for i, j in b.items()} + anchor = {j8: a[i4] for j8, i4 in i8from4.items() if i4 in a} + pending, last = {}, -1 + for j8, g in enumerate(I8): + if j8 in anchor: last = anchor[j8] + elif j8 not in i8from4: pending.setdefault(last, []).append(copy.deepcopy(g)); stats['kept_own'] += 1 + else: stats['dropped_by_stage'] += 1 + out = list(pending.get(-1, [])) + for k, g in enumerate(O4): + if k in o2i: + i4 = o2i[k] + if i4 in b: + g8 = copy.deepcopy(I8[b[i4]]) + if I4[i4][-1] != g[-1]: g8[-1] = copy.deepcopy(g[-1]); stats['frames_changed'] += 1 + out.append(g8) + else: + out.append(copy.deepcopy(g)); stats['introduced'] += 1 + out.extend(pending.get(k, [])) + return out + + +def main(): + ap = argparse.ArgumentParser() + for k in ('--shadow-input', '--shadow-output', '--input', '--map', '--gk-dir', '--out'): ap.add_argument(k, type=Path, required=True) + a = ap.parse_args(); assert not a.out.exists() + sys.path.insert(0, str(a.gk_dir)); import gk_word as G, gk_common as C + G.V = C.V = 112 + rd = lambda p: json.loads(gzip.decompress(p.read_bytes())) + enc = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode(); sha = lambda x: hashlib.sha256(x).hexdigest() + I4, O4, I8 = rd(a.shadow_input), rd(a.shadow_output), rd(a.input) + fm = {int(k): int(v) for k, v in json.loads(a.map.read_text())['map'].items()} + assert all(fm[k] == k for k in fm if k < 448), 'only ids >= 448 may move' + R = I8['report']['R']; assert sorted(fm.values()) == list(range(224 + R)), 'map is not onto the K-triangle registers' + assert I4['report'].get('R', 504) == 504 and len(fm) + len(set(range(728)) - set(fm)) == 728 + rem = set(range(728)) - set(fm) + rn = lambda r: fm[r] + touches = lambda g: any(r in rem for r in regs(g)) + def rg(g): + g = copy.deepcopy(g); g[1] = rn(g[1]) + if g[0] == 'add': g[2] = rn(g[2]) + return g + def rn_word(w): + w = copy.deepcopy(w) + for s in ('A', 'B', 'cut', 'precondition', 'cleanup'): + if s in w: w[s] = [rg(g) for g in w[s] if not touches(g)] + for k in ('start_extra', 'helper_final'): + if k in w: w[k] = {str(rn(int(r))): f for r, f in w[k].items() if int(r) not in rem} + return w + I4r, O4r = rn_word(I4), rn_word(O4) + O8 = copy.deepcopy(I8); stats = {s: Counter() for s in ('A', 'B')} + for s in ('A', 'B'): O8[s] = transfer_section(I4r[s], O4r[s], I8[s], stats[s]) + for k in ('start_extra', 'target_levels'): + x, y = I4r.get(k, {}), O4r.get(k, {}); d = dict(I8.get(k, {})) + for r in set(x) | set(y): + if x.get(r) != y.get(r): + if r in y: d[r] = y[r] + else: d.pop(r, None) + if k in O4 or k in I8: O8[k] = dict(sorted(d.items(), key=lambda kv: int(kv[0]))) + for k in O4: + if k not in ('A', 'B', 'cleanup', 'report', 'start_extra', 'target_levels', 'cut', 'precondition'): + assert O4r[k] == I4r[k], 'stage changed an unported field: ' + k + O8['cleanup'] = [inverse(e) for e in reversed(O8['A'] + O8['B']) if not 112 <= e[1] < 224] + H = G.profile(O8) + ws = [9 - len(G.basis(O8['start_extra'].get(str(224 + h), []))) for h in range(R)] + O8['report'] = dict(I8['report'], local_profile={str(k): v for k, v in sorted(H.items())}, local_rank_mass=sum(k * v for k, v in H.items()), + width_inventory={str(k): v for k, v in sorted(Counter(ws).items())}) + a.out.mkdir(parents=True); (a.out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(enc(O8), mtime=0)) + receipt = dict(status='PORTED_STAGE_PENDING_NATIVE_AUDIT', R=R, removed_504_helpers=sorted(rem), + shadow_input_content_sha256=sha(enc(I4)), shadow_output_content_sha256=sha(enc(O4)), input_content_sha256=sha(enc(I8)), + output_content_sha256=sha(enc(O8)), sections={s: dict(v) for s, v in stats.items()}, local_profile=O8['report']['local_profile'], + scope='Transfer construction only; exactness, frame chains and profile are certified by the native audit run on the output.') + (a.out / 'PORT-STAGE.json').write_text(json.dumps(receipt, indent=2, sort_keys=True) + '\n', newline='\n'); print(json.dumps(receipt, indent=2)) + + +main() diff --git a/research/pr643-improvement-20261013/witness/code/cold_end_controls.py b/research/pr643-improvement-20261013/witness/code/cold_end_controls.py new file mode 100644 index 0000000000..f265fcc3c7 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/cold_end_controls.py @@ -0,0 +1,198 @@ +"""cold_end_controls.py COLD-END-WORD.json.gz ROUTING OUTDIR : raw-word negative controls for the cold low-frame ends and the +refactored cleanup accepted by hpe_audit_and_transport.py. Every mutation MUST be rejected (AssertionError); the +unmutated word MUST pass. Apache-2.0. DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.""" +import copy, gzip, json, shutil, sys, tempfile +from pathlib import Path +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import hpe_audit_and_transport as atc + +src, routing, outdir = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3]) +word = json.load(gzip.open(src)) +v, R = word['report']['v'], word['report']['R']; n = 2*v + R +regs = lambda e: [e[1]] + ([e[2]] if e[0] == 'add' else []) +meta = word['refactored_cleanup'] +cold = [int(h) for h in meta['cold_low_frame_ended_helpers']] +npre = meta['premix_gates']; nlow = meta['lower_frame_gates'] +early = word['early_cleanup']; eidx = {i for i, _ in early} +rest = [i for i in range(len(word['cleanup'])) if i not in eidx] + + +def trial(w): + """None if the transport audit accepts w, else the AssertionError message.""" + tmp = Path(tempfile.mkdtemp()) + p = tmp/'w.json.gz'; p.write_bytes(gzip.compress(json.dumps(w).encode(), mtime=0)) + try: + atc.run(p, routing, tmp/'out') + return None + except AssertionError as e: + return repr(e.args[0]) if e.args else 'AssertionError' + finally: + shutil.rmtree(tmp, ignore_errors=True) + + +# Pinned rejection reasons: each mutant must fail at this assertion of hpe_audit_and_transport.py (message substring). +ENDPOINT, COLDPRE, CONE = "'arbitrary-dirt endpoint'", 'touches a cold hyperplane-ended helper', 'hpe cone pre-check (row / column)' +WHY = dict(premix_to_precondition=COLDPRE, premix_dropped=COLDPRE, e_premix_dropped=ENDPOINT, lower_dropped=ENDPOINT, + remainder_dropped=ENDPOINT, coefficient=ENDPOINT, into_full=ENDPOINT, dyadic=ENDPOINT, frame_below="'nonmonotone'", + nonmonotone="'nonmonotone'", other_frame=CONE, cone=CONE, extra_end=COLDPRE, marker='cleanup is not the literal reversed inverse', + target='refactored cleanup touches a target', profile_pin='paid local profile differs from the reported local_profile', + entering_precondition='zero-frame precondition/compensation touches an entering helper') +assert trial(word) is None, 'unmutated cold-end word must pass' +results = [] + + +def reject(name, mut, why): + """the mutation must be rejected, and for the pinned reason (a substring of the audit's assertion message).""" + w = copy.deepcopy(word); mut(w) + msg = trial(w) + assert msg is not None, 'cold-end mutation accepted: ' + name + assert why in msg, 'cold-end mutation %r rejected for the wrong reason: %s' % (name, msg[:300]) + results.append(name); print('rejected', name, '|', why, flush=True) + + +h0 = cold[0] +i0, U0 = next((i, f) for i, f in early if h0 in regs(word['cleanup'][i])) +r0 = rest[len(rest)//2] + + +def premix_to_precondition(w): # premix before the wrappers; compensation then reads the cold ends + w['precondition'] = w['precondition'] + w['A'][:npre]; w['A'] = w['A'][npre:] + + +def lower_gate_into_full(w): # a lower-frame gate on a cold-ended helper executed in the FULL remainder instead + w['early_cleanup'] = [x for x in w['early_cleanup'] if x[0] != i0] + + +def drop_cleanup_gate(w, i): # remove the gate AND its early_cleanup entry: a structurally valid word missing one gate + w['cleanup'].pop(i) + w['early_cleanup'] = [[j - (j > i), f] for j, f in w['early_cleanup'] if j != i] + + +def other_frame(w): # a different frame of the same dimension as the cold end (another cold helper's) + f = next(w['helper_final'][str(h)] for h in cold if w['helper_final'][str(h)] != w['helper_final'][str(h0)]) + w['helper_final'][str(h0)] = f + + +def extra_cold_end(w): # declare a premixed partner of h0 cold-ended at h0's frame: fails the row/column cone + p = next(r for e in w['A'][:npre] for r in regs(e) if r != h0 and h0 in regs(e)) + w['helper_final'][str(p)] = w['helper_final'][str(h0)] + + +reject('premix placed in the zero-frame precondition (before the cold wrappers)', premix_to_precondition, WHY['premix_to_precondition']) +reject('one premix gate dropped (the compensation then reads a cold-ended helper)', lambda w: w['A'].pop(npre - 1), WHY['premix_dropped']) +reject('one lower-frame cleanup gate dropped (gate and its early_cleanup entry)', lambda w: drop_cleanup_gate(w, i0), WHY['lower_dropped']) +reject('one FULL-remainder gate dropped', lambda w: drop_cleanup_gate(w, r0), WHY['remainder_dropped']) +reject('lower-frame gate coefficient changed', lambda w: w['cleanup'][i0].__setitem__(3, w['cleanup'][i0][3] * 2), WHY['coefficient']) +reject('lower-frame gate moved into the FULL remainder (touches a cold-ended helper at FULL)', lower_gate_into_full, WHY['into_full']) +reject('lower-frame gate frame below its registers\' frames', lambda w: next(x for x in w['early_cleanup'] if x[0] == i0).__setitem__(1, U0[:-1]), WHY['frame_below']) +reject('cold end at another dim-4 frame', other_frame, WHY['other_frame']) +# PROFILE-PIN control: without its helper_final entry the cold-ended helper is a valid FULL-ended helper; the word is +# rejected because its reported paid profile (which counts the low end) no longer matches the frame chains. +reject('profile pin: cold end dropped (valid FULL end, but the reported profile counts the low end)', lambda w: w['helper_final'].pop(str(h0)), WHY['profile_pin']) +reject('extra cold end on a premixed partner (the compensation reads it before its wrapper)', extra_cold_end, WHY['extra_end']) +reject('refactored-cleanup marker removed (literal-inverse rule applies)', lambda w: w.pop('refactored_cleanup'), WHY['marker']) +reject('remainder gate retargeted to a target register', lambda w: w['cleanup'][r0].__setitem__(1, v + 3), WHY['target']) +reject('non-dyadic remainder coefficient', lambda w: w['cleanup'][r0].__setitem__(4 if w['cleanup'][r0][0] == 'add' else 3, 3 * w['cleanup'][r0][4 if w['cleanup'][r0][0] == 'add' else 3]), WHY['dyadic']) +reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('5', w['report']['local_profile']['5'] - 1), WHY['profile_pin']) +ent = [int(h) for h in meta.get('entering_low_frame_ended_helpers', [])] +for e0 in ent: # ENTERING LOW-FRAME ENDS (ColdSupply extension; every entering end; absent for words without them) + j0 = next(i for i, e in enumerate(word['A'][:npre]) if e0 in regs(e)) + k0, Ue = next((i, f) for i, f in early if e0 in regs(word['cleanup'][i])) + def to_pre(w, j0=j0): w['precondition'].append(w['A'][j0]); w['A'].pop(j0) + def other_hp(w, e0=e0, Ue=Ue): w['helper_final'][str(e0)] = next(f for h, f in w['helper_final'].items() if len(f) == len(Ue) and sorted(f) != sorted(Ue)) + reject('entering end %d: premix gate dropped' % e0, lambda w, j0=j0: w['A'].pop(j0), WHY['e_premix_dropped']) + reject('entering end %d: premix gate at frame [] instead of its entrance E' % e0, lambda w, j0=j0: w['A'][j0].__setitem__(-1, []), WHY['nonmonotone']) + reject('entering end %d: premix gate moved into the zero-frame precondition' % e0, to_pre, WHY['entering_precondition']) + reject('entering end %d: lower-frame gate dropped (gate and its early_cleanup entry)' % e0, lambda w, k0=k0: drop_cleanup_gate(w, k0), WHY['lower_dropped']) + reject('entering end %d: profile pin: end dropped (valid FULL end, but the reported profile counts the low end)' % e0, lambda w, e0=e0: w['helper_final'].pop(str(e0)), WHY['profile_pin']) + reject('entering end %d: end at another hyperplane' % e0, other_hp, WHY['cone']) +# Pinned rejection reasons of the COLD-BEYOND mutants (substrings of hpe_audit_and_transport.py assertion messages). +MYWHY = dict(tw_precondition=COLDPRE, tw_dropped=COLDPRE, tw_coefficient=COLDPRE, tw_other_block=COLDPRE, + tw_entering='zero-frame compensation reads an entering helper', + ab_dropped=ENDPOINT, ab_coefficient=ENDPOINT, ab_early=ENDPOINT, ab_live=ENDPOINT, ab_centre=ENDPOINT, + ab_lower="'nonmonotone'", ab_higher="'nonmonotone'", + sh_dropped=ENDPOINT, sh_coefficient=ENDPOINT, rel_dropped=ENDPOINT, rel_coefficient=ENDPOINT, rel_live=ENDPOINT, + h8_other=CONE, h8_lower=ENDPOINT) +# COLD-BEYOND primitives (present only when the word carries them): frame-[] target writes in the premix (explicit +# post-wrapper compensation of an ended helper's dirt) and forward absorptions into dead registers. +nw = meta.get('premix_target_writes', 0) +if nw: + wi = [i for i in range(npre) if v <= word['A'][i][1] < 2*v] + assert len(wi) == nw + + def writes_to_precondition(w): # the target writes run before the cold wrappers (inside the zero-frame precondition) + g = [w['A'][i] for i in wi]; w['precondition'] = w['precondition'] + g + w['A'] = [e for i, e in enumerate(w['A']) if i not in set(wi)] + reject('premix target writes placed in the zero-frame precondition (before the cold wrappers)', writes_to_precondition, MYWHY['tw_precondition']) + reject('one premix target write dropped (compensation must read an ended helper)', lambda w: w['A'].pop(wi[0]), MYWHY['tw_dropped']) + reject('premix target write coefficient changed', lambda w: w['A'][wi[0]].__setitem__(3, w['A'][wi[0]][3] * 2), MYWHY['tw_coefficient']) + # (reading another register that carries the SAME weight of the ended helper's dirt is a valid variant, so the mutant reads + # the same factory slot of the next block, which carries none of it) + entering_regs = sorted(int(r) for r in word.get('start_extra', {})) + reject('premix target write reads an entering helper', lambda w: w['A'][wi[0]].__setitem__(2, entering_regs[0]), MYWHY['tw_entering']) + reject('premix target write reads a cold helper of another block', lambda w: w['A'][wi[0]].__setitem__(2, 2*v + (w['A'][wi[0]][2] - 2*v + 16) % 224), MYWHY['tw_other_block']) +ab = meta.get('forward_absorption_A_indices', []) +if any(len(word['helper_final'][str(h)]) == 8 for h in cold): + # with dim-8 cold ends, the centre-retargeted absorption first leaks an ended helper's dirt into the cut's targets + MYWHY['ab_centre'] = COLDPRE +if ab: + # the ColdBeyond U_b absorption (q += -1/2 g); ColdThird's extra absorptions have their own controls below + a0 = next(a for a in ab if word['A'][a][3] * 2 == -word['A'][a][4]); g0 = word['A'][a0] + + def absorption_moved_early(w): # absorbed before the absorbed register's last kernel write + e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[2] == w['A'][i][1] and w['A'][i][-1] == g0[-1]) + w['A'].insert(j, e) + + def absorption_into_live(w): # q += a g moved right after g's previous frame-mate gate, while q is still live + e = w['A'].pop(a0); j = max(i for i in range(npre, a0) if g0[1] in regs(w['A'][i])) + w['A'].insert(j, e) + reject('forward absorption dropped', lambda w: w['A'].pop(a0), MYWHY['ab_dropped']) + reject('forward absorption into a centre (a live register read by the cut)', lambda w: w['A'][a0].__setitem__(1, next(c for c in word['centers'] if c not in g0[1:3] and c not in cold)), MYWHY['ab_centre']) + reject('forward absorption coefficient changed', lambda w: w['A'][a0].__setitem__(3, w['A'][a0][3] * 2), MYWHY['ab_coefficient']) + reject('forward absorption placed before the absorbed register\'s last kernel write', absorption_moved_early, MYWHY['ab_early']) + reject('forward absorption placed while the absorbing register is still live', absorption_into_live, MYWHY['ab_live']) + reject('forward absorption at a lower frame than its registers', lambda w: w['A'][a0].__setitem__(-1, w['A'][a0][-1][:-1]), MYWHY['ab_lower']) + reject('forward absorption at a higher frame (FULL) than its registers', lambda w: w['A'][a0].__setitem__(-1, [256, 128, 64, 32, 16, 8, 4, 2, 1]), MYWHY['ab_higher']) +# COLD-THIRD primitives (present only when the word carries them): several absorptions after one input gate, dirt-release +# absorptions (a dead port takes a live helper's value so that a hyperplane unit's column has no dirt on it), and cold ends at +# a dim-8 frame with lifted partners. +hyper = [h for h in cold if len(word['helper_final'][str(h)]) == 8] +if hyper and ab: + sh = next(a for a, b in zip(ab, ab[1:]) if b == a + 1) # two absorptions sharing one input anchor + rel = next(a for a in ab if a - 1 not in ab and a + 1 not in ab and word['A'][a][2] in hyper and word['A'][a][3] * 2 != -word['A'][a][4]) + hh = hyper[0]; ih = next(i for i, f in early if hh in regs(word['cleanup'][i])) + reject('second absorption sharing an input anchor dropped', lambda w: w['A'].pop(sh + 1), MYWHY['sh_dropped']) + reject('shared-anchor absorption coefficient changed', lambda w: w['A'][sh + 1].__setitem__(3, w['A'][sh + 1][3] * 2), MYWHY['sh_coefficient']) + reject('dirt-release absorption dropped', lambda w: w['A'].pop(rel), MYWHY['rel_dropped']) + reject('dirt-release absorption coefficient changed', lambda w: w['A'][rel].__setitem__(3, w['A'][rel][3] * 2), MYWHY['rel_coefficient']) + jr = max(i for i in range(npre, rel) if word['A'][i][0] == 'add' and word['A'][i][2] == word['A'][rel][1]) + + def release_while_read(w): # the release runs before a kernel gate that still READS the port (port live) + e = w['A'].pop(rel); w['A'].insert(jr, e) + reject('dirt-release absorption moved before a kernel gate that still reads the port', release_while_read, MYWHY['rel_live']) +if hyper: + # dim-8 cold-end controls once PER DISTINCT dim-8 terminal frame (each family of dim-8 cold ends keeps its own controls) + fams = [] + for h in hyper: + if sorted(word['helper_final'][str(h)]) not in [sorted(word['helper_final'][str(x)]) for x in fams]: fams.append(h) + for hh in fams: + ih = next(i for i, f in early if hh in regs(word['cleanup'][i])) + Uh = word['helper_final'][str(hh)] + reject('dim-8 cold end %d (frame %s) at another dim-8 frame' % (hh, Uh), lambda w, hh=hh: w['helper_final'].__setitem__(str(hh), next(f for h, f in w['helper_final'].items() if len(f) == 8 and sorted(f) != sorted(w['helper_final'][str(hh)]))), MYWHY['h8_other']) + reject('dim-8 cold end %d (frame %s): one lower-frame gate dropped (gate and its early_cleanup entry)' % (hh, Uh), lambda w, ih=ih: drop_cleanup_gate(w, ih), MYWHY['h8_lower']) + reject('dim-8 cold end %d (frame %s): profile pin (end dropped)' % (hh, Uh), lambda w, hh=hh: w['helper_final'].pop(str(hh)), WHY['profile_pin']) +# FACTORED ACCUMULATOR (CarrierBypass; present only when the word carries one): a lower-frame tail gate a += x*g on two +# non-ended registers whose accumulator a is afterwards read by a dim-8 cold end's tail gate (h += y*a at its U). +ended_all = {int(h) for h in word['helper_final']} +tailg = [(i, word['cleanup'][i]) for i, _ in early] +acc = None +for k, (i, e) in enumerate(tailg): + if e[0] == 'add' and e[1] not in ended_all and e[2] not in ended_all and len(next(f for j, f in early if j == i)) < 8: + if any(t[0] == 'add' and t[2] == e[1] and t[1] in hyper for _, t in tailg[k + 1:]): + acc = i; break +if acc is not None: + reject('factored accumulator gate zeroed', lambda w: w['cleanup'][acc].__setitem__(3, 0), ENDPOINT) + reject('factored accumulator gate coefficient doubled', lambda w: w['cleanup'][acc].__setitem__(3, w['cleanup'][acc][3] * 2), ENDPOINT) +outdir.mkdir(parents=True, exist_ok=True) +(outdir/'COLD-END-CONTROLS.json').write_text(json.dumps(dict(status='PASS_COLD_END_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n') +print('PASS', len(results), 'cold-end raw-word mutations rejected') diff --git a/research/pr643-improvement-20261013/witness/code/construct_k_triangle.py b/research/pr643-improvement-20261013/witness/code/construct_k_triangle.py new file mode 100644 index 0000000000..763a2b3f5f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/construct_k_triangle.py @@ -0,0 +1,374 @@ +# Round20 early-coordinate-center / own-Y variant, prepared for icekylinx +# with OpenAI Codex assistance. Apache-2.0. Scalar elementary-operation +# helpers below are retained from the attributed PR514 construct_partial.py. +# Adapted by OpenAI Codex for isolated structural research. +# Modified from PR425 by icekylinx with Codex assistance. +"""Full discovery word for Hamming packets with borrowed X and Y registers. + +This changes the scalar architecture. It is not accepted by the old restricted +gx interface: source bases may change until full-frame cleanup, and targets use +an explicitly inverted output basis. No supplier admission is asserted. +""" +import copy,gzip,json,math,time +import itertools as it +from collections import Counter,defaultdict +from fractions import Fraction as Q +from pathlib import Path + +import sys +INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text()) +P=D['binary_ports'];R=D['root_lines'];v=120;h=9 +modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz')) +# AtomScout: leaver-read K-triangles (schedule from atom1.py / rog.py CP-SAT) +TRI=json.loads(Path(sys.argv[3]).read_text()) +FULLT={(tuple(tr['p']),tr['e']) for tr in TRI['triangles']} +TRI_COORDS={t+8 for tr in TRI['triangles'] for t,_,_ in tr['reads']} +COPYL=[] +NH=504-3*len(FULLT)+len(COPYL) + +def basis(vectors): + b={} + for x in vectors: + for p in sorted(b,reverse=True): + if x>>p&1:x^=b[p] + if x: + p=x.bit_length()-1 + for q in b: + if b[q]>>p&1:b[q]^=x + b[p]=x + return tuple(b[p] for p in sorted(b,reverse=True)) +def inside(a,b):return basis(a+b)==b +def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0]) +FULL=basis([1<len(M):M.append(rr) + if len(M)==8:break + assert len(M)==8 + linear(regs,M,F) + for i,r in zip(c,regs): + assert rows[r]=={s:Q(R[s][i]) for s in ids} + block_totals[c,i]=r + +# All centers are complete while Y is still at zero. This is the crucial +# difference from an illegal early-own-Y prefix using the old center order. +centers=[] +for i in range(8): + regs=[block_totals[c,i] for c in sorted(blocks) if i in c] + F=hyper(P[frame[i]]);a=regs[0] + for b in regs[1:]:add(a,b,1,F) + centers.append(a) +centers += [frame[i] for i in range(8)] +center_frames=[cur[r] for r in centers] +assert list(map(len,center_frames))==[8]*8+[1]*8 +assert all(cur[v+t]==() for t in range(v)) + +phase=B +for t,(r,coef,F) in sorted(own_rows.items()): + if t in TRI_COORDS:continue + assert cur[r]==F + add(v+t,r,coef,F) +# requests are needed for TRI coefficients +requests=defaultdict(list) +for pid,pair in enumerate(pairs): + if not pair['selected']:continue + (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix'] + requests[key1].append((t,-Q(mat[0][0],2))) + requests[key2].append((u,-Q(mat[0][1],2))) +reqcoef={t:(key,coef) for key,reqs in requests.items() for t,coef in reqs} +def face_info(c,p,eps): + z=blocks[c];keys=[(pp,ee) for pp in it.combinations(c,2) for ee in (-1,1)] + r_local,alpha=z['outputs'][keys.index((p,eps))] + j=[j for j in range(40,len(z['events'])) if z['events'][j][0]==r_local];assert len(j)==1 + return j[0],Q(alpha) +tri_join_counts=Counter() +lcopy={} +for s8 in COPYL: + r=s8+8;c=alloc();add(c,r,1,cur[r]);lcopy[r]=c +for tr in TRI['triangles']: + p,eps=tuple(tr['p']),tr['e'] + for t8,blk,loc in tr['reads']: + t=t8+8;blk=tuple(blk);r=maps[blk][loc];r0=r;r=lcopy.get(r,r) + key,coef=reqcoef[t];assert key[1]==p and key[2]==eps,(key,p,eps) + if blk==key[0]: + rr,c0,F0=own_rows[t];assert rr==r0;q=c0 + else: + j,alpha=face_info(blk,p,eps);ev=blocks[blk]['events'][j];assert loc in ev[:2] + q=coef*alpha + F=basis(cur[v+t]+cur[r]);assert inside(F,hyper(P[t])),('TRI frame',t) + tri_join_counts[len(F)]+=1;add(v+t,r,q,F) + +packets={} +for c,z in sorted(blocks.items()): + mp=maps[c] + keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)] + skipev={face_info(c,p,eps)[0] for p,eps in keys if (p,eps) in FULLT} + for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]): + if j not in early[c] and 40+j not in skipev: + t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F)) + for key,(r,alpha) in zip(keys,z['outputs']): + if tuple(key) in FULLT:skip();continue + a=mp[r];b=alloc();add(b,a,1,cur[a]) + consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d)) + assert len(consumers)==2 + for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha)) + +# Both tetrahedra use the same partition. A selected key has exactly two +# selected Y loads and no ordinary M consumer. Supply its two raw halves in +# opposite orders and never form that M. Other keys retain the old M path. +second=[];first_join_counts=Counter() +for key,reqs in sorted(requests.items()): + assert len(reqs)==2 + c,p,eps=key + if (p,eps) in FULLT:continue + ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds + for j,(target,coef) in enumerate(sorted(reqs)): + first_source,second_source=(a,b) if j==0 else (b,a) + r,alpha=packets[first_source,p,eps,second_source] + F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target])) + first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F) + r,alpha=packets[second_source,p,eps,c] + second.append((target,r,coef*alpha)) + +Ms={} +for c in sorted(blocks): + for p in it.combinations(c,2): + ds=sorted(d for d in blocks if d!=c and set(p)<=set(d)) + for eps in (-1,1): + if (c,p,eps) in requests:continue + (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds] + F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F) + Ms[c,p,eps]=(a,alpha) + +consumers=defaultdict(list) +for pid,pair in enumerate(pairs): + for key in pair['keys']:consumers[key].append(pid) +slots={} +for key,uses in sorted(consumers.items()): + assert len(uses)==2 + if key in requests: + assert all(pairs[i]['selected'] for i in uses) + continue + assert all(not pairs[i]['selected'] for i in uses) + a,alpha=Ms[key] + for j,pid in enumerate(uses): + if j==0:r=a + else:r=alloc();add(r,a,1,cur[a]) + slots[pid,key]=(r,alpha) +assert len(cur)-240==NH,len(cur)-240 + +selected_join_counts=Counter() +for target,r,coef in second: + F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target])) + selected_join_counts[len(F)]+=1;add(v+target,r,coef,F) +output_basis=[] +for pair in pairs: + if not pair['selected']:continue + (t,u),mat=pair['targets'],pair['matrix'] + F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u])) + add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F) + z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z)) + +for pid,pair in enumerate(pairs): + if pair['selected']:continue + (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix'] + (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2] + F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta + ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta + add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F) + add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u])) + +for t in range(v): + expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {} + assert rows[v+t]==expected,('side identity',t) + +scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)] +precondition=[] +for t,u,z in output_basis: + a,b=scatter[t].copy(),scatter[u].copy() + scatter[t]=[x/2-y/z for x,y in zip(a,b)] + scatter[u]=[x/2+y/z for x,y in zip(a,b)] + precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]], + ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]]) +for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL) +H[8]+=8;H[1]+=8 +assert sum(r*z for r,z in H.items())==9*NH+240*8+72,sum(r*z for r,z in H.items()) + +def apply(e,matrix): + if e[0]=='add': + _,t,s,a,b,*_=e;q=Q(a,b) + for j,x in list(matrix[s].items()): + z=matrix[t].get(j,Q(0))+q*x + if z:matrix[t][j]=z + else:matrix[t].pop(j,None) + else: + _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()} +def inverse(e): + e=copy.deepcopy(e) + if e[0]=='add':e[3]*=-1 + else:e[2],e[3]=e[3],e[2] + e[-1]=list(FULL);return e +cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q] +cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v] +matrix=[{r:Q(1)} if r>i)&1);u=q^(1<>i&1 else 0)for i in order]+[1<0 and all(x['R']==R for x in registry.values()),'providers disagree on helper count R' + assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY' + assert replay['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz')and replay['local_programs_sha256']==sha(directory/'LOCAL-PROGRAMS.json.gz') + widths=[len(pc['frames'][pc['final'][2*V+h]])-len(pc['frames'][pc['start'][2*V+h]])for h in range(R)] # HPE: residual width |final|-|start| + assert widths==plan['provider_registry'][provider_id]['widths'] + for name in provider_files: + value=sha(directory/name);assert value==plan['provider_registry'][provider_id]['artifact_sha256'][name] + source_artifacts[f'providers/{provider_id}/{name}']=value + registry[provider_id]=dict(local_programs=programs,canonical_word_sha256=sha(directory/'CANONICAL-WORD.json.gz'),local_programs_sha256=sha(directory/'LOCAL-PROGRAMS.json.gz'),local_program_checks=checks,exact_local_clifford_recipe_sha256=sha(directory/'CLIFFORD-RECIPES.json'),residual_adapter_sha256=sha(directory/'RESIDUAL-ADAPTERS.json'),v=V,h=9,R=R,ports=pc['ports'],centers=pc['centers'],widths=widths) +assert len(roles)==72*R # one whole-owner role per (call, provider helper) +selected={(c['stage'],c['replica']):c for c in plan['provider_calls']} +assert len(selected)==72 and set(selected)==set(call_order) +assert Counter(c['provider']for c in selected.values())==COUNTS +per_call_widths={(c['stage'],c['replica']):c['widths']for c in plan['per_call_widths']} +for key,c in selected.items(): + assert c['time']==at[key] and c['provider']in registry + assert per_call_widths[key]==registry[c['provider']]['widths'] +for key in('local_programs','exact_local_clifford_recipe_sha256','residual_adapter_sha256'):t.pop(key) +t['local_providers']=registry +rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={} +for e in parent['execution_schedule']: + if e['kind']=='idle_cover_sweep': + for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair'] +bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0 +for z in roles: + s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V) + assert 0<=s<9 and 0<=rep=0 and off+w<=rank[i] + assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1] + B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i] + occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[] + order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M + sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma + route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9 + cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells + digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n') +for c in t['calls']: + k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R)) + c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f2*max(paid)**2 + +assert all(c['local_program_sha256']==registry[c['provider_id']]['local_program_checks'][c['orientation']]['sha256']for c in t['calls']) +t['provider_dispatch']='For each indivisible local_cover_sweep, execute local_providers[call.provider_id].local_programs[call.orientation] with that provider residual adapters and Clifford recipes. The sweep provider_id must equal its call provider_id.' +raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0)) +res=dict(status='EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE', + template_sha256=hashlib.sha256(raw).hexdigest(), + parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(), + live=DATA,physical=physical,global_profile=dict(sorted(paid.items())), + rank_mass=sum(r*n for r,n in paid.items()),deficit=2560,maxchild=max(paid), + hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering, + unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(), + cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles), + asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(), + source_artifacts=source_artifacts,provider_counts=dict(Counter(c['provider_id']for c in t['calls'])), + scope='Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required.') +(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2)) diff --git a/research/pr643-improvement-20261013/witness/code/generated_identity.py b/research/pr643-improvement-20261013/witness/code/generated_identity.py new file mode 100644 index 0000000000..74a9b60479 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/generated_identity.py @@ -0,0 +1,62 @@ +"""Proof-relevant identities for generated artifacts, independent of gzip streams. + +Immutable source archives retain their exact byte hashes. For freshly emitted +artifacts, gzip identity is the exact decompressed payload and JSON identity +retains every field. Only CLIFFORD-REVIEW's root timing field is excluded. +Literal receipt references are checked against actual files before replacing +the three gzip references (and the phase recipe reference) with content hashes. +Prepared with OpenAI Codex assistance; Apache-2.0. +""" +from pathlib import Path +import copy +import gzip +import hashlib +import json +import math + +if not __debug__: + raise RuntimeError('Assertions must remain enabled') + +FILES=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json', + 'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json', + 'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json') + +def sha(path): + return hashlib.sha256(Path(path).read_bytes()).hexdigest() + +def json_identity(value): + return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False).encode('utf-8')).hexdigest() + +def payload_identity(path): + return hashlib.sha256(gzip.decompress(Path(path).read_bytes())).hexdigest() + +def phase_value(directory,value=None): + directory=Path(directory) + value=copy.deepcopy(json.loads((directory/'CLIFFORD-REVIEW.json').read_bytes())if value is None else value) + assert value['canonical_word_sha256']==sha(directory/'CANONICAL-WORD.json.gz'),'stale phase canonical word reference' + assert value['recipe_sha256']==sha(directory/'CLIFFORD-RECIPES.json'),'stale phase recipe reference' + seconds=value.pop('seconds') + assert type(seconds)in(int,float) and math.isfinite(seconds) and seconds>=0,'invalid phase timing metadata' + value['canonical_word_sha256']=payload_identity(directory/'CANONICAL-WORD.json.gz') + value['recipe_sha256']=json_identity(json.loads((directory/'CLIFFORD-RECIPES.json').read_bytes())) + return value + +def native_value(directory,value=None): + directory=Path(directory) + value=copy.deepcopy(json.loads((directory/'INDEPENDENT-LOCAL-REPLAY.json').read_bytes())if value is None else value) + for field,name in [('canonical_word_sha256','CANONICAL-WORD.json.gz'),('local_programs_sha256','LOCAL-PROGRAMS.json.gz')]: + assert value[field]==sha(directory/name),'stale native artifact reference: '+field + value[field]=payload_identity(directory/name) + return value + +def artifact_identities(directory): + directory=Path(directory) + result={} + for name in FILES: + path=directory/name + if name.endswith('.gz'): + result[name]=payload_identity(path) + else: + value=phase_value(directory)if name=='CLIFFORD-REVIEW.json'else native_value(directory)if name=='INDEPENDENT-LOCAL-REPLAY.json'else json.loads(path.read_bytes()) + result[name]=json_identity(value) + return result diff --git a/research/pr643-improvement-20261013/witness/code/generated_identity_controls.py b/research/pr643-improvement-20261013/witness/code/generated_identity_controls.py new file mode 100644 index 0000000000..b4c133c107 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/generated_identity_controls.py @@ -0,0 +1,228 @@ +"""Actual gzip/receipt portability and consistently rebound semantic controls. + +Only scratch copies of generated provider files are changed. Each assembly +control recomputes raw artifact links, all seven portable identities and the +owner/invoice digests. This tests identity admission, not a replacement for the +full physical replay. Prepared with OpenAI Codex assistance; Apache-2.0. +""" +import argparse +import copy +import gzip +import hashlib +import json +import math +import shutil +import tempfile +from pathlib import Path + +import os +assert os.environ.get('GAIN_PR564_SOURCE'), 'Explicit engine source required' +from assemble import assemble +from witness import PROVIDERS,SPOT +from generated_identity import FILES, artifact_identities, json_identity, sha + +if not __debug__: + raise RuntimeError('Assertions required; refusing optimized verification') + + +def read(path): + raw = path.read_bytes() + return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw) + + +def write_json(path, value): + # Nonfinite numbers are emitted only by deliberate invalid-timing controls. + path.write_text(json.dumps(value, indent=2)+'\n', encoding='utf-8', newline='\n') + + +def write_gzip(path, value): + payload = json.dumps(value, sort_keys=True, separators=(',', ':')).encode() + path.write_bytes(gzip.compress(payload, compresslevel=1, mtime=123456789)) + + +def refresh_links(directory): + """Rebind only the three actual gzip references and the phase recipe link.""" + native = read(directory/'INDEPENDENT-LOCAL-REPLAY.json') + native['canonical_word_sha256'] = sha(directory/'CANONICAL-WORD.json.gz') + native['local_programs_sha256'] = sha(directory/'LOCAL-PROGRAMS.json.gz') + write_json(directory/'INDEPENDENT-LOCAL-REPLAY.json', native) + phase = read(directory/'CLIFFORD-REVIEW.json') + phase['canonical_word_sha256'] = sha(directory/'CANONICAL-WORD.json.gz') + phase['recipe_sha256'] = sha(directory/'CLIFFORD-RECIPES.json') + write_json(directory/'CLIFFORD-REVIEW.json', phase) + + +def rebound(owner, invoice, pid, directory): + """Return complete consistent receipt links to the changed actual files.""" + identities = artifact_identities(directory) + o, i = copy.deepcopy(owner), copy.deepcopy(invoice) + p = i['providers'][pid] + for name in FILES: + raw = sha(directory/name) + p['artifacts'][name] = raw + o['source_artifacts']['providers/'+pid+'/'+name] = raw + p['semantic_artifact_sha256'] = identities + o['provider_artifact_semantic_sha256'][pid] = identities + phase = identities['CLIFFORD-REVIEW.json'] + o['provider_phase_semantic_sha256'][pid] = phase + i['provider_phase_semantic_sha256'][pid] = phase + owner_hash = json_identity(o) + i['owner_audit_sha256'] = owner_hash + return o, i, owner_hash, json_identity(i), identities + + +def run(base, audit, out, provider_root=None): + assert not out.exists() + out.parent.mkdir(parents=True, exist_ok=True) + source = provider_root or base/'providers' + owner_path, invoice_path = audit/'OWNERS-AND-PROFILE.json', audit/'PREFIX-AND-INVOICE.json' + owner, invoice = read(owner_path), read(invoice_path) + baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path)) + accepted, rejected, references, source_identities = [], [], [], {} + raw_changed = {} + with tempfile.TemporaryDirectory(prefix='generated-identity-controls-', dir=out.parent) as td: + scratch = Path(td) + for pid in sorted(PROVIDERS): + original = source/pid + ids = artifact_identities(original) + assert ids == PROVIDERS[pid]['artifact_semantic_sha256'] + source_identities[pid] = dict(raw={name:sha(original/name) for name in FILES}, semantic=ids) + # The optional provider-root can use another Python/zlib environment. + o, i, oh, ih, _ = rebound(owner, invoice, pid, original) + assert assemble(o, i, oh, ih)['kappa'] == baseline['kappa'] + + def fresh(tag): + directory = scratch/(pid+'-'+tag) + directory.mkdir() + for name in FILES: + shutil.copyfile(original/name, directory/name) + return directory + + def reject_semantics(tag, mutate, changed_file): + directory = fresh(tag) + mutate(directory) + refresh_links(directory) + o, i, oh, ih, new_ids = rebound(owner, invoice, pid, directory) + assert new_ids[changed_file] != ids[changed_file], (tag, 'mutation disappeared from identity') + try: + assemble(o, i, oh, ih) + except AssertionError: + rejected.append(dict(provider=pid, case=tag, changed_identity=changed_file, + all_raw_and_semantic_links_rebound=True)) + else: + raise AssertionError('semantic mutation accepted: '+tag) + + def json_mutation(name, change): + def mutate(directory): + value = read(directory/name) + change(value) + write_json(directory/name, value) + return mutate + + directory = fresh('recompression') + changed = [] + for name in ('CANONICAL-WORD.json.gz', 'LOCAL-PROGRAMS.json.gz'): + before = (directory/name).read_bytes() + payload = gzip.decompress(before) + after = gzip.compress(payload, compresslevel=1, mtime=123456789) + assert after != before and gzip.decompress(after) == payload + (directory/name).write_bytes(after) + changed.append(name) + refresh_links(directory) + o, i, oh, ih, new_ids = rebound(owner, invoice, pid, directory) + assert new_ids == ids + assert assemble(o, i, oh, ih)['kappa'] == baseline['kappa'] + accepted.append(dict(provider=pid, case='recompressed_same_payloads', changed_raw_artifacts=changed, + all_seven_identities_unchanged=True, all_raw_links_rebound=True)) + raw_changed[pid] = {name:[sha(original/name),sha(directory/name)] for name in changed} + + # A stale literal link must fail before any normalization can hide it. + for tag, name, receipt, field in ( + ('stale_native_word_link','CANONICAL-WORD.json.gz','INDEPENDENT-LOCAL-REPLAY.json','canonical_word_sha256'), + ('stale_native_program_link','LOCAL-PROGRAMS.json.gz','INDEPENDENT-LOCAL-REPLAY.json','local_programs_sha256'), + ('stale_phase_word_link','CANONICAL-WORD.json.gz','CLIFFORD-REVIEW.json','canonical_word_sha256'), + ('stale_phase_recipe_link','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','recipe_sha256')): + directory = fresh(tag) + value = read(directory/receipt) + value[field] = '0'*64 + write_json(directory/receipt, value) + try: + artifact_identities(directory) + except AssertionError: + references.append(dict(provider=pid, case=tag, rejected_before_projection=True)) + else: + raise AssertionError('stale literal reference normalized away: '+tag) + + def change_scalar(directory): + programs = read(directory/'LOCAL-PROGRAMS.json.gz') + event = next(e for e in programs['forward'] if e[0]=='scalar' and e[1][0]=='add') + event[1][3] = -event[1][3] + write_gzip(directory/'LOCAL-PROGRAMS.json.gz', programs) + reject_semantics('changed_actual_scalar', change_scalar, 'LOCAL-PROGRAMS.json.gz') + + def change_frame(directory): + word = read(directory/'CANONICAL-WORD.json.gz') + r = 2*112 + SPOT[2] # PR558 helper 294 (register 518) or its helper-map image: an entering helper + old = word['start'][r] + replacement = next(j for j,f in enumerate(word['frames']) + if j != old and len(f) == len(word['frames'][old])) + word['start'][r] = replacement + write_gzip(directory/'CANONICAL-WORD.json.gz', word) + reject_semantics('changed_actual_start_frame_same_rank', change_frame, 'CANONICAL-WORD.json.gz') + reject_semantics('native_false_restoration', json_mutation('INDEPENDENT-LOCAL-REPLAY.json', + lambda x:x['local']['forward'].__setitem__('private_work_erased',False)), + 'INDEPENDENT-LOCAL-REPLAY.json') + reject_semantics('native_wrong_column_count', json_mutation('INDEPENDENT-LOCAL-REPLAY.json', + lambda x:x['local']['backward'].__setitem__('all_exact_columns',x['local']['backward']['all_exact_columns']-1)), + 'INDEPENDENT-LOCAL-REPLAY.json') + reject_semantics('native_changed_profile', json_mutation('INDEPENDENT-LOCAL-REPLAY.json', + lambda x:x['paid_profiles']['forward'].__setitem__('1',x['paid_profiles']['forward']['1']+1)), + 'INDEPENDENT-LOCAL-REPLAY.json') + reject_semantics('phase_false_global_equality', json_mutation('CLIFFORD-REVIEW.json', + lambda x:x.__setitem__('all_child_equalities_include_global_phase',False)), + 'CLIFFORD-REVIEW.json') + + # This event hash is proof data, even when its value equals a gzip hash. + def change_event_hash(directory): + value = read(directory/'LOCAL-CHECKS.json') + value['forward']['sha256'] = sha(directory/'CANONICAL-WORD.json.gz') + write_json(directory/'LOCAL-CHECKS.json', value) + assert artifact_identities(directory)['LOCAL-CHECKS.json'] == json_identity(value) + reject_semantics('local_event_hash_is_not_a_container_reference', change_event_hash, 'LOCAL-CHECKS.json') + reject_semantics('unrelated_native_root_seconds_retained', json_mutation('INDEPENDENT-LOCAL-REPLAY.json', + lambda x:x.__setitem__('seconds',7)), 'INDEPENDENT-LOCAL-REPLAY.json') + reject_semantics('nested_phase_seconds_retained', json_mutation('CLIFFORD-REVIEW.json', + lambda x:x.__setitem__('additional_evidence',{'seconds':7})), 'CLIFFORD-REVIEW.json') + + for tag,value in [('negative',-1),('boolean',True),('string','1'),('nan',float('nan')), + ('infinity',float('inf'))]: + directory = fresh('invalid-timing-'+tag) + phase = read(directory/'CLIFFORD-REVIEW.json');phase['seconds'] = value + write_json(directory/'CLIFFORD-REVIEW.json', phase) + try: + artifact_identities(directory) + except AssertionError: + references.append(dict(provider=pid,case='invalid_phase_seconds_'+tag, + rejected_before_projection=True)) + else: + raise AssertionError('invalid timing silently erased: '+tag) + n=len(PROVIDERS) + assert len(accepted)==n and len(rejected)==9*n and len(references)==9*n + assert {x['provider']for x in accepted}=={x['provider']for x in rejected}=={x['provider']for x in references}==set(PROVIDERS) + report=dict(status='PASS_GENERATED_ARTIFACT_RECOMPRESSION_AND_REBOUND_MUTATIONS', + kappa=baseline['kappa'], source_owner_sha256=sha(owner_path),source_invoice_sha256=sha(invoice_path), + source_providers=source_identities,recompression_changed_raw_hashes=raw_changed, + accepted=accepted,semantic_mutations_rejected=rejected,invalid_references_or_metadata_rejected=references, + counts=dict(recompression_accepted=n,semantic_rejected=9*n,reference_or_metadata_rejected=9*n), + scope='Actual copied gzip streams and receipt JSON are changed. All seven content identities, raw source links and owner/invoice digests are recomputed consistently before assembly. Only identical decompressed payloads are accepted; scalar, same-rank frame, native proof fields, global phase, event hashes and unrelated seconds remain pinned. Literal references and invalid phase timing are rejected before normalization. Full physical replay remains a separate prerequisite.') + write_json(out,report) + print(report['status'],report['counts']) + + +if __name__=='__main__': + parser=argparse.ArgumentParser(description=__doc__) + for name in ('base','audit','out'): + parser.add_argument('--'+name,type=Path,required=True) + parser.add_argument('--provider-root',type=Path) + args=parser.parse_args() + run(args.base,args.audit,args.out,args.provider_root) diff --git a/research/pr643-improvement-20261013/witness/code/hpe_adapters_local.py b/research/pr643-improvement-20261013/witness/code/hpe_adapters_local.py new file mode 100644 index 0000000000..8f77ccf02d --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/hpe_adapters_local.py @@ -0,0 +1,116 @@ +"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding. Apache-2.0. +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. The wrapper construction follows PR #458 +(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first); +S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers R_E^-1 before the whole local invocation and L_E^-1 after its +full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically. +usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json +Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive +constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that L_E^-1 S_E R_E^-1 has exactly the +tableau and zero-state vector (global phase included) of fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong +translation, wrong width) must be rejected.""" +import copy, gzip, json, sys +from pathlib import Path +# Package-path adaptation only; the exact wrapper mathematics is unchanged. +import os +R = Path(os.environ['MULTICOLD_SOURCE']) / 'vendor/pr558/vendor/pr552/complex-global/vendor531' # HPE: the pinned vendor531 clifford_exact +sys.path.insert(0, str(R / 'vendor/clifford')) +from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity +n = 9; FULL = tuple(1 << i for i in range(n)) +def monomial_op(rec): + """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)""" + out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset'])) + return out.then(Op(n, identity(n), [('phase', rec['phase'])])) +def S_of(U, END=FULL): + # HPE: a helper that starts at E=U and ends at END has residual T_END T_E^-1 (END = FULL is the inherited case) + return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, tuple(END))) +def wrapped_ok(U, rec, END=FULL): + """exactly: L^-1 S R^-1 = C_[w] x I (apply order: R^-1, S, L^-1), w = dim END - dim E""" + w = len(END) - len(U); S = S_of(U, END); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left']) + net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w)) + return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state() +def _contains(a, b): + a = list(a) + for x in b: + for y in sorted(a, reverse=True): + if x >> (y.bit_length() - 1) & 1: x ^= y + if x: return False + return True +def main(): + c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v'] + starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0 and c['final'][r] == 1}) + # HPE: (entrance, terminal) pairs of helpers ending at a proper subspace; key 'E:U'. Inherited words have none. + ends = sorted({(c['start'][r], c['final'][r]) for r in range(2 * v, len(c['start'])) if c['final'][r] != 1}) + # COLD-HPE: e == 0 (a cold helper, entrance = bottom, T_0 = I) is allowed: the (0, U) recipe is keyed '0:U' + assert all(len(frames[u]) < n and _contains(frames[u], frames[e]) for e, u in ends) + cold_ends = [(e, u) for e, u in ends if e == 0] + recipes = {} + for f in starts: + U = frames[f]; rec, compiled = lower_child(S_of(U)) + recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right']) + for e, u in ends: + E, U = frames[e], frames[u]; rec, compiled = lower_child(S_of(E, U)) + recipes['%d:%d' % (e, u)] = dict(frame=e, terminal=u, vectors=list(E), terminal_vectors=list(U), entrance_rank=len(E), + terminal_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right']) + Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes), sort_keys=True, separators=(',', ':')) + '\n') + # ---- independent decode of the serialized file + data = json.loads(Path(sys.argv[2]).read_text())['recipes'] + dot = lambda a, b: bin(a & b).count('1') & 1 + detail = [] + for f in starts: + rec = data[str(f)]; U = frames[f] + assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f) + detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U), + totally_isotropic=all(dot(a, b) == 0 for a in U for b in U))) + hdetail = [] + for e, u in ends: # HPE: independent decode, residual width = dim U - dim E + rec = data['%d:%d' % (e, u)]; E, U = frames[e], frames[u] + assert wrapped_ok(E, rec, U), ('HPE wrapper product is not C_[w] x I', e, u) + hdetail.append(dict(frame=e, terminal=u, entrance_rank=len(E), terminal_rank=len(U), residual_width=len(U) - len(E))) + controls = [] + def reject(name, fn): + f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec) + if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name) + controls.append(name) + reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4)) + reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1)) + reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4)) + reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left']))) + reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1)) + if ends: # HPE controls on the first (E, U) pair + e, u = next((p for p in ends if p[0] != 0), ends[0]); rec0 = data['%d:%d' % (e, u)] # COLD-HPE: an entering pair if any (= ends[0] without cold ends) + def hreject(name, ok): + if ok: raise AssertionError('HPE mutation accepted: ' + name) + controls.append(name) + hreject('hpe: U-wrapper decoded against a FULL ending', wrapped_ok(frames[e], rec0)) + hreject('hpe: width misreported as 9 - dim E', wrapped_ok(frames[e], dict(rec0, rank=n - len(frames[e])), frames[u])) + other = next(f for f in range(len(frames)) if f != u and len(frames[f]) == len(frames[u]) and _contains(frames[f], frames[e])) + hreject('hpe: wrong terminal hyperplane', wrapped_ok(frames[e], rec0, frames[other])) + fe = next(((e2, u2) for e2, u2 in ends if str(e2) in data), None) + if fe: # an entrance shared with FULL-ended helpers: R_{E,FULL} must not serve as R_{E,U} + r2 = data['%d:%d' % fe] + hreject('hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}', wrapped_ok(frames[fe[0]], dict(r2, right=data[str(fe[0])]['right']), frames[fe[1]])) + hreject('hpe: wrong global phase', wrapped_ok(frames[e], dict(rec0, left=dict(rec0['left'], phase=(rec0['left']['phase'] + 1) % 4)), frames[u])) + if cold_ends: # COLD-HPE controls on the first cold pair (0, U): factor_iff_pre says only R_{0,U} itself may precede + e, u = cold_ends[0]; recc = data['%d:%d' % (e, u)]; E, U = frames[e], frames[u] + ID = dict(matrix_rows=[1 << i for i in range(n)], offset=0, quadratic_rows=[0] * n, linear_Z4=[0] * n, phase=0) + assert monomial_op(ID).tab == identity(n) # the control's wrapper really is the identity + def creject(name, ok): + if ok: raise AssertionError('cold HPE mutation accepted: ' + name) + controls.append(name) + creject('cold hpe: identity pre wrapper instead of R_{0,U}', wrapped_ok(E, dict(recc, right=ID), U)) + creject('cold hpe: identity post wrapper instead of L_{0,U}', wrapped_ok(E, dict(recc, left=ID), U)) + creject('cold hpe: no wrappers (cold FULL convention L = R = I)', wrapped_ok(E, dict(recc, left=ID, right=ID), U)) + creject('cold hpe: U-wrapper decoded against a FULL ending', wrapped_ok(E, recc)) + creject('cold hpe: width misreported as 9', wrapped_ok(E, dict(recc, rank=n), U)) + other = next(f for f in range(len(frames)) if f != u and len(frames[f]) == len(frames[u])) + creject('cold hpe: wrong terminal hyperplane', wrapped_ok(E, recc, frames[other])) + creject('cold hpe: wrong global phase', wrapped_ok(E, dict(recc, right=dict(recc['right'], phase=(recc['right']['phase'] + 1) % 4)), U)) + ent = next((p for p in ends if p[0] != 0 and p[1] == u), None) + same = lambda x, y: monomial_op(x).tab == monomial_op(y).tab and monomial_op(x).zero_state() == monomial_op(y).zero_state() + if ent and not same(data['%d:%d' % ent]['right'], recc['right']): # an entering helper ending at the same U: its R_{E,U} must not serve as R_{0,U} + creject('cold hpe: pre wrapper resolved to an entering recipe R_{E,U}', wrapped_ok(E, dict(recc, right=data['%d:%d' % ent]['right']), U)) + res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), **({'hyperplane_end_pairs': hdetail} if ends else {}), **({'cold_hyperplane_end_pairs': len(cold_ends)} if cold_ends else {}), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail), + all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail) + Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n') + print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight']) +if __name__ == '__main__': main() diff --git a/research/pr643-improvement-20261013/witness/code/hpe_audit_and_transport.py b/research/pr643-improvement-20261013/witness/code/hpe_audit_and_transport.py new file mode 100644 index 0000000000..d5d3509d90 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/hpe_audit_and_transport.py @@ -0,0 +1,304 @@ +"""Rebuild arbitrary-dirt compensation and transport a changed local word. + +Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0. +Adapted from PR425/433 (icekylinx), PR484's audit_gk.py +(DreamingOfClouds), and Round19's 112-port transport. This auditor does not +import a constructor, a nominated compensation table, or a global price. +Only the changed scalar word and its actual frame chains are checked here. +""" +import argparse +import copy +import gzip +import hashlib +import json +import time +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def content_hash(path): + data = path.read_bytes() + return hashlib.sha256(gzip.decompress(data) if path.suffix == '.gz' else data).hexdigest() + + +def basis(vs): + pivots = {} + for x in vs: + for k in sorted(pivots, reverse=True): + if x >> k & 1: + x ^= pivots[k] + if x: + k = x.bit_length() - 1 + for j in pivots: + if pivots[j] >> k & 1: + pivots[j] ^= x + pivots[k] = x + return tuple(pivots[k] for k in sorted(pivots, reverse=True)) + + +def apply(e, rows): + if e[0] == 'scale': + _, target, a, b, *_ = e + q = Q(a, b) + assert q + rows[target] = {j: q*x for j, x in rows[target].items()} + else: + _, target, source, a, b, *_ = e + assert target != source + q = Q(a, b) + for j, x in list(rows[source].items()): + value = rows[target].get(j, Q(0)) + q*x + if value: + rows[target][j] = value + else: + rows[target].pop(j, None) + + +def inverse(e): + e = copy.deepcopy(e) + if e[0] == 'add': + e[3] *= -1 + else: + e[2], e[3] = e[3], e[2] + return e + + +def dual(e): + e = inverse(e) + if e[0] == 'add': + e[1], e[2] = e[2], e[1] + return e + + +def state_maps(prefix, n): + """P = exact state map of the prefix (precondition + compensation + A + cut + B), and P^-1 (rows as sparse dicts).""" + P = [{r: Q(1)} for r in range(n)] + for e in prefix: + apply(e, P) + Pinv = [{r: Q(1)} for r in range(n)] + for e in reversed(prefix): + apply(inverse(e), Pinv) + return P, Pinv + + +def cone_violations(P, Pinv, hpe, mapping, endB, final, frames): + """COLD-HPE / CONE PRE-CHECK. Necessary conditions for helper h (raw index) to end at U = final[h] under ANY + monotone common-frame cleanup of the end-of-B state P (frames only climb, every gate at a common frame): + row (J26-H dependency bound): every g in supp(row h of P^-1) has end-of-B frame <= U -- h is rebuilt from them; + column (dirt-column lemma): every g != h with P[g][h] != 0 has end-of-B frame <= U -- the column of P at h, + restricted to rows whose frame is not <= U, changes only by invertible row operations unless h is read at a + frame not <= U, so it can reach e_h only if it is already zero there. + Both are implied by the exact endpoint replay plus the frame checks below; here they fail FAST, with the reason.""" + inside = lambda a, b: basis(frames[a] + frames[b]) == frames[b] + viol = [] + for h in hpe: + U = final[mapping[h]] + viol += [('row', h, g) for g, x in sorted(Pinv[h].items()) if x and not inside(endB[mapping[g]], U)] + viol += [('column', h, g) for g in range(len(P)) if g != h and P[g].get(h) and not inside(endB[mapping[g]], U)] + return viol + + +def run(raw_path, routing_path, out): + start_time = time.monotonic() + word, routing = read(raw_path), read(routing_path) + v, h, helpers = word['report']['v'], word['report']['h'], word['report']['R'] + assert h == 9 and v == 112 and routing['v'] == v + n = 2*v + helpers + ident = lambda: [{r: Q(1)} for r in range(n)] + main = word['A'] + word['cut'] + word['B'] + assert all(not v <= e[2] < 2*v for e in word['A'] + word['B'] + if e[0] == 'add' and not v <= e[1] < 2*v) + matrix = ident() + for e in main: + apply(e, matrix) + dirty = [{} for _ in range(n)] + for r in range(v, 2*v): + dirty[r] = {j: x for j, x in matrix[r].items() if j >= 2*v} + for e in word['precondition']: + apply(e, dirty) + compensation = [['add', r, j, -q.numerator, q.denominator, []] + for r in range(v, 2*v) for j, q in sorted(dirty[r].items())] + entering = set(map(int, word.get('start_extra', {}))) + assert all(e[2] not in entering for e in compensation), 'zero-frame compensation reads an entering helper' + cleanup = [inverse(e) for e in reversed(word['A'] + word['B']) + if not v <= e[1] < 2*v] + if 'refactored_cleanup' in word: + # REFACTORED CLEANUP (cold low-frame ends): the cleanup is not the literal reversed inverse of A+B but another exact + # factorisation of the same inverse. Nothing about it is trusted: it may only touch non-target registers (T rows + # stay the compensated data accumulators), every gate is dyadic (checked below), and the arbitrary-dirt endpoint + # replay below must be exact in BOTH orientations for the full reordered program. Inherited words keep the literal + # assertion (the else branch), so their outputs are unchanged. + assert all(not v <= r < 2*v for e in word['cleanup'] for r in ([e[1]] + ([e[2]] if e[0] == 'add' else []))), 'refactored cleanup touches a target' + assert all(e[0] in ('add', 'scale') for e in word['cleanup']) + cleanup = word['cleanup'] + else: + assert [e[:-1] for e in cleanup] == [e[:-1] for e in word['cleanup']], 'cleanup is not the literal reversed inverse of A+B' + # HPE: hyperplane-ended helpers. 'early_cleanup' = [[cleanup index, frame vectors], ...] are cleanup gates executed + # right after B (before the final climbs) at the given frame; 'helper_final' = {helper: frame vectors} replaces FULL as + # that helper's terminal frame. The scalar program is the reordered one and is replayed exactly below, so a move that + # does not commute with the skipped cleanup prefix is rejected by the arbitrary-dirt endpoint assertion. + early = [(int(i), f) for i, f in word.get('early_cleanup', [])] + helper_final = {int(r): f for r, f in word.get('helper_final', {}).items()} + early_idx = [i for i, _ in early] + assert len(set(early_idx)) == len(early_idx) and all(0 <= i < len(cleanup) for i in early_idx) + assert all(2*v <= r < n for r in helper_final) + # COLD-HPE: a COLD helper (not in start_extra, entrance frame 0 = bottom) may also end at a proper subspace U. + # It is the E = bottom instance of #593's theorems: its wrappers are the (0, U) recipes R_{0,U}, L_{0,U} (checked + # exactly by hpe_adapters_local), emitted as residual_adapter events like an entering helper's. + cold_hpe = sorted(r for r in helper_final if r not in entering) + # COLD-HPE wrapper order: R_{0,U}^-1 is emitted with the entry adapters, after the zero-frame precondition and + # compensation, so (exactly as for an entering helper, asserted above) nothing before it may touch a cold-ended helper. + assert all(r not in set(cold_hpe) for e in word['precondition'] + compensation for r in ([e[1]] + ([e[2]] if e[0] == 'add' else []))), 'zero-frame precondition/compensation touches a cold hyperplane-ended helper before its wrapper' + # ENTERING helpers (start frame E != 0): their wrapper R_E^-1 precedes every gate on them, so the zero-frame precondition + # and compensation may not touch them either (mirrors hpe_emit_local's start-frame-0 rule here, at the scalar audit). + assert all(r not in entering for e in word['precondition'] + compensation for r in ([e[1]] + ([e[2]] if e[0] == 'add' else []))), 'zero-frame precondition/compensation touches an entering helper' + tail =[word['cleanup'][i][:-1] + [f] for i, f in early] + rest = [e for i, e in enumerate(word['cleanup']) if i not in set(early_idx)] + program = word['precondition'] + compensation + main + tail + rest + for backward in (False, True): + actual = ident() + for e in program: + apply(dual(e) if backward else e, actual) + expected = ident() + for t in range(v): + expected[t if backward else v+t][v+t if backward else t] = Q(-1 if backward else 1) + assert actual == expected, ('arbitrary-dirt endpoint', backward) + # The native scalar compiler allows dyadic additions and signed binary scales. + for e in program: + q = Q(e[3], e[4]) if e[0] == 'add' else Q(e[2], e[3]) + assert q.denominator & (q.denominator-1) == 0 + if e[0] == 'scale': + a = abs(q.numerator) + assert a and a & (a-1) == 0 + + tau = lambda x: x ^ (43 if (x & 43).bit_count() % 2 else 0) + ports = routing['ports'] + assert len(set(ports)) == v and set(map(tau, word['ports'])) == set(ports) + mapping = {i: ports.index(tau(p)) for i, p in enumerate(word['ports'])} + mapping.update({v+i: v+mapping[i] for i in range(v)}) + mapping.update({r: r for r in range(2*v, n)}) + full = tuple(1 << i for i in range(h-1, -1, -1)) + frames, frame_ids = [(), full], {(): 0, full: 1} + + def fid(vectors): + frame = basis(vectors) + if frame not in frame_ids: + frame_ids[frame] = len(frames) + frames.append(frame) + return frame_ids[frame] + + def transform(e): + e = copy.deepcopy(e) + e[1] = mapping[e[1]] + if e[0] == 'add': + e[2] = mapping[e[2]] + if e[-1] is not None: + e[-1] = fid([tau(x) for x in e[-1]]) + return e + + canonical = {key: [transform(e) for e in word[key]] + for key in ('A', 'B', 'cut', 'cleanup', 'precondition')} + canonical['compensation'] = [transform(e) for e in compensation] + if tail: + canonical['tail'] = [transform(e) for e in tail] # HPE (absent for inherited words: identical output) + canonical['cleanup'] = [transform(e) for e in rest] # HPE (full cleanup minus the early gates) + canonical['start'] = [fid([p]) for p in ports] + [0]*(v+helpers) + for r, frame in word.get('start_extra', {}).items(): + assert 2*v <= int(r) < n + canonical['start'][int(r)] = fid([tau(x) for x in frame]) + canonical['final'] = ([1]*v + + [fid(x for x in range(1, 1 << h) if (x & p).bit_count() % 2 == 0) for p in ports] + + [1]*helpers) + for r, frame in helper_final.items(): # HPE + canonical['final'][r] = fid([tau(x) for x in frame]) + canonical.update(h=h, v=v, R=helpers, ports=ports, frames=frames, + centers=[mapping[r] for r in word['centers']], + center_frames=[fid(tau(x) for x in frame) for frame in word['center_frames']]) + levels = {mapping[v+int(t)]-v: fid(tau(x) for x in frame) + for t, frame in word.get('target_levels', {}).items()} + canonical['target_levels'] = {str(t): f for t, f in levels.items()} + current, paid, edges = canonical['start'].copy(), Counter(), set() + + def climb(r, f): + old = current[r] + assert basis(frames[old] + frames[f]) == frames[f], ('nonmonotone', r, old, f) + if old != f: + degree = len(frames[f]) - len(frames[old]) + assert degree > 0 + paid[degree] += 1 + edges.add((old, f)) + current[r] = f + + for part in ('A', 'B'): + if part == 'B': + assert all(current[r] == f for r, f in zip(canonical['centers'], canonical['center_frames'])) + assert all(current[v+t] == levels.get(t, 0) for t in range(v)) + for r, frame in zip(canonical['centers'], canonical['center_frames']): + served = {levels.get(e[1]-v, 0) for e in canonical['cut'] if e[2] == r} + old = frame + for f in sorted(served, key=lambda f: -len(frames[f])): + assert basis(frames[old] + frames[f]) == frames[old] + if old != f: + paid[len(frames[old])-len(frames[f])] += 1 + edges.add((old, f)) + edges.add((f, old)) + old = f + for e in canonical[part]: + for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): + climb(r, e[-1]) + if helper_final: # COLD-HPE / CONE PRE-CHECK at the end-of-B frames + P, Pinv = state_maps(word['precondition'] + compensation + main, n) + cone = cone_violations(P, Pinv, sorted(helper_final), mapping, current.copy(), canonical['final'], frames) + assert not cone, ('hpe cone pre-check (row / column)', cone[:8]) + for e in canonical.get('tail', []): # HPE: early cleanup gates at their common frame + for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): + climb(r, e[-1]) + for r, f in enumerate(canonical['final']): + climb(r, f) + # HPE: the remaining cleanup runs at FULL, so it may touch only registers whose terminal frame is FULL; a + # hyperplane-ended helper is touched by nothing after its tail gates. + for e in canonical['cleanup']: + assert all(canonical['final'][r] == 1 for r in [e[1]] + ([e[2]] if e[0] == 'add' else [])), ('cleanup on non-FULL end', e) + assert all(len(frames[canonical['final'][r]]) < h for r in helper_final) + assert dict(paid) == {int(r): count for r, count in word['report']['local_profile'].items()}, 'paid local profile differs from the reported local_profile' + canonical['local_profile'] = dict(sorted(paid.items())) + canonical['edges'] = sorted(edges) + out.mkdir(parents=True, exist_ok=False) + payload = json.dumps(canonical, sort_keys=True, separators=(',', ':')).encode() + (out/'CANONICAL-WORD.json.gz').write_bytes(gzip.compress(payload, mtime=0)) + (out/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word, sort_keys=True, separators=(',', ':')).encode(), mtime=0)) + receipt = dict(status='PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES', + input_content_sha256=content_hash(raw_path), routing_content_sha256=content_hash(routing_path), + canonical_content_sha256=hashlib.sha256(payload).hexdigest(), + live_columns_each_orientation=n, helpers=helpers, + compensation_additions=len(compensation), scalar_operations=len(program), + center_rank_sum=sum(map(len, word['center_frames'])), + local_profile=dict(sorted(paid.items())), local_rank_mass=sum(r*z for r, z in paid.items()), + widths=[len(frames[canonical['final'][r]])-len(frames[canonical['start'][r]]) for r in range(2*v, n)], + frames=len(frames), directed_edges=len(edges), + tau=43, target_port_order_matches_baseline=True, + seconds=time.monotonic()-start_time, + scope='Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. Phase lowering, wrappers, global owners and global assembly are separate.') + if tail or helper_final: + receipt.update(hyperplane_ended_helpers=sorted(helper_final), early_cleanup_gates=len(tail)) + if cold_hpe: # COLD-HPE (absent for words without cold ends) + receipt.update(cold_hyperplane_ended_helpers=cold_hpe) + if 'refactored_cleanup' in word: # REFACTORED CLEANUP (absent for inherited words) + receipt.update(refactored_cleanup_gates=len(word['cleanup']), refactored_cleanup=word['refactored_cleanup']) + (out/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(receipt, indent=2)+'\n') + print(json.dumps({k: value for k, value in receipt.items() if k != 'widths'}, indent=2), flush=True) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--raw', type=Path, required=True) + parser.add_argument('--routing', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + run(args.raw, args.routing, args.out) diff --git a/research/pr643-improvement-20261013/witness/code/hpe_audit_local.py b/research/pr643-improvement-20261013/witness/code/hpe_audit_local.py new file mode 100644 index 0000000000..17bccb64fd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/hpe_audit_local.py @@ -0,0 +1,171 @@ +# Local-only extraction of the attributed PR514 / PR433 independent replay. +# Prepared for icekylinx with OpenAI Codex assistance. Apache-2.0. +# The complete local checker and its negative controls are retained verbatim. +# Global hosting is verified separately for the changed 112-port geometry. +import copy,gzip,hashlib,json,sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +OUT=Path(sys.argv[1]) +c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz')) +ir={'local_programs':json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'))} +v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames'] +levels={int(t):f for t,f in c.get('target_levels',{}).items()} +entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0] +plain={r for r in range(n) if r not in set(entering)} + +def contains(a,b): + for x in a: + for y in b: + if x>>(y.bit_length()-1)&1:x^=y + if x:return False + return True +hpe={r for r in range(2*v,n) if c['final'][r]!=1} # HPE: helpers whose terminal frame is a proper subspace U of FULL +assert all(len(frames[c['final'][r]])0 + hist[rank]+=1;cur[r]=b + elif tag=='center': + _,k,a,b,rank=event + assert phases[-1]=='centers' and private=={('C',k):a} + cf=c['center_frames'][k];cr=len(frames[cf]) + # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child + assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a]) + assert rank==abs(len(frames[a])-len(frames[b]))>0 + chain.setdefault(k,[]).append((a,b)) + private['C',k]=b;hist[rank]+=1;centers.append(k) + elif tag=='scalar': + _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None + if target[0]=='C' and op=='clear': + assert private.get(target,f)==f + private.pop(target,None) + else: + for r in (target,source): + if r is None:continue + if r[0]=='L':assert cur[r[1]]==f and (r[1] not in wset or (r[1] in pre_seen and r[1] not in post_seen)),('common frame / wrapper order',r,cur[r[1]],f) + else: + if r==target and r not in private:private[r]=f + assert private[r]==f + if op=='clear':rows[target]={};norm[target]=Q(0) + elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source] + elif op=='scale': + q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator + assert a&(a-1)==0 and b&(b-1)==0 + rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q) + else: + q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator + assert source!=target and b&(b-1)==0 + # Independent symbolic replay of the cleared coefficient work. + w=0 + for bit in bin(a)[2:]:w=2*w+int(bit) + assert Q(w,b)*(1 if q>0 else -1)==q + prefix=max(prefix,Q(a)*norm[source]) + norm[target]=norm.get(target,Q(0))+abs(q)*norm[source] + row=rows.setdefault(target,{}) + for j,x in list(rows[source].items()): + z=row.get(j,Q(0))+q*x + if z:row[j]=z + else:row.pop(j,None) + prefix=max(prefix,norm[target]) + else:raise AssertionError(tag) + assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private + assert sorted(r for k,r,_ in wrappers if k=='pre')==wrapped and sorted(r for k,r,_ in wrappers if k=='post')==wrapped # GK + for k,st in chain.items(): # GK: the steps of each centre chain link up and end at the centre frame + cf=c['center_frames'][k] + if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1)) + else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1)) + assert all(not row for reg,row in rows.items() if reg[0]=='C') + for r in range(n): + expected={r:Q(1)} + if back and r i0])) +reject('early gate frame below its registers\' frames', lambda w: w['early_cleanup'][0].__setitem__(1, U0[:-1])) +reject('hyperplane end on a non-entering helper', lambda w: (w['start_extra'].pop(h0))) +reject('profile not updated (paid climbs misreported)', lambda w: w['report']['local_profile'].__setitem__('1', w['report']['local_profile']['1']-3)) +reject('profile without 8 partner U->FULL climb charges', lambda w: w['report']['local_profile'].__setitem__('1', w['report']['local_profile']['1']-8)) +reject('duplicate early gate', lambda w: w['early_cleanup'].append(list(w['early_cleanup'][0]))) + +# Constructor controls for build_hpe's commutation rule (an early gate h -= p may skip earlier cleanup gates on p only +# when they commute with it, i.e. only read p). base = the word without its hyperplane ends; a skipped gate that WRITES +# the partner (an addition into p or a scale of p) or touches h must make build_hpe.apply refuse the recipe, while a +# skipped gate that only reads p is accepted. +import build_hpe +base = copy.deepcopy(word); base.pop('early_cleanup'); base.pop('helper_final') +hf = {int(h) for h in word['helper_final']} +changes = [] +for i, U in word['early_cleanup']: # pair each early gate with its helper via the gate's target + h = cl[i][1] + assert h in hf and word['helper_final'][str(h)] == U + changes.append(dict(helper=h, cleanup_index=i, frame=U)) +z0 = changes[0]; g0 = cl[z0['cleanup_index']]; p0 = g0[2] +x0 = next(r for r in range(2*v, n) if r not in {z['helper'] for z in changes} | {cl[z['cleanup_index']][2] for z in changes}) +NONCOMMUTE = 'cleanup gate does not commute with the skipped cleanup gates on its registers' +ONEGATE = 'helper must have exactly this one cleanup gate' + + +def build_with(w): + return build_hpe.apply(w, changes) + + +def inserted(pre): + """base with gate `pre` inserted at cleanup position 0; the changes' indices shift by one""" + w = copy.deepcopy(base); w['cleanup'].insert(0, pre) + return w, [dict(z, cleanup_index=z['cleanup_index'] + 1) for z in changes] + + +def cfail(name, w, ch, expect): + """the constructor must refuse with the pinned message `expect`""" + try: + build_hpe.apply(w, ch) + except AssertionError as e: + assert expect in str(e), ('constructor control %r failed with the wrong message: %s' % (name, e)) + results.append('constructor: ' + name); print('rejected constructor:', name, '--', expect, flush=True); return + raise AssertionError('HPE constructor mutation accepted: ' + name) + + +build_hpe.apply(*inserted(['add', x0, p0, -1, 1, FULL])) # positive: a skipped gate that only reads the partner commutes +cfail('skipped cleanup gate adds into the partner', *inserted(['add', p0, x0, -1, 1, FULL]), NONCOMMUTE) +cfail('skipped cleanup gate scales the partner', *inserted(['scale', p0, -1, 1, FULL]), NONCOMMUTE) +cfail('extra cleanup gate reading the helper (one-gate rule)', *inserted(['add', x0, z0['helper'], -1, 1, FULL]), ONEGATE) +cfail('extra cleanup gate adding into the helper (one-gate rule)', *inserted(['add', z0['helper'], x0, -1, 1, FULL]), ONEGATE) +# Real helpers admitted only by the commutation rule: their partner has an earlier cleanup gate x -= p (reads p). +# Flipping that gate in place to p -= x (writes p) must be refused by the commutation assert. +first = {} +for i, e in enumerate(cl): + for r in regs(e): first.setdefault(r, i) +relaxed = [z for z in changes if any(first[r] < z['cleanup_index'] for r in regs(cl[z['cleanup_index']]))] +for z in relaxed: + i = z['cleanup_index']; p = cl[i][2] + j = next(j for j in range(i) if p in regs(cl[j])) + e = cl[j]; assert e[0] == 'add' and e[2] == p and e[1] != p, ('skipped gate on a relaxed helper is not a reader', j, e) + build_hpe.apply(copy.deepcopy(base), changes) # positive: the real word's own changes + w = copy.deepcopy(base); w['cleanup'][j] = ['add', p, e[1]] + e[3:] + cfail('real helper %d: skipped gate %d flipped from %d -= %d to %d -= %d' % (z['helper'], j, e[1], p, p, e[1]), w, changes, NONCOMMUTE) +print('relaxed helpers', [z['helper'] for z in relaxed], flush=True) +outdir.mkdir(parents=True, exist_ok=True) +(outdir/'HPE-ATC-CONTROLS.json').write_text(json.dumps(dict(status='PASS_HPE_RAW_WORD_CONTROLS', word=str(src), rejected=results), indent=1) + '\n') +print('PASS', len(results), 'HPE raw-word mutations rejected') diff --git a/research/pr643-improvement-20261013/witness/code/hpe_emit_local.py b/research/pr643-improvement-20261013/witness/code/hpe_emit_local.py new file mode 100644 index 0000000000..534fdc71f7 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/code/hpe_emit_local.py @@ -0,0 +1,163 @@ +# GK: modified copy of PR #433's complex_emit.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5 +# (Anthropic), via Claude Code. Every change is marked "GK:". On a word without start_extra / target_levels the behaviour +# and every written file equal PR #433's (regression anchor in verify.py). +import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__))) +# Adapted from PR425 by icekylinx with Codex assistance. +"""Emit both local programs, integrate the fixed nine-stage geometry, and bill. + +The expanded scalar interface is justified in PROOF.txt. This script does not +claim a Lean proof or discharge the inherited all-size/analytic interfaces. +""" +import copy,gzip,hashlib,importlib.util,json,math +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +OUT=Path(_sys.argv[1]);cp=OUT/'CANONICAL-WORD.json.gz' +c=json.load(gzip.open(cp)) +frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R +def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest() +def basis(vs): + b={} + for x in vs: + for p in sorted(b,reverse=True): + if x>>p&1:x^=b[p] + if x: + p=x.bit_length()-1 + for q in b: + if b[q]>>p&1:b[q]^=x + b[p]=x + return tuple(b[p] for p in sorted(b,reverse=True)) +def dual(e): + e=list(e) + if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1 + else:e[2],e[3]=e[3],e[2] + return e +def scalar(e,back): + e=dual(e) if back else list(e) + if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]] + return ['scale',['L',e[1]],e[2],e[3]] +def primitive_bound(e): + if e[0] in ('clear','copy'):return 1 + q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3]) + a,b=abs(q.numerator),q.denominator + assert b&(b-1)==0 + if e[0]=='scale': + assert a&(a-1)==0 + return abs(a.bit_length()-b.bit_length())+int(q<0) + # Exact binary Horner multiplication on a cleared private stream, repeated + # halving, signed accumulation into the target, then clear the private stream. + return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1) + +def emit(back): + out=[];cur=c['start'].copy() + def event(e):out.append(e) + def scal(e,f):event(['scalar',e,f]) + event(['phase','zero_frame_precondition']) + for e in c['precondition']+c['compensation']: + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + assert all(c['start'][r]==0 for r in regs) + scal(scalar(e,back),0) + event(['phase','entry_adapters']) + # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate + # that touches it and L_E^-1 follows the full-frame cleanup. Words without entrances emit PR #433's events. + entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0] + hpe={r for r in range(2*v,n) if c['final'][r]!=1} # HPE: hyperplane-ended helpers (terminal frame != FULL) + # COLD-HPE: a cold helper (start frame 0) ending at U also carries the paid wrappers R_{0,U}^-1 / L_{0,U}^-1 (the + # E = bottom instance of #593); without cold ends wrapped == entering and the event stream is the inherited one. + wrapped=sorted(set(entering)|hpe) + for r,f in enumerate(c['start']): + if r in wrapped:event(['residual_adapter','pre',r,f]+([c['final'][r]] if c['final'][r]!=1 else [])) # HPE: R_{E,U}^-1 names U + else:event(['adapter','old_to_new',r,f]) + def climb(r,f,part): + old=cur[r] + if old==f:return + assert basis(frames[old]+frames[f])==tuple(frames[f]) + rank=len(frames[f])-len(frames[old]);assert rank>0 + event(['climb',part,r,old,f,rank]);cur[r]=f + # HPE: 'cleanup_tail' = early cleanup gates at their own frames; emitted only when the word has them, so a word + # without hyperplane-ended helpers yields exactly the inherited event stream. + for part in ('A','centers','B')+(('cleanup_tail',) if c.get('tail') else ())+('final',): + event(['phase',part]) + if part in ('A','B','cleanup_tail'): + for e in (c['tail'] if part=='cleanup_tail' else c[part]): + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + for r in regs:climb(r,e[-1],part) + scal(scalar(e,back),e[-1]) + elif part=='centers': + # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends + # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level + lv=lambda r:c.get('target_levels',{}).get(str(r-v),0) + assert all(cur[r]==lv(r) for r in range(v,2*v)) + for k,r in enumerate(c['centers']): + cf=c['center_frames'][k];assert cur[r]==cf + terms=[e for e in c['cut'] if e[2]==r] + path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x])) + C=['C',k] + if not back: + scal(['clear',C],cf);scal(['copy',C,['L',r]],cf) + for a in range(len(path)): + if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])]) + for e in terms: + if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a]) + scal(['clear',C],path[-1]) + else: + scal(['clear',C],path[-1]) + for a in range(len(path)-1,-1,-1): + for e in terms: + if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a]) + if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])]) + scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf) + else: + for r,f in enumerate(c['final']):climb(r,f,part) + event(['phase','exit_adapters']) + for r,f in enumerate(c['final']): + if r not in hpe:event(['adapter','new_to_old',r,f]) # HPE: no old-convention exit for a helper that ends at U; its post wrapper is L_{E,U}^-1 + event(['phase','full_frame_cleanup']) + for e in c['cleanup']: + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + assert all(c['final'][r]==1 for r in regs) + scal(scalar(e,back),1) + for r in wrapped:event(['residual_adapter','post',r,c['start'][r]]+([c['final'][r]] if r in hpe else [])) # HPE: 5th field = terminal frame U # GK: L_E^-1 after the full-frame cleanup + event(['phase','done']) + return out + +def check_local(events,back): + # Literal scalar replay of the emitted stream, including center lifetimes. + state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0 + for e in events: + if e[0]=='climb':assert not live;paid[e[5]]+=1 + elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1 + elif e[0]=='scalar': + op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op) + if tag=='clear': + state[t]={} + if t[0]=='C' and t[1] in live:live.remove(t[1]) + elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1]) + elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()} + else: + s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{}) + if t[0]=='C' and t[1] not in live:live.append(t[1]) + for j,x in list(state.get(s,{}).items()): + z=row.get(j,Q(0))+q*x + if z:row[j]=z + else:row.pop(j,None) + assert not live and all(not row for r,row in state.items() if r[0]=='C') + for r in range(n): + expected={r:Q(1)} + if back and r PR552 -> +PR531 invoice_final.py, whose notices and sources are preserved in the package. +Every call selects a hash-bound provider. Shared compiler reserves use maxima; +primitive work, coefficient work, local children and wrappers are also summed +from actual selected provider/orientation records. +""" +import argparse, gzip, hashlib, json +import sys as _s,pathlib as _p;_s.path.insert(0,str(_p.Path(__file__).resolve().parent)) +from witness import * +from generated_identity import artifact_identities +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +assert __debug__, 'Assertions required' + +def read(path): + data=path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix=='.gz' else data) +def filehash(path): return hashlib.sha256(path.read_bytes()).hexdigest() +def contenthash(path): + data=path.read_bytes() + return hashlib.sha256(gzip.decompress(data) if path.suffix=='.gz' else data).hexdigest() +def programhash(events): + return hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest() + +def recount_provider(local_dir, registry): + cp=local_dir/'CANONICAL-WORD.json.gz'; pp=local_dir/'LOCAL-PROGRAMS.json.gz' + rp=local_dir/'INDEPENDENT-LOCAL-REPLAY.json' + w,programs,replay=read(cp),read(pp),read(rp) + checks=read(local_dir/'LOCAL-CHECKS.json') + assert set(programs)=={'forward','backward'} + assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY' + assert replay['canonical_word_sha256']==filehash(cp)==registry['canonical_word_sha256'] + assert replay['local_programs_sha256']==filehash(pp)==registry['local_programs_sha256'] + assert programs==registry['local_programs'] + assert checks==registry['local_program_checks'] + assert filehash(local_dir/'CLIFFORD-RECIPES.json')==registry['exact_local_clifford_recipe_sha256'] + assert filehash(local_dir/'RESIDUAL-ADAPTERS.json')==registry['residual_adapter_sha256'] + v,helpers,h,m=w['v'],w['R'],w['h'],73 + assert (v,h)==(112,9) and type(helpers) is int and helpers>0 + assert registry['v']==v and registry['R']==helpers and registry['h']==h + assert registry['ports']==w['ports'] and registry['centers']==w['centers'] + assert replay['v']==v and replay['helpers']==helpers + n=2*v+helpers + widths = [len(w['frames'][w['final'][r]])-len(w['frames'][w['start'][r]]) for r in range(2*v, 2*v+helpers)] # HPE: |final|-|start| + terminal_codim = sum(h-len(w['frames'][w['final'][r]]) for r in range(2*v, 2*v+helpers)) # HPE: 0 for FULL-ended helpers + ends = {r: f for r, f in enumerate(w['final']) if r >= 2*v and f != 1} + assert len(widths) == helpers + entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0} + entering = len(entrances) + wrapped = {**entrances, **{r: 0 for r in ends if r not in entrances}} # COLD-HPE: cold hyperplane-ended helpers carry wrappers too + cold_ends = len(wrapped) - len(entrances) + assert entering == replay['entering_helpers'] + local = {} + for orientation, events in programs.items(): + # Endpoint equality and native frames were already independently + # replayed on all n columns in the hash-bound receipt above. + env = {('L', r): Q(1) for r in range(n)} + peak = Q(1) + real = macros = workops = 0 + paid = Counter() + wrappers = {'pre': set(), 'post': set()} + for event in events: + tag = event[0] + if tag == 'climb': + paid[event[5]] += 1 + elif tag == 'center': + paid[event[4]] += 1 + elif tag == 'residual_adapter': + _, kind, register, frame, *end = event + assert kind in wrappers and wrapped.get(register) == frame + assert end == ([ends[register]] if register in ends else []) # HPE: R_{E,U}^-1 and L_{E,U}^-1 name U + assert register not in wrappers[kind] + wrappers[kind].add(register) + elif tag == 'scalar': + macros += 1 + scalar = event[1] + op, target = scalar[0], tuple(scalar[1]) + if op == 'clear': + env[target] = Q(0) + count = 1 + elif op == 'copy': + env[target] = env[tuple(scalar[2])] + count = 1 + elif op == 'scale': + q = Q(scalar[2], scalar[3]) + numerator, denominator = abs(q.numerator), q.denominator + assert numerator and numerator & (numerator-1) == 0 + assert denominator & (denominator-1) == 0 + env[target] *= abs(q) + count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0) + elif op == 'add': + source = tuple(scalar[2]) + q = Q(scalar[3], scalar[4]) + numerator, denominator = abs(q.numerator), q.denominator + assert source != target and numerator > 0 + assert denominator & (denominator-1) == 0 + acc, count = 0, 1 # clear coefficient work + for i, bit in enumerate(bin(numerator)[2:]): + if i: + acc *= 2 + count += 1 + peak = max(peak, acc*env[source]) + if bit == '1': + acc += 1 + count += 1 + peak = max(peak, acc*env[source]) + value = Q(acc) + for _ in range(denominator.bit_length()-1): + value /= 2 + count += 1 + peak = max(peak, value*env[source]) + assert value == abs(q) + count += 2 # signed accumulation and work clear + env[target] = env.get(target, Q(0)) + abs(q)*env[source] + workops += count + else: + raise AssertionError(op) + real += 2*count + peak = max(peak, env[target]) + else: + assert tag in ('adapter', 'phase') + assert wrappers['pre'] == wrappers['post'] == set(wrapped) + assert all(value == 0 for register, value in env.items() if register[0] == 'C') + prior = replay['local'][orientation] + assert prior['all_exact_columns'] == n and prior['private_work_erased'] + assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits'] + bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1 + assert bits == prior['prefix_bits_upper'] + assert real == checks[orientation]['real_component_primitive_bound'] + assert macros == checks[orientation]['scalar_macros'] + assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()} + assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()} + local[orientation] = dict( + events=len(events), macros=macros, real_component_primitives=real, + prefix_l1=str(peak), prefix_bits=bits, + coefficient_work_primitive_count=workops, all_exact_columns=n, + dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True, + private_centres_and_coefficient_work_cleared=True, + pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']), + endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json') + + centres = len(w['centers']) + children = sum(checks['forward']['paid_profile'].values()) + assert checks['forward']['paid_profile'] == checks['backward']['paid_profile'] + macro_bound = max(row['macros'] for row in local.values()) + compiler = 64*(m+1)**3 + adapters = 16*(macro_bound+children+n+centres)+64*m + primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler + + assert widths==registry['widths'] + artifacts={f.name:filehash(f) for f in local_dir.iterdir() if f.is_file()} + phase_review=read(local_dir/'CLIFFORD-REVIEW.json') + return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n, + entering_helpers=entering,entrance_rank=sum(len(w['frames'][f]) for f in w['start'][2*v:]), + terminal_codimension=terminal_codim, hyperplane_ended_helpers=len(ends), # HPE: always reported (0 for FULL-ended words) + **({'cold_hyperplane_ended_helpers': cold_ends} if cold_ends else {}), # COLD-HPE: absent without cold ends + width_inventory=dict(sorted(Counter(widths).items())),widths=widths, + local_adapters=adapters,local_primitive_bound=primitive_bound, + compiler=compiler,children=children,artifacts=artifacts, + paid_profile=checks['forward']['paid_profile'], + program_hashes={o:programhash(events) for o,events in programs.items()},semantic_artifact_sha256=artifact_identities(local_dir)) + + +def run(base, hosted, audit, out, retained_invoice=None): + local_dir=base/'split-centres' + parent=read(local_dir/'GLOBAL-TEMPLATE.json.gz') + template_path=hosted/'GLOBAL-TEMPLATE.json.gz' + template=read(template_path); summary=read(hosted/'HOSTED.json') + owners=read(audit/'OWNERS-AND-PROFILE.json'); control=read(audit/'ASYNC-AUDIT.json') + template_hash=contenthash(template_path) + assert template_hash==control['complex_template_sha256']==owners['template_sha256']==summary['template_sha256'] + assert owners['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE' + assert template['recipe']==parent['recipe'] + assert 'local_programs' not in template + assert set(template['local_providers'])==set(PIDS) + providers={pid:recount_provider(base/'providers'/pid,registry) + for pid,registry in template['local_providers'].items()} + for pid,p in providers.items(): + assert owners['provider_phase_semantic_sha256'][pid]==control['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] + # The fresh controller admission must cite precisely these provider bytes. + for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json', + 'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json', + 'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'): + path='providers/'+pid+'/'+name + assert summary['source_artifacts'][path]==p['artifacts'][name] + assert owners['source_artifacts'][path]==p['artifacts'][name] + # R is read from the provider words (all must agree); the parent dedicated-bank + # envelope keeps its own helper count R0 from the parent split-centres word. + assert len({p['helpers'] for p in providers.values()})==1,'providers disagree on helper count R' + v,h,m,centres=112,9,73,8 + helpers=next(iter(providers.values()))['helpers']; n=2*v+helpers + assert all((p['v'],p['h'],p['centres'],p['n'])==(v,h,centres,n) for p in providers.values()) + parent_helpers=read(local_dir/'CANONICAL-WORD.json.gz')['R'] + stages,replicas,blocks_per_stream=9,8,4 + call_count=len(template['calls']) + assert call_count==stages*replicas==control['complete_invocations'] + assert control['one_owner_per_complete_invocation'] + assert len({(c['stage'],c['replica']) for c in template['calls']})==call_count + parent_calls={(c['stage'],c['replica']):c for c in parent['calls']} + sweeps=[e for e in template['execution_schedule'] if e['kind']=='local_cover_sweep'] + assert len(sweeps)==call_count + selected=[]; selected_paid=Counter(); provider_counts=Counter(); orientation_counts=Counter() + scalar=coefficient_work=macros=0; wrapper_factors=0 + factors_per_wrapper=2*(m-1) + for c in template['calls']: + pid,orientation=c['provider_id'],c['orientation']; p=providers[pid] + old=parent_calls[(c['stage'],c['replica'])] + assert orientation==old['orientation'] and c['owners'][:2*v]==old['owners'][:2*v] + assert c['local_program_sha256']==p['program_hashes'][orientation] + r=p['local'][orientation] + scalar+=r['real_component_primitives']; coefficient_work+=r['coefficient_work_primitive_count']; macros+=r['macros'] + wrapper_factors+=(r['pre_wrappers']+r['post_wrappers'])*factors_per_wrapper + provider_counts[pid]+=1; orientation_counts[(pid,orientation)]+=1 + selected_paid.update({int(k):v for k,v in p['paid_profile'].items()}) + selected.append(dict(stage=c['stage'],replica=c['replica'],provider_id=pid,orientation=orientation, + program_sha256=c['local_program_sha256'],events=r['events'],macros=r['macros'], + real_component_primitives=r['real_component_primitives'], + coefficient_work_primitive_count=r['coefficient_work_primitive_count'], + entering_helpers=p['entering_helpers'],entrance_rank=p['entrance_rank'], + pre_wrappers=r['pre_wrappers'],post_wrappers=r['post_wrappers'])) + assert provider_counts==COUNTS + # The sweep registry is executable: no hidden use of the historical supplier. + by_call={(c['stage'],c['replica']):c for c in template['calls']} + for e in sweeps: + c=by_call[(e['stage'],e['replica'])] + assert e['provider_id']==c['provider_id'] + assert set(p['compiler'] for p in providers.values())=={64*(m+1)**3} + compiler=64*(m+1)**3 + adapters=max(p['local_adapters'] for p in providers.values()) + primitive_bound=max(p['local_primitive_bound'] for p in providers.values()) + bridge_steps=sum(event['kind']=='bridge' for event in parent['recipe']) + bridge_sweeps=sum(event['kind']=='bridge' for event in template['execution_schedule']) + assert bridge_sweeps==replicas*bridge_steps + bridge_additions=2*v*bridge_sweeps + shifts=blocks_per_stream*v*replicas; moves=2*shifts + parent_live,parent_physical=parent['live'],parent['physical'] + data_stock=2*v*blocks_per_stream*replicas + assert (parent_live-data_stock)%stages==0 + parent_banks=(parent_live-data_stock)//stages + assert parent_banks>=0 and parent_physical==parent_live+parent_helpers+centres+2 + nonlocal_items=(4*v*replicas*stages+2*v*replicas*stages+2*call_count*helpers + +sum(child['replicas'] for child in parent['idle_children'])+stages*parent_banks + +bridge_additions+shifts+moves+parent_live+parent_physical+wrapper_factors) + outside=8*nonlocal_items+64*m + parent_pervertex=(scalar+bridge_additions+shifts+moves+parent_live + +(call_count*adapters+outside)*compiler+64*parent_physical) + live,physical=template['live'],template['physical'] + mass,profile=owners['rank_mass'],owners['paid_profile'] + assert m*live-mass==owners['deficit']==2560 + assert mass==sum(int(r)*count for r,count in profile.items()) + assert physical==live+helpers+centres+2 + assert live==owners['live'] and physical==owners['physical'] + assert live<=parent_live and physical<=parent_physical + assert not template['bank_padding']['families'] + assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged'] + # The old dedicated-bank geometry is only a conservative reserve envelope. + # Its singular program is never used as evidence for a mixed invocation. + rebased=parent_pervertex+65*(physical-parent_physical)+(live-parent_live) + used=max(rebased,parent_pervertex); retained=None; payload=512 + if retained_invoice is not None: + previous=read(retained_invoice) + assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload + previous_bound=previous['conservative_pervertex_used'] + used=max(used,previous_bound+parent_pervertex) + retained=dict(sha256=filehash(retained_invoice),previous_pervertex_allowance=previous_bound, + added_complete_new_pervertex=parent_pervertex,policy='Retain old allowance and add entire fresh mixed recount.') + half=m//2; group=2**(half*half) + for i in range(1,half+1): group*=2**(2*i)-1 + stock,streamed_mass=group*physical,group*mass + logical=group*used+64; router=compiler*(logical+1)*(stock+1)**2 + g_bound,e_bound,c0=2**30000,2**100000,2**210000 + total_mass=streamed_mass+e_bound + literal=2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m + row=2*stock.bit_length()+9909+252+2*payload + maxchild=max(map(int,profile)) + inequalities=dict(local_primitive_bound=primitive_bound<2**48, + logical=logical<2**6050,router=router2*maxchild*maxchild) + assert all(inequalities.values()) + localbits=max(r['prefix_bits'] for p in providers.values() for r in p['local'].values()) + input_l2_bits=(m+1)//2 + required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4 + assert required_prefix R helper map +# (verify.py checks the spec value against the constructor's HELPER-MAP.json) +SPOT=tuple(SPEC.get('width_spot_helpers',(270,282,294,306))) +PIDS=tuple(sorted(set(DISPATCH.values()))) +COUNTS=dict(Counter(DISPATCH.values())) +assert DISCOVER or set(PROVIDERS)==set(PIDS),'spec providers differ from dispatch providers' +def lookup(key): + """Dotted spec path; a segment may itself contain dots when it names a file (split at most once per known file suffix).""" + v=SPEC;parts=key.split('.') + while parts: + for n in range(len(parts),0,-1): + k='.'.join(parts[:n]) + if isinstance(v,dict) and k in v:v=v[k];parts=parts[n:];break + else:raise KeyError('spec has no key %s'%key) + return v +def pin(key,got): + """Strict mode: got must equal the spec value at dotted key; the failure names the key.""" + if DISCOVER: + if os.environ.get('WITNESS_RECORD'): # discovery bookkeeping only: append (key, value) for the spec writer + with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10)) + return got + want=lookup(key) + assert got==want,'SPEC MISMATCH %s: expected %s got %s'%(key,json.dumps(want)[:400],json.dumps(got,default=str)[:400]) + return got +def partner(pid): + """A different provider for substitution controls (next in sorted order).""" + assert len(PIDS)>1 + return PIDS[(PIDS.index(pid)+1)%len(PIDS)] diff --git a/research/pr643-improvement-20261013/witness/data/EXPECTED.json b/research/pr643-improvement-20261013/witness/data/EXPECTED.json new file mode 100644 index 0000000000..bb0b39efab --- /dev/null +++ b/research/pr643-improvement-20261013/witness/data/EXPECTED.json @@ -0,0 +1,1422 @@ +{ + "schema": "witness-expected/1", + "witness_sha256": "05cabf96dca0eb8f7cc2541c9702eaff5e7b3219f22e37a4bcb82a78398d940c", + "build": { + "jp8_504": { + "steps": [ + { + "input_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d", + "omission_controls": 6, + "output_content_sha256": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d" + }, + { + "input_content_sha256": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d", + "omission_controls": 32, + "output_content_sha256": "055c0fb41d8b0d506674f62d0227833a74eabd19a022a1dfeb72c3952b7a030f" + }, + {}, + { + "input_content_sha256": "055c0fb41d8b0d506674f62d0227833a74eabd19a022a1dfeb72c3952b7a030f", + "omission_controls": 135, + "rank5_controls": 8, + "joint_negative_controls": 15, + "output_content_sha256": "6c361b33967bb62d878b3acef44a4ac2c70970e99f36a11906b03811495de533" + } + ], + "base_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d", + "word_content_sha256": "6c361b33967bb62d878b3acef44a4ac2c70970e99f36a11906b03811495de533" + }, + "jp8": { + "steps": [ + { + "input_content_sha256": "a78f4e2114212d2f4b567cc9ef4e3b31ace0c19983009cec562a642831a84c34", + "shadow_input_content_sha256": "aad9b01b30bb8a2c5ce8d9415afafc88b0ab288986eb3d068a2bbba8e45bef51", + "shadow_output_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d", + "output_content_sha256": "2f15196f7f6589749676d5b3a3e193997567b996621b6166f081739ecbd5b9bf" + }, + { + "input_content_sha256": "2f15196f7f6589749676d5b3a3e193997567b996621b6166f081739ecbd5b9bf", + "shadow_input_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d", + "shadow_output_content_sha256": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d", + "output_content_sha256": "d1e6e83d61009650261c17ee59f44cdce1528b8908d4dc5b5437a789847ae5ba" + }, + { + "input_content_sha256": "d1e6e83d61009650261c17ee59f44cdce1528b8908d4dc5b5437a789847ae5ba", + "shadow_input_content_sha256": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d", + "shadow_output_content_sha256": "055c0fb41d8b0d506674f62d0227833a74eabd19a022a1dfeb72c3952b7a030f", + "output_content_sha256": "c5280629e7b9fc03ddd6be63fb9218935c21c015a5e5052ad14dfa34ae68466f" + }, + { + "input_content_sha256": "c5280629e7b9fc03ddd6be63fb9218935c21c015a5e5052ad14dfa34ae68466f", + "shadow_input_content_sha256": "055c0fb41d8b0d506674f62d0227833a74eabd19a022a1dfeb72c3952b7a030f", + "shadow_output_content_sha256": "6c361b33967bb62d878b3acef44a4ac2c70970e99f36a11906b03811495de533", + "output_content_sha256": "8aa907460a478d49c67dac4b96ce842a2811f0283cfa7723288ba9b82f07d80f" + }, + { + "input_content_sha256": "8aa907460a478d49c67dac4b96ce842a2811f0283cfa7723288ba9b82f07d80f", + "negative_controls": 48, + "output_content_sha256": "b7a36c11d0f49a027bbbcb6185a4484a65c176ac9597afd3fa28eaad58a8a0ce" + }, + { + "input_content_sha256": "b7a36c11d0f49a027bbbcb6185a4484a65c176ac9597afd3fa28eaad58a8a0ce", + "negative_controls": 21, + "output_content_sha256": "a51b37b5bd5e9e66ea14e9759f88cb6181bab041cb09aecd08e7a11956100016" + }, + { + "input_content_sha256": "a51b37b5bd5e9e66ea14e9759f88cb6181bab041cb09aecd08e7a11956100016", + "negative_controls": 51, + "output_content_sha256": "b82c7888e7fad97b752cec3fd5be459df2ad35fdcdf15434beb04f4bf0c05922" + } + ], + "helper_map_sha256": "688d5115b221be68c96970822cc04ff698e2a84432fa7db9cb59057f6fe55def", + "base_content_sha256": "a78f4e2114212d2f4b567cc9ef4e3b31ace0c19983009cec562a642831a84c34", + "word_content_sha256": "b82c7888e7fad97b752cec3fd5be459df2ad35fdcdf15434beb04f4bf0c05922" + }, + "jp8b": { + "steps": [ + { + "input_content_sha256": "a78f4e2114212d2f4b567cc9ef4e3b31ace0c19983009cec562a642831a84c34", + "shadow_input_content_sha256": "aad9b01b30bb8a2c5ce8d9415afafc88b0ab288986eb3d068a2bbba8e45bef51", + "shadow_output_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d", + "output_content_sha256": "2f15196f7f6589749676d5b3a3e193997567b996621b6166f081739ecbd5b9bf" + }, + { + "input_content_sha256": "2f15196f7f6589749676d5b3a3e193997567b996621b6166f081739ecbd5b9bf", + "shadow_input_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d", + "shadow_output_content_sha256": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d", + "output_content_sha256": "d1e6e83d61009650261c17ee59f44cdce1528b8908d4dc5b5437a789847ae5ba" + }, + { + "input_content_sha256": "d1e6e83d61009650261c17ee59f44cdce1528b8908d4dc5b5437a789847ae5ba", + "shadow_input_content_sha256": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d", + "shadow_output_content_sha256": "055c0fb41d8b0d506674f62d0227833a74eabd19a022a1dfeb72c3952b7a030f", + "output_content_sha256": "c5280629e7b9fc03ddd6be63fb9218935c21c015a5e5052ad14dfa34ae68466f" + }, + { + "input_content_sha256": "c5280629e7b9fc03ddd6be63fb9218935c21c015a5e5052ad14dfa34ae68466f", + "shadow_input_content_sha256": 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calls and st2's jp8 as a second provider jp8b on one call, with an exact per-time-Hall owner map (exact-window MIP warm-started from st2u4's map)", + "summary": "Provider menu {jp8 (st2u4's u4 chain), jp8b (st2's jp8 chain)}; ck dropped. The global controls need two dispatched providers; st2u4 used ck on one call, twin uses st2's jp8 word there instead, which the aggregate LP prices lower (pinned at time 5: LP bound 523258.896187 with jp8b vs 523259.058061 with ck; BrainAdversary twinlp.py). Owner search (BrainAdversary twinmip.py mipA) with H4aFinish's solve_h.py (objective sum F(r) = r*(73/r)^b, b = 0.001636): exact-window MIP at dispatch jp8 x71, jp8b x1 (time 5) over base + st2u4's aggregate-LP patterns with weight >= 0.01, warm-started from st2u4's map, gap 1e-9, 1 thread, 900 s; the solver stdout was lost, so its status/gap line was not recorded (the 900 s limit was reached). mkplan.py --locals (jp8 = st2u4's jp8 local, jp8b = st2's jp8 local) reproduces data/PLAN.json byte for byte. 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"recipe": "pkg:data/recipes/k492-jp8-hyperplane_end.json" + }, + { + "type": "cold_end", + "recipe": "pkg:data/recipes/k492-jp8-cold_end.json.gz" + } + ] + }, + "jp8b": { + "base": { + "kind": "k_triangle", + "schedule": "pkg:data/TRI-SCHEDULE.json" + }, + "steps": [ + { + "type": "port_stage", + "shadow_input": "raw504", + "shadow_output": "promoted558" + }, + { + "type": "port_stage", + "shadow_input": "promoted558", + "shadow_output": "jp8_504:0" + }, + { + "type": "port_stage", + "shadow_input": "jp8_504:0", + "shadow_output": "jp8_504:1" + }, + { + "type": "port_stage", + "shadow_input": "jp8_504:1", + "shadow_output": "jp8_504:3" + }, + { + "type": "frame_regroup", + "recipe": "pkg:data/recipes/k492-jp8-frame_regroup.json" + }, + { + "type": "hyperplane_end", + "recipe": "pkg:data/recipes/k492-jp8-hyperplane_end.json" + }, + { + "type": "cold_end", + "recipe": "pkg:data/recipes/k492-jp8b-cold_end.json.gz" + } + ] + } + }, + "dispatch": { + "mode": "fixed", + "menu": [ + "jp8", + "jp8b" + ], + "plan": "pkg:data/PLAN.json", + "origin": "at the dispatch jp8 ×71, jp8b ×1 (st2u4's dispatch with ck at time 5 replaced by jp8b)", + "plan_rule": "the window MIP's PLAN with the provider registry re-derived from the admitted provider locals (widths over the word's R helpers) and `profile`/`assignment_sha256` recomputed from the map (Stack492 mkplan.py)" + }, + "owners": { + "warm_owners": "pkg:data/search/WARM-OWNERS.json.gz", + "exact_windows": true, + "origin": "an exact per-time-Hall exact-window MIP solution (900 s, warm-started from complex-571-cold14-st2u4's map; solver status/gap not recorded)", + "warm_owners_origin": "complex-571-cold14-st2u4's `data/OWNERS.json.gz` (= PR637's owners), the warm start of the MIP", + "search": { + "method": "fixed_dispatch_exact_window_milp", + "tool": "solve_h.py (H4aFinish copy)", + "b": 0.001636, + "aggregate_lp_comparison": { + "tool": "twinlp.py", + "ck_at_5": 523259.058061, + "jp8b_at_5": 523258.896187 + }, + "mip": { + 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aggregate LP with ck pinned at time 5 (the comparison run)", + "WARM-PLAN.json": "the window MIP's PLAN for st2u4's map, matching WARM-OWNERS.json.gz", + "TEMPLATE-PLAN.json": "the PLAN whose windows/order/registry template the nominator reuses" + } + }, + "search_inputs": { + "LP-PATTERNS-AGG.json": "pkg:data/search/LP-PATTERNS-AGG.json", + "DISPATCH.json": "pkg:data/search/DISPATCH.json", + "LP-PATTERNS-TWIN-AGG.json": "pkg:data/search/LP-PATTERNS-TWIN-AGG.json", + "LP-PATTERNS-CTL-AGG.json": "pkg:data/search/LP-PATTERNS-CTL-AGG.json", + "WARM-PLAN.json": "pkg:data/search/WARM-PLAN.json", + "TEMPLATE-PLAN.json": "pkg:data/search/TEMPLATE-PLAN.json" + } + }, + "bar": "0.001636523543003976", + "gain_baseline_kappa": "0.001601260169988325", + "credits": [ + "**BrainAdversary (research agent)**: the twin-provider dispatch (jp8b replacing ck) and its owner solve.", + "**CarrierBypass (research agent)**: the u4 premix-only dim-8 cold ends with factored row partners and the patched cold_end controls.", + "**jeremydiviney**: PR627 (the two factored jp8 cold ends 590/581 and their tails; the warm-start owner map).", + "**ColdThird (research agent)**: the h4a cold ends and the widened forward-absorption allowlist (PROOF-NOTE.md).", + "**This package**: porting the PR604/B3 chains onto the K-triangle skeleton (port_stage, frame_regroup), the R-generalised global code (GlobalR) and the owner solve.", + "**AtomScout (research agent)**: the leaver-read K-triangle atom and TRI-SCHEDULE.", + "**icekylinx**: PR531 (construct_504.py, the direct-delivery source the K-triangle constructor extends).", + "**This package**: the second cold end per block and the two cold_end primitives (PROOF-NOTE.md).", + "**DreamingOfClouds**: PR604 (the cold_end construction, its verifier changes and controls), PR599, PR516, PR509, PR484.", + "**jeremykothe2**: PR601, PR600, PR596, PR593, PR592 and PR591 (hyperplane-ended helpers and the HPE verifier).", + "**DominikScholz**: PR571 and PR569 (including PR569's window-MILP nominator nominate_width7.py, which the owner search adapts).", + "**eumemic**: PR564, PR561, PR562, PR558, PR550, PR543, PR507.", + "**chafreaky**: PR583, PR572, PR551.", + "**icekylinx**: PR535 and PR531.", + "**Dugongue**: PR552 and PR514.", + "**Douglas Colkitt / CrocSwap**: maintenance.", + "**The original OpenAI #109 framework.**" + ], + "chains_origin": "two jp8 words: jp8 = complex-571-cold14-st2u4's jp8 chain (u4), jp8b = complex-571-cold14-st2's jp8 chain; ck is not used", + "shadows": { + "jp8_504": { + "base": "frozen558_promoted", + "steps": [ + { + "type": "cold_kernel", + "recipe": "multicold:data/EIGHT-COLD.json" + }, + { + "type": "multicut", + "recipe": "multicold:data/EIGHT-MULTICOLD.json" + }, + { + "type": "frozen558_scalar_audits" + }, + { + "type": "joint_prefix", + "recipe": "joint_prefix:data/JOINT-PREFIX.json", + "variant": "eightcold", + "kernel_recipes": "joint_prefix:data/EIGHTCOLD-JOINT-KERNELS.json" + } + ] + } + }, + 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"c919c366ef1d3528f1884e47dfce858ab3164b099740e4c17cde6f697b3ec458" +} diff --git a/research/pr643-improvement-20261013/witness/extras/check_declarations.py b/research/pr643-improvement-20261013/witness/extras/check_declarations.py new file mode 100644 index 0000000000..1c80a9411b --- /dev/null +++ b/research/pr643-improvement-20261013/witness/extras/check_declarations.py @@ -0,0 +1,56 @@ +"""Check that declarative inputs and outputs exactly reconstruct the replay SPEC.""" +from pathlib import Path +import hashlib +import json + +P = Path(__file__).resolve().parents[1] +read = lambda name: json.loads((P / 'data' / name).read_bytes()) + +def need(value, message): + if not value: + raise ValueError(message) + +def merge(a, b): + need(all(a[k] == b[k] for k in a.keys() & b.keys()), 'conflicting declaration') + return a | b + +w, e, s, plan = map(read, ('WITNESS.json', 'EXPECTED.json', 'SPEC.json', 'PLAN.json')) +need((w['schema'], e['schema'], s['schema']) == ('witness/1', 'witness-expected/1', 'witness-spec/1'), 'schemas') +need(w['geometry'] == dict(v=112, h=9, helpers=492, centres=8, stages=9, replicas=8, + cold_helpers=[264, 276, 288, 300]), 'fixed native geometry') +need(hashlib.sha256((P / 'data/WITNESS.json').read_bytes()).hexdigest() == e['witness_sha256'], 'witness hash') +need(w['name'] == s['name'], 'name') +for key in ('data', 'call_order'): + need(w[key] == s[key], key) +need(sorted(w['dispatch']) == sorted(s['dispatch']), 'same complete dispatch') +need(len({(stage, replica) for stage, replica, _ in w['dispatch']}) == len(w['dispatch']), 'unique dispatch keys') +need(w['dispatch'] == [[c['stage'], c['replica'], c['provider']] for c in plan['provider_calls']], 'literal dispatch') +need(w['call_order'] == plan['order'], 'literal chronology') +for name, filename in (('plan_sha256', 'PLAN.json'), ('owners_sha256', 'OWNERS.json.gz')): + need(hashlib.sha256((P / 'data' / filename).read_bytes()).hexdigest() == w['data'][name], filename) +need(merge(e['global'], {'gain_baseline_kappa': w['gain_baseline_kappa']}) == s['expected'], 'global outputs') +provider_outputs = {} +for pid, declaration in e['providers'].items(): + declaration = dict(declaration) + for group in ('artifacts', 'expected_local'): + nested = declaration.pop(group) + declaration = merge(declaration, {group + '.' + key: value for key, value in nested.items()}) + provider_outputs[pid] = declaration +need(provider_outputs == s['providers'], 'provider outputs with literal dotted receipt keys') +need(s['width_spot_helpers'] == w['geometry']['cold_helpers'], 'mapped width spot helpers') +build = dict(w['build']) +need(set(e['build']) == set(w['build']['providers']) | set(w['build']['shadows']), 'all provider and shadow outputs') +for group in ('providers', 'shadows'): + build[group] = {} + for pid, declaration in w['build'][group].items(): + a, b = dict(declaration), dict(e['build'][pid]) + left, right = a.pop('steps'), b.pop('steps') + base_outputs = {'content_sha256': b.pop('base_content_sha256')} + if 'helper_map_sha256' in b: + base_outputs['helper_map_sha256'] = b.pop('helper_map_sha256') + a['base'] = merge(a['base'], base_outputs) + need(len(left) == len(right), 'construction step count') + build[group][pid] = merge(a, b) + build[group][pid]['steps'] = [merge(x, y) for x, y in zip(left, right)] +need(build == s['build'], 'complete typed build with shadows') +print('PASS declarative inputs and outputs reconstruct SPEC', flush=True) diff --git a/research/pr643-improvement-20261013/witness/extras/check_native_owners.py b/research/pr643-improvement-20261013/witness/extras/check_native_owners.py new file mode 100644 index 0000000000..fe40c5b717 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/extras/check_native_owners.py @@ -0,0 +1,104 @@ +"""Independent candidate native profile, widths, owner intervals and exact moment. + +Chi Zhao, with substantial OpenAI Codex assistance. Apache-2.0. The independent rational +interval engine is Chafik Boukhalfa's retained PR626 extras/exact_intervals.py. +This checker does not import PR627 construction or global accounting code. +""" +import argparse +import gzip +import hashlib +import importlib.util +import json +from collections import Counter, defaultdict +from fractions import Fraction as Q +from pathlib import Path + +ap = argparse.ArgumentParser() +ap.add_argument('--package', type=Path, required=True) +ap.add_argument('--replay', type=Path, required=True) + +ap.add_argument('--out', type=Path, required=True) + +a = ap.parse_args() + +def read(p): + raw = p.read_bytes() + return json.loads(gzip.decompress(raw) if p.suffix == '.gz' else raw) + +def need(value, message): + if not value: + raise ValueError(message) + +spec = read(a.package/'data/SPEC.json') +plan = read(a.package/'data/PLAN.json') +roles = read(a.package/'data/OWNERS.json.gz') +reference = Path(__file__).resolve().parent/'REFERENCE.json' +need(hashlib.sha256(reference.read_bytes()).hexdigest() == 'bb06a02cb1927ef7e39e79f97d38a04c1865e8c271b2cb66533d5ca4b4974a21', 'reference geometry pin') +old = read(reference) +expected_changes = old['expected_width_changes'] +for key in ('order', 'windows', 'pairs', 'sides'): + need(plan[key] == old[key], 'inherited geometry '+key) +widths = {} +profiles = {} +for pid in ('jp8', 'jp8b'): + word = read(a.replay/(pid+'-local')/'CANONICAL-WORD.json.gz') + program = read(a.replay/(pid+'-local')/'LOCAL-PROGRAMS.json.gz') + need((word['v'], word['h'], word['R']) == (112,9,492), 'native shape') + widths[pid] = [len(word['frames'][word['final'][h]]) - len(word['frames'][word['start'][h]]) for h in range(224,716)] + profiles[pid] = Counter(e[-1] for e in program['forward'] if e[0] in ('climb','center')) + need(profiles[pid] == Counter(e[-1] for e in program['backward'] if e[0] in ('climb','center')), 'reflected profile') + need(widths[pid] == spec['providers'][pid]['complete_contract']['widths'], 'native width declarations') + changes = [(i,u,v) for i,(u,v) in enumerate(zip(old['provider_registry'][pid]['widths'],widths[pid])) if u != v] + need([list(c) for c in changes] == expected_changes[pid], 'reviewed native width changes') + need(profiles[pid] == Counter({int(r):n for r,n in plan['provider_registry'][pid]['actual_paid_profile'].items()}), 'native paid registry profile') +calls = {c['time']:c for c in plan['provider_calls']} +need(set(calls) == set(range(72)), 'complete calls') +need(len(plan['provider_calls']) == 72 and all(c['provider'] in widths for c in calls.values()), 'unique valid dispatch') +paid = sum((profiles[c['provider']] for c in calls.values()), Counter()) +used = defaultdict(set) +helpers = defaultdict(set) +families = defaultdict(set) +for r in roles: + t = r['time']; c = calls[t]; h = r['helper'] + need((c['stage'],c['replica']) == (r['stage'],r['replica']) == tuple(plan['order'][t]), 'call ordering') + need(0 <= h < 492 and h not in helpers[t], 'helper uniqueness') + need(0 <= r['port'] < 112 and 0 <= r['owner_replica'] < 8, 'owner/port range') + need(r['family'] not in families[t], 'family uniqueness') + helpers[t].add(h); families[t].add(r['family']) + width = widths[c['provider']][h] + need(r['width'] == width, 'actual width') + need(r['family'] == r['owner_replica']*896+(2*plan['pairs'][str(r['child'])]+plan['sides'][str(r['child'])])*112+r['port'], 'physical family') + need(r['copy'] == r['owner_replica']*112+r['port'], 'physical copy') + key = r['owner_replica'],r['child'],r['port'] + cap,window = plan['windows'][str(key[0])+','+str(key[1])] + need(t in window and 0 <= r['offset'] <= r['offset']+width <= cap, 'window and capacity') + cells = set(range(r['offset'],r['offset']+width)) + need(not cells & used[key], 'disjoint intervals') + used[key].update(cells) +need(len(roles) == 35424 and all(helpers[t] == set(range(492)) for t in calls), 'all roles') +idle = Counter() +for key,(cap,_) in plan['windows'].items(): + rep,ch = map(int,key.split(',')) + for port in range(112): + cells = used[rep,ch,port] + need(cells == set(range(len(cells))), 'compact interval') + if len(cells) < cap: + idle[cap-len(cells)] += 1 +paid.update(idle) +need(dict(paid) == {int(k):v for k,v in plan['profile'].items()} == {int(k):v for k,v in spec['expected']['global_profile'].items()}, 'native plus idle profile') +need(sum(k*v for k,v in paid.items()) == 520704, 'rank mass') +need(73*7168-sum(k*v for k,v in paid.items()) == 2560, 'deficit') +interval_path = Path(__file__).resolve().parent/'exact_intervals.py' +need(hashlib.sha256(interval_path.read_bytes()).hexdigest() == 'aa3c2327c5d3742248b720a87b2de0bbe2e34ed2af89a578e3c8d5bd2656a9cf', 'independent interval engine pin') +s = importlib.util.spec_from_file_location('independent_intervals', interval_path) +E = importlib.util.module_from_spec(s); s.loader.exec_module(E) +q = Q(spec['expected']['complex_lower']); lower = upper = Q(0) +for rank,count in paid.items(): + lo,hi = E.log(Q(73,rank)); lo,hi = E.exp(q*lo,q*hi) + lower += Q(rank*count,73*7168)*lo; upper += Q(rank*count,73*7168)*hi +need(upper < 1, 'strict exact moment') +kappa = Q(spec['expected']['kappa']); old_kappa = Q('0.001636542223442109') +need(kappa <= q/(1+q) and kappa > old_kappa, 'strict frontier gain and conversion') +report = dict(status='PASS_INDEPENDENT_NATIVE_OWNERS_AND_MOMENT', roles=len(roles), calls=len(calls), native_profiles={p:dict(c) for p,c in profiles.items()}, idle=dict(idle), global_profile=dict(paid), complex_lower=str(q), moment_lower=str(lower), moment_upper=str(upper), strict_margin_lower=str(1-upper), kappa=str(kappa), reference643_kappa=str(old_kappa), absolute_kappa_gain=str(kappa-old_kappa), relative_kappa_gain=str(kappa/old_kappa-1), interval_engine_sha256=hashlib.sha256(interval_path.read_bytes()).hexdigest(), scope='Literal finite native profile and width/owner interval accounting with a separate rational moment engine; strict supplier/physical/phase/outer admission is checked by the separate full replay.') +a.out.write_text(json.dumps(report,indent=2)+'\n') +print(report['status']) diff --git a/research/pr643-improvement-20261013/witness/extras/check_owner_controls.py b/research/pr643-improvement-20261013/witness/extras/check_owner_controls.py new file mode 100644 index 0000000000..a54d716d97 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/extras/check_owner_controls.py @@ -0,0 +1,27 @@ +"""Targeted rejection controls for the independent owner/moment checker. +Chi Zhao, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse,copy,gzip,json,subprocess,sys,tempfile +from pathlib import Path +from fractions import Fraction as Q +ap=argparse.ArgumentParser();ap.add_argument('--package',type=Path,required=True);ap.add_argument('--replay',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args() +checker=Path(__file__).resolve().with_name('check_native_owners.py') +original={name:json.loads(gzip.decompress((a.package/'data'/name).read_bytes()) if name.endswith('.gz') else (a.package/'data'/name).read_bytes()) for name in ('SPEC.json','PLAN.json','OWNERS.json.gz')} +cases=[('positive',None),('wrong_width','actual width'),('duplicate_helper','helper uniqueness'),('wrong_family','physical family'),('wrong_profile','native plus idle profile'),('false_moment','strict exact moment')];results=[] +for name,expected in cases: + data=copy.deepcopy(original);roles=data['OWNERS.json.gz'];spec=data['SPEC.json'] + if name=='wrong_width':roles[0]['width']+=1 + if name=='duplicate_helper':roles[1]['helper']=roles[0]['helper'] + if name=='wrong_family':roles[0]['family']+=100000 + if name=='wrong_profile':spec['expected']['global_profile']['1']+=1 + if name=='false_moment':spec['expected']['complex_lower']=str(Q(spec['expected']['complex_lower'])+Q(1,10**8)) + with tempfile.TemporaryDirectory(prefix='combined-owner-control-')as tmp: + root=Path(tmp);(root/'data').mkdir() + for filename,value in data.items(): + raw=json.dumps(value).encode();(root/'data'/filename).write_bytes(gzip.compress(raw,mtime=0) if filename.endswith('.gz') else raw) + p=subprocess.run([sys.executable,'-I','-O','-B',str(checker),'--package',str(root),'--replay',str(a.replay),'--out',str(root/'result.json')],capture_output=True,text=True) + if expected is None: + if p.returncode:raise RuntimeError(p.stderr) + elif not p.returncode or 'ValueError: '+expected not in p.stderr:raise RuntimeError(name+' unexpected result '+p.stdout+p.stderr) + results.append(dict(name=name,status='PASS'if expected is None else'REJECTED',expected_reason=expected)) +a.out.write_text(json.dumps(dict(status='PASS_INDEPENDENT_OWNER_CONTROLS',isolated_optimized=True,cases=results),indent=2)+'\n');print('PASS independent positive and five rejection controls') diff --git a/research/pr643-improvement-20261013/witness/extras/check_u4_portable.py b/research/pr643-improvement-20261013/witness/extras/check_u4_portable.py new file mode 100644 index 0000000000..ef3b93eea1 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/extras/check_u4_portable.py @@ -0,0 +1,88 @@ +"""Independent exact U4 scalar isolation, frame, and focused mutation checks. +Chi Zhao, with substantial OpenAI Codex assistance. Apache-2.0. +No construction or admission modules are imported. +""" +import argparse,copy,gzip,hashlib,json +from pathlib import Path +from fractions import Fraction as F +from collections import Counter + +ENDS=(233,265,425,441) +U=(256,128,64,32,16,8,6,1) +EXPECTED={'jp8':{1:2526,2:398,3:448,4:168,5:64,6:4},'ck':{1:2608,2:548,3:304,4:168,5:66,6:4}} +def need(ok,message): + if not ok:raise ValueError(message) +def basis(vs): + p={} + for x in vs: + while x: + k=x.bit_length()-1 + if k in p:x^=p[k] + else:p[k]=x;break + return tuple(p.values()) +def check(w,provider): + n=716 + need((w['report']['v'],w['report']['R'])==(112,492),'native shape') + P=[{i:F(1)}for i in range(n)] + def apply(e): + need(e[0] in ('add','scale'),'scalar primitive') + if e[0]=='scale':P[e[1]]={j:v*F(e[2],e[3])for j,v in P[e[1]].items()} + else: + t,s=e[1:3];c=F(e[3],e[4]) + for j,v in list(P[s].items()): + z=P[t].get(j,F(0))+c*v + if z:P[t][j]=z + else:P[t].pop(j,None) + early={i for i,_ in w['early_cleanup']} + tail=[w['cleanup'][i][:-1]+[f]for i,f in w['early_cleanup']] + for e in w['A']+w['cut']+w['B']+tail:apply(e) + ended=set(map(int,w['helper_final'])) + for h in ended: + need(P[h]=={h:F(1)},'ended row isolation') + need(all(not P[j].get(h)for j in range(n)if j!=h),'ended column isolation') + for i,e in enumerate(w['cleanup']): + if i not in early:apply(e) + need(all(P[j]=={j:F(1)}for j in range(n)if not 112<=j<224),'non-target FULL restoration') + cur=[()for _ in range(n)] + for j,v in enumerate(w['ports']):cur[j]=(v,) + for h,f in w['start_extra'].items():cur[int(h)]=basis(f) + profile=Counter() + def climb(r,f): + f=basis(f) + need(len(basis(cur[r]+f))==len(f),'monotone frame containment') + if len(f)>len(cur[r]):profile[len(f)-len(cur[r])]+=1 + cur[r]=f + for e in w['A']+w['B']+tail: + for j in (e[1:3]if e[0]=='add' else e[1:2]):climb(j,tuple(e[-1])) + for h in ENDS: + need(str(h) not in w['start_extra'],'new helper cold') + need(len(cur[h])==len(basis(cur[h]+U))==8,'new terminal frame') + need(tuple(w['helper_final'][str(h)])==U,'declared new terminal frame') + for h in range(n): + if 112<=h<224:continue + climb(h,tuple(w['helper_final'].get(str(h),[1<=2:q/=2;k+=1 + def s(z): + lo=2*sum((z**(2*j+1)/Q(2*j+1)for j in range(80)),Q(0));hi=lo+2*z**161/(161*(1-z*z));return lo,hi + a,b=s((q-1)/(q+1));c,d=s(Q(1,3));return down(a+k*c),up(b+k*d) +def exp(a,b): + def s(x): + term=total=Q(1) + for j in range(1,17):term*=x/j;total+=term + return total,term*x/17/(1-x/18) + need(0<=a<=b= 0 and off + width <= cap, 'interval exceeds owner') + cells = set(range(off, off + width)) + index = (owner, child, port) + require(not occupied[index] & cells, 'overlapping intervals') + occupied[index].update(cells) + expected = {(t, h) for t, call in enumerate(calls) + for h in range(len(registry[call['provider']]['widths']))} + require(roles == expected, 'missing or extra role') + idle = Counter() + for win_key, (cap, _) in template['windows'].items(): + owner, child = map(int, win_key.split(',')) + for port in range(112): + cells = occupied[owner, child, port] + require(cells == set(range(len(cells))), 'owner intervals are not compacted') + if len(cells) < cap: + idle[cap - len(cells)] += 1 + profile = Counter() + for call in calls: + profile.update({int(r): n for r, n in registry[call['provider']]['actual_paid_profile'].items()}) + profile.update(idle) + require(dict(profile) == {int(r): n for r, n in template['profile'].items()}, 'paid profile mismatch') + require(sum(r * n for r, n in profile.items()) == template['rank_mass'] == 520704, 'rank mass mismatch') + require(73 * template['live'] - template['rank_mass'] == template['deficit'] == 2560, 'deficit mismatch') + return dict(roles=len(roles), idle_profile=dict(sorted(idle.items())), + profile=dict(sorted(profile.items())), rank_mass=520704, + dispatch=dict(Counter(c['provider'] for c in calls))) + + +def negative_controls(rows, template): + mutations = [('duplicate', lambda r: r.append(copy.deepcopy(r[0]))), + ('width', lambda r: r[0].update(width=r[0]['width'] + 1)), + ('offset', lambda r: r[0].update(offset=1000)), + ('family', lambda r: r[0].update(family=-1))] + for name, mutate in mutations: + bad = copy.deepcopy(rows) + mutate(bad) + try: + validate(bad, template) + except ValueError: + continue + raise ValueError(f'negative control unexpectedly accepted: {name}') + return [name for name, _ in mutations] + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--base-data', type=Path, required=True, + help='data directory of exact pinned PR643 package') + parser.add_argument('--out', type=Path, required=True) + parser.add_argument('--negative-controls', action='store_true') + args = parser.parse_args() + source = json.loads((HERE / 'SOURCE.json').read_text()) + base_plan = (args.base_data / 'PLAN.json').read_bytes() + base_owners = (args.base_data / 'OWNERS.json.gz').read_bytes() + require(sha(base_plan) == source['base']['plan_sha256'], 'base plan pin mismatch') + require(sha(base_owners) == source['base']['owners_sha256'], 'base owners pin mismatch') + moves_data = (HERE / 'OWNER-MOVES.json.gz').read_bytes() + template_data = (HERE / 'OWNER-TEMPLATE.json').read_bytes() + require(sha(moves_data) == source['moves_sha256'], 'moves pin mismatch') + require(sha(template_data) == source['template_sha256'], 'template pin mismatch') + original = json.loads(gzip.decompress(base_owners)) + rows = {key(row): row for row in original} + require(len(rows) == len(original) == source['roles'], 'base role inventory mismatch') + moves = json.loads(gzip.decompress(moves_data)) + require(len(moves) == source['changed_literal_rows'], 'move count mismatch') + require(len({key(row) for row in moves}) == len(moves), 'duplicate recorded move') + for row in moves: + require(key(row) in rows, 'move refers to absent base role') + rows[key(row)] = row + rows = [rows[k] for k in sorted(rows)] + template = json.loads(template_data) + receipt = validate(rows, template) + if args.negative_controls: + receipt['rejected_controls'] = negative_controls(rows, template) + payload = json.dumps(rows, sort_keys=True, separators=(',', ':')).encode() + require(sha(payload) == source['target_owners_content_sha256'], 'reconstructed payload mismatch') + data = gzip.compress(payload, compresslevel=9, mtime=0) + data = data[:9] + b'\xff' + data[10:] + args.out.mkdir(parents=True, exist_ok=True) + (args.out / 'OWNERS.json.gz').write_bytes(data) + receipt.update(status='PASS_LITERAL_OWNER_EXPORT', owners_sha256=sha(data), + owners_content_sha256=sha(payload), + published_owners_sha256=source['target_owners_sha256'], + scope='Owner structure only; full native supplier and exact assembly replay remain required.') + (args.out / 'EXPORT.json').write_text(json.dumps(receipt, indent=2) + '\n') + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/pr643-improvement-20261013/witness/owner-search/search_neighborhood.py b/research/pr643-improvement-20261013/witness/owner-search/search_neighborhood.py new file mode 100644 index 0000000000..be61df67b1 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/owner-search/search_neighborhood.py @@ -0,0 +1,62 @@ +"""Bounded CP-SAT owner search. Chi Zhao with substantial OpenAI Codex assistance. Apache-2.0.""" +from ortools.sat.python import cp_model +from pathlib import Path +from collections import defaultdict,Counter +import json,gzip,random,time,hashlib,math +import argparse +ap=argparse.ArgumentParser();ap.add_argument('--base-data',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);args=ap.parse_args() +p=json.loads((args.base_data/'PLAN.json').read_text());rows=json.loads(gzip.decompress((args.base_data/'OWNERS.json.gz').read_bytes()));bins=defaultdict(list) +for i,r in enumerate(rows):bins[r['owner_replica'],r['child'],r['port']].append(i) +cap=lambda b:p['windows'][f'{b[0]},{b[1]}'][0] +allow=lambda b:set(p['windows'][f'{b[0]},{b[1]}'][1]) +gap=lambda b:cap(b)-sum(rows[i]['width']for i in bins[b]) + +for key in p['windows']: + r,ch=map(int,key.split(',')) + for port in range(112):bins[r,ch,port] +partial=[b for b in bins if 0>p&1:x^=b[p] + if x: + p=x.bit_length()-1 + for q in b: + if b[q]>>p&1:b[q]^=x + b[p]=x + return tuple(b[p] for p in sorted(b,reverse=True)) +def inside(a,b):return basis(a+b)==b +def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0]) +FULL=basis([1<len(M):M.append(rr) + if len(M)==8:break + assert len(M)==8 + linear(regs,M,F) + for i,r in zip(c,regs): + assert rows[r]=={s:Q(R[s][i]) for s in ids} + block_totals[c,i]=r + +# All centers are complete while Y is still at zero. This is the crucial +# difference from an illegal early-own-Y prefix using the old center order. +centers=[] +for i in range(8): + regs=[block_totals[c,i] for c in sorted(blocks) if i in c] + F=hyper(P[frame[i]]);a=regs[0] + for b in regs[1:]:add(a,b,1,F) + centers.append(a) +centers += [frame[i] for i in range(8)] +center_frames=[cur[r] for r in centers] +assert list(map(len,center_frames))==[8]*8+[1]*8 +assert all(cur[v+t]==() for t in range(v)) + +phase=B +for t,(r,coef,F) in sorted(own_rows.items()): + assert cur[r]==F + add(v+t,r,coef,F) + +packets={} +for c,z in sorted(blocks.items()): + mp=maps[c] + for j,(e,F) in enumerate(list(zip(z['events'],z['event_frames']))[40:]): + if j not in early[c]: + t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F)) + keys=[(p,eps) for p in it.combinations(c,2) for eps in (-1,1)] + for key,(r,alpha) in zip(keys,z['outputs']): + a=mp[r];b=alloc();add(b,a,1,cur[a]) + consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d)) + assert len(consumers)==2 + for target,r in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(r,Q(alpha)) + +# Both tetrahedra use the same partition. A selected key has exactly two +# selected Y loads and no ordinary M consumer. Supply its two raw halves in +# opposite orders and never form that M. Other keys retain the old M path. +requests=defaultdict(list) +for pid,pair in enumerate(pairs): + if not pair['selected']:continue + (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix'] + requests[key1].append((t,-Q(mat[0][0],2))) + requests[key2].append((u,-Q(mat[0][1],2))) +second=[];first_join_counts=Counter() +for key,reqs in sorted(requests.items()): + assert len(reqs)==2 + c,p,eps=key + ds=sorted(d for d in blocks if d!=c and set(p)<=set(d));a,b=ds + for j,(target,coef) in enumerate(sorted(reqs)): + first_source,second_source=(a,b) if j==0 else (b,a) + r,alpha=packets[first_source,p,eps,second_source] + F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target])) + first_join_counts[len(F)]+=1;add(v+target,r,coef*alpha,F) + r,alpha=packets[second_source,p,eps,c] + second.append((target,r,coef*alpha)) + +Ms={} +for c in sorted(blocks): + for p in it.combinations(c,2): + ds=sorted(d for d in blocks if d!=c and set(p)<=set(d)) + for eps in (-1,1): + if (c,p,eps) in requests:continue + (a,alpha),(b,beta)=[packets[d,p,eps,c] for d in ds] + F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F) + Ms[c,p,eps]=(a,alpha) + +consumers=defaultdict(list) +for pid,pair in enumerate(pairs): + for key in pair['keys']:consumers[key].append(pid) +slots={} +for key,uses in sorted(consumers.items()): + assert len(uses)==2 + if key in requests: + assert all(pairs[i]['selected'] for i in uses) + continue + assert all(not pairs[i]['selected'] for i in uses) + a,alpha=Ms[key] + for j,pid in enumerate(uses): + if j==0:r=a + else:r=alloc();add(r,a,1,cur[a]) + slots[pid,key]=(r,alpha) +assert len(cur)-240==504 + +selected_join_counts=Counter() +for target,r,coef in second: + F=basis(cur[v+target]+cur[r]);assert inside(F,hyper(P[target])) + selected_join_counts[len(F)]+=1;add(v+target,r,coef,F) +output_basis=[] +for pair in pairs: + if not pair['selected']:continue + (t,u),mat=pair['targets'],pair['matrix'] + F=basis(cur[v+t]+cur[v+u]);assert inside(F,hyper(P[t])) and inside(F,hyper(P[u])) + add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F) + z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F);output_basis.append((t,u,z)) + +for pid,pair in enumerate(pairs): + if pair['selected']:continue + (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix'] + (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2] + F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta + ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta + add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F) + add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u])) + +for t in range(v): + expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {} + assert rows[v+t]==expected,('side identity',t) + +scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)] +precondition=[] +for t,u,z in output_basis: + a,b=scatter[t].copy(),scatter[u].copy() + scatter[t]=[x/2-y/z for x,y in zip(a,b)] + scatter[u]=[x/2+y/z for x,y in zip(a,b)] + precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]], + ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]]) +for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL) +H[8]+=8;H[1]+=8 +assert sum(r*z for r,z in H.items())==9*504+240*8+72 + +def apply(e,matrix): + if e[0]=='add': + _,t,s,a,b,*_=e;q=Q(a,b) + for j,x in list(matrix[s].items()): + z=matrix[t].get(j,Q(0))+q*x + if z:matrix[t][j]=z + else:matrix[t].pop(j,None) + else: + _,t,a,b,*_=e;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()} +def inverse(e): + e=copy.deepcopy(e) + if e[0]=='add':e[3]*=-1 + else:e[2],e[3]=e[3],e[2] + e[-1]=list(FULL);return e +cut=[['add',v+t,centers[i],q.numerator,q.denominator,None] for t,row in enumerate(scatter) for i,q in enumerate(row) if q] +cleanup=[inverse(e) for e in reversed(A+B) if not v<=e[1]<2*v] +matrix=[{r:Q(1)} if r= 2 * V} +for e in w['precondition']: apply(e, dirty) +comp = [] +for r in range(V, 2 * V): + for j, x in sorted(dirty[r].items()): + assert not w['start_extra'].get(str(j)); comp.append(['add', r, j, -x.numerator, x.denominator, []]) +expected = ident(); expected_back = ident() +for t in range(V): expected[V + t][t] = Q(1); expected_back[t][V + t] = Q(-1) +correct = w['precondition'] + comp + main + w['cleanup'] +assert replay(correct) == expected and replay([inverse(e, True) for e in correct]) == expected_back +# locate every new gate by exact content in A/B +located = [] +for K in recipe['kernels']: + pos = [] + for gt in K['gates']: + q = Q(gt['coefficient']); gate = ['add', gt['donor'], K['pivot'], -q.numerator, q.denominator, K['frame']] + hits = [(part, i) for part in ('A', 'B') for i, e in enumerate(w[part]) if e == gate] + assert len(hits) == 1, (K['pivot'], gt, hits) + pos.append(hits[0]) + located.append((K['pivot'], pos)) +controls = [] +for pivot, pos in located: + for omitted in [[p] for p in pos] + [pos]: + om = set(omitted) + A = [e for i, e in enumerate(w['A']) if ('A', i) not in om]; B = [e for i, e in enumerate(w['B']) if ('B', i) not in om] + cleanup = [inverse(e) for e in reversed(A + B) if not V <= e[1] < 2 * V] + program = w['precondition'] + comp + A + w['cut'] + B + cleanup + assert replay(program) != expected and replay([inverse(e, True) for e in program]) != expected_back + controls.append(dict(pivot=pivot, omitted=[list(p) for p in omitted], forward_rejected=True, reflected_rejected=True)) +r = dict(status='PASS_EXACT_MULTICUT_KERNEL_OMISSION_CONTROLS', word_sha256=hashlib.sha256(a.word.read_bytes()).hexdigest(), + columns_each_orientation=N, correct_compensation_frozen=True, compensation_entries=len(comp), controls=controls, + scope='Each new multi-cut donor gate and each entire new kernel omitted. Cleanup is regenerated, correct compensation is held fixed, and both exact scalar orientations reject each mutant.') +a.out.write_text(json.dumps(r, indent=2) + '\n'); print(r['status'], len(controls)) diff --git a/research/pr643-improvement-20261013/witness/vendor/joint_prefix/code/build_joint_prefix.py b/research/pr643-improvement-20261013/witness/vendor/joint_prefix/code/build_joint_prefix.py new file mode 100644 index 0000000000..1dcb2ebe2c --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/joint_prefix/code/build_joint_prefix.py @@ -0,0 +1,64 @@ +#!/usr/bin/env python3 +"""Apply the literal57-gate joint prefix to either complete eight-cold provider. + +Derived from Dominik Scholz's PR571 compose_prefix.py, commit +b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3. Exact source hashes are in +data/JOINT-PREFIX.json. The plain variant keeps each retained event's own frame, +instead of copying width-seven-only frame expansions. OpenAI Codex assistance; +Apache-2.0. No optimization, external replay directory or network is required. +""" +import argparse,copy,gzip,hashlib,json,sys +from collections import Counter +from pathlib import Path + +def main(): + if not __debug__:raise RuntimeError('Assertions required') + parser=argparse.ArgumentParser(description=__doc__) + for name in ('input','recipe','gk-dir','out'):parser.add_argument('--'+name,type=Path,required=True) + parser.add_argument('--variant',choices=('eightcold','width7'),required=True) + args=parser.parse_args();assert not args.out.exists() + sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() + recipe=json.loads(args.recipe.read_bytes());pin=recipe['variants'][args.variant] + raw=gzip.decompress(args.input.read_bytes());assert hashlib.sha256(raw).hexdigest()==pin['input_content_sha256'] + original=json.loads(raw);word=copy.deepcopy(original) + sys.path.insert(0,str(args.gk_dir.resolve()));import gk_word as g,gk_common as co + g.V=co.V=112;g.DATA=co.DATA=7168 + oldn,newn=recipe['old_prefix_length'],recipe['new_prefix_length'];assert(oldn,newn)==(69,57) + assert [event[:-1]for event in word['A'][:oldn]]==recipe['old_scalar_prefix'] + events={tuple(e[:-1]):e for e in word['A'][:oldn]};assert len(events)==oldn + prefix=[copy.deepcopy(events[tuple(e)])for e in recipe['new_scalar_prefix']] + assert len(prefix)==len({tuple(e[:-1])for e in prefix})==newn + word['A']=prefix+word['A'][oldn:] + for key,frame in recipe['removed_start_frames'].items(): + assert word['start_extra'][key]==frame + del word['start_extra'][key] + assert set(recipe['removed_start_frames'])=={'523','525','599','601'} + assert word['B']==original['B'] and word['A'][newn:]==original['A'][oldn:] + word['cleanup']=[g.inverse(e,g.FULL)for e in reversed(word['A']+word['B'])if not 112<=e[1]<224] + before,after=g.profile(original),g.profile(word);widths=co.widths_of(word);oldwidths=co.widths_of(original) + delta={r:after[r]-before[r]for r in set(after)|set(before)if after[r]!=before[r]} + assert delta=={1:-12,2:-16,3:16} + assert dict(before)=={int(r):n for r,n in pin['profile_before'].items()} + assert dict(after)=={int(r):n for r,n in pin['profile_after'].items()} + changes={str(h):[x,y]for h,(x,y)in enumerate(zip(oldwidths,widths))if x!=y} + assert changes==pin['changed_helper_widths']=={str(h):[8,9]for h in(299,301,375,377)} + assert Counter(widths)==Counter({int(r):n for r,n in pin['width_inventory'].items()}) + responses=g.responses(word);assert all(not responses[int(r)-224]for r in word['start_extra']) + word['report'].update(local_profile=dict(after),local_rank_mass=sum(r*n for r,n in after.items()), + entrance_rank=sum(9-w for w in widths),entering_helpers=sum(w<9 for w in widths),width_inventory=dict(Counter(widths))) + encoded=g.dump(word);encoded=encoded[:9]+b'\xff'+encoded[10:] + assert hashlib.sha256(gzip.decompress(encoded)).hexdigest()==pin['output_content_sha256'] + args.out.mkdir(parents=True);target=args.out/'FULL-WORD.json.gz';target.write_bytes(encoded) + result=dict(status='PASS_LITERAL_JOINT_PREFIX_EXACT_RESPONSE_AND_FRAME_PROFILE',variant=args.variant, + source_content_sha256=pin['input_content_sha256'],word_content_sha256=pin['output_content_sha256'], + word_sha256=sha(target),recipe_sha256=sha(args.recipe),constructor_sha256=sha(Path(__file__)), + old_prefix=oldn,new_prefix=newn,retained_event_frames_unchanged=True,A_tail_unchanged=True,B_unchanged=True, + removed_start_frames=recipe['removed_start_frames'],all_entering_response_columns_zero=True, + profile_before=dict(before),profile_after=dict(after),profile_delta=delta, + width_inventory=dict(Counter(widths)),changed_helper_widths=changes, + scope='Exact construction and frame-chain profile only. Full scalar/native/wrapper/phase, ' + 'omission, physical owner and invoice/moment checks remain separate.') + (args.out/'CONSTRUCTION.json').write_text(json.dumps(result,indent=2)+'\n',encoding='utf-8',newline='\n') + print(result['status'],args.variant) + +if __name__=='__main__':main() diff --git a/research/pr643-improvement-20261013/witness/vendor/joint_prefix/data/EIGHTCOLD-JOINT-KERNELS.json b/research/pr643-improvement-20261013/witness/vendor/joint_prefix/data/EIGHTCOLD-JOINT-KERNELS.json new file mode 100644 index 0000000000..af8755011b --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/joint_prefix/data/EIGHTCOLD-JOINT-KERNELS.json @@ -0,0 +1,1085 @@ +{ + "kernels": [ + { + "pivot": 486, + "frame": [ + 120 + ], + "gates": [ + { + "part": "A", + "index": 49, + "donor": 462, + "coefficient": "1" + } + ] + }, + { + "pivot": 487, + "frame": [ + 120 + ], + "gates": [ + { + "part": "A", + "index": 50, + "donor": 463, + "coefficient": "1" + } + ] + }, + { + "pivot": 488, + "frame": [ + 96 + ], + "gates": [ + { + "part": "A", + "index": 25, + "donor": 474, + "coefficient": "1" + } + ] + }, + { + "pivot": 489, + "frame": [ + 96 + ], + "gates": [ + { + "part": "A", + "index": 26, + "donor": 475, + "coefficient": "1" + } + ] + }, + { + "pivot": 498, + "frame": [ + 126 + ], + "gates": [ + { + "part": "A", + "index": 55, + "donor": 464, + "coefficient": "1" + } + ] + }, + { + "pivot": 499, + "frame": [ + 126 + ], + "gates": [ + { + "part": "A", + "index": 56, + "donor": 465, + "coefficient": "1" + } + ] + }, + { + "pivot": 500, + "frame": [ + 102 + ], + "gates": [ + { + "part": "A", + "index": 39, + "donor": 476, + "coefficient": "1" + } + ] + }, + { + "pivot": 501, + "frame": [ + 102 + ], + "gates": [ + { + "part": "A", + "index": 40, + "donor": 477, + "coefficient": "1" + } + ] + }, + { + "pivot": 534, + "frame": [ + 126 + ], + "gates": [ + { + "part": "A", + "index": 53, + "donor": 466, + "coefficient": "-1/2" + } + ] + }, + { + "pivot": 535, + "frame": [ + 126 + ], + "gates": [ + { + "part": "A", + "index": 54, + "donor": 467, + "coefficient": "-1/2" + } + ] + }, + { + "pivot": 536, + "frame": [ + 96 + ], + "gates": [ + { + "part": "A", + "index": 27, + "donor": 480, + "coefficient": "-1/2" + } + ] + }, + { + "pivot": 537, + "frame": [ + 96 + ], + "gates": [ + { + "part": "A", + "index": 28, + "donor": 481, + "coefficient": "-1/2" + } + ] + }, + { + "pivot": 538, + "frame": [ + 96 + ], + "gates": [ + { + "part": "A", + "index": 29, + "donor": 490, + "coefficient": "1" + } + ] + }, + { + "pivot": 539, + "frame": [ + 96 + ], + "gates": [ + { + "part": "A", + "index": 30, + "donor": 491, + "coefficient": "1" + } + ] + }, + { + "pivot": 540, + "frame": [ + 126 + ], + "gates": [ + { + "part": "A", + "index": 45, + "donor": 504, + "coefficient": "1" + } + ] + }, + { + "pivot": 541, + "frame": [ + 126 + ], + "gates": [ + { + "part": "A", + "index": 46, + "donor": 505, + "coefficient": "1" + } + ] + }, + { + "pivot": 546, + 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{ + "part": "B", + "index": 507, + "donor": 115, + "coefficient": "1", + "donor_state": [ + 115, + 1 + ], + "split_donor": false, + "target_donor": true + }, + { + "part": "B", + "index": 575, + "donor": 179, + "coefficient": "-1", + "donor_state": [ + 179, + 0 + ], + "split_donor": true, + "target_donor": true + }, + { + "part": "B", + "index": 722, + "donor": 543, + "coefficient": "1", + "donor_state": [ + 543, + 0 + ], + "split_donor": true + } + ], + "profile_delta": { + "1": 3, + "2": 1, + "3": -2 + } + }, + { + "pivot": 531, + "frame": [ + 30 + ], + "gates": [ + { + "part": "B", + "index": 550, + "donor": 155, + "coefficient": "1", + "donor_state": [ + 155, + 1 + ], + "split_donor": false, + "target_donor": true + }, + { + "part": "B", + "index": 617, + "donor": 219, + "coefficient": "-1", + "donor_state": [ + 219, + 0 + ], + "split_donor": true, + "target_donor": true + }, + { + "part": "B", + "index": 740, + "donor": 555, + "coefficient": "1", + "donor_state": [ + 555, + 0 + ], + "split_donor": true + } + ], + "profile_delta": { + "1": 3, + "2": 1, + "3": -2 + } + }, + { + "pivot": 494, + "frame": [ + 24 + ], + "gates": [ + { + "part": "B", + "donor": 566, + "coefficient": "1", + "index": 379 + }, + { + "part": "B", + "donor": 640, + "coefficient": "-2", + "index": 380 + }, + { + "part": "B", + "donor": 688, + "coefficient": "-1", + "index": 382 + }, + { + "part": "B", + "donor": 642, + "coefficient": "2", + "index": 381 + }, + { + "part": "B", + "donor": 690, + "coefficient": "1", + "index": 383 + } + ] + } + ], + "scope": "All57 new A-prefix gates, all25 PR568 multi-cut gates and five inherited494 gates; each individual gate and each whole kernel.", + "provenance": { + "source_commit": "b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3", + "source_recipe_sha256": "836d839e744b1cbee5b3a47b4d6f766e9d822161fe3640794f9a0f051d2ad20d", + "word_content_sha256": "6c361b33967bb62d878b3acef44a4ac2c70970e99f36a11906b03811495de533", + "note": "Part, index and frame are exact 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"providers/words/zero/CONSTRUCTION.json": "684ec2e57240e0f376c133d801a8f4e0d3d5f30cc427f0334b66e4eaceaea183", + "providers/words/zero/FULL-WORD.json.gz": "2d8dbb9f163f29cdab2e210674dd873895d2628144aef88b2e4d354dee6c5fd1", + "stages/fourcold-mixed-screen/COMPLETE.json": "b29ab797ce529b97f539f46a2576efd3d9c0782d19962a5a22c28b5de260a58e", + "stages/fourcold-mixed-screen/K2.json": "f6baa328dba7e5b98f923b9339ffaced9b0133860154575d73af046f523d6105", + "stages/fourcold-mixed-screen/K3.json": "8fd24d1333eba66f8f67f34dcfc71280eacd4ec36c4202350765ab4abb7b479a", + "stages/fourcold-mixed-screen/K4.json": "320c9c572e7e8149563feba33039aecaa88a280f7f306b9f33850737988e2a3c", + "stages/fourcold-mixed-screen/K5.json": "05a8e247722a8ede7accf71b200abece6ae5072f48ab50c601a5aa51986f60bb", + "stages/fourcold-mixed-screen/K6.json": "664d249d2a335578d0bbf10e161faaae12ec935b1d0394f9e12aa21937761271", + "stages/fourcold-mixed-screen/K7.json": "2e325a44479bc882476d7c7691b469e9db04f9c6a1f8f4e33679fc7970fd1814", + "stages/fourcold-mixed-screen/SOURCE.json": "8d1fc167260195a16f48cfc5d9dd74653cef69197b56de15234ff9879995ed09", + "stages/screen_stages.py": "406f46288b31add60ee49ad616e721ce0a18e5eb72b7b9a7dd8664466a4dd8db" + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/larger_gain/README.md b/research/pr643-improvement-20261013/witness/vendor/larger_gain/README.md new file mode 100644 index 0000000000..fc05b0876e --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/larger_gain/README.md @@ -0,0 +1,175 @@ +# Larger-gain research after PR564 + +The new direction is to create residual helpers of width seven, which can +share a rank-sixteen owner with a width-nine helper. The current width-eight +helpers cannot make that exact pair. Thirty-two coordinated entrance-frame +promotions per selected call create this option while preserving the scalar +program. This changes the available packing patterns, rather than extending +the already saturated width-five-to-four promotion family. + +The frozen literal nomination uses 63 width-seven providers and nine ordinary +four-cold providers. Its complete profile has native rate +`b = 0.001602631813774414678548` and nominal grid value +`kappa = 0.001600067494703216`, about 0.4352% above PR564. Full global admission +passes: physical chronology and all sixteen owner mutations, the complete +finite invoice, both exact moment engines, all 47 outer constraints for each +model, and rejection of all 89 invalid assembly variants. The conservative +model also passes at `kappa = 0.001600067491919801`. See the +[frozen result and artifact bindings](global/width7/RESULT.json). + +The separately completed four-cold fallback is already fully admitted at +`kappa = 0.001593675235313849`, a 0.03396% gain. See its +[result and artifact bindings](global/fourcold/RESULT.json) and the +[independent adapter review](geometry/FOUR-COLD-SEAM-REVIEW.md). + +## Latest state and scope + +Research ran in an isolated checkout based on PR564. Publication is based on +main and includes only this package; PR564 is an explicit external dependency. The +repository has an `origin` remote; its main branch and PRs through 566 were +fetched. The [state record](STATE.json) pins every inspected head: + +- `origin/main`: `db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`. +- [PR564](https://github.com/CrocSwap/integer-mult-bounds/pull/564): + `c18417b02b80594b2ca1c8c21185d28befafc935`, numerical baseline + `kappa = 0.001593134158181640`. +- [PR565](https://github.com/CrocSwap/integer-mult-bounds/pull/565) and + [PR566](https://github.com/CrocSwap/integer-mult-bounds/pull/566) add formal + compact counting and input preparation. PR566 reports a concrete six-tape + composition with bound `22n+17`. These are not a higher kappa or a general + worst-case constant-time indexing theorem. + +The complete unchanged PR564 verifier was freshly run: all 36 stages passed, +including its providers, phases, physical owners, finite invoice, two moment +engines and outer assembly. Source hashes, receipts and the stage log are +retained in [baseline564](baseline564/BASELINE.json). + +Every new numerical result here has the same conditional finite-construction +boundary as the inherited package. All-size compilation, common labels and +mutable bases, normalized residual realization, correlated whole-call +hosting, precision/tape and analytic transfer remain assumptions. No +unconditional multiplication theorem, complete Lean proof, or general O(1) +indexing theorem is claimed. + +## What changed locally + +Three additional exact suffix relations reduce three width-nine helpers to +width eight in each zero-, four- and eight-promotion provider. Their combined +paid change is `3 H1 + 6 H2 - 6 H3`. The relations were reconstructed for each +provider: copying the same insertion cuts blindly was invalid. The actual +words, all-column scalar checks, dirty-helper restoration, omitted-kernel +controls and phase recipes are retained under [providers](providers/README.md). + +Next, 32 entrance-frame promotions create width-seven helpers. Their combined +paid change is `32 H1 + 160 H2 - 128 H3`. The fully checked eight-promotion +provider therefore has local profile + +```text +H = {1:2352, 2:592, 3:328, 4:192, 5:56, 6:56, 8:8} +helper widths = {4:8, 5:48, 7:32, 8:128, 9:288} +``` + +All three versions passed 728 columns in both orientations, exact restoration, +native frames, eleven local negative controls, 3005 phase edges and 224 +endpoint adapters. Their source-bound bundles are in +[providers/width7](providers/width7/). + +The packing search must respect complete helper ownership. A width-count +solution initially failed literal expansion because it demanded incompatible +shared owners from the same invocation. Additional subset constraints excluded +that solution. The retained nominee checks actual invocation windows, whole +owners, distinct roles and disjoint prefixes. + +## Exact bounds that keep the search focused + +The strongest negative result is an exact dual certificate for the current +PR564 providers. Within its present capacities and live stock, no repacking, +provider remix or finite cloning can reach the next `10^-18` kappa grid point. +The proof enumerates every 4/5/8/9 pattern in capacities 8/16/32/48, relaxes +integrality and chronology, and checks the resulting 548 dual inequalities +with two independent rational engines. See +[the proof and scope](patterns/PROOF.md). + +Additional width-five-to-four promotions are affine continuations of the +existing cost/inventory family. Forty more pass local checks but do not +improve the four-cold capacity ceiling. Width-seven promotions change that +conclusion by introducing new bin patterns. The exact upper bound for the +32-promotion family is approximately `0.001600564129863655`. Combining it +with forty more width-four promotions raises the relaxed upper bound only to +`0.001600616266460206`. Neither is an admitted result: these deliberately +ignore physical conflicts. All sixty available width-seven promotions also +passed local checks, but their additional cost yields no further relaxed gain. + +The larger alphabet was also tested at five, seven, nine and eleven stages, +allowing arbitrary fractional provider mixtures, all mixed-width auxiliary +banks, and no chronology conflicts. Exact upper bounds are approximately: + +| Stages | Dimension | Kappa upper bound | +| --- | ---: | ---: | +| 5 | 41 | 0.001395406 | +| 7 | 57 | 0.001577285 | +| 9 | 73 | 0.001600617 | +| 11 | 89 | 0.001554605 | + +These are rounded upward for display. The nine-stage optimum uses no banks. +The other stage counts remain below PR564 even in this enlarged model. +The [stage proof, exact receipts and reproduction commands](geometry/README.md) +describe the padding and provider assumptions; these are not universal bounds +over every possible local construction. + +## Where a materially larger gain could come from + +The next useful target is the local packet factory, especially expensive +helper paths. An exact sensitivity experiment removes each candidate's actual +paid frame path and residual demand, with all other costs retained. Under the +optimistic assumption that a new word replaces that work for free, saving six +selected helper paths per call crosses a 1% target; saving 32 crosses 5%. +This identifies the cost budget a new construction must beat. It does not +show that the existing helpers are removable. See the measured paths and +adjacent exact threshold checks in [HELPER-TARGETS.md](geometry/HELPER-TARGETS.md). + +The 5% target would also outgrow the currently composed PR543 bit supplier. +[PR555](https://github.com/CrocSwap/integer-mult-bounds/pull/555) already reports +bit rate `0.001733052823330162099157`, enough headroom in principle; its +source-bound replay and new composition were not performed here. + +Several structural shortcuts were checked and failed within explicit scopes: +lossless binary dimension reduction, hyperplane puncturing, seven-center +decoding with too few deletions, retaining 120 ports at the old center bill, +literal tensor lifts, direct clone-free ordinary packet reads, and a full +tetrahedron Walsh output basis with unchanged packets. The geometry and +provider notes retain exact receipts and explain what each test leaves open. +In particular, a joint packet refactorization, a sparse mixed output basis, +or joint reselection of entrance kernel/gauge bases remains a substantive +direction beyond the affine local promotions tried here. + +## Verification and attribution + +The full provider and global reproduction uses an explicit immutable PR564 +source package. The output directory must be new: + +```sh +python3 -B research/larger-gain/global/reproduce.py \ + --source /path/to/pinned-PR564/research/complex-allcold \ + --work /tmp/width7-reproduction +``` + +The exact capacity exclusions can be replayed without SciPy. Set the same +source package for the supplementary model screens: + +```sh +GAIN_PR564_SOURCE=/path/to/pinned-PR564/research/complex-allcold \ + python3 -B research/larger-gain/patterns/verify_ceiling_controls.py +``` + +This checks every retained capacity dual and rejects deliberately corrupted +source pins, potentials, dimensions, rates and signs. The stage receipts have +their separate standard-library verifier. SciPy nominates solutions only; +exact rational checks establish the stated exclusions. + +The new providers preserve their source credits and immutable input hashes. +Modified global adapters retain the complete invoice and all inherited +guards; the patch and source/adapted hashes are included. See [NOTICE](NOTICE). +Prepared with substantial OpenAI Codex assistance. The publication adds only +this research package; its PR564 dependency is external and pinned. No +upstream scientific package was modified. diff --git a/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/build_entrance_promotions.py b/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/build_entrance_promotions.py new file mode 100644 index 0000000000..37e6c0684e --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/build_entrance_promotions.py @@ -0,0 +1,82 @@ +#!/usr/bin/env python3 +"""Compose paid entrance-frame promotions, preserving every scalar operation. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +import copy +import gzip +import hashlib +import json +from pathlib import Path +import sys + +from coupled_frames_base import Chains, basis +from search_suffix_kernels import entropy + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--word', type=Path, required=True) + parser.add_argument('--recipes', type=Path, required=True) + parser.add_argument('--gk-dir', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + assert __debug__ and not args.out.exists() + sys.path.insert(0, str(args.gk_dir.resolve())) + import gk_word as g + import gk_common as co + g.V = co.V = 112 + g.DATA = co.DATA = 7168 + raw = gzip.decompress(args.word.read_bytes()) + original = json.loads(raw) + word = copy.deepcopy(original) + recipes = json.loads(args.recipes.read_text()) + assert len({recipe['pivot'] for recipe in recipes}) == len(recipes) + graph = Chains(word) + changed = set() + for recipe in recipes: + pivot = recipe['pivot'] + assert basis(tuple(word['start_extra'][str(pivot)])) == basis(tuple(recipe['old_frame'])) + frame = basis(tuple(recipe['new_frame'])) + assert len(frame) == len(recipe['old_frame']) + 1 + start = graph.regs[pivot][0] + seed = graph.next[start, pivot] + closure = graph.closure(seed, frame, 'raise', len(graph.nodes)) + assert closure is not None + for node, value in closure.items(): + graph.nodes[node]['F'] = value + changed.add(node) + word['start_extra'][str(pivot)] = list(frame) + for node in changed: + point = graph.nodes[node] + word[point['section']][point['index']][-1] = list(point['F']) + before, after = g.profile(original), g.profile(word) + delta = {r: after[r] - before[r] for r in set(after) | set(before) if after[r] != before[r]} + assert sum(r * n for r, n in delta.items()) == -len(recipes) + for section in ('A', 'cut', 'B', 'cleanup', 'precondition'): + assert [event[:-1] for event in word[section]] == [event[:-1] for event in original[section]] + widths = co.widths_of(word) + word['report'].update(local_profile=dict(after), local_rank_mass=sum(r * n for r, n in after.items()), + entrance_rank=sum(9 - width for width in widths), + entering_helpers=sum(width < 9 for width in widths), + width_inventory=dict(Counter(widths))) + args.out.mkdir(parents=True) + encoded = g.dump(word) + (args.out / 'FULL-WORD.json.gz').write_bytes(encoded) + (args.out / 'RECIPES.json').write_text(json.dumps(recipes, indent=2) + '\n') + receipt = dict(status='PASS_COUPLED_ENTRANCE_PROMOTION_CONSTRUCTION', + source_content_sha256=hashlib.sha256(raw).hexdigest(), + word_content_sha256=hashlib.sha256(gzip.decompress(encoded)).hexdigest(), + changed_gates=len(changed), promotions=len(recipes), + scalar_operations_unchanged=True, profile_before=dict(before), profile_after=dict(after), + profile_delta=delta, local_entropy_delta=entropy(delta), + widths_after=dict(Counter(widths)), + scope='Exact coupled frame-chain construction only; native, phase, hosting, ' + 'invoice and moment admission remain separate.') + (args.out / 'CONSTRUCTION.json').write_text(json.dumps(receipt, indent=2) + '\n') + print(json.dumps(receipt, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/coupled_frames_base.py b/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/coupled_frames_base.py new file mode 100644 index 0000000000..90a01f0641 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/coupled_frames_base.py @@ -0,0 +1,373 @@ +#!/usr/bin/env python3 +"""Bounded coupled frame search on the pinned PR531 scalar word. + +Extends the frame-chain idea in icekylinx's coalesce_frames.py (retained in +research/direct-delivery504-global/code) to both propagation directions and +all A/B gates. Scalar coefficients/order, entrances, exits and cut frames stay +fixed. Exact entropy comparisons guide discovery; a new nonlinear moment, +Clifford recipes and global binding must still be checked independently. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +import copy +from fractions import Fraction +from functools import lru_cache +import gzip +import hashlib +import json +import math +from pathlib import Path +import random + +ROOT = Path(__file__).resolve().parents[2] +SOURCE = ROOT / 'research/direct-delivery504-global/evidence/local/FULL-WORD.json.gz' + + +def require(ok, detail): + if not ok: + raise ValueError(detail) + + +@lru_cache(None) +def basis(vectors): + pivots = {} + for x in vectors: + for p in sorted(pivots, reverse=True): + if x >> p & 1: + x ^= pivots[p] + if x: + p = x.bit_length() - 1 + for q in pivots: + if pivots[q] >> p & 1: + pivots[q] ^= x + pivots[p] = x + return tuple(pivots[p] for p in sorted(pivots, reverse=True)) + + +@lru_cache(None) +def span(frame): + values = {0} + for x in frame: + values |= {y ^ x for y in values} + return frozenset(values) + + +@lru_cache(None) +def meet(a, b): + return basis(tuple(sorted(span(a) & span(b)))) + + +@lru_cache(None) +def join(a, b): + return basis(a + b) + + +def contained(a, b): + return join(a, b) == b + + +def exact_gain(delta): + """exp(old entropy - new entropy), using unchanged total rank mass.""" + require(sum(r * n for r, n in delta.items()) == 0, 'rank mass changed') + result = Fraction(1) + for r, n in delta.items(): + result *= Fraction(r) ** (r * n) + return result + + +class Chains: + def __init__(self, word): + self.word = word + self.v = len(word['ports']) + self.h = word['report']['h'] + self.full = basis(tuple(1 << i for i in range(self.h))) + self.nodes = [] + self.regs = [[] for _ in range(2 * self.v + word['report']['R'])] + self.mutable = [] + starts = [(p,) for p in word['ports']] + [()] * (self.v + word['report']['R']) + for r, frame in word.get('start_extra', {}).items(): + starts[int(r)] = tuple(frame) + levels = {int(t): basis(tuple(f)) for t, f in word.get('target_levels', {}).items()} + for r, f in enumerate(starts): + self.add([r], f, 'start', None) + for section in ('A', 'B'): + if section == 'B': + for r, f in zip(word['centers'], word['center_frames']): + self.add([r], f, 'barrier', None) + for t in range(self.v): + self.add([self.v + t], levels.get(t, ()), 'barrier', None) + for i, event in enumerate(word[section]): + regs = event[1:3] if event[0] == 'add' else event[1:2] + self.mutable.append(self.add(regs, event[-1], section, i)) + for r in range(len(self.regs)): + f = self.full + if self.v <= r < 2 * self.v: + port = word['ports'][r - self.v] + f = basis(tuple(x for x in range(1, 1 << self.h) if not (x & port).bit_count() % 2)) + self.add([r], f, 'final', None) + self.prev, self.next = {}, {} + for r, chain in enumerate(self.regs): + for x, y in zip(chain, chain[1:]): + self.next[x, r] = y + self.prev[y, r] = x + # The emitter has no implicit climb at a cut: lock its actual final + # incident gate too. This prevents free unbilled barrier transitions. + self.locked = {k for k, n in enumerate(self.nodes) if n['section'] not in ('A', 'B')} + for k, n in enumerate(self.nodes): + if n['section'] == 'barrier': + for r in n['regs']: + p = self.prev[k, r] + require(self.nodes[p]['F'] == n['F'], 'initial cut mismatch') + self.locked.add(p) + self.lower, self.upper = {}, {} + for k, n in enumerate(self.nodes): + value = () + if k in self.locked: + value = n['F'] + else: + for r in n['regs']: + value = join(value, self.lower[self.prev[k, r]]) + self.lower[k] = value + for k in reversed(range(len(self.nodes))): + n = self.nodes[k] + value = self.full + if k in self.locked: + value = n['F'] + else: + for r in n['regs']: + value = meet(value, self.upper[self.next[k, r]]) + self.upper[k] = value + self.center_profile = Counter() + for r, f in zip(word['centers'], word['center_frames']): + current = basis(tuple(f)) + served = {levels.get(e[1] - self.v, ()) for e in word['cut'] if e[2] == r} + for g in sorted(served, key=lambda x: (-len(x), x)): + require(contained(g, current), 'center descent not nested') + if current != g: + self.center_profile[len(current) - len(g)] += 1 + current = g + + def add(self, regs, frame, section, index): + k = len(self.nodes) + self.nodes.append(dict(regs=list(regs), F=basis(tuple(frame)), section=section, index=index)) + for r in regs: + self.regs[r].append(k) + return k + + def profile(self): + result = self.center_profile.copy() + for r, chain in enumerate(self.regs): + for x, y in zip(chain, chain[1:]): + f, g = self.nodes[x]['F'], self.nodes[y]['F'] + require(contained(f, g), ('nonmonotone', r, x, y)) + if self.nodes[y]['section'] == 'barrier': + require(f == g, 'unbilled cut transition') + if f != g: + result[len(g) - len(f)] += 1 + return result + + def closure(self, seed, wanted, direction, limit): + changed, queue = {}, [(seed, wanted)] + links = self.next if direction == 'raise' else self.prev + operation = join if direction == 'raise' else meet + while queue: + k, want = queue.pop() + old = changed.get(k, self.nodes[k]['F']) + new = operation(old, want) + if new == old: + continue + if k in self.locked: + return None + changed[k] = new + if len(changed) > limit: + return None + for r in self.nodes[k]['regs']: + j = links[k, r] + neighbor = changed.get(j, self.nodes[j]['F']) + valid = contained(new, neighbor) if direction == 'raise' else contained(neighbor, new) + if not valid: + queue.append((j, new)) + return changed + + def delta(self, changed): + edges = {(self.prev[k, r], k, r) for k in changed for r in self.nodes[k]['regs']} + edges |= {(k, self.next[k, r], r) for k in changed for r in self.nodes[k]['regs']} + result = Counter() + for x, y, _ in edges: + f, g = self.nodes[x]['F'], self.nodes[y]['F'] + nf, ng = changed.get(x, f), changed.get(y, g) + require(contained(nf, ng), 'invalid closure') + if f != g: + result[len(g) - len(f)] -= 1 + if nf != ng: + result[len(ng) - len(nf)] += 1 + return {r: n for r, n in result.items() if n} + + def options(self, seed, direction, depth, lattice=False): + links = self.next if direction == 'raise' else self.prev + options = [] + for r in self.nodes[seed]['regs']: + found, k, steps = [], seed, 0 + while (k, r) in links and steps < 128: + k = links[k, r] + f = self.nodes[k]['F'] + if f not in found: + found.append(f) + steps += 1 + if len(found) >= depth or k in self.locked: + break + options.append(found) + result = set(x for row in options for x in row) + if len(options) == 2: + operation = meet if direction == 'raise' else join + result |= {operation(a, b) for a in options[0] for b in options[1]} + f = self.nodes[seed]['F'] + if lattice: + if direction == 'raise': + # All covers of F in the allowed subspace interval. + result |= {join(f, (x,)) for x in span(self.upper[seed]) - span(f)} + else: + # Every codimension-one subspace is the kernel of a nonzero + # functional in F's basis coordinates. Keep the fixed lower. + for functional in range(1, 1 << len(f)): + pivot = (functional & -functional).bit_length() - 1 + kernel = basis(tuple(f[i] ^ (f[pivot] if functional >> i & 1 else 0) + for i in range(len(f)) if i != pivot)) + if contained(self.lower[seed], kernel): + result.add(kernel) + return sorted({join(f, g) if direction == 'raise' else meet(f, g) for g in result} - {f}, + key=lambda g: (len(g), g)) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--word', type=Path, default=SOURCE) + parser.add_argument('--out', type=Path, required=True) + parser.add_argument('--passes', type=int, default=3) + parser.add_argument('--depth', type=int, default=4) + parser.add_argument('--closure-limit', type=int, default=256) + parser.add_argument('--lattice', action='store_true') + parser.add_argument('--neutral-rounds', type=int, default=0, + help='Seeded equal-entropy moves between strict descent passes.') + parser.add_argument('--seed', type=int, default=12026) + args = parser.parse_args() + require(args.passes > 0 and args.depth > 0 and args.closure_limit > 0, 'positive limits required') + require(args.neutral_rounds >= 0, 'neutral rounds must be nonnegative') + require(not args.out.exists(), 'use a new output directory') + source = args.word.read_bytes() + original = json.loads(gzip.decompress(source)) + word = copy.deepcopy(original) + graph = Chains(word) + before = graph.profile() + require(dict(before) == {int(r): n for r, n in word['report']['local_profile'].items()}, 'input profile mismatch') + trace, attempts, blocked, feasible = [], 0, 0, 0 + rng = random.Random(args.seed) + seen = {tuple(n['F'] for n in graph.nodes)} + neutral_moves = 0 + for pass_number in range(args.passes + args.neutral_rounds): + accepted = 0 + for direction in ('raise', 'lower'): + order = reversed(graph.mutable) if direction == 'raise' else iter(graph.mutable) + for k in order: + if k in graph.locked: + continue + best = None + for target in graph.options(k, direction, args.depth, args.lattice): + attempts += 1 + changed = graph.closure(k, target, direction, args.closure_limit) + if not changed: + blocked += 1 + continue + feasible += 1 + delta = graph.delta(changed) + ratio = exact_gain(delta) + if ratio > 1 and (best is None or ratio > best[0]): + best = ratio, changed, delta + if best is None: + continue + ratio, changed, delta = best + updates = [] + for j, frame in sorted(changed.items()): + node = graph.nodes[j] + updates.append(dict(section=node['section'], index=node['index'], + old=list(node['F']), new=list(frame))) + node['F'] = frame + trace.append(dict(pass_number=pass_number, direction=direction, + entropy_gain_ratio=str(ratio), delta=delta, updates=updates)) + accepted += 1 + print(json.dumps(dict(pass_number=pass_number, accepted=accepted, attempts=attempts, + profile=dict(sorted(graph.profile().items())))), flush=True) + if not accepted: + if pass_number >= args.neutral_rounds: + break + choices = list(graph.mutable) + rng.shuffle(choices) + moved = False + for k in choices: + if k in graph.locked: + continue + directions = ['raise', 'lower'] + rng.shuffle(directions) + for direction in directions: + candidates = graph.options(k, direction, args.depth, args.lattice) + rng.shuffle(candidates) + for target in candidates: + attempts += 1 + changed = graph.closure(k, target, direction, args.closure_limit) + if not changed: + blocked += 1 + continue + feasible += 1 + delta = graph.delta(changed) + if exact_gain(delta) != 1: + continue + state = tuple(changed.get(j, n['F']) for j,n in enumerate(graph.nodes)) + if state in seen: + continue + seen.add(state) + updates = [] + for j, frame in sorted(changed.items()): + n = graph.nodes[j] + updates.append(dict(section=n['section'], index=n['index'], old=list(n['F']), new=list(frame))) + n['F'] = frame + trace.append(dict(pass_number=pass_number, direction=direction, + entropy_gain_ratio='1', delta=delta, updates=updates)) + neutral_moves += 1 + moved = True + break + if moved: + break + if moved: + break + if not moved: + break + after = graph.profile() + for k in graph.mutable: + node = graph.nodes[k] + word[node['section']][node['index']][-1] = list(node['F']) + for section in ('A', 'B'): + require([e[:-1] for e in word[section]] == [e[:-1] for e in original[section]], 'scalar word changed') + require(all(word[k] == original[k] for k in original if k not in ('A', 'B', 'report')), 'fixed data changed') + require(sum(r*n for r,n in before.items()) == sum(r*n for r,n in after.items()), 'rank mass changed') + word['report']['local_profile'] = dict(sorted(after.items())) + word['report']['status'] = 'COUPLED_FRAME_SEARCH_CANDIDATE_REQUIRES_PHASE_AND_GLOBAL_REPLAY' + payload = gzip.compress(json.dumps(word, sort_keys=True, separators=(',', ':')).encode(), mtime=0) + gain = exact_gain({r:after[r]-before[r] for r in before.keys() | after.keys()}) + result = dict(status='LOCAL_CANDIDATE' if gain > 1 else 'NO_GAIN_IN_BOUNDED_SEARCH', + source_sha256=hashlib.sha256(source).hexdigest(), output_sha256=hashlib.sha256(payload).hexdigest(), + parameters=dict(passes=args.passes, depth=args.depth, closure_limit=args.closure_limit, + lattice=args.lattice, neutral_rounds=args.neutral_rounds, seed=args.seed), + attempts=attempts, blocked=blocked, feasible=feasible, accepted_groups=len(trace), + neutral_moves=neutral_moves, + profile_before=dict(sorted(before.items())), profile_after=dict(sorted(after.items())), + entropy_saving=sum(r*(before[r]-after[r])*math.log(73/r) for r in before.keys() | after.keys()), + trace=trace, scope='Scalar word and frame chains only; phases, ownership bindings and exact assembly remain separate.') + args.out.mkdir(parents=True) + (args.out / 'FULL-WORD.json.gz').write_bytes(payload) + (args.out / 'SEARCH.json').write_text(json.dumps(result, indent=2) + '\n') + print(json.dumps({k:v for k,v in result.items() if k != 'trace'}, sort_keys=True), flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/search_suffix_kernels.py b/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/search_suffix_kernels.py new file mode 100644 index 0000000000..34c588349a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/larger_gain/providers/search_suffix_kernels.py @@ -0,0 +1,269 @@ +#!/usr/bin/env python3 +"""Exact bounded search for additional cold entrances in the PR564 word. + +This changes actual scalar donor gates and prices actual frame-chain splits. +It is a discovery screen, not a phase/hosting/recurrence certificate. +Prepared with OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +import copy +from fractions import Fraction as Q +from functools import lru_cache +import gzip +import hashlib +import importlib.util +import json +import math +from pathlib import Path +import sys +import time + + +@lru_cache(None) +def basis(vectors): + pivots = {} + for x in vectors: + for k in sorted(pivots, reverse=True): + if x >> k & 1: + x ^= pivots[k] + if x: + k = x.bit_length() - 1 + for j in pivots: + if pivots[j] >> k & 1: + pivots[j] ^= x + pivots[k] = x + return tuple(pivots[k] for k in sorted(pivots, reverse=True)) + + +@lru_cache(None) +def span(frame): + values = {0} + for x in frame: + values |= {y ^ x for y in values} + return frozenset(values) + + +def inside(a, b): + return basis(a + b) == b + + +def add(row, other, coefficient): + for key, value in other.items(): + new = row.get(key, Q(0)) + coefficient * value + if new: + row[key] = new + else: + row.pop(key, None) + + +def linear_basis(columns, donors): + result = {} + for donor in donors: + row = columns[donor].copy() + combination = {donor: Q(1)} + while row: + key = min(row) + if key not in result: + q = row[key] + row = {j: v / q for j, v in row.items()} + combination = {j: v / q for j, v in combination.items()} + result[key] = row, combination + break + q = row[key] + other, relation = result[key] + add(row, other, -q) + add(combination, relation, -q) + return result + + +def solve(column, eliminated): + row, answer = column.copy(), {} + while row: + key = min(row) + if key not in eliminated: + return None + other, relation = eliminated[key] + q = row[key] + add(row, other, -q) + add(answer, relation, q) + return answer + + +def frames(word, selected_part='B'): + size = 2 * len(word['ports']) + word['report']['R'] + full = basis(tuple(1 << j for j in range(word['report']['h']))) + current = [(p,) for p in word['ports']] + [()] * (size - len(word['ports'])) + for r, frame in word['start_extra'].items(): + current[int(r)] = basis(tuple(frame)) + first = {} + before = [] + for part in ('A', 'B'): + for index, event in enumerate(word[part]): + if part == selected_part: + before.append(current.copy()) + for r in event[1:3] if event[0] == 'add' else event[1:2]: + first.setdefault(r, (part, index, basis(tuple(event[-1])))) + current[r] = basis(tuple(event[-1])) + after, nxt = [None] * len(word[selected_part]), [full] * size + for index in reversed(range(len(word['B']))): + event = word['B'][index] + for r in event[1:3] if event[0] == 'add' else event[1:2]: + nxt[r] = basis(tuple(event[-1])) + if selected_part == 'B': + after[index] = nxt.copy() + if selected_part == 'A': + for register, frame in zip(word['centers'], word['center_frames']): + nxt[register] = basis(tuple(frame)) + for index in reversed(range(len(word['A']))): + event = word['A'][index] + for register in event[1:3] if event[0] == 'add' else event[1:2]: + nxt[register] = basis(tuple(event[-1])) + after[index] = nxt.copy() + return first, before, after + + +def entropy(delta): + return sum(n * r * math.log(r) for r, n in delta.items()) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--word', type=Path, required=True) + parser.add_argument('--gk-dir', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + parser.add_argument('--step', type=int, default=1) + parser.add_argument('--max-rank', type=int, default=2) + parser.add_argument('--part', choices=('A', 'B'), default='B') + parser.add_argument('--retain', type=int, default=12) + args = parser.parse_args() + assert __debug__ and args.step > 0 and 1 <= args.max_rank <= 3 + assert not args.out.exists() + args.out.mkdir(parents=True) + sys.path.insert(0, str(args.gk_dir.resolve())) + import gk_word as g + import gk_common as co + g.V = co.V = 112 + g.DATA = co.DATA = 7168 + raw = gzip.decompress(args.word.read_bytes()) + word = json.loads(raw) + original_profile = g.profile(word) + first, before, after = frames(word, args.part) + untouched = {r: data for r, data in first.items() + if r >= 224 and str(r) not in word['start_extra'] + and (args.part == 'A' or data[0] == 'B')} + options = {} + for r, (_, _, frame) in untouched.items(): + lines = sorted(span(frame) - {0}) + values = {(x,) for x in lines} + if args.max_rank >= 2: + values |= {basis((x, y)) for x in lines for y in lines if x != y} + if args.max_rank >= 3 and len(frame) <= 3: + values.add(frame) + options[r] = sorted(v for v in values if len(v) <= args.max_rank) + columns = [{} for _ in range(728)] + for target in range(112): + columns[112 + target] = {target: Q(1)} + if args.part == 'A': + for event in reversed(word['cut'] + word['B']): + if event[0] == 'add': + add(columns[event[2]], columns[event[1]], Q(event[3], event[4])) + else: + columns[event[1]] = {t: q * Q(event[2], event[3]) + for t, q in columns[event[1]].items()} + counts = Counter() + found = {} + start = time.monotonic() + last = max(data[1] if data[0] == args.part else len(word[args.part]) - 1 + for data in untouched.values()) + for index in reversed(range(len(word[args.part]))): + event = word[args.part][index] + if event[0] == 'add': + add(columns[event[2]], columns[event[1]], Q(event[3], event[4])) + else: + columns[event[1]] = {t: q * Q(event[2], event[3]) + for t, q in columns[event[1]].items()} + if index > last or index % args.step: + continue + cur, nxt = before[index], after[index] + for pivot, (first_part, first_index, first_frame) in untouched.items(): + if first_part == args.part and index > first_index: + continue + for frame in options[pivot]: + counts['exact_span_queries'] += 1 + donors = [r for r in range(728) if r != pivot and not 112 <= r < 224 + and columns[r] and inside(cur[r], frame) and inside(frame, nxt[r])] + # Prefer donors that avoid splitting a paid climb. This is only + # a basis choice; the existence test still uses every donor. + def score(r): + a, e, b = len(cur[r]), len(frame), len(nxt[r]) + delta = Counter({b - a: -1}) if b > a else Counter() + if e > a: + delta[e - a] += 1 + if b > e: + delta[b - e] += 1 + return -entropy(delta), r + donors.sort(key=score) + relation = solve(columns[pivot], linear_basis(columns, donors)) + if relation is None: + continue + counts['exact_relations'] += 1 + if any(q.denominator & (q.denominator - 1) for q in relation.values()): + counts['nondyadic_relations'] += 1 + continue + key = (pivot, frame, tuple(sorted(relation.items()))) + if key in found: + counts['duplicate_relations'] += 1 + continue + changed = copy.deepcopy(word) + gates = [['add', r, pivot, -q.numerator, q.denominator, list(frame)] + for r, q in sorted(relation.items())] + changed[args.part][index:index] = gates + changed['start_extra'][str(pivot)] = list(frame) + changed['cleanup'] = [g.inverse(e, g.FULL) + for e in reversed(changed['A'] + changed['B']) + if not 112 <= e[1] < 224] + profile = g.profile(changed) + delta = {r: profile[r] - original_profile[r] + for r in set(profile) | set(original_profile) + if profile[r] != original_profile[r]} + assert sum(r * n for r, n in delta.items()) == -len(frame) + changed['report']['local_profile'] = dict(profile) + # Optimistic global entropy credits released rank at a size-48 + # remainder. It screens candidates, never certifies hosting. + estimate = entropy(delta) + len(frame) * (1 + math.log(48)) + candidate = dict(part=args.part, index=index, pivot=pivot, frame=frame, + coefficients={str(r): str(q) for r, q in relation.items()}, + inserted_gates=len(gates), profile_delta=delta, + local_entropy_delta=entropy(delta), + optimistic_entropy_gain=estimate) + found[key] = (candidate, changed) + if index % 100 == 0: + print(json.dumps(dict(cut=index, queries=counts['exact_span_queries'], + found=len(found), seconds=time.monotonic() - start)), flush=True) + ordered = sorted(found.values(), key=lambda pair: (-pair[0]['optimistic_entropy_gain'], + pair[0]['inserted_gates'], pair[0]['pivot'])) + for index, (candidate, changed) in enumerate(ordered[:args.retain]): + name = 'candidate-%03d' % index + (args.out / (name + '.json')).write_text(json.dumps(candidate, indent=2) + '\n') + (args.out / (name + '.json.gz')).write_bytes(g.dump(changed)) + report = dict(status='PASS_EXACT_BOUNDED_SUFFIX_SCREEN', + source_sha256=hashlib.sha256(args.word.read_bytes()).hexdigest(), + source_content_sha256=hashlib.sha256(raw).hexdigest(), + part=args.part, cuts_step=args.step, max_frame_rank=args.max_rank, + untouched_pivots={str(r): data for r, data in untouched.items()}, + counts=dict(counts), distinct_relations=len(found), + candidates=[candidate for candidate, _ in ordered], + seconds=time.monotonic() - start, + scope='Exact rational span test over all currently frame-compatible non-target donors; ' + 'one deterministic cost-ordered donor basis per pivot/frame/cut. ' + 'Rank limit and selected part are explicit. Nondyadic bases are skipped, ' + 'not proofs of absence of another dyadic solution. New words require ' + 'native, phase, owner, invoice and moment admission.') + (args.out / 'SEARCH.json').write_text(json.dumps(report, indent=2) + '\n') + print(json.dumps(dict(status=report['status'], distinct_relations=len(found), + counts=dict(counts), seconds=report['seconds'])), flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/LICENSE b/research/pr643-improvement-20261013/witness/vendor/multicold/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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--- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/MANIFEST.json @@ -0,0 +1,210 @@ +{ + "code/assemble.py": "3fedbccb09d469f8ee366b4302e51448de6d25793a78a12c5f9a8d9667a755eb", + "code/assembly_controls.py": "a0f2349ba8fe8404b8b76c869f12dd7e250a775b2e05b3c9c00e6889ad4c8a45", + "code/audit_allcold.py": "7950e5c01488a9146bdbaf19ab4fd0c33cd25a4d63fb56ef995ef2e45ac7ec1a", + "code/audit_kernel_controls.py": "5100459211f43ba048bf82c3942bbedb8b224272b24722a14f0dcd808a38aafa", + "code/audit_multicold_controls.py": "3ff631f0bdc7e707d4296ff441802cc26da9c6556650469f09ab7253558b4017", + "code/bind_providers_portable.py": "01e62fee1f1dcf1b7b34338d555dacd5cd1d7d10d6b9a605d0913d959f8c7ecf", + "code/build_cold_kernel.py": "aa556a1988f7d4c52bd82fd2a648769f7094bd75ba79582c15ec441d710e213b", + "code/build_four_portable.py": "417b1dc4dca485dfbbaa820e552cae9bf3932bbace6ea16ce93aa0590c3c184e", + "code/build_multicut_kernels.py": 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"1a0e92f610f96a5e642310a2823b152cf573c0d1630b9c174fcc8388d1ffd2a2" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/NOTICE.md b/research/pr643-improvement-20261013/witness/vendor/multicold/NOTICE.md new file mode 100644 index 0000000000..9e71745270 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/NOTICE.md @@ -0,0 +1,17 @@ +# Attribution and scope + +The seven multi-cut cold kernels, their constructor and omission audit, the new literal owner assignment, the rebinding of all three providers and this package were prepared by the WidthScreen and ReopenLoop research agents with Claude Code (Anthropic) assistance. They extend eumemic/Codex PR564 (`research/complex-allcold`, head `c18417b02b80594b2ca1c8c21185d28befafc935`), which remains frozen and is not modified by this package. The owner allocator adapts higherbeing's open allocator (`research/complex-delivery-map-open-allocator`, CP-SAT aggregate model with Hall conditions). The per-pattern edge colouring follows the realization script in `research/experiment-log/negative-searches/partial-own-coordinated`. Neither tool is an admission dependency. Apache-2.0 applies; LICENSE is included. + +The notice of the PR564 package follows unchanged. + +# Attribution and scope + +The all-call cold-kernel composition, literal owner assignment, independent admission, packaging and exact assembly were prepared for eumemic with OpenAI Codex assistance. Apache-2.0 applies; LICENSE is included. No independent human-authorship or unconditional all-size theorem claim is made. + +This work combines eumemic/Codex PR561's cold-kernel word and mixed controller, head `210dfa4896e77a8fb5e22ca5a970b0fb0ac984a6`, with PR562's zero/four/eight provider construction and admission, head `27070553cfbf094148a74170481738f8b747d82e`. Their notices are copied at `proof/PR561-NOTICE.md` and `proof/PR562-NOTICE.md`. New owner assignments and all three complete cold native providers are verified independently here. All previous public heads and claims remain frozen. + +Full unchanged source packages of PR558 (`060b137c8a6f9d73fd7864c7f8cf2736d6441774`) and Rohan Arun's PR559 (`d858c0b2edcc704ef370b3c96dc51a75439b77b0`) are retained in vendor/. Their licenses, source pins, original authorship and AI disclosures are preserved. The native exact-complex recurrence credits PR559; its transfer to this all-call cold controller is reviewed separately. + +The retained ancestry includes Dugongue PR552, chafreaky PR551, icekylinx PR531/PR535, PR484/PR507/PR514 whole-owner/controller work, eumemic/Codex PR550, and the PR275 finite-frontier assembly. Original notices credit DreamingOfClouds with Claude Opus 5.5 through Claude Code, icekylinx with OpenAI Codex assistance, and Rohan Arun's earlier Claude and current Codex work. They are not replaced by this notice. + +The unchanged PR543 bit supplier is cited at `2065fe4f72a914d907f1046603f5a36f17018535`; its pinned complete profile is repriced but no fresh bit-circuit replay is claimed. Original Clifford and three-stage cover notes were reviewed at `12a4934d15006e8c10f9b2264f13f8f341be802b`. All inherited common-label/mutable-source, compiler, hosting, precision/tape, analytic and bit H1–H5 contracts remain conditional. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/README.md b/research/pr643-improvement-20261013/witness/vendor/multicold/README.md new file mode 100644 index 0000000000..28e72fb0a0 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/README.md @@ -0,0 +1,44 @@ +# Eight cold helpers in every complete complex invocation + +κ = 0.001596133352130093 (conditional). + +The complex supplier has b = 0.00159868506668458107128. The unchanged cited PR543 bit cap is c = 0.001653826988146798944268, so complex binds. A separately verified conservative complex model yields κ = 0.001596133349380077. The gain over PR564 (κ = 0.001593134158181640) is 2.999e-6, or 0.188%. + +PR564 made one helper per call cold: helper 270 enters at rank one, so its residual width drops from nine to eight. This package adds seven more cold helpers to every provider. Each one is killed by a *multi-cut* kernel: its donor gates `donor += -q·pivot @E` sit at different cuts rather than at one cut. The pivot holds only its initial dirt until its first original touch, so the gates cancel its complete dirty response if and only if an exact dyadic relation holds among the donor columns at their cuts. + +- Helper-donor kernels: helpers 282, 294 and 306 (registers 506@[24], 518@[30], 530@[30]). Each uses four or five gates on helper donors, one of which is another B-first helper split at its first frame. Each changes the local profile by `{1:+1,2:+2,3:-2}`. +- Target-donor kernels: helpers 271, 283, 295 and 307 (registers 495@[24], 507@[24], 519@[30], 531@[30]). Each uses three B-part gates: two on output targets, like the post-centre gauge compensation, and one on a B-first partner. Each changes the local profile by `{1:+3,2:+1,3:-2}`. + +Every B-first width-nine helper needs another B-first helper as its split donor, so this family has at most 16/2 = 8 cold helpers per word. All eight are used. + +All 72 calls keep PR564's dispatch: 15 zero-pivot, two four-pivot and 55 eight-pivot words. All three now carry the eight cold helpers. With p promoted pivots: + +- The width inventory is `{4:p, 5:56-p, 8:164, 9:284}`. +- The local paid profile is `e1·(2316+2p) + e2·(452-2p) + e3·(456-p) + e4·(184+p) + 56e5 + 56e6 + 8e8`. +- There are 220 entering helpers, and the entrance rank is 388+p. + +A new literal owner assignment realizes the inventory. It was found with an aggregate CP-SAT model with per-call Hall conditions, adapted from the open allocator in `research/complex-delivery-map-open-allocator`, then a per-pattern Kőnig edge colouring. Its idle profile is `{1:93,2:93,3:2118,7:1,48:1713}`, against PR564's `{3:2364,7:172,48:1668}`. + +The complete paid profile is `{1:167741,2:31741,3:34502,4:13696,5:4032,6:4032,7:1,8:576,48:1713}`. It is reconstructed from both actual reflected scalar event lists and the complete physical controller. All 36,288 helpers have one whole owner, with no auxiliary banks. The audit checks 3,209 orthogonal chart types, 27,679 cross-replica roles and 4,018 positive idle remainders. Live stock is 7168, physical stock 7682, rank mass 520704 and deficit 2560. + +Run it with standard-library Python 3 and a fresh output directory outside this source package: + +```sh +python3 -B verify.py --work /tmp/multicold-replay +``` + +Assertions must remain enabled. The verifier: + +- Fully reconstructs frozen PR558 and the four-pivot source. +- Rebuilds PR564's three one-cold words with their six cold-kernel omission controls each. +- Applies the seven frozen multi-cut kernels to each word. It checks exact zero complete dirty response by forward replay, legal frame chains and the pinned profile delta, and runs 32 omission controls per provider (every new gate alone and every whole kernel, in both exact orientations). +- Re-runs, on each final word, the inherited 44-kernel and four/eight promotion omission audits. +- Checks all 728 scalar columns in both orientations, all 504 arbitrary dirty helpers restored, both reflected ledgers, all 2929 exact phase edges and 224 endpoint adapters per provider, and the normalized wrappers. +- Binds the three fresh native providers and checks the complete physical assignment with 16 controller mutants. +- Emits a fresh complete finite invoice and checks both exact recurrence/assembly models with 54 malformed-receipt controls. + +The fresh invoice charges 11,598,720 scalar primitives, 5,743,456 coefficient-work primitives and 4,561,920 elementary wrapper factors. Prefix 225 is below 512; the physical row coefficient 16,467 is below 20,161. Full group/router, adapter, literal, mass, precision, tape, idle and all-size obligations remain charged. Two rational moment engines reject the adjacent supplier endpoint, and both models pass seven bootstrap levels and 47 strict outer constraints with next-grid and parameter controls. + +The native complex moment credits rohanarun's PR559 exactly as in PR564. Only the generic complex bad-residue surcharge is omitted; the conservative witness is verified first, and the PR543 bit fallback remains. + +This remains conditional on the inherited all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, analytic transfer and PR543 H1–H5 assumptions. Finite exact replay is not an unconditional theorem, a full Lean proof or a practical speed claim. 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"aa556a1988f7d4c52bd82fd2a648769f7094bd75ba79582c15ec441d710e213b", + "git_blob_sha1": "e77f484b90fdfbc461537fed2efdc205dfcbd98f" + } + }, + "derivations": { + "controller": "PR562 and PR561 mixed providers adapted to three one-cold providers and new literal owner assignment.", + "invoice": "Fresh actual-provider recount based on preserved PR531/PR561/PR562 lineage.", + "assembly": "Both retained rational engines and outer engine; native recurrence credits PR559; new complete-profile and receipt admission.", + "recipes": "Zero/four cold recipes recomputed on the actual promoted words; eight uses frozen PR561 recipe." + }, + "disclosure": "Prepared with OpenAI Codex assistance; all prior notices, licenses and AI disclosures retained." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/assemble.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/assemble.py new file mode 100644 index 0000000000..fbdb655e1e --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/assemble.py @@ -0,0 +1,206 @@ +"""Hardened all72 one-cold three-provider 0/4/8 assembly with the native exact-complex moment. + +Prepared with OpenAI Codex assistance. The rational engines and outer +constraints are retained from PR547/PR548 and their preserved ancestry. +The bit operator is the cited unchanged PR543 supplier. The complex owner +and invoice inputs must be freshly emitted by the packaged physical replay. +All conservative admission guards and conservative moment/outer witnesses run +before the PR559 native-complex correction. The bit surcharge is retained. +""" +from pathlib import Path +from fractions import Fraction as Q +from decimal import Decimal, localcontext +import argparse,json,hashlib,importlib.util +from collections import Counter +assert __debug__, 'Assertions required' +P=Path(__file__).resolve().parent.parent +read=lambda p:json.loads(p.read_text()) +sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +hash_ok=lambda x:isinstance(x,str) and len(x)==64 and all(t in '0123456789abcdef'for t in x) +digest=lambda x:hashlib.sha256(json.dumps(x,separators=(',',':')).encode()).hexdigest() +def load(n): + s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +M,B,A=[load(n)for n in ('moment','base_two_moment','outer')] +def dec(x): + with localcontext()as ctx:ctx.prec=70;return str(Decimal(x.numerator)/Decimal(x.denominator)) +PROVIDERS={'rank5_eight_cold': {'semantic_phase_sha256': 'ac32ac4b9cd18a383df1b28c9e2a06389e57d75d8e1e1454ab0adeeb97ad7cec', 'promoted': 8, 'width_digest': 'c981156345ace92e314d8a14d5991f5a0fe60275baef0894311b568bc81a166d', 'program_hashes': {'backward': '9a28d43dfc68e4f9af4e3b0b261000971fe4e6e16260ee09c9e92f4ad048370f', 'forward': 'de1b6c0c8cd6bcebaab701bff3d24363e27b5c3e09ee48f5842dba666bcabcec'}, 'artifacts': {'CANONICAL-WORD.json.gz': '94dba75199d70b744be5604386b8eca6767f0b0e1aeee06b2bd0e4e1db858940', 'LOCAL-PROGRAMS.json.gz': 'c4581db41fd2a07aa82655a07c0c4bb041b7f5ae96ef11d4cd33294dc66022f7', 'LOCAL-CHECKS.json': '57b8a93866ebfb23b81225264229742a980ab60b7dd6ff1df014ba43c8d0ead8', 'INDEPENDENT-LOCAL-REPLAY.json': '05a6ff6313baf97f9a2a4be1abcf502919912643b2f9be40a8ad566059e84da2', 'CLIFFORD-RECIPES.json': 'b32e904cac5f4ac2b9a80a50dfd112ced1e44a2eab1ee24149c501f0d6979748', 'RESIDUAL-ADAPTERS.json': 'baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275'}}, 'rank5_four_cold': {'semantic_phase_sha256': '309e6f87773cadac4d9b5dc487b5f4e5a2a5e325be4c71914fc87bd6f704a25f', 'promoted': 4, 'width_digest': '6aaea7c35332e8125a696c83168cc0b9a2eac0522981c4d4a51d389895651a6b', 'program_hashes': {'backward': '6d9e3f75b3d0dc0c9d823b3a384cd017d6e5a545f311fcd6492c765150343bbd', 'forward': 'ca1620641c24cb27ebede47be1de72d56aba33992cc0836a0a85708869731b6e'}, 'artifacts': {'CANONICAL-WORD.json.gz': 'f9a70b887fe3ae0eb179bc55d67ad6cf02c6aee3b8018831ba63f9c6aa910e34', 'LOCAL-PROGRAMS.json.gz': 'ed06ac327779d03561b5617ef4dd6c380c9a861fe64e227b348bf9b1699846c2', 'LOCAL-CHECKS.json': 'dd0468946f78090a686fc40825337cb2a4fba7a9d16fb746d28e7ee57c40c484', 'INDEPENDENT-LOCAL-REPLAY.json': '46a90f09fd73b537c6e13cf3aa7b45507ce137781c6519c8c3850630513c4057', 'CLIFFORD-RECIPES.json': '54bd631952843286d5e60d1faeadd25450156c66a2a31277d4d8d4cdcc29547f', 'RESIDUAL-ADAPTERS.json': 'ddeab3b37b16eca2c90c2a8d4afa124e86b611319c8f0a9632bfefbaa7667a0e'}}, 'rank5_zero_cold': {'semantic_phase_sha256': '85fddde1d9c2b3adc304469363813d36847cc211a8e8bab599c5320d1013cda7', 'promoted': 0, 'width_digest': 'd9a77d61f35ee60461f24a8fef1b76479688bb49c0a61a46342599a6fef9346f', 'program_hashes': {'backward': '58bade4d6398856987fa0ec9c2e86fe255aa3a0a5ae4486fe144da8790ccd71a', 'forward': '0aaf8bdcbc9d069897d63af3e7d0c221bfce22fc087595993118427a23ad54ee'}, 'artifacts': {'CANONICAL-WORD.json.gz': '0e5ee1dcdede94e34693340b0ada9063af107f86fcf90b2b99b63cfcb2ba0940', 'LOCAL-PROGRAMS.json.gz': '4681802b1948ad1f7689e770afca5801419487e012e359c59aaff5645dd2ae29', 'LOCAL-CHECKS.json': 'a545ee98750f79cb7c02c5a5b05a64b1ae5873ed489c302a4d969b5851591d80', 'INDEPENDENT-LOCAL-REPLAY.json': '8dffb8de35e53454f319443b0fd9413306c222e6bfcf2734c1f854b7a3f9db44', 'CLIFFORD-RECIPES.json': '7f5c487e420e44c2070fcfe252be7fddd6c7ef6193b347d1984b6150392f333a', 'RESIDUAL-ADAPTERS.json': 'e4fce8ca73ad20a86711837dd6fe1efad5a335689352791a635969e4d1be4391'}}} +DISPATCH={(0, 0): 'rank5_eight_cold', (0, 1): 'rank5_eight_cold', (1, 0): 'rank5_eight_cold', (0, 2): 'rank5_eight_cold', (1, 1): 'rank5_eight_cold', (2, 0): 'rank5_eight_cold', (0, 3): 'rank5_eight_cold', (1, 2): 'rank5_eight_cold', (2, 1): 'rank5_eight_cold', (3, 0): 'rank5_eight_cold', (0, 4): 'rank5_eight_cold', (1, 3): 'rank5_eight_cold', (2, 2): 'rank5_eight_cold', (3, 1): 'rank5_eight_cold', (4, 0): 'rank5_eight_cold', (0, 5): 'rank5_eight_cold', (1, 4): 'rank5_eight_cold', (2, 3): 'rank5_eight_cold', (3, 2): 'rank5_eight_cold', (4, 1): 'rank5_eight_cold', (5, 0): 'rank5_eight_cold', (0, 6): 'rank5_eight_cold', (1, 5): 'rank5_eight_cold', (2, 4): 'rank5_eight_cold', (3, 3): 'rank5_eight_cold', (4, 2): 'rank5_eight_cold', (5, 1): 'rank5_eight_cold', (0, 7): 'rank5_eight_cold', (6, 0): 'rank5_eight_cold', (1, 6): 'rank5_eight_cold', (2, 5): 'rank5_eight_cold', (3, 4): 'rank5_eight_cold', (4, 3): 'rank5_eight_cold', (5, 2): 'rank5_eight_cold', (6, 1): 'rank5_eight_cold', (1, 7): 'rank5_eight_cold', (7, 0): 'rank5_eight_cold', (2, 6): 'rank5_eight_cold', (3, 5): 'rank5_eight_cold', (4, 4): 'rank5_eight_cold', (5, 3): 'rank5_eight_cold', (6, 2): 'rank5_zero_cold', (7, 1): 'rank5_eight_cold', (2, 7): 'rank5_eight_cold', (8, 0): 'rank5_eight_cold', (3, 6): 'rank5_zero_cold', (4, 5): 'rank5_four_cold', (5, 4): 'rank5_eight_cold', (6, 3): 'rank5_eight_cold', (7, 2): 'rank5_zero_cold', (8, 1): 'rank5_eight_cold', (3, 7): 'rank5_eight_cold', (4, 6): 'rank5_zero_cold', (5, 5): 'rank5_zero_cold', (6, 4): 'rank5_eight_cold', (7, 3): 'rank5_eight_cold', (8, 2): 'rank5_zero_cold', (4, 7): 'rank5_zero_cold', (5, 6): 'rank5_eight_cold', (6, 5): 'rank5_eight_cold', (7, 4): 'rank5_zero_cold', (8, 3): 'rank5_zero_cold', (5, 7): 'rank5_zero_cold', (6, 6): 'rank5_eight_cold', (7, 5): 'rank5_four_cold', (8, 4): 'rank5_zero_cold', (6, 7): 'rank5_zero_cold', (7, 6): 'rank5_zero_cold', (8, 5): 'rank5_zero_cold', (7, 7): 'rank5_eight_cold', (8, 6): 'rank5_eight_cold', (8, 7): 'rank5_zero_cold'} +CALL_ORDER=[(0, 0), (0, 1), (1, 0), (0, 2), (1, 1), (2, 0), (0, 3), (1, 2), (2, 1), (3, 0), (0, 4), (1, 3), (2, 2), (3, 1), (4, 0), (0, 5), (1, 4), (2, 3), (3, 2), (4, 1), (5, 0), (0, 6), (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (0, 7), (6, 0), (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1), (1, 7), (7, 0), (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1), (2, 7), (8, 0), (3, 6), (4, 5), (5, 4), (6, 3), (7, 2), (8, 1), (3, 7), (4, 6), (5, 5), (6, 4), (7, 3), (8, 2), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (5, 7), (6, 6), (7, 5), (8, 4), (6, 7), (7, 6), (8, 5), (7, 7), (8, 6), (8, 7)] +def assemble(owner,invoice,owner_sha,invoice_sha): + # These are admission receipts, not optional collections of successful rows. + # Require both orientations and every finite check before pricing anything. + assert owner['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE' + assert invoice['status']=='PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE' + assert all(hash_ok(x)for x in (owner_sha,invoice_sha,owner['template_sha256'],owner['controller_audit_sha256'],invoice['parent_template_sha256'])) + checks={'local_primitive_bound','logical','router','literal','mass','precision','tape','row','halving'} + assert set(invoice['strict_checks'])==checks + assert all(invoice['strict_checks'][name] is True for name in checks) + assert set(invoice['providers'])==set(PROVIDERS) + assert invoice['provider_counts']=={'rank5_eight_cold':55,'rank5_zero_cold':15,'rank5_four_cold':2} + assert owner['all_live_owners_per_call_distinct'] is True + assert owner['owners_per_call']==728 and owner['actual_helper_owner_charts']==36288 + assert owner['rank_mass']==520704 + assert owner['actual_73column_sigmas']==3209 and owner['cross_replica_helper_roles']==27679 + assert owner['explicit_idle_remainder_children']==4018 + assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==72 + assert invoice['live']==owner['live'] and invoice['physical']==owner['physical'] + assert invoice['helpers']==504 and invoice['centres']==8 + assert invoice['physical_stock_identity']==dict(data_and_owner_families=7168,local_helpers=504,private_centres=8,coefficient_work=2) + assert sum(invoice['physical_stock_identity'].values())==invoice['physical'] + assert invoice['controller_audit_sha256']==owner['controller_audit_sha256'] + for pid,p in invoice['providers'].items(): + promoted=PROVIDERS[pid]['promoted'] + assert set(p['local'])=={'forward','backward'} + assert p['helpers']==504 and p['centres']==8 and p['n']==728 and p['v']==112 and p['h']==9 + assert p['entering_helpers']==220 and p['entrance_rank']==388+promoted + assert p['width_inventory']=={str(r):n for r,n in {4:promoted,5:56-promoted,8:164,9:284}.items()if n} + assert all(type(w) is int and 00 + assert prior['added_complete_new_pervertex']==pervertex + assert prior['policy']=='Retain old allowance and add entire fresh mixed recount.' + used=max(used,prior['previous_pervertex_allowance']+pervertex) + assert invoice['conservative_pervertex_used']==used + finite=invoice['finite'] + assert 02*48*48) + assert actual_checks==invoice['strict_checks'] and all(actual_checks.values()) + bit_path=P/'inputs/PR543-EXPECTED.json';bit_data=bit_path.read_bytes() + assert hashlib.sha1(b'blob '+str(len(bit_data)).encode()+b'\0'+bit_data).hexdigest()=='b61d859826246e0c3dabbe096e57ad7015eadfd5' + bit=json.loads(bit_data)['nine'] + c=Q(bit['bit_lower']);conservative_b=Q('0.001598685063925764864431');b=Q('0.00159868506668458107128') + expected={1:167741,2:31741,3:34502,4:13696,5:4032,6:4032,7:1,8:576,48:1713} + H={int(r):n for r,n in owner['paid_profile'].items()};assert H==expected + assert owner['template_sha256']==invoice['template_sha256'] and owner_sha==invoice['owner_audit_sha256'] + assert owner['live']==7168 and owner['physical']==7682 and owner['deficit']==2560 + assert owner['hosted_residuals']==36288 and owner['banked_residuals']==0 + def check_moment(side,h,m,W,lower,deficit,bad): + assert m*W-sum(r*n for r,n in h.items())==deficit and m*m>2*max(h)**2 + rows=[] + for z,accept in [(lower,True),(lower+Q(1,10**24),False)]: + l,u=M.moment(h,m,W,z,bad);ll,uu=B.moment(m,W,list(h.items()),z) + if bad: + fl,fu=B.moment(m,W,[(1,32*m*m*sum(h.values()))],z);ll+=fl/10**16;uu+=fu/10**16 + assert (u<1 and uu<1)if accept else(l>1 and ll>1) + rows.append(dict(side=side,surcharge=bad,endpoint=str(z),accept=accept,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)])) + return rows + bitH={int(r):n for r,n in bit['profile'].items()} + bit_moments=check_moment('bit',bitH,64,bit['bit']['live'],c,9984,True) + conservative_moments=check_moment('conservative_complex',H,73,owner['live'],conservative_b,2560,True) + assert bit['bit']['two_level_coefficient_bits']0 + ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512) + cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a) + q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18) + bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}} + outer=A.assembly(chain[-1],bb,bridge,k,eta=eta,beta=beta);assert len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values()) + controls=[] + for name,kk,ee,be in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]: + try:A.assembly(chain[-1],bb,bridge,kk,eta=ee,beta=be) + except AssertionError:controls.append(name) + else:raise AssertionError(name) + return k,cuts,outer,controls + conservative_k,conservative_cuts,conservative_outer,conservative_controls=outer_witness(conservative_b) + assert conservative_k==Q('0.001596133349380077') + # Only after every conservative supplier/admission/outer check succeeds is + # the reviewed native exact-complex recurrence selected. Bit charge stays. + native_moments=check_moment('complex',H,73,owner['live'],b,2560,False) + k,cuts,outer,controls=outer_witness(b) + assert k==Q('0.001596133352130093') + assert M.moment(H,73,owner['live'],b,True)[0]>1 + assert M.moment(bitH,64,bit['bit']['live'],c+Q(1,10**24),False)[1]<1 + model_controls=['native_complex_endpoint_rejected_with_old_surcharge','omitting_bit_surcharge_would_fail_next_endpoint_rejection'] + moments=bit_moments+native_moments + input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'inputs/PR543-EXPECTED.json':sha(bit_path)} + input_hashes.update({'engines/'+name+'.py':sha(P/'engines'/(name+'.py'))for name in ('moment','base_two_moment','outer')}) + return dict(status='PASS_FRESH_MIXED_048_ALLCOLD_NATIVE_EXACT_ASSEMBLY',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex',gain_over_pinned558_percent=dec(100*(k/Q('0.001592517889315014')-1)),complex_profile=H,provider_counts=invoice['provider_counts'],surcharge_model={'complex':False,'bit':True},conservative_complex_lower=str(conservative_b),conservative_complex_decimal=dec(conservative_b),conservative_kappa=str(conservative_k),conservative_kappa_decimal=dec(conservative_k),conservative_moments=conservative_moments,conservative_bootstrap=conservative_cuts,conservative_outer={n:str(v)for n,v in conservative_outer['strict_constraints'].items()},conservative_controls=conservative_controls,model_controls=model_controls,native_correction_gain=dec(k-conservative_k),template_sha256=owner['template_sha256'],input_sha256=input_hashes,bit_supplier=dict(pr=543,repository='eumemic/integer-mult-bounds',commit='2065fe4f72a914d907f1046603f5a36f17018535',path='research/e8-bit-r420/EXPECTED.json',git_blob_sha1='b61d859826246e0c3dabbe096e57ad7015eadfd5',replay_scope='Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit.'),moments=moments,bootstrap=cuts,outer={n:str(v)for n,v in outer['strict_constraints'].items()},controls=controls,scope='Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. Three fixed one-cold per-invocation providers composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.') +if __name__=='__main__': + import sys + package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists() + owner_path=C/'audit/OWNERS-AND-PROFILE.json';invoice_path=C/'audit/PREFIX-AND-INVOICE.json' + owner,invoice=read(owner_path),read(invoice_path) + assert owner['template_sha256']==read(C/'hosted/HOSTED.json')['template_sha256'] + r=assemble(owner,invoice,sha(owner_path),sha(invoice_path));out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],r['kappa_decimal']) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/assembly_controls.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/assembly_controls.py new file mode 100644 index 0000000000..b81574bfb6 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/assembly_controls.py @@ -0,0 +1,242 @@ +"""Independent admission controls for the three-provider native-complex assembly. + +Prepared with OpenAI Codex assistance; Apache-2.0. Mutation receipts are +rebound to their new owner digest, so unrelated stale hashes cannot conceal +an incomplete width, provider, orientation, paid-profile or finite check. +The fresh physical replay remains a separate prerequisite. +""" +import argparse +import copy +import hashlib +import json +from pathlib import Path +from assemble import assemble + +assert __debug__, 'Assertions required' +P = Path(__file__).resolve().parent +sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest() +digest = lambda x: hashlib.sha256(json.dumps(x, sort_keys=True, separators=(',', ':')).encode()).hexdigest() + + +def verify(owner_path, invoice_path): + owner = json.loads(owner_path.read_text()) + invoice = json.loads(invoice_path.read_text()) + baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path)) + + def empty_maps(o, i): + i['strict_checks'] = {} + i['providers'] = {} + + def missing_backward(o, i): + del i['providers']['rank5_four_cold']['local']['backward'] + + def understated_stock(o, i): + o['physical'] -= 1 + i['physical'] -= 1 + i['physical_stock_identity']['coefficient_work'] -= 1 + + def changed_profile(o, i): + o['paid_profile']['1'] += 2 + o['paid_profile']['2'] -= 1 + + def changed_widths(o, i): + widths = i['providers']['rank5_eight_cold']['widths'] + a, b = widths.index(4), widths.index(9) + widths[a] += 1 + widths[b] -= 1 + + def permuted_widths(o, i): + widths = i['providers']['rank5_eight_cold']['widths'] + a, b = widths.index(4), widths.index(9) + widths[a], widths[b] = widths[b], widths[a] + + def compensating_profiles(o, i): + # The two dishonest profiles cancel exactly in the 55+2 weighted aggregate. + p, q = i['providers']['rank5_eight_cold'], i['providers']['rank5_four_cold'] + p['paid_profile']['1'] += 2 + q['paid_profile']['1'] -= 55 + p['children'] += 2 + q['children'] -= 55 + + def wrong_orientation(o, i): + c = next(c for c in i['selected_calls'] if c['stage'] == 0) + c['orientation'] = 'backward' + p = i['providers'][c['provider_id']] + z = p['local']['backward'] + c['program_sha256'] = p['program_hashes']['backward'] + for name in ('events', 'macros', 'real_component_primitives', + 'coefficient_work_primitive_count', 'pre_wrappers', 'post_wrappers'): + c[name] = z[name] + i['selected_real_component_primitives'] = sum(c['real_component_primitives'] for c in i['selected_calls']) + i['selected_coefficient_work_primitive_count'] = sum(c['coefficient_work_primitive_count'] for c in i['selected_calls']) + + def forged_program_hash(o, i): + i['providers']['rank5_four_cold']['program_hashes']['forward'] = '0' * 64 + for c in i['selected_calls']: + if c['provider_id'] == 'rank5_four_cold': + c['program_sha256'] = '0' * 64 + + def wrong_selected_call(o, i): + c = next(c for c in i['selected_calls'] if c['provider_id'] == 'rank5_four_cold') + d = next(c for c in i['selected_calls'] if (c['stage'], c['replica']) == (4, 4)) + c['replica'], d['replica'] = d['replica'], c['replica'] + + def understated_prefix(o, i): + for p in i['providers'].values(): + for z in p['local'].values(): + z['prefix_bits'], z['prefix_l1'] = 1, '1' + i['global_prefix_bits'] = 1 + 37 + 72 + 72 + 4 + + def stale_zero_program(o, i): + p = i['providers']['rank5_zero_cold'] + p['program_hashes'] = copy.deepcopy(i['providers']['rank5_eight_cold']['program_hashes']) + for c in i['selected_calls']: + if c['provider_id'] == 'rank5_zero_cold': + c['program_sha256'] = p['program_hashes'][c['orientation']] + + def moved_providers(o, i): + a = next(c for c in i['selected_calls'] if (c['stage'], c['replica']) == (4, 5)) + b = next(c for c in i['selected_calls'] if (c['stage'], c['replica']) == (4, 4)) + a['provider_id'], b['provider_id'] = b['provider_id'], a['provider_id'] + for c in (a, b): + p = i['providers'][c['provider_id']] + c['program_sha256'] = p['program_hashes'][c['orientation']] + c['entering_helpers'], c['entrance_rank'] = p['entering_helpers'], p['entrance_rank'] + + def reordered_calls(o, i): + i['selected_calls'][0], i['selected_calls'][1] = i['selected_calls'][1], i['selected_calls'][0] + + def permuted_four_widths(o, i): + widths = i['providers']['rank5_four_cold']['widths'] + a, b = widths.index(4), widths.index(5) + widths[a], widths[b] = widths[b], widths[a] + + def stale_zero_profile(o, i): + p = i['providers']['rank5_zero_cold'] + p['paid_profile'] = copy.deepcopy(i['providers']['rank5_eight_cold']['paid_profile']) + p['children'] = sum(p['paid_profile'].values()) + + controls = [ + ('empty_certification_maps', empty_maps), + ('missing_provider_backward_orientation', missing_backward), + ('failed_invoice_status', lambda o, i: i.__setitem__('status', 'FAIL')), + ('nonboolean_precision_check', lambda o, i: i['strict_checks'].__setitem__('precision', 'true')), + ('wrong_owner_role_count', lambda o, i: o.__setitem__('actual_helper_owner_charts', 36287)), + ('understated_physical_stock', understated_stock), + ('changed_profile_same_rank_mass', changed_profile), + ('insufficient_finite_C0', lambda o, i: i['finite'].__setitem__('required_C0_bits', 210001)), + ('unpaid_scalar_primitive', lambda o, i: i['providers']['rank5_four_cold']['local']['forward'].__setitem__('real_component_primitives', 161064)), + ('wrong_local_artifact_binding', lambda o, i: i['providers']['rank5_four_cold']['artifacts'].__setitem__('LOCAL-PROGRAMS.json.gz', '0' * 64)), + ('false_dirty_restoration', lambda o, i: i['providers']['rank5_four_cold']['local']['backward'].__setitem__('all_dirty_helper_columns_restored', False)), + ('missing_finite_check', lambda o, i: i['strict_checks'].pop('halving')), + ('width_inventory_wrong_same_total', changed_widths), + ('width_order_wrong_same_inventory', permuted_widths), + ('compensating_false_provider_profiles', compensating_profiles), + ('wrong_reflected_orientation_selfconsistent_totals', wrong_orientation), + ('forged_provider_and_call_program_hash', forged_program_hash), + ('four_provider_at_wrong_call', wrong_selected_call), + ('wrong_declared_provider_count', lambda o, i: i['provider_counts'].__setitem__('rank5_four_cold', 3)), + ('missing_selected_call', lambda o, i: i['selected_calls'].pop()), + ('wrong_selected_primitive_sum', lambda o, i: i.__setitem__('selected_real_component_primitives', i['selected_real_component_primitives'] - 1)), + ('wrong_selected_coefficient_work_sum', lambda o, i: i.__setitem__('selected_coefficient_work_primitive_count', i['selected_coefficient_work_primitive_count'] - 1)), + ('unpaid_wrapper_factors', lambda o, i: i.__setitem__('wrapper_elementary_factors_charged', i['wrapper_elementary_factors_charged'] - 144)), + ('wrong_local_compiler', lambda o, i: i['providers']['rank5_four_cold'].__setitem__('compiler', 1)), + ('wrong_global_compiler', lambda o, i: i.__setitem__('compiler', 1)), + ('wrong_local_adapter_charge', lambda o, i: i['providers']['rank5_four_cold'].__setitem__('local_adapters', 1)), + ('wrong_global_adapter_maximum', lambda o, i: i.__setitem__('local_adapters', 1)), + ('wrong_local_primitive_bound', lambda o, i: i['providers']['rank5_four_cold'].__setitem__('local_primitive_bound', 1)), + ('understated_exact_prefix_and_global_sum', understated_prefix), + ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)), + ('wrong_row_prefix_reserve', lambda o, i: i.__setitem__('row_prefix_extra', 0)), + ('wrong_parent_geometry_charge', lambda o, i: i.__setitem__('unhosted_pervertex', 1)), + ('wrong_rebased_geometry_charge', lambda o, i: i.__setitem__('hosted_rebased_pervertex', 1)), + ('wrong_complete_pervertex_envelope', lambda o, i: i.__setitem__('conservative_pervertex_used', 1)), + ('wrong_prior_added_complete_invoice', lambda o, i: i['retained_prior_overcharge'].__setitem__('added_complete_new_pervertex', 1)), + ('wrong_finite_router_bits', lambda o, i: i['finite'].__setitem__('router_bits', 1)), + ('wrong_finite_literal_bits', lambda o, i: i['finite'].__setitem__('literal_bits', 1)), + ('wrong_finite_physical_stock_bits', lambda o, i: i['finite'].__setitem__('physical_stock_bits', 1)), + ('wrong_finite_row_coefficient', lambda o, i: i['finite'].__setitem__('physical_row_coefficient', 1)), + ] + controls.extend([ + ('missing_zero_provider', lambda o, i: i['providers'].pop('rank5_zero_cold')), + ('missing_eight_provider_backward', lambda o, i: i['providers']['rank5_eight_cold']['local'].pop('backward')), + ('stale_zero_program_and_consistent_selected_hashes', stale_zero_program), + ('stale_zero_profile_with_consistent_child_total', stale_zero_profile), + ('reordered_complete_calls', reordered_calls), + ('relocated_four_and_eight_providers_same_counts', moved_providers), + ('four_provider_widths_permuted_same_inventory', permuted_four_widths), + ('understated_explicit_idle_remainders', lambda o, i: o.__setitem__('explicit_idle_remainder_children', 4017)), + ('understated_actual_chart_types', lambda o, i: o.__setitem__('actual_73column_sigmas', 3208)), + ('wrong_cross_replica_role_count', lambda o, i: o.__setitem__('cross_replica_helper_roles', 27678)), + ]) + def cold_width_permutation(o, i): + w = i['providers']['rank5_four_cold']['widths'] + j = w.index(9) + w[270], w[j] = w[j], w[270] + def no_cold_wrappers(o, i): + for p in i['providers'].values(): + p['entering_helpers'] = 212 + for z in p['local'].values():z['pre_wrappers'] = z['post_wrappers'] = 212 + for c in i['selected_calls']: + c['entering_helpers'] = c['pre_wrappers'] = c['post_wrappers'] = 212 + i['wrapper_elementary_factors_charged'] = 72*424*144 + def synchronized_forged_recipe(o, i): + pid = 'rank5_zero_cold';name = 'CLIFFORD-RECIPES.json' + i['providers'][pid]['artifacts'][name] = '0'*64 + o['source_artifacts']['providers/'+pid+'/'+name] = '0'*64 + def synchronized_forged_phase_semantics(o, i): + pid = 'rank5_zero_cold' + i['providers'][pid]['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] = '0'*64 + o['provider_phase_semantic_sha256'][pid] = i['provider_phase_semantic_sha256'][pid] = '0'*64 + controls.extend([ + ('synchronized_forged_phase_review_semantics', synchronized_forged_phase_semantics), + ('cold_helper_width_permuted_same_inventory', cold_width_permutation), + ('old_no_cold_wrapper_counts_selfconsistent', no_cold_wrappers), + ('synchronized_forged_source_recipe_hash', synchronized_forged_recipe), + ]) + rejected = [] + for name, mutate in controls: + o, i = copy.deepcopy(owner), copy.deepcopy(invoice) + mutate(o, i) + oh = digest(o) + i['owner_audit_sha256'] = oh + try: + assemble(o, i, oh, digest(i)) + except (AssertionError, KeyError): + rejected.append(name) + else: + raise AssertionError('Invalid admission receipt accepted: ' + name) + try: + assemble(owner, invoice, '0' * 64, sha(invoice_path)) + except AssertionError: + rejected.append('wrong_owner_receipt_hash') + else: + raise AssertionError('Wrong owner digest accepted') + assert len(rejected) == 54 + assert baseline['controls'] == ['next_grid', 'zero_eta', 'zero_beta', 'unit_beta'] + assert baseline['conservative_controls'] == baseline['controls'] + assert baseline['surcharge_model'] == {'complex': False, 'bit': True} + assert len(baseline['model_controls']) == 2 + return dict( + status='PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS', + valid_receipt_kappa=baseline['kappa'], + input_sha256=baseline['input_sha256'], + assembler_sha256=sha(P / 'assemble.py'), + rejected_controls=rejected, + exact_outer_controls=baseline['controls'], + conservative_outer_controls=baseline['conservative_controls'], + recurrence_model_controls=baseline['model_controls'], + scope='Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay.', + ) + + +if __name__ == '__main__': + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--owner', type=Path, required=True) + ap.add_argument('--invoice', type=Path, required=True) + ap.add_argument('--out', type=Path, required=True) + a = ap.parse_args() + assert not a.out.exists() + result = verify(a.owner, a.invoice) + a.out.write_text(json.dumps(result, indent=2) + '\n') + print(result['status'], len(result['rejected_controls'])) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_allcold.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_allcold.py new file mode 100644 index 0000000000..932c04afcf --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_allcold.py @@ -0,0 +1,220 @@ +"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit. +Imports no emitter, optimizer, expander, edge-coloring, or source hosting code. +CLI: BASE HOSTED REPORT [--mutation-controls] +Each provider is independently read from BASE/providers, never from a baseline width histogram. +OpenAI Codex three-provider 0/4/8 extension; retains all inherited independent controller checks. +All72 one-cold dispatch is frozen from PROVIDER-CALLS SHA256 049ad6640f9f3b0e329a4eaba8c390cf560791a12f22f25f0bace59153a05f4e. +""" +import sys,json,gzip,hashlib,copy +assert __debug__, 'Assertions must remain enabled' +from pathlib import Path +from collections import Counter,defaultdict +BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz') +ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json') +ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json') +sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +provider_ids=('rank5_zero_cold','rank5_four_cold','rank5_eight_cold') +providers={};registry={};phase_semantic_hashes={} +required_artifacts={'work/complex-nine-native/DATA-PHASES.json'} +provider_files=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json', + 'INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json') +for pid in provider_ids: + p=BASE/'providers'/pid + c=read(p/'CANONICAL-WORD.json.gz');checks=read(p/'LOCAL-CHECKS.json') + programs=read(p/'LOCAL-PROGRAMS.json.gz');replay=read(p/'INDEPENDENT-LOCAL-REPLAY.json') + phase=read(p/'CLIFFORD-REVIEW.json');adapters=read(p/'RESIDUAL-ADAPTERS.json')['recipes'] + widths=[c['h']-len(c['frames'][c['start'][2*c['v']+h]])for h in range(c['R'])] + promoted={'rank5_zero_cold':0,'rank5_four_cold':4,'rank5_eight_cold':8}[pid] + assert all(widths[h]==8 for h in (270,271,282,283,294,295,306,307)) and Counter(widths)==Counter({r:n for r,n in{4:promoted,5:56-promoted,8:164,9:284}.items()if n}) + canonical_sha=sha(p/'CANONICAL-WORD.json.gz');programs_sha=sha(p/'LOCAL-PROGRAMS.json.gz') + assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY' + assert replay['canonical_word_sha256']==canonical_sha and replay['local_programs_sha256']==programs_sha + assert replay['v']==c['v'] and replay['helpers']==c['R'] + assert set(programs)==set(checks)==set(replay['local'])==set(replay['paid_profiles'])=={'forward','backward'} + for orientation,events in programs.items(): + ck=checks[orientation];rr=replay['local'][orientation] + assert hashlib.sha256(json.dumps(events,sort_keys=True,separators=(',',':')).encode()).hexdigest()==ck['sha256'] + assert ck['events']==len(events) and ck['all_columns']==2*c['v']+c['R'] + assert ck['private_centers_cleared'] and ck['private_coefficient_stream_cleared_after_each_macro'] + assert rr['all_exact_columns']==2*c['v']+c['R'] and rr['private_work_erased'] + literal=Counter(e[-1]for e in events if e[0]in('climb','center')) + assert dict(literal)=={int(r):n for r,n in ck['paid_profile'].items()}=={int(r):n for r,n in c['local_profile'].items()} + assert ck['paid_profile']==replay['paid_profiles'][orientation] + assert phase['canonical_word_sha256']==canonical_sha and phase['recipe_sha256']==sha(p/'CLIFFORD-RECIPES.json') + assert phase['all_child_equalities_include_global_phase'] + phase_semantic_hashes[pid]=hashlib.sha256(json.dumps({k:v for k,v in phase.items()if k!='seconds'},sort_keys=True,separators=(',',':')).encode()).hexdigest() + for h,w in enumerate(widths): + assert 0>i)&1==0);a=q^(1<>i&1 else 0)for i in order]+[1<2*max(paid)**2 + return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72) + +r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256'] +assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items()) +controls=[] +def reject(name,mut): + if '--mutation-controls' not in sys.argv[4:]:return + q=copy.deepcopy(ct);mut(q) + try:audit(q) + except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name) + else:raise AssertionError('ACCEPTED '+name) +enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4) +reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)])) +reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0])) +reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA)) +reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1)) +reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72)) +reject('omit idle remainder',lambda q:q['idle_children'].pop()) +reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1)) +special=lambda q:next(c for c in q['calls']if(c['stage'],c['replica'])==(4,5)) +changed=next(h for h in range(R)if providers['rank5_four_cold']['widths'][h]!=providers['rank5_eight_cold']['widths'][h]) +assert providers['rank5_four_cold']['widths'][changed]==5 and providers['rank5_eight_cold']['widths'][changed]==4 +reject('wrong provider at a four-pivot invocation',lambda q:special(q).__setitem__('provider_id','rank5_eight_cold')) +reject('stale per-call local program hash',lambda q:special(q).__setitem__('local_program_sha256',registry['rank5_eight_cold']['local_program_checks'][special(q)['orientation']]['sha256'])) +reject('stale serialized four-pivot provider program',lambda q:q['local_providers']['rank5_four_cold'].__setitem__('local_programs',registry['rank5_eight_cold']['local_programs'])) +reject('unbound residual adapter hash',lambda q:q['local_providers']['rank5_four_cold'].__setitem__('residual_adapter_sha256','0'*64)) +reject('wrong provider width registry',lambda q:q['local_providers']['rank5_four_cold']['widths'].__setitem__(changed,4)) +reject('wrong per-call width at a four-pivot invocation',lambda q:special(q)['owners'][2*V+changed][1].__setitem__(3,4)) +reject('wrong sweep provider',lambda q:next(e for e in q['execution_schedule']if e['kind']=='local_cover_sweep'and(e['stage'],e['replica'])==(4,5)).__setitem__('provider_id','rank5_eight_cold')) +reject('cold helper width silently restored to nine',lambda q:q['local_providers']['rank5_four_cold']['widths'].__setitem__(270,9)) +reject('missing cold helper wrapper binding',lambda q:q['local_providers']['rank5_zero_cold'].__setitem__('residual_adapter_sha256','0'*64)) +report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],provider_phase_semantic_sha256=phase_semantic_hashes,widths_by_provider={pid:dict(sorted(Counter(providers[pid]['widths']).items()))for pid in provider_ids},provider_counts=dict(Counter(c['provider_id']for c in ct['calls'])),all_provider_program_phase_and_wrapper_bindings=True,scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses three per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.') +REPORT.parent.mkdir(parents=True,exist_ok=True) +REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2)) + +owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],provider_phase_semantic_sha256=phase_semantic_hashes,controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest()) +(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n') + +# Literal residual frames are a compact export of the already checked offsets, +# not another global replay. Every row names its actual inherited axes. +frames=[] +for z in ct['idle_children']: + axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes'])) + tail=axes[z['pending_offset']:] + assert len(tail)==z['rank'] + frames.append(dict(z,orthogonal_axes=tail)) +frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode() +portable=bytearray(gzip.compress(frame_raw,mtime=0));portable[9]=255 +(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(bytes(portable)) +frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'], + uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames), + rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())), + source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(), + scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.') +(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n') + diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_kernel_controls.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_kernel_controls.py new file mode 100644 index 0000000000..771231cd4c --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_kernel_controls.py @@ -0,0 +1,41 @@ +"""Exact new-kernel omission controls with the correct compensation frozen.""" +import argparse,copy,gzip,hashlib,json +from fractions import Fraction as Q +from pathlib import Path +if not __debug__:raise SystemExit('Assertions required.') +ap=argparse.ArgumentParser();ap.add_argument('--word',type=Path,required=True);ap.add_argument('--recipe',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();w=json.loads(gzip.decompress(a.word.read_bytes()));recipe=json.loads(a.recipe.read_text());V=112;N=728 +def inverse(e,dual=False): + e=copy.deepcopy(e) + if e[0]=='add': + e[3]*=-1 + if dual:e[1],e[2]=e[2],e[1] + else:e[2],e[3]=e[3],e[2] + return e +def ident():return[{r:Q(1)}for r in range(N)] +def apply(e,rows): + if e[0]=='scale': + t=e[1];q=Q(e[2],e[3]);rows[t]={j:q*x for j,x in rows[t].items()};return + t,s=e[1:3];q=Q(e[3],e[4]) + for j,x in list(rows[s].items()): + z=rows[t].get(j,Q(0))+q*x + if z:rows[t][j]=z + else:rows[t].pop(j,None) +def replay(es): + rows=ident() + for e in es:apply(e,rows) + return rows +main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(N)] +for r in range(V,2*V):dirty[r]={j:x for j,x in mx[r].items()if j>=2*V} +for e in w['precondition']:apply(e,dirty) +comp=[] +for r in range(V,2*V): + for j,x in sorted(dirty[r].items()):assert not w['start_extra'].get(str(j));comp.append(['add',r,j,-x.numerator,x.denominator,[]]) +expected=ident();expected_back=ident() +for t in range(V):expected[V+t][t]=Q(1);expected_back[t][V+t]=Q(-1) +correct=w['precondition']+comp+main+w['cleanup'];assert replay(correct)==expected and replay([inverse(e,True)for e in correct])==expected_back +indices=list(range(recipe['index'],recipe['index']+len(recipe['coefficients'])));controls=[] +for omitted in [[i]for i in indices]+[indices]: + B=[e for i,e in enumerate(w['B'])if i not in omitted];cleanup=[inverse(e)for e in reversed(w['A']+B)if not V<=e[1]<2*V];program=w['precondition']+comp+w['A']+w['cut']+B+cleanup + assert replay(program)!=expected and replay([inverse(e,True)for e in program])!=expected_back + controls.append(dict(omitted_B_indices=omitted,forward_rejected=True,reflected_rejected=True)) +r=dict(status='PASS_EXACT_NEW_KERNEL_OMISSION_CONTROLS',word_sha256=hashlib.sha256(a.word.read_bytes()).hexdigest(),columns_each_orientation=N,correct_compensation_frozen=True,compensation_entries=len(comp),controls=controls,scope='Each new donor gate and entire new kernel omitted. Cleanup is regenerated, correct compensation is held fixed, and both exact scalar orientations reject each mutant.');a.out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],len(controls)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_multicold_controls.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_multicold_controls.py new file mode 100644 index 0000000000..30cac3cf87 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/audit_multicold_controls.py @@ -0,0 +1,75 @@ +"""Exact multi-cut cold-kernel omission controls with the correct compensation frozen. +Generalises PR564's audit_kernel_controls.py: for every recipe kernel, each new donor +gate alone and the entire kernel are omitted; cleanup is regenerated, the correct +word's frame-zero compensation is held fixed, and both exact scalar orientations +must reject every mutant.""" +import argparse, copy, gzip, hashlib, json +from fractions import Fraction as Q +from pathlib import Path +if not __debug__: raise SystemExit('Assertions required.') +ap = argparse.ArgumentParser(); ap.add_argument('--word', type=Path, required=True); ap.add_argument('--recipe', type=Path, required=True); ap.add_argument('--out', type=Path, required=True); a = ap.parse_args() +w = json.loads(gzip.decompress(a.word.read_bytes())); recipe = json.loads(a.recipe.read_text()); V = 112; N = 728 + + +def inverse(e, dual=False): + e = copy.deepcopy(e) + if e[0] == 'add': + e[3] *= -1 + if dual: e[1], e[2] = e[2], e[1] + else: e[2], e[3] = e[3], e[2] + return e + + +def ident(): return [{r: Q(1)} for r in range(N)] + + +def apply(e, rows): + if e[0] == 'scale': + t = e[1]; q = Q(e[2], e[3]); rows[t] = {j: q * x for j, x in rows[t].items()}; return + t, s = e[1:3]; q = Q(e[3], e[4]) + for j, x in list(rows[s].items()): + z = rows[t].get(j, Q(0)) + q * x + if z: rows[t][j] = z + else: rows[t].pop(j, None) + + +def replay(es): + rows = ident() + for e in es: apply(e, rows) + return rows + + +main = w['A'] + w['cut'] + w['B']; mx = replay(main); dirty = [{} for _ in range(N)] +for r in range(V, 2 * V): dirty[r] = {j: x for j, x in mx[r].items() if j >= 2 * V} +for e in w['precondition']: apply(e, dirty) +comp = [] +for r in range(V, 2 * V): + for j, x in sorted(dirty[r].items()): + assert not w['start_extra'].get(str(j)); comp.append(['add', r, j, -x.numerator, x.denominator, []]) +expected = ident(); expected_back = ident() +for t in range(V): expected[V + t][t] = Q(1); expected_back[t][V + t] = Q(-1) +correct = w['precondition'] + comp + main + w['cleanup'] +assert replay(correct) == expected and replay([inverse(e, True) for e in correct]) == expected_back +# locate every new gate by exact content in A/B +located = [] +for K in recipe['kernels']: + pos = [] + for gt in K['gates']: + q = Q(gt['coefficient']); gate = ['add', gt['donor'], K['pivot'], -q.numerator, q.denominator, K['frame']] + hits = [(part, i) for part in ('A', 'B') for i, e in enumerate(w[part]) if e == gate] + assert len(hits) == 1, (K['pivot'], gt, hits) + pos.append(hits[0]) + located.append((K['pivot'], pos)) +controls = [] +for pivot, pos in located: + for omitted in [[p] for p in pos] + [pos]: + om = set(omitted) + A = [e for i, e in enumerate(w['A']) if ('A', i) not in om]; B = [e for i, e in enumerate(w['B']) if ('B', i) not in om] + cleanup = [inverse(e) for e in reversed(A + B) if not V <= e[1] < 2 * V] + program = w['precondition'] + comp + A + w['cut'] + B + cleanup + assert replay(program) != expected and replay([inverse(e, True) for e in program]) != expected_back + controls.append(dict(pivot=pivot, omitted=[list(p) for p in omitted], forward_rejected=True, reflected_rejected=True)) +r = dict(status='PASS_EXACT_MULTICUT_KERNEL_OMISSION_CONTROLS', word_sha256=hashlib.sha256(a.word.read_bytes()).hexdigest(), + columns_each_orientation=N, correct_compensation_frozen=True, compensation_entries=len(comp), controls=controls, + scope='Each new multi-cut donor gate and each entire new kernel omitted. Cleanup is regenerated, correct compensation is held fixed, and both exact scalar orientations reject each mutant.') +a.out.write_text(json.dumps(r, indent=2) + '\n'); print(r['status'], len(controls)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/bind_providers_portable.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/bind_providers_portable.py new file mode 100644 index 0000000000..57394f71bb --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/bind_providers_portable.py @@ -0,0 +1,60 @@ +"""Bind freshly verified 0/4/8 one-cold providers to the frozen literal owner plan. +Prepared with OpenAI Codex assistance; Apache-2.0. All byte-stable native +files are pinned to the plan. Only validated phase-receipt timing/serialization +and directory fields are rebound; no dispatch, width or owner choice changes. +""" +import argparse,copy,gzip,hashlib,json,shutil +from collections import Counter +from pathlib import Path +assert __debug__, 'Assertions required' +ap=argparse.ArgumentParser(description=__doc__) +for name in ('baseline','zero','four','eight','plan','out'):ap.add_argument('--'+name,type=Path,required=True) +a=ap.parse_args();assert not a.out.exists();a.out.mkdir(parents=True) +def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +base=a.out/'base';shutil.copytree(a.baseline/'complex-global/base',base) +dirs={'rank5_zero_cold':a.zero,'rank5_four_cold':a.four,'rank5_eight_cold':a.eight} +promotions={'rank5_zero_cold':0,'rank5_four_cold':4,'rank5_eight_cold':8} +for pid,src in dirs.items():shutil.copytree(src,base/'providers'/pid) +plan=read(a.plan);original=copy.deepcopy(plan);sources={} +assert set(plan['provider_registry'])==set(dirs) +assert Counter(c['provider']for c in plan['provider_calls'])=={'rank5_zero_cold':15,'rank5_four_cold':2,'rank5_eight_cold':55} +stable=('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json','RESIDUAL-ADAPTERS.json') +for pid,desc in plan['provider_registry'].items(): + d=base/'providers'/pid;p=promotions[pid] + word,program,checks,native,phase=[read(d/name)for name in('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json')] + assert (word['v'],word['h'],word['R'],len(word['centers']))==(112,9,504,8) + assert word['ports']==desc['ports'] and word['centers']==desc['centers'] + widths=[9-len(word['frames'][f])for f in word['start'][224:]] + assert all(widths[h]==8 for h in (270,271,282,283,294,295,306,307)) + assert widths==desc['widths'] and Counter(widths)==Counter({4:p,5:56-p,8:164,9:284}) + assert native['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY' + assert len(native['negative_controls_rejected'])==11 + assert native['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and native['local_programs_sha256']==sha(d/'LOCAL-PROGRAMS.json.gz') + assert phase['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES' + assert phase['canonical_word_sha256']==sha(d/'CANONICAL-WORD.json.gz') and phase['recipe_sha256']==sha(d/'CLIFFORD-RECIPES.json') + assert phase['all_child_equalities_include_global_phase'] is True and phase['endpoint_adapters']==224 and phase['directed_edges']==2929 + assert set(program)==set(checks)=={'forward','backward'} + expected={1:2316+2*p,2:452-2*p,3:456-p,4:184+p,5:56,6:56,8:8} + for orientation,events in program.items(): + profile=Counter() + for e in events: + if e[0]=='climb':profile[e[5]]+=1 + elif e[0]=='center':profile[e[4]]+=1 + assert dict(profile)==expected=={int(r):n for r,n in checks[orientation]['paid_profile'].items()}=={int(r):n for r,n in native['paid_profiles'][orientation].items()} + assert hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest()==checks[orientation]['sha256'] + for name in stable: + assert sha(d/name)==desc['artifact_sha256'][name],(pid,name,'changed non-timing artifact') + if name.endswith('.gz'):assert(d/name).read_bytes()[9]==255,(pid,name,'nonportable gzip header') + for c in plan['provider_calls']: + if c['provider']==pid: + assert c['orientation']==('forward'if c['stage']%2==0 else'backward') + assert c['local_program_sha256']==checks[c['orientation']]['sha256'] + desc['directory']='providers/'+pid + desc['artifact_sha256']={name:sha(d/name)for name in desc['artifact_sha256']} + sources[pid]=dict(artifact_sha256=desc['artifact_sha256'],canonical_content_sha256=hashlib.sha256(json.dumps(word,sort_keys=True,separators=(',',':')).encode()).hexdigest(),all_phase_edges=2929) +plan['runtime_source_plan_sha256']=sha(a.plan) +(a.out/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n') +receipt=dict(status='PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING',source_plan_sha256=sha(a.plan),runtime_plan_sha256=sha(a.out/'PLAN.json'),providers=sources,only_rebound_fields=['provider_registry.directory','provider_registry.artifact_sha256.CLIFFORD-REVIEW.json','runtime_source_plan_sha256']) +(a.out/'BINDING.json').write_text(json.dumps(receipt,indent=2)+'\n') +print(receipt['status']) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_cold_kernel.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_cold_kernel.py new file mode 100644 index 0000000000..e77f484b90 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_cold_kernel.py @@ -0,0 +1,38 @@ +"""Frozen earlier-cut kernel constructor; Apache-2.0. + +Prepared by OpenAI Codex. Direct supplier provenance: PR558, using PR552's +weighted word and the research session's exact earlier-cut suffix relation. +This script establishes scalar relation/frame construction only. Its output +requires fresh native, phase, mixed-owner, invoice and assembly verification. +""" +import argparse,copy,gzip,hashlib,json,sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +if not __debug__:raise SystemExit('Assertions required.') +ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--recipe',type=Path,required=True);ap.add_argument('--gk-dir',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args() +sys.path.insert(0,str(a.gk_dir.resolve()));import gk_word as g,gk_common as co +g.V=co.V=112;g.DATA=co.DATA=7168 +raw=gzip.decompress(a.input.read_bytes());recipe=json.loads(a.recipe.read_text());assert hashlib.sha256(raw).hexdigest()==recipe['input_content_sha256'];w=json.loads(raw);old=copy.deepcopy(w);P=g.profile(w);part=recipe['part'];index=recipe['index'];pivot=recipe['pivot'];E=co.basis(recipe['frame']);assert part=='B'and 224<=pivot<728 and str(pivot)not in w['start_extra'] +regs=lambda e:e[1:3]if e[0]=='add'else e[1:2] +assert all(pivot not in regs(e)for e in w['A']+w['cut']+w['B'][:index]),'pivot must be untouched before the chosen cut' +cols=[{}for _ in range(728)] +for t in range(112):cols[112+t]={t:Q(1)} +def add(a,b,q): + for j,x in b.items(): + z=a.get(j,Q(0))+q*x + if z:a[j]=z + else:a.pop(j,None) +for e in reversed(w['B'][index:]): + if e[0]=='add':add(cols[e[2]],cols[e[1]],Q(e[3],e[4])) + else:cols[e[1]]={t:x*Q(e[2],e[3])for t,x in cols[e[1]].items()} +residual=cols[pivot].copy();new=[] +for donor,coefficient in sorted(recipe['coefficients'].items(),key=lambda z:int(z[0])): + donor=int(donor);q=Q(coefficient);assert donor!=pivot and donor not in range(112,224);assert q.denominator&(q.denominator-1)==0 + add(residual,cols[donor],-q);new.append(['add',donor,pivot,-q.numerator,q.denominator,list(E)]) +assert not residual,'exact suffix dirty-response relation failed' +w['B']=w['B'][:index]+new+w['B'][index:];w['start_extra'][str(pivot)]=list(E);w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not 112<=e[1]<224];PP=g.profile(w);delta={r:PP[r]-P[r]for r in set(P)|set(PP)if PP[r]!=P[r]};assert delta=={int(r):n for r,n in recipe['profile_delta'].items()};assert sum(r*n for r,n in delta.items())==-len(E) +w['report']['local_profile']=dict(PP);encoded=g.dump(w);assert hashlib.sha256(gzip.decompress(encoded)).hexdigest()==recipe['output_content_sha256'] +a.out.mkdir(parents=True,exist_ok=False);(a.out/'FULL-WORD.json.gz').write_bytes(encoded) +r=dict(status='PASS_FROZEN_EARLIER_CUT_KERNEL_CONSTRUCTION',input_content_sha256=hashlib.sha256(raw).hexdigest(),output_content_sha256=hashlib.sha256(gzip.decompress(encoded)).hexdigest(),pivot=pivot,changed_helper=pivot-224,entrance_frame=list(E),inserted_gates=len(new),exact_suffix_relation=True,pivot_untouched_before_cut=True,profile_before=dict(P),profile_after=dict(PP),delta=delta,helper_width_before=9,helper_width_after=9-len(E),scope='Literal scalar donor word, fixed-cut suffix response, exact frame chains and cleanup constructed. Native/all-column, phase, owner, invoice and assembly checks remain separate. No claimed homogeneous resource gain.') +(a.out/'KERNEL-CONSTRUCTION.json').write_text(json.dumps(r,indent=2)+'\n');print(json.dumps(r,indent=2)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_four_portable.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_four_portable.py new file mode 100644 index 0000000000..b55f70b228 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_four_portable.py @@ -0,0 +1,48 @@ +"""Reconstruct the frozen four-pivot supplier from the verified zero word. +Prepared with OpenAI Codex assistance; Apache-2.0. Derived from PR558's +complete-group promotion. Gzip metadata is normalized to OS byte255 while +the decompressed word is pinned to the exploratory construction. Neither a +solver nor a platform-dependent header selects any mathematics. +""" +import argparse,copy,gzip,hashlib,json,sys +from collections import Counter +from pathlib import Path +assert __debug__, 'Assertions required' +ap=argparse.ArgumentParser(description=__doc__) +for name in ('input','recipe','gk-dir','out'):ap.add_argument('--'+name,type=Path,required=True) +a=ap.parse_args();assert not a.out.exists() +sys.path.insert(0,str(a.gk_dir));import gk_word as g,gk_common as co +g.V=co.V=112;g.DATA=co.DATA=7168 +sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +r=json.loads(a.recipe.read_text());assert sha(a.input)==r['source_sha256'] +w=json.loads(gzip.decompress(a.input.read_bytes()));before=copy.deepcopy(w) +assert dict(g.profile(w))=={int(k):n for k,n in r['local_before'].items()} +assert len(r['changes'])==1;ch=r['changes'][0] +assert ch['group']==10 and ch['pivots']==[419,421,422,423] and ch['gates']==12 +assert len(g.basis(ch['old_E']))==4 and len(g.basis(ch['new_E']))==5 and g.span(ch['old_E'])<=g.span(ch['new_E']) +for h in ch['pivots']: + assert w['start_extra'][str(224+h)]==ch['old_E'];w['start_extra'][str(224+h)]=ch['new_E'] +kernel=w['B'][320:488];count=0 +assert len(kernel)==168 and all(e[0]=='add'for e in kernel) +assert not {e[1]for e in kernel}&{e[2]for e in kernel} +for e in kernel: + if e[2]-224 in ch['pivots']: + assert e[-1]==ch['old_E'];e[-1]=ch['new_E'];count+=1 +assert count==12 +w['B'][320:488]=sorted(kernel,key=lambda e:len(e[-1])) +w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not 112<=e[1]<224] +profile=dict(g.profile(w));widths=dict(Counter(g.widths_of(w))) +assert profile=={int(k):n for k,n in r['local_after'].items()} +assert widths=={int(k):n for k,n in r['widths'].items()} +assert Counter(tuple(e[:-1])for e in before['B'])==Counter(tuple(e[:-1])for e in w['B']) +assert {k:v for k,v in before.items()if k not in {'B','cleanup','start_extra','report'}}=={k:v for k,v in w.items()if k not in {'B','cleanup','start_extra','report'}} +w['report'].update(local_profile=profile,width_inventory=widths,local_rank_mass=sum(k*n for k,n in profile.items()),status='FOUR_RANK5_PIVOTS_PENDING_MIXED_NATIVE_ADMISSION') +raw=g.dump(w);assert raw[:3]==b'\x1f\x8b\x08' and len(raw)>=18 +raw=raw[:9]+b'\xff'+raw[10:] +assert hashlib.sha256(raw).hexdigest()==r['word_sha256'] +assert hashlib.sha256(gzip.decompress(raw)).hexdigest()==r['word_content_sha256'] +a.out.mkdir(parents=True);(a.out/'FULL-WORD.json.gz').write_bytes(raw) +(a.out/'PROMOTION.json').write_bytes(a.recipe.read_bytes()) +receipt=dict(status='PASS_FROZEN_FOUR_PIVOT_CONSTRUCTION',source_sha256=sha(a.input),recipe_sha256=sha(a.recipe),word_sha256=r['word_sha256'],word_content_sha256=r['word_content_sha256'],local_profile=profile,width_inventory=widths,scalar_B_multiset_unchanged=True,complete_commuting_kernel_group=True) +(a.out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n') +print(receipt['status'],receipt['word_sha256']) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_multicut_kernels.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_multicut_kernels.py new file mode 100644 index 0000000000..bb5f7b438f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/build_multicut_kernels.py @@ -0,0 +1,94 @@ +"""Frozen multi-cut cold-kernel constructor; Apache-2.0. + +Generalises PR564's build_cold_kernel.py: a cold pivot (untouched before its +first new gate) may receive its donor gates donor += -q*pivot @E at several +cuts. The pivot holds only its initial dirt until its first original touch, so +the new gates kill its complete dirty response iff the exact suffix relation +sum_g q_g * col_{cut_g}[donor_g] = col[pivot] holds. This script inserts the +recipe gates kernel by kernel (positions refer to the word before that kernel), +then checks: donors are not targets/pivot/centres, dyadic coefficients, the +pivot's first touch is a new gate, the exact complete dirty response of the +pivot is zero (forward replay), frame legality and the exact profile delta via +gk_word.profile, and the pinned output content hash. Native all-column, +phase, owner, invoice and assembly checks remain separate. +""" +import argparse, copy, gzip, hashlib, json, sys +from fractions import Fraction as Q +from pathlib import Path +if not __debug__: raise SystemExit('Assertions required.') +ap = argparse.ArgumentParser() +for k in ('input', 'recipe', 'gk-dir', 'out'): ap.add_argument('--' + k, type=Path, required=True) +a = ap.parse_args() +sys.path.insert(0, str(a.gk_dir.resolve())); import gk_word as g, gk_common as co +g.V = co.V = 112; g.DATA = co.DATA = 7168 +V = 112; N = 728 +raw = gzip.decompress(a.input.read_bytes()); recipe = json.loads(a.recipe.read_text()) +assert hashlib.sha256(raw).hexdigest() == recipe['input_content_sha256'] +w = json.loads(raw) +regs = lambda e: e[1:3] if e[0] == 'add' else e[1:2] + + +def dirty_response(word, pivot): + rows = {} + def get(r): return rows.setdefault(r, {r: Q(1)}) + for e in word['A'] + word['cut'] + word['B']: + if e[0] == 'scale': + q = Q(e[2], e[3]); rows[e[1]] = {j: q * x for j, x in get(e[1]).items()} + else: + t, s = e[1], e[2]; q = Q(e[3], e[4]); src = get(s); tgt = get(t) + for j, x in list(src.items()): + z = tgt.get(j, Q(0)) + q * x + if z: tgt[j] = z + else: tgt.pop(j, None) + return {r: rows[r][pivot] for r in range(V, 2 * V) if r in rows and rows[r].get(pivot)} + + +receipts = [] +for K in recipe['kernels']: + P0 = g.profile(w) + pivot = K['pivot']; E = co.basis(K['frame']) + assert 2 * V <= pivot < N and str(pivot) not in w['start_extra'] + before = dirty_response(w, pivot); assert before, 'pivot already has zero response' + ins = {'A': {}, 'B': {}} + for gt in K['gates']: + d = gt['donor']; q = Q(gt['coefficient']) + assert d != pivot and d not in w['centers'] + if V <= d < 2 * V: + # gauge-type (target) donor: only after the centre scatter, like the post-centre gauge compensation + assert gt['part'] == 'B' and gt.get('target_donor') is True + assert q and q.denominator & (q.denominator - 1) == 0 + assert gt['part'] in ('A', 'B') and 0 <= gt['index'] <= len(w[gt['part']]) + ins[gt['part']].setdefault(gt['index'], []).append(['add', d, pivot, -q.numerator, q.denominator, list(E)]) + assert all(pivot not in regs(e) for e in w['cut'] if e[0] == 'add') + new_ids = {id(e) for part in ins for lst in ins[part].values() for e in lst} + for part in ('B', 'A'): + for i in sorted(ins[part], reverse=True): + w[part][i:i] = ins[part][i] + allg = w['A'] + w['B'] + first_old = next(k for k, e in enumerate(allg) if pivot in regs(e) and id(e) not in new_ids) + assert all(id(e) in new_ids or pivot not in regs(e) for e in allg[:first_old]) + assert sum(id(e) in new_ids for e in allg[:first_old]) == len(K['gates']), 'every new gate must precede the first original pivot touch' + w['start_extra'][str(pivot)] = list(E) + w['cleanup'] = [g.inverse(e, g.FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V] + after = dirty_response(w, pivot) + assert not after, ('exact multi-cut relation failed', pivot, after) + PP = g.profile(w) + delta = {r: PP[r] - P0[r] for r in set(P0) | set(PP) if PP[r] != P0[r]} + assert delta == {int(r): n for r, n in K['profile_delta'].items()}, (pivot, delta) + assert sum(r * n for r, n in delta.items()) == -len(E) + receipts.append(dict(pivot=pivot, changed_helper=pivot - 2 * V, entrance_frame=list(E), inserted_gates=len(K['gates']), + cuts=sorted({(gt['part'], gt['index']) for gt in K['gates']}), profile_delta=delta, + prior_dirty_targets=len(before), exact_zero_response=True, helper_width_before=9, + helper_width_after=9 - len(E))) +w['report']['local_profile'] = {str(k): n for k, n in sorted(g.profile(w).items())} +w['report']['entering_helpers'] = sum(1 for x in g.widths_of(w) if x < 9) +w['report']['entrance_rank'] = sum(9 - x for x in g.widths_of(w)) +encoded = g.dump(w) +assert hashlib.sha256(gzip.decompress(encoded)).hexdigest() == recipe['output_content_sha256'], hashlib.sha256(gzip.decompress(encoded)).hexdigest() +a.out.mkdir(parents=True, exist_ok=False); (a.out / 'FULL-WORD.json.gz').write_bytes(encoded) +r = dict(status='PASS_FROZEN_MULTICUT_COLD_KERNEL_CONSTRUCTION', input_content_sha256=recipe['input_content_sha256'], + output_content_sha256=recipe['output_content_sha256'], kernels=receipts, + local_profile=w['report']['local_profile'], entering_helpers=w['report']['entering_helpers'], + entrance_rank=w['report']['entrance_rank'], + scope='Literal multi-cut donor gates, exact complete dirty-response cancellation, exact frame chains and regenerated cleanup. Native all-column, phase, owner, invoice and assembly checks remain separate.') +(a.out / 'KERNEL-CONSTRUCTION.json').write_text(json.dumps(r, indent=2) + '\n'); print(json.dumps(r, indent=2)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/emit_allcold.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/emit_allcold.py new file mode 100644 index 0000000000..2c405712cb --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/emit_allcold.py @@ -0,0 +1,140 @@ +"""Three-provider whole-owner derivative, adapted with OpenAI Codex assistance. +Based on PR514 and its credited PR484/507 lineage. +CLI: --base VERIFIED_VARIANT --owners ASYNC-OWNERS.json.gz --plan ASYNC-PLAN.json --out OUT +No optimizer or unpublished word builder runs. The frozen map explicitly names +one whole helper per family per complete invocation, plus borrowed spectators. +""" +import sys,json,gzip,hashlib,copy,argparse +from pathlib import Path +from collections import Counter,defaultdict +parser=argparse.ArgumentParser(description=__doc__) +parser.add_argument('--base',type=Path,required=True);parser.add_argument('--owners',type=Path,required=True);parser.add_argument('--plan',type=Path,required=True);parser.add_argument('--out',type=Path,required=True) +a=parser.parse_args();BASE,MAP,PLAN,OUT=(p.resolve()for p in(a.base,a.owners,a.plan,a.out));assert not OUT.exists();OUT.mkdir(parents=True) +class OH: + @staticmethod + def idle_basis(q): + z=next(i for i in range(9)if not(q>>i)&1);u=q^(1<>i&1 else 0)for i in order]+[1<=0 and off+w<=rank[i] + assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1] + B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i] + occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[] + order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M + sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma + route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9 + cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells + digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n') +for c in t['calls']: + k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R)) + c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f2*max(paid)**2 + +assert all(c['local_program_sha256']==registry[c['provider_id']]['local_program_checks'][c['orientation']]['sha256']for c in t['calls']) +t['provider_dispatch']='For each indivisible local_cover_sweep, execute local_providers[call.provider_id].local_programs[call.orientation] with that provider residual adapters and Clifford recipes. The sweep provider_id must equal its call provider_id.' +raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0)) +res=dict(status='EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE', + template_sha256=hashlib.sha256(raw).hexdigest(), + parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(), + live=DATA,physical=physical,global_profile=dict(sorted(paid.items())), + rank_mass=sum(r*n for r,n in paid.items()),deficit=2560,maxchild=max(paid), + hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering, + unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(), + cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles), + asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(), + source_artifacts=source_artifacts,provider_counts=dict(Counter(c['provider_id']for c in t['calls'])), + scope='Three actual verified local providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required.') +(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/code/invoice_allcold.py b/research/pr643-improvement-20261013/witness/vendor/multicold/code/invoice_allcold.py new file mode 100644 index 0000000000..dc3676d2a4 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/code/invoice_allcold.py @@ -0,0 +1,314 @@ +"""Fresh call-specific mixed-provider finite invoice. + +Prepared with OpenAI Codex assistance, Apache-2.0. The scalar/Horner recount +and finite inequalities are adapted from the retained PR558 -> PR552 -> +PR531 invoice_final.py, whose notices and sources are preserved in the package. +Every call selects a hash-bound provider. Shared compiler reserves use maxima; +primitive work, coefficient work, local children and wrappers are also summed +from actual selected provider/orientation records. +""" +import argparse, gzip, hashlib, json +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +assert __debug__, 'Assertions required' + +def read(path): + data=path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix=='.gz' else data) +def filehash(path): return hashlib.sha256(path.read_bytes()).hexdigest() +def contenthash(path): + data=path.read_bytes() + return hashlib.sha256(gzip.decompress(data) if path.suffix=='.gz' else data).hexdigest() +def programhash(events): + return hashlib.sha256(json.dumps(events,separators=(',',':')).encode()).hexdigest() + +def recount_provider(local_dir, registry): + cp=local_dir/'CANONICAL-WORD.json.gz'; pp=local_dir/'LOCAL-PROGRAMS.json.gz' + rp=local_dir/'INDEPENDENT-LOCAL-REPLAY.json' + w,programs,replay=read(cp),read(pp),read(rp) + checks=read(local_dir/'LOCAL-CHECKS.json') + assert set(programs)=={'forward','backward'} + assert replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY' + assert replay['canonical_word_sha256']==filehash(cp)==registry['canonical_word_sha256'] + assert replay['local_programs_sha256']==filehash(pp)==registry['local_programs_sha256'] + assert programs==registry['local_programs'] + assert checks==registry['local_program_checks'] + assert filehash(local_dir/'CLIFFORD-RECIPES.json')==registry['exact_local_clifford_recipe_sha256'] + assert filehash(local_dir/'RESIDUAL-ADAPTERS.json')==registry['residual_adapter_sha256'] + v,helpers,h,m=w['v'],w['R'],w['h'],73 + assert (v,helpers,h)==(112,504,9) + assert registry['v']==v and registry['R']==helpers and registry['h']==h + assert registry['ports']==w['ports'] and registry['centers']==w['centers'] + assert replay['v']==v and replay['helpers']==helpers + n=2*v+helpers + widths = [h-len(w['frames'][f]) for f in w['start'][2*v:]] + assert len(widths) == helpers + entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0} + entering = len(entrances) + assert entering == replay['entering_helpers'] + local = {} + for orientation, events in programs.items(): + # Endpoint equality and native frames were already independently + # replayed on all n columns in the hash-bound receipt above. + env = {('L', r): Q(1) for r in range(n)} + peak = Q(1) + real = macros = workops = 0 + paid = Counter() + wrappers = {'pre': set(), 'post': set()} + for event in events: + tag = event[0] + if tag == 'climb': + paid[event[5]] += 1 + elif tag == 'center': + paid[event[4]] += 1 + elif tag == 'residual_adapter': + _, kind, register, frame = event + assert kind in wrappers and entrances.get(register) == frame + assert register not in wrappers[kind] + wrappers[kind].add(register) + elif tag == 'scalar': + macros += 1 + scalar = event[1] + op, target = scalar[0], tuple(scalar[1]) + if op == 'clear': + env[target] = Q(0) + count = 1 + elif op == 'copy': + env[target] = env[tuple(scalar[2])] + count = 1 + elif op == 'scale': + q = Q(scalar[2], scalar[3]) + numerator, denominator = abs(q.numerator), q.denominator + assert numerator and numerator & (numerator-1) == 0 + assert denominator & (denominator-1) == 0 + env[target] *= abs(q) + count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0) + elif op == 'add': + source = tuple(scalar[2]) + q = Q(scalar[3], scalar[4]) + numerator, denominator = abs(q.numerator), q.denominator + assert source != target and numerator > 0 + assert denominator & (denominator-1) == 0 + acc, count = 0, 1 # clear coefficient work + for i, bit in enumerate(bin(numerator)[2:]): + if i: + acc *= 2 + count += 1 + peak = max(peak, acc*env[source]) + if bit == '1': + acc += 1 + count += 1 + peak = max(peak, acc*env[source]) + value = Q(acc) + for _ in range(denominator.bit_length()-1): + value /= 2 + count += 1 + peak = max(peak, value*env[source]) + assert value == abs(q) + count += 2 # signed accumulation and work clear + env[target] = env.get(target, Q(0)) + abs(q)*env[source] + workops += count + else: + raise AssertionError(op) + real += 2*count + peak = max(peak, env[target]) + else: + assert tag in ('adapter', 'phase') + assert wrappers['pre'] == wrappers['post'] == set(entrances) + assert all(value == 0 for register, value in env.items() if register[0] == 'C') + prior = replay['local'][orientation] + assert prior['all_exact_columns'] == n and prior['private_work_erased'] + assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits'] + bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1 + assert bits == prior['prefix_bits_upper'] + assert real == checks[orientation]['real_component_primitive_bound'] + assert macros == checks[orientation]['scalar_macros'] + assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()} + assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()} + local[orientation] = dict( + events=len(events), macros=macros, real_component_primitives=real, + prefix_l1=str(peak), prefix_bits=bits, + coefficient_work_primitive_count=workops, all_exact_columns=n, + dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True, + private_centres_and_coefficient_work_cleared=True, + pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']), + endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json') + + centres = len(w['centers']) + children = sum(checks['forward']['paid_profile'].values()) + assert checks['forward']['paid_profile'] == checks['backward']['paid_profile'] + macro_bound = max(row['macros'] for row in local.values()) + compiler = 64*(m+1)**3 + adapters = 16*(macro_bound+children+n+centres)+64*m + primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler + + assert widths==registry['widths'] + artifacts={f.name:filehash(f) for f in local_dir.iterdir() if f.is_file()} + phase_review=read(local_dir/'CLIFFORD-REVIEW.json') + semantic_phase=hashlib.sha256(json.dumps({k:v for k,v in phase_review.items()if k!='seconds'},sort_keys=True,separators=(',',':')).encode()).hexdigest() + return dict(local=local,helpers=helpers,centres=centres,v=v,h=h,n=n, + entering_helpers=entering,entrance_rank=sum(h-width for width in widths), + width_inventory=dict(sorted(Counter(widths).items())),widths=widths, + local_adapters=adapters,local_primitive_bound=primitive_bound, + compiler=compiler,children=children,artifacts=artifacts, + paid_profile=checks['forward']['paid_profile'], + program_hashes={o:programhash(events) for o,events in programs.items()},semantic_artifact_sha256={'CLIFFORD-REVIEW.json':semantic_phase}) + + +def run(base, hosted, audit, out, retained_invoice=None): + local_dir=base/'split-centres' + parent=read(local_dir/'GLOBAL-TEMPLATE.json.gz') + template_path=hosted/'GLOBAL-TEMPLATE.json.gz' + template=read(template_path); summary=read(hosted/'HOSTED.json') + owners=read(audit/'OWNERS-AND-PROFILE.json'); control=read(audit/'ASYNC-AUDIT.json') + template_hash=contenthash(template_path) + assert template_hash==control['complex_template_sha256']==owners['template_sha256']==summary['template_sha256'] + assert owners['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE' + assert template['recipe']==parent['recipe'] + assert 'local_programs' not in template + assert set(template['local_providers'])=={'rank5_zero_cold','rank5_four_cold','rank5_eight_cold'} + providers={pid:recount_provider(base/'providers'/pid,registry) + for pid,registry in template['local_providers'].items()} + for pid,p in providers.items(): + assert owners['provider_phase_semantic_sha256'][pid]==control['provider_phase_semantic_sha256'][pid]==p['semantic_artifact_sha256']['CLIFFORD-REVIEW.json'] + # The fresh controller admission must cite precisely these provider bytes. + for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json', + 'INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-RECIPES.json', + 'CLIFFORD-REVIEW.json','RESIDUAL-ADAPTERS.json'): + path='providers/'+pid+'/'+name + assert summary['source_artifacts'][path]==p['artifacts'][name] + assert owners['source_artifacts'][path]==p['artifacts'][name] + v,helpers,h,m,centres,n=112,504,9,73,8,728 + stages,replicas,blocks_per_stream=9,8,4 + call_count=len(template['calls']) + assert call_count==stages*replicas==control['complete_invocations'] + assert control['one_owner_per_complete_invocation'] + assert len({(c['stage'],c['replica']) for c in template['calls']})==call_count + parent_calls={(c['stage'],c['replica']):c for c in parent['calls']} + sweeps=[e for e in template['execution_schedule'] if e['kind']=='local_cover_sweep'] + assert len(sweeps)==call_count + selected=[]; selected_paid=Counter(); provider_counts=Counter(); orientation_counts=Counter() + scalar=coefficient_work=macros=0; wrapper_factors=0 + factors_per_wrapper=2*(m-1) + for c in template['calls']: + pid,orientation=c['provider_id'],c['orientation']; p=providers[pid] + old=parent_calls[(c['stage'],c['replica'])] + assert orientation==old['orientation'] and c['owners'][:2*v]==old['owners'][:2*v] + assert c['local_program_sha256']==p['program_hashes'][orientation] + r=p['local'][orientation] + scalar+=r['real_component_primitives']; coefficient_work+=r['coefficient_work_primitive_count']; macros+=r['macros'] + wrapper_factors+=(r['pre_wrappers']+r['post_wrappers'])*factors_per_wrapper + provider_counts[pid]+=1; orientation_counts[(pid,orientation)]+=1 + selected_paid.update({int(k):v for k,v in p['paid_profile'].items()}) + selected.append(dict(stage=c['stage'],replica=c['replica'],provider_id=pid,orientation=orientation, + program_sha256=c['local_program_sha256'],events=r['events'],macros=r['macros'], + real_component_primitives=r['real_component_primitives'], + coefficient_work_primitive_count=r['coefficient_work_primitive_count'], + entering_helpers=p['entering_helpers'],entrance_rank=p['entrance_rank'], + pre_wrappers=r['pre_wrappers'],post_wrappers=r['post_wrappers'])) + assert provider_counts==Counter(rank5_zero_cold=15,rank5_four_cold=2,rank5_eight_cold=55) + # The sweep registry is executable: no hidden use of the historical supplier. + by_call={(c['stage'],c['replica']):c for c in template['calls']} + for e in sweeps: + c=by_call[(e['stage'],e['replica'])] + assert e['provider_id']==c['provider_id'] + assert set(p['compiler'] for p in providers.values())=={64*(m+1)**3} + compiler=64*(m+1)**3 + adapters=max(p['local_adapters'] for p in providers.values()) + primitive_bound=max(p['local_primitive_bound'] for p in providers.values()) + bridge_steps=sum(event['kind']=='bridge' for event in parent['recipe']) + bridge_sweeps=sum(event['kind']=='bridge' for event in template['execution_schedule']) + assert bridge_sweeps==replicas*bridge_steps + bridge_additions=2*v*bridge_sweeps + shifts=blocks_per_stream*v*replicas; moves=2*shifts + parent_live,parent_physical=parent['live'],parent['physical'] + data_stock=2*v*blocks_per_stream*replicas + assert (parent_live-data_stock)%stages==0 + parent_banks=(parent_live-data_stock)//stages + assert parent_banks>=0 and parent_physical==parent_live+helpers+centres+2 + nonlocal_items=(4*v*replicas*stages+2*v*replicas*stages+2*call_count*helpers + +sum(child['replicas'] for child in parent['idle_children'])+stages*parent_banks + +bridge_additions+shifts+moves+parent_live+parent_physical+wrapper_factors) + outside=8*nonlocal_items+64*m + parent_pervertex=(scalar+bridge_additions+shifts+moves+parent_live + +(call_count*adapters+outside)*compiler+64*parent_physical) + live,physical=template['live'],template['physical'] + mass,profile=owners['rank_mass'],owners['paid_profile'] + assert m*live-mass==owners['deficit']==2560 + assert mass==sum(int(r)*count for r,count in profile.items()) + assert physical==live+helpers+centres+2 + assert live==owners['live'] and physical==owners['physical'] + assert live<=parent_live and physical<=parent_physical + assert not template['bank_padding']['families'] + assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged'] + # The old dedicated-bank geometry is only a conservative reserve envelope. + # Its singular program is never used as evidence for a mixed invocation. + rebased=parent_pervertex+65*(physical-parent_physical)+(live-parent_live) + used=max(rebased,parent_pervertex); retained=None; payload=512 + if retained_invoice is not None: + previous=read(retained_invoice) + assert previous['compiler']==compiler and previous['charged_prefix_bits']==payload + previous_bound=previous['conservative_pervertex_used'] + used=max(used,previous_bound+parent_pervertex) + retained=dict(sha256=filehash(retained_invoice),previous_pervertex_allowance=previous_bound, + added_complete_new_pervertex=parent_pervertex,policy='Retain old allowance and add entire fresh mixed recount.') + half=m//2; group=2**(half*half) + for i in range(1,half+1): group*=2**(2*i)-1 + stock,streamed_mass=group*physical,group*mass + logical=group*used+64; router=compiler*(logical+1)*(stock+1)**2 + g_bound,e_bound,c0=2**30000,2**100000,2**210000 + total_mass=streamed_mass+e_bound + literal=2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m + row=2*stock.bit_length()+9909+252+2*payload + maxchild=max(map(int,profile)) + inequalities=dict(local_primitive_bound=primitive_bound<2**48, + logical=logical<2**6050,router=router2*maxchild*maxchild) + assert all(inequalities.values()) + localbits=max(r['prefix_bits'] for p in providers.values() for r in p['local'].values()) + input_l2_bits=(m+1)//2 + required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4 + assert required_prefix=18 + return raw[:9]+b'\xff'+raw[10:] +gzip.compress=compress_portable +script=Path(sys.argv[1]).resolve() +sys.argv=sys.argv[1:] +sys.path.insert(0,str(script.parent)) +runpy.run_path(str(script),run_name='__main__') diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/data/EIGHT-COLD.json b/research/pr643-improvement-20261013/witness/vendor/multicold/data/EIGHT-COLD.json new file mode 100644 index 0000000000..aaa42ba132 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/data/EIGHT-COLD.json @@ -0,0 +1,28 @@ +{ + "part": "B", + "index": 368, + "pivot": 494, + "frame": [ + 24 + ], + "distance": 294, + "dyadic": true, + "coefficients": { + "566": "1", + "640": "-2", + "688": "-1", + "642": "2", + "690": "1" + }, + "profile_delta": { + "3": -2, + "2": 2, + "1": 1 + }, + "entropy_delta": -0.4713744313795125, + "inserted_gates": 5, + "input_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d", + "output_content_sha256": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d", + "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/558", + "source_head": "060b137c8a6f9d73fd7864c7f8cf2736d6441774" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/data/EIGHT-MULTICOLD.json b/research/pr643-improvement-20261013/witness/vendor/multicold/data/EIGHT-MULTICOLD.json new file mode 100644 index 0000000000..c16e7460cb --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/data/EIGHT-MULTICOLD.json @@ -0,0 +1,381 @@ +{ + "input_content_sha256": "edb55811a9d38802c311c74bdd2d4d1b2f3eaf37d06e4178eef0785c2fa4b57d", + "output_content_sha256": "055c0fb41d8b0d506674f62d0227833a74eabd19a022a1dfeb72c3952b7a030f", + "kernels": [ + { + "pivot": 506, + "frame": [ + 24 + ], + "gates": [ + { + "part": "B", + "index": 173, + "donor": 652, + "coefficient": "-2", + "donor_state": [ + 652, + 1 + ], + "split_donor": false + }, + { + 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Counts are inputs, not proved by this script. +80-term rational logarithms and 12-term exponentials independently enclose +the two moments. The accompanying written review addresses their realization. +""" +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +GRID = 10**30 + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def log_unit(x): + require(1 <= x <= 2, "logarithm range") + z = (x-1)/(x+1) + lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0)) + return lo, lo+2*z**161/(161*(1-z*z)) + + +def log_bounds(x): + k = 0 + while x > 2: + x /= 2 + k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + # Outward rational rounding keeps later certificates compact. + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + + +def exp_bounds(x): + require(0 <= x < 1, "exponential range") + term = total = Q(1) + for j in range(1, 13): + term *= x/j + total += term + tail = term*x/13/(1-x/14) + return total, total+tail + + +def moment(m, W, entries, saving): + lo = hi = Q(0) + for t, count in entries: + t, count = int(t), int(count) + require(0 < t < m and count > 0, "improper child") + l, u = log_bounds(Q(m, t)) + lower = exp_bounds(saving*l)[0] + upper = exp_bounds(saving*u)[1] + lo += Q(t*count, m*W)*lower + hi += Q(t*count, m*W)*upper + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/engines/moment.py b/research/pr643-improvement-20261013/witness/vendor/multicold/engines/moment.py new file mode 100644 index 0000000000..7d697cb452 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/engines/moment.py @@ -0,0 +1,113 @@ +"""Independent prospective ordinary five-stage cost, never supplier admission. + +Consumes a raw one-invocation ledger made from the actual source/internal/target +paths. No packed profile is used as an input. Missing physical/finite/compiler +obligations must remain explicit in the accompanying report. +""" +from collections import Counter +from decimal import Decimal, localcontext, ROUND_FLOOR +from fractions import Fraction as F +from functools import lru_cache +from math import factorial +import hashlib, json, sys +from pathlib import Path + +DYAD = 1 << 224 + +def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) +def ceil(x): return -floor(-x) + +@lru_cache(None) +def logarithm(x): + """Mercator bounds after binary reduction; ln(2) via two Mercator sums. + + For 1 <= y < 2, log(y) is an alternating series in z=y-1. + We instead reduce to 1 <= y < 3/2, and bound log(3/2) and + log(2) by the same alternating series at z=1/2 and z=1/3, + using log(2)=log(3/2)+log(4/3). All sums are exact rationals. + """ + assert x >= 1 + k = 0 + while x >= 2: x /= 2; k += 1 + j = int(x >= F(3, 2)) + if j: x /= F(3, 2) + def mercator(y): + z=y-1 + assert 0 <= z <= F(1,2) + # An even partial sum is below log; the next term bounds its tail. + t=z; s=F(0) + for n in range(1, 225): + s += (t if n & 1 else -t)/n + t *= z + return s, s+t/225 + a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3)) + return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f) + +def exponential(l,u): + assert 0 <= l <= u < F(1,10) + def poly(x): + s=t=F(1) + for j in range(1,25): t=t*x/j; s+=t + return s,t + lo,_=poly(l);hi,last=poly(u) + return floor(lo),ceil(hi+last*u/25/(1-u/26)) + +def moment(H,m,W,a,bad=False): + lo=hi=F(0) + for r,n in H.items(): + assert 0 < r < m and n > 0 + l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u) + p=F(r*n,m*W);lo+=p*e;hi+=p*f + if bad: + # Existing envelope shape, only conditionally portable to the new cover. + l,u=logarithm(F(m));e,f=exponential(a*l,a*u) + p=F(32*m*sum(H.values()),10**16*W) + lo+=p*e;hi+=p*f + return floor(lo),ceil(hi) + +def decimal(x): + with localcontext() as c: + c.prec=70 + return str(Decimal(x.numerator)/Decimal(x.denominator)) + +def certify(H,m,W,bad=False): + with localcontext() as c: + c.prec=70 + terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()] + fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0) + lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003') + for _ in range(210): + a=(lo+hi)/2 + if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a + else:hi=a + q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR)) + lo=F(q,10**24);hi=lo+F(1,10**24) + lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad) + assert lv[1]<10 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2 + assert 1-eps*(1+c)==eta-eps*eta/4 + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/inputs/PR543-EXPECTED.json b/research/pr643-improvement-20261013/witness/vendor/multicold/inputs/PR543-EXPECTED.json new file mode 100644 index 0000000000..b61d859826 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/inputs/PR543-EXPECTED.json @@ -0,0 +1,239 @@ +{ + "word": { + "file": "data/bitE8mut-r420.json.gz", + "file_sha256": "9721a3819efd68307f66f00d84a952eb28eb7c3ad2ce79653ce295c98a764784", + "content_sha256": "e597e3885c0a8daa262afa5985ee2930443329126aece76d33159d81882bdcc2", + "plan_sha256": "d5c2494b4baae801143049e172db303b3c8e25a002e9d9715a1d79dcb2d74c58", + "R": 420, + "retained_totals": 9, + "gates": { + "D": 120, + "A": 2064, + "B": 837, + "C": 2661 + }, + "local_histogram": { + "1": 1320, + "2": 1440, + "4": 60, + "5": 120, + "8": 9 + }, + "legality": { + "records": 29874, + "common_frame_ADDs": 26916, + "rank_mass": 5112 + }, + "five_stage_columns": 900, + "five_stage_payload_bits": 100, + "nine_stage_columns": 1380, + "nine_stage_payload_bits": 100, + "eleven_stage_columns": 1620, + "eleven_stage_payload_bits": 100 + }, + "interface": { + "hypotheses": { + "H1_no_target_feeds_z": true, + "H2_D_frame0_targets_from_helpers": true, + "H3_A_z_only_scatter_targets_B_split": true, + "H4_C_literal_reverse_at_full": true, + "H5_V_identity": true + }, + "conclusion": { + "U_block_form": true, + "J_identity": true, + "K_equals_D": true, + "C_is_U_inverse": true + }, + "interleaving": { + "z_gates_A": 2064, + "source_writes_A": 0, + "z_gates_B": 597, + "source_writes_B": 597, + "helper_writes_B": 0, + "sources_rewritten_B": 120, + "B_z_write_frame_dims": { + "4": 477, + "6": 120 + }, + "B_z_operand_kinds": { + "source<-helper": 120, + "source<-source": 477 + }, + "B_z_operand_kinds_by_dim": { + "dim4:source<-source": 477, + "dim6:source<-helper": 120 + }, + "B_z_writes_after_a_target_read_of_the_same_register": 597, + "B_target_reads_of_registers_rewritten_earlier_in_B": 120, + "target_reads_of_targets": 0, + "cleanup_gates": 2661 + } + }, + "nine": { + "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly)", + "bit_lower": "413456747036699736067/250000000000000000000000", + "bit_lower_decimal": "0.001653826988146798944268", + "profile": { + "1": 380160, + "2": 426624, + "4": 32640, + "5": 34560, + "6": 15360, + "7": 23040, + "8": 2592, + "42": 3456 + }, + "bit": { + "live": 30720, + "physical": 30729, + "maxchild": 42, + "rank_mass": 1956096, + "hosted_residuals": 120960, + "bank_assignments": 0, + "prefix_bits": 189, + "charged_prefix_bits": 192, + "coefficient_bits": 189, + "two_level_coefficient_bits": 416, + "charged_two_level_coefficient_bits": 512, + "row_coefficient": 18355, + "halving_depth": 2 + }, + "kappa": { + "pr535": { + "kappa": "793733736881443/500000000000000000", + "kappa_decimal": "0.001587467473762886", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "binding_component": "complex" + }, + "pr531": { + "kappa": "1517760977820331/1000000000000000000", + "kappa_decimal": "0.001517760977820331", + "complex_lower": "304013615566499291631/200000000000000000000000", + "binding_component": "complex" + } + } + }, + "eleven": { + "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting)", + "bit_lower": "82015816228313440961/50000000000000000000000", + "bit_lower_decimal": "0.00164031632456626881922", + "profile": { + "1": 116160, + "2": 130560, + "4": 9120, + "5": 10560, + "6": 3839, + "7": 7680, + "8": 792, + "14": 1, + "56": 3497 + }, + "bit": { + "live": 9600, + "physical": 9609, + "maxchild": 56, + "rank_mass": 745536, + "hosted_residuals": 36960, + "prefix_bits": 4710, + "charged_prefix_bits": 4736, + "coefficient_bits": 4710, + "three_level_coefficient_bits": 14185, + "charged_three_level_coefficient_bits": 14208, + "row_coefficient": 19431, + "halving_depth": 3 + }, + "emitted_program_sha256": "3de4325e0df33ca85116d05cbcc6810f025d6083e5134d128236769c97699f51", + "kappa": { + "pr535": { + "kappa": "793733736881443/500000000000000000", + "kappa_decimal": "0.001587467473762886", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "binding_component": "complex" + }, + "pr531": { + "kappa": "1517760977820331/1000000000000000000", + "kappa_decimal": "0.001517760977820331", + "complex_lower": "304013615566499291631/200000000000000000000000", + "binding_component": "complex" + } + } + }, + "controls": { + "pr510_r480_nine": { + "word": "vendor/pr510/e8-r480-dead-totals/data/bitE8mut-r480.json.gz", + "bit_lower": "396861776523137034277/250000000000000000000000", + "bit_lower_decimal": "0.001587447106092548137108", + "kappa": { + "pr535": { + "kappa": "1584931111785787/1000000000000000000", + "kappa_decimal": "0.001584931111785787", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "binding_component": "bit" + }, + "pr531": { + "kappa": "1517760977820331/1000000000000000000", + "kappa_decimal": "0.001517760977820331", + "complex_lower": "304013615566499291631/200000000000000000000000", + "binding_component": "complex" + }, + "pr484": { + "kappa": "662515748707749/500000000000000000", + "kappa_decimal": "0.001325031497415498", + "complex_lower": "663394767670133/500000000000000000", + "binding_component": "complex" + }, + "pr471": { + "kappa": "260706019542937/200000000000000000", + "kappa_decimal": "0.001303530097714685", + "complex_lower": "1305231506267591/1000000000000000000", + "binding_component": "complex" + }, + "pr458": { + "kappa": "323880830669511/250000000000000000", + "kappa_decimal": "0.001295523322678044", + "complex_lower": "1297203880559577927527/1000000000000000000000000", + "binding_component": "complex" + } + } + }, + "pr493_r489_eleven": { + "word": "../e8-bit-carrier-skeleton/data/bit/bitE8mut-r489.json.gz", + "bit_lower": "391360506745414227149/250000000000000000000000", + "bit_lower_decimal": "0.001565442026981656908596", + "emitted_program_sha256": "e37b52e4861c39154b5891460fb45df8651c92cd68961078f8f06596f057c822", + "kappa": { + "pr535": { + "kappa": "97687203033227/62500000000000000", + "kappa_decimal": "0.001562995248531632", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "binding_component": "bit" + }, + "pr531": { + "kappa": "1517760977820331/1000000000000000000", + "kappa_decimal": "0.001517760977820331", + "complex_lower": "304013615566499291631/200000000000000000000000", + "binding_component": "complex" + }, + "pr484": { + "kappa": "662515748707749/500000000000000000", + "kappa_decimal": "0.001325031497415498", + "complex_lower": "663394767670133/500000000000000000", + "binding_component": "complex" + }, + "pr471": { + "kappa": "260706019542937/200000000000000000", + "kappa_decimal": "0.001303530097714685", + "complex_lower": "1305231506267591/1000000000000000000", + "binding_component": "complex" + }, + "pr458": { + "kappa": "323880830669511/250000000000000000", + "kappa_decimal": "0.001295523322678044", + "complex_lower": "1297203880559577927527/1000000000000000000000000", + "binding_component": "complex" + } + } + } + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/CONSTRUCTION.md b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/CONSTRUCTION.md new file mode 100644 index 0000000000..1d4b6d6c17 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/CONSTRUCTION.md @@ -0,0 +1,25 @@ +# Actual words and whole-call composition + +## Seven multi-cut cold kernels (this package) + +Each provider word first receives PR564's single-cut kernel for helper 270 (below). `code/build_multicut_kernels.py` then inserts seven more kernels from the frozen recipes `data/{ZERO,FOUR,EIGHT}-MULTICOLD.json`. A kernel for pivot p at entrance frame E is a list of gates `d += -q*p @E`, each at its own position (part, index). All gates precede p's first original touch, and p carries only its initial dirt there. The gates therefore cancel p's complete dirty response if and only if `sum_g q_g * col_{cut_g}[d_g] = col[p]` over the actual suffix columns. The constructor checks this by an exact forward replay of every output row. It also requires dyadic q, donors that are not data registers, pivots or centres, legal frame chains under gk_word.profile, the pinned profile delta and the pinned output content hash. + +Pivots 506@[24], 518@[30] and 530@[30] use helper donors, one of which is a B-first helper split at its first frame; each has delta `{1:+1,2:+2,3:-2}`. Pivots 495@[24], 507@[24], 519@[30] and 531@[30] use two output-target donors and one B-first partner, all in part B; each has delta `{1:+3,2:+1,3:-2}`. All seven pivots enter at rank one, so eight helpers per word have residual width eight. `code/audit_multicold_controls.py` locates every new gate by exact content and rejects all 32 omission mutants (each gate, each whole kernel) in both exact orientations, with cleanup regenerated and correct compensation frozen. The changed words then pass the unchanged native, phase, wrapper, controller, invoice and assembly admissions. + +## PR564 single-cut kernel (inherited) + +For each zero/four/eight provider, helper 270 is register 494 and is untouched before B index 368. The frozen constructor independently reconstructs the actual suffix responses and checks + + q494 = q566 - 2q640 + 2q642 - q688 + q690. + +Five opposite donor updates on frame [24] kill that future dirty response; cleanup is rebuilt from the actual changed word. The entry frame has rank one and the helper's residual width becomes eight. The changed scalar word, compensation, inverse transpose and both frame ledgers are then verified natively; the construction relation alone is not admission. + +In PR564, with p=0,4,8 promoted pivots, the local paid profile was `e1*(2301+2p)+e2*(442-2p)+e3*(470-p)+e4*(184+p)+56e5+56e6+8e8` with width inventory `{4:p,5:56-p,8:157,9:291}`. With the seven multi-cut kernels it is `e1*(2316+2p)+e2*(452-2p)+e3*(456-p)+e4*(184+p)+56e5+56e6+8e8`, width inventory `{4:p,5:56-p,8:164,9:284}`, 220 nonzero entrance helpers and entrance rank 388+p. The exact call dispatch retains 15/2/55 counts, but every selected provider now includes the cold kernel. + +The complete literal owner map is frozen in data/OWNERS.json.gz; the audit derives physical windows through all individual bridges, same-call family uniqueness, residual offsets, spectator axes, orthogonal charts and remaining idle children. Local sums plus the idle profile `{1:93,2:93,3:2118,7:1,48:1713}` of the new literal owner map yield the complete printed profile. No profile-only homogeneous substitution is used. The solver is a discovery tool, not an admission dependency. + +All source and all wrapper/scalar/phase work remain charged. The fresh invoice sums the actual selected provider and orientation primitives, uses conservative shared compiler maxima, and retains the prior allowance as an overcharge. Reusing frozen arithmetic engines does not reuse the old invoice: the assembler independently reconstructs its stock/group/router/literal/precision/tape/row inequalities from fresh receipts. + +Uniform fixed dispatch across the full orthogonal group preserves the PR559 native complex cover argument. Right translation by each checked orthogonal owner chart is a bijection, and every chosen scalar/phase program is exact on all columns. The native moment removes no real bit exception or finite work. Both the conservative complex moment and native exact-complex moment are certified, with unchanged PR543 bit fallback and inherited all-size/analytic assumptions. + +Exploratory packing optimality receipts describe only the stated one-cold complete-group family and retained capacities. They are not global bounds over other words, cuts, kernels, owner inventories or controllers, and are not needed for the constructive record. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-EXACT-FRONTIER.json b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-EXACT-FRONTIER.json new file mode 100644 index 0000000000..adc6d105ec --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-EXACT-FRONTIER.json @@ -0,0 +1,208 @@ +{ + "status": "PASS_EXACT_TWO_ENGINE_FULL_GROUP_ONE_COLD_MIXED_FRONTIER_OPTIMAL_AT_112_GROUPS_72_COLD", + "basis": [ + 1, + 6, + 8, + 15, + 38, + 142, + 147, + 545, + 546 + ], + "basis_solution": [ + "5376", + "172", + "2964", + "448", + "3584", + "1668", + "1916", + "112", + "72" + ], + "basis_inverse": [ + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1/2", + "1", + "1", + "0", + "-1", + "-1", + "-1/2", + "0", + "-1/2" + 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The family allows arbitrary full\nrank-five groups per invocation, zero/one specified earlier cold kernel per\ninvocation, all4/5/8/9 bin patterns, and drops chronology constraints. It does\nnot exclude additional cold kernels, other local words, or cloned geometry.\n" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-OWNER-RECEIPT.json b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-OWNER-RECEIPT.json new file mode 100644 index 0000000000..15247d2f59 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-OWNER-RECEIPT.json @@ -0,0 +1,448 @@ +{ + "status": "PASS_LITERAL_MIXED048_ALLCOLD_OWNER_ASSIGNMENT_PENDING_LOCAL_AND_NATIVE_ADMISSION", + "source_word_sha256": "bab53c1749361779e4bc267fd9d1c899ccd09d61459eb6fea54edce44f16feec", + "source_plan_sha256": "0299973329086dad569269931a33d41b9f76868e747b3418e4b340720059de6f", + "owners_sha256": "5e9e6e0a61db061fef6489b4e803ac35b6c38f7419d6a51769e5438d324ed1df", + "roles": 36288, + "per_call_width_inventory": [ + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 52, + "4": 4 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 52, + "4": 4 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 56 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 48, + "4": 8 + }, + { + "9": 291, + "8": 157, + "5": 56 + } + ], + "idle_profile": { + "3": 2364, + "7": 172, + "48": 1668 + }, + "complete_paid_profile": { + "1": 166568, + "2": 30928, + "3": 35756, + "4": 13696, + "5": 4032, + "6": 4032, + "7": 172, + "8": 576, + "48": 1668 + }, + "rank_mass": 520704, + "deficit": 2560, + "window_count": 144, + "scope": "Every literal helper assigned once; exact one-family-per-invocation, source windows, offsets, disjoint axes and per-call widths checked. Exact native owner/controller/spectator audits, both moment engines and finite invoice still required.", + "parent_template_sha256": "ab8448de2036a23d9b55a196a8846512dc24fdf09855c1e0f0caa5b7a6965f7b", + "role_serialization": "final asynchronous call time, then ascending helper" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-PROVIDERS.json b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-PROVIDERS.json new file mode 100644 index 0000000000..3ba0e6f3cd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/EXPLORATORY-PROVIDERS.json @@ -0,0 +1,148 @@ +{ + "status": "PASS_ZERO_AND_FOUR_COLD_LOCAL_COMPLETE", + "script": "/private/tmp/pr558-allcold/verify_zero_four.py", + "script_sha256": "512be5db19ac347a7187688fe5cfdf37ee03fec2c68074e5df68b4b1eda90ae0", + "providers": { + "rank5_zero_cold": { + "root": "/private/tmp/pr558-allcold/providers/rank5_zero_cold", + "raw": "/private/tmp/pr558-allcold/zero-word/FULL-WORD.json.gz", + "recipe": "/private/tmp/pr558-allcold/recipes/ZERO-COLD.json", + "profile": { + "1": 2301, + "2": 442, + "3": 470, + "4": 184, + "5": 56, + "6": 56, + "8": 8 + }, + "widths": { + "9": 291, + "8": 157, + "5": 56 + }, + "programs": { + "forward": { + "sha256": "2e6c329a14d95ad5d22a9672bb3a9136b96c0f0997d9cdb7bb5f0f0d05e17504", + "events": 21486, + "scalar_macros": 16291, + "real_component_primitive_bound": 161308, + "paid_profile": { + "1": 2301, + "2": 442, + "3": 470, + "4": 184, + "5": 56, + "6": 56, + "8": 8 + }, + "all_columns": 728, + "private_centers_cleared": true, + "private_coefficient_stream_cleared_after_each_macro": true + }, + "backward": { + "sha256": "3edefeeeeed2f234ae0c72483363c38af87efbd415547425692e851cee69dc0f", + "events": 21486, + "scalar_macros": 16291, + "real_component_primitive_bound": 161356, + "paid_profile": { + "1": 2301, + "2": 442, + "3": 470, + "4": 184, + "5": 56, + "6": 56, + "8": 8 + }, + "all_columns": 728, + "private_centers_cleared": true, + "private_coefficient_stream_cleared_after_each_macro": true + } + }, + "raw_content_sha256": "7d503f7d259e4413762d33a4b7b6855a4637aa42eac99b78ff8a0500ea9b9cf7", + "canonical_sha256": "cfaaf0e6e033641e29ef926a1150b670f339a95993ebd7d8b37b24f58d5e7eb5", + "canonical_content_sha256": "e878beff358f01a19a22f7a59480663c1de1f7d6b201f082355344e65f75e732", + "phase_edges": 2929, + "endpoint_adapters": 224, + "wrapper_frames": 23, + "kernel_controls_both_orientations": 6, + "inherited_kernel_controls": 44, + "promotion_controls": 0, + "native_controls": 11, + "wrapper_controls": 5, + "receipt_sha256": "f0c5f5f38429102230e6d321ba73f470d476b6612090431802151b0454eec1a9" + }, + "rank5_four_cold": { + "root": "/private/tmp/pr558-allcold/providers/rank5_four_cold", + "raw": "/private/tmp/pr558-allcold/four-word/FULL-WORD.json.gz", + "recipe": "/private/tmp/pr558-allcold/recipes/FOUR-COLD.json", + "profile": { + "1": 2309, + "2": 434, + "3": 466, + "4": 188, + "5": 56, + "6": 56, + "8": 8 + }, + "widths": { + "9": 291, + "8": 157, + "5": 52, + "4": 4 + }, + "programs": { + "forward": { + "sha256": "ed1ec8bc7f62806188df0b8f1516a958709c4cf7064c925b328f9a0240a9f321", + "events": 21486, + "scalar_macros": 16291, + "real_component_primitive_bound": 161308, + "paid_profile": { + "1": 2309, + "2": 434, + "3": 466, + "4": 188, + "5": 56, + "6": 56, + "8": 8 + }, + "all_columns": 728, + "private_centers_cleared": true, + "private_coefficient_stream_cleared_after_each_macro": true + }, + "backward": { + "sha256": "cd5fd9340f3064053b39e65fa053447e2a9f3545c038c073e328d2158469aca5", + "events": 21486, + "scalar_macros": 16291, + "real_component_primitive_bound": 161356, + "paid_profile": { + "1": 2309, + "2": 434, + "3": 466, + "4": 188, + "5": 56, + "6": 56, + "8": 8 + }, + "all_columns": 728, + "private_centers_cleared": true, + "private_coefficient_stream_cleared_after_each_macro": true + } + }, + "raw_content_sha256": "e722b4de2f8def94a0b420e6f294be6b8b22d6bc83e65117ba369b8810c0d09d", + "canonical_sha256": "d8b15de893feb4f0c93b456341a43e34aea7ffd0b3044a6d5ad44ac9efaa6d72", + "canonical_content_sha256": "23802c1cd35143aa21b6699cee2805013c9e042eaef8b3ad63d18f6d0a45e794", + "phase_edges": 2929, + "endpoint_adapters": 224, + "wrapper_frames": 23, + "kernel_controls_both_orientations": 6, + "inherited_kernel_controls": 44, + "promotion_controls": 4, + "native_controls": 11, + "wrapper_controls": 5, + "receipt_sha256": "24e7f533ccfbeddabf544da23dfd3ebef61153e9da0962e6d093e85be1b2e670" + } + }, + "eight_cold_already_verified": "/private/tmp/complex-mixed-coldkernel-final-clean-replay/cold-local", + "scope": "Actual raw and portable native zero/four providers only. Both reflected scalar/frame ledgers, arbitrary dirt/private restoration, exact wrappers and complete phase edges passed. Global controller, complete invoice and assembly are independent remaining obligations." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR561-NOTICE.md b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR561-NOTICE.md new file mode 100644 index 0000000000..ff0c32addd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR561-NOTICE.md @@ -0,0 +1,9 @@ +# Attribution and scope + +The new call-specific cold-kernel construction, mixed-provider emitter and independent controller audit, finite invoice, packaging and exact assembly were prepared for eumemic with OpenAI Codex assistance. Apache-2.0 applies; LICENSE is included. No claim of independent human authorship or an unconditional all-size multiplication theorem is made. + +The full source package of eumemic/Codex [PR558](https://github.com/CrocSwap/integer-mult-bounds/pull/558), commit `060b137c8a6f9d73fd7864c7f8cf2736d6441774`, is copied unchanged at `vendor/pr558`. Its original notices, source pins, license and AI disclosures are preserved. Its ancestry includes Dugongue PR552 (`33c33af0b7697155be1ea708e08cbd3f0707d94c`), chafreaky PR551 (`e7faafc4fec401d24080e5b2df12f964f1cfe123`), icekylinx PR531/PR535, the PR484/PR507/PR514 owner-controller lineage, and eumemic/Codex PR550 (`c7337040822978f1611ce9d9d44e7bb96d887e23`). The retained attribution to DreamingOfClouds with Claude Opus 5.5 through Claude Code and to icekylinx with OpenAI Codex assistance is not replaced by this notice. + +The exact moment and outer engines are unchanged retained copies. The bit supplier is cited unchanged PR543, commit `2065fe4f72a914d907f1046603f5a36f17018535`; this package reprices its pinned complete profile but does not claim a fresh bit-circuit replay. The assembly uses the inherited finite-frontier method from PR275. + +The new emitter and independent owner auditor adapt the preserved PR531/PR514 implementation by binding each invocation to its own complete scalar provider and dimensions. The fresh invoice adapts PR531's exact scalar/Horner and finite accounting to sum actual selected calls and charge shared compiler maxima. Copied source paths and their hashes are recorded in SOURCE-PINS.json. All prior public heads and claims remain frozen. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR562-NATIVE-TRANSFER.txt b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR562-NATIVE-TRANSFER.txt new file mode 100644 index 0000000000..5c60dfe105 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR562-NATIVE-TRANSFER.txt @@ -0,0 +1,147 @@ +Independent source-scope review of PR559 for the three-provider 0/4/8 complex cover +Prepared with OpenAI Codex assistance. 2026-10-12 UTC. + +Conclusion + +The native exact-complex moment is conditionally justified for +the exact three-provider template bound by the final packaged physical replay. +The PR559 reasoning applies to this actual three-provider controller, provided the +same inherited all-size exact-complex compiler and outer-transfer contracts are +retained. The bit bad-residue surcharge must remain. This is not a new proof of +those inherited contracts and is not an unconditional multiplication theorem. + +Source verification + +I downloaded PR559 at head 000ede8d8354bbf2e1f0f881d0a668dac979d953, +read its PROOF.md and complete arithmetic verifier, and reproduced its published +b = 0.001594507311629175685644 and kappa = 0.001591968905569359. +The manifest-bound replay passed. The later PR559 head +d858c0b2edcc704ef370b3c96dc51a75439b77b0 extends the same proof to PR558. +Its current PR558 arithmetic replay independently passed with b = +0.001595058050537679100938 and kappa = 0.001592517892053334; its retained +PR552 regression also passed. The two source identities and numerical results +are preserved separately, rather than treating the initial PR552 result as +the current PR559 record. Independently fetched original notes at commit +12a4934d15006e8c10f9b2264f13f8f341be802b match the vendored note bytes and Git blob +identities: + + general-clifford-frames.tex: + blob 0367eeb005298601f28a673861d6f71bf1d0ebbb + SHA256 c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54 + three-stage-cover-assembly.tex: + blob 983ffb6ac8fb9117360cd0797c00c05dfa071c9d + SHA256 ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d + +I also read the original three-stage complex and bit cover notes, the retained +PR552 local emitter/auditor/controller invoice interfaces, the generic combined +assembly code, and the actual new mixed emitter, audit and invoice bindings. + +Why the two recurrence terms differ + +The original complex cover uses a finite binary orthogonal group. Exact +Gaussian-dyadic Clifford representatives exist for every selected binary frame; +each nested frame transition lowers to finite rank-zero adapters surrounding its +single paid coordinate Fourier child. Endpoint and dirty-tail identities are +operator equalities, including exact phases, rather than success statements on +a subset of residue classes. The full orthogonal-cover multiplicity cancels from +the normalized child moment, but remains fully charged in the finite invoice. + +The adjacent bit construction instead has width-dependent GL_m(R_w) selectors. +It proves good-class whole-rank execution and a real local-ring fallback on a +small exceptional residue fraction. The bound adds 32*m^2 rank-one fallback +children on a 10^-16 fraction of each ideal edge. This separate bit obligation +is not created merely because fixed binary GL matrices are used to choose exact +complex Clifford representatives. + +The conservative assembly used the same bad=True arithmetic helper for both +suppliers, thereby adding that bit fallback to the already exhaustive complex +profile. Under the exact-complex compiler contract, it is sufficient to charge + + sum_r H[r] * (r/73)^(1-b) / 7168. + +Only the extra complex fallback term is omitted. No paid child, idle remainder, +Clifford adapter, scalar/Horner primitive, wrapper, group router, precision, +tape, external-row or all-size obligation is omitted. + +Transfer to the actual mixed controller + +All three selected providers have been independently replayed on all 728 arbitrary +scalar columns in both reflected orientations, including all 504 dirty helper +columns and private-work erasure. Their native event lists, actual local paid +profiles, phase recipes and normalization adapters are bound into the emitted +provider registry. Exactly 55 calls use rank5_eight, 15 use rank5_zero and two use rank5_four. +The two four-pivot calls are (stage 4, replica 5) and (stage 7, replica 5); +the entire 72-call order and provider map are frozen in the independent auditor +and hardened assembler. The call, sweep, orientation and program hashes agree. +Provider selection does not depend on the cover group element or on a residue +class. Every cover vertex uses the same finite schedule and selected programs. + +The independent controller audit reconstructed all 36,288 helper owner roles, +including availability windows through individual bridges, one whole physical +owner per helper invocation, disjoint residual slots, actual spectator axes, +3,018 orthogonal 73-column chart types, and all 4,240 positive idle remainders. +Its complete profile is: + + {1:166496, 2:30784, 3:35907, 4:13696, 5:4032, 6:4032, + 7:208, 8:576, 39:1, 48:1660}. + +Each fixed orthogonal owner chart acts by right translation on the full retained +cover group; right translation is a bijection. This supplies the same complete +construction at every group vertex. Different fixed providers at different +schedule positions do not introduce an exceptional subset. No enumeration of +the enormous entire orthogonal group is claimed: the finite chart checks and +exact group-translation argument are distinct parts of the reasoning. + +The fresh mixed finite invoice recounts actual selected-provider scalar/Horner +work and wrappers, uses conservative shared compiler maxima, and retains the +full group stock and router charge. All nine finite checks pass; prefix 225 is +below payload 512, physical row coefficient 16,467 is below 20,161, and the +halving check is 73^2 = 5,329 > 2*48^2 = 4,608. Those guards are unchanged by the +recurrence correction. + +Independent exact arithmetic + +The two rational engines give the accepted supplier endpoint + b = 0.001595125099152880684647 +and reject b + 10^-24. The old contaminated complex model rejects the new +endpoint, demonstrating that the numerical difference is precisely a recurrence +choice and not a hidden change to source or owners. With the unchanged cited +PR543 bit cap c = 0.001653826988146798944268, including its fallback term, seven +bootstrap levels and all 47 strict outer inequalities yield + kappa = 0.001592584727281865. +The next 10^-18 kappa grid point is rejected by that assembly witness. +The gain over the conservative mixed kappa 0.001592584724544791 is 2.737074e-12. +The final ASSEMBLY.json retains the exact rational intervals, all 47 +inequalities for each recurrence, seven bootstrap levels for each, and source +hashes. The conservative endpoint b = 0.001595125096407067070240 and its +complete outer witness pass before the native correction is applied. The +separate ASSEMBLY-CONTROLS.json rejects 50 admission mutations while +rebinding mutated owner digests; it also records the four strict outer +parameter controls for both witnesses and the two recurrence-model controls. + +Required conditions and limits + +1. Completed recursive children must implement the exact Gaussian-dyadic complex + operators on all roles under the inherited all-size compiler/common-label + interface; the finite replay does not prove arbitrary-size realization. +2. Selected providers must remain fixed per complete invocation and uniformly + transported across the complete finite orthogonal cover. A new provider with + actual exceptional residue classes would require a new fallback analysis. +3. Dirty restoration, both reflected scalar/frame ledgers, exact Clifford phases, + wrapper normalization, complete paid profiles, owner windows and residual + remainders remain admission requirements, all checked for this template. +4. Full finite group/router and literal scalar/Horner/adapter charges, completed + call precision, fixed tape/exact recovery and external-row contracts remain. +5. The PR543 bit compiler, mutable-source/local-ring selector and H1-H5 conditions, + including its complete bad-class fallback, remain separate assumptions. +6. The inherited analytic/outer transfer remains conditional. This review changes + no operator and proves no unconditional theorem, practical speedup or general + optimality claim. Published heads have not been edited. + +Attribution + +This recurrence correction follows rohanarun's PR559 source-scope review and +credits the original exact Clifford/complex-cover notes by icekylinx and prior +compiler/hosting authors. The 0/4/8 words and reassigned whole owners retain PR558, +Dugongue PR552 and eumemic PR543 provenance. This independent application and +arithmetic check were prepared with OpenAI Codex assistance. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR562-NOTICE.md b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR562-NOTICE.md new file mode 100644 index 0000000000..bbf3ffd9e5 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PR562-NOTICE.md @@ -0,0 +1,11 @@ +# Attribution and scope + +The new 0/4/8 per-invocation selection, literal whole-owner reassignment, controller binding, independent admission, packaging and exact composition were prepared for eumemic with OpenAI Codex assistance. Apache-2.0 applies; LICENSE is included. No claim of independent human authorship or an unconditional all-size theorem is made. + +The unchanged full source of eumemic/Codex PR558, head `060b137c8a6f9d73fd7864c7f8cf2736d6441774`, is preserved at `vendor/pr558`. This includes its original notices, license, source pins and AI disclosures, and the ancestry of Dugongue PR552 (`33c33af0b7697155be1ea708e08cbd3f0707d94c`), chafreaky PR551 (`e7faafc4fec401d24080e5b2df12f964f1cfe123`), icekylinx PR531/PR535, PR484/PR507/PR514 hosting/controller work, and eumemic/Codex PR550 (`c7337040822978f1611ce9d9d44e7bb96d887e23`). The original attribution to DreamingOfClouds with Claude Opus 5.5 through Claude Code and icekylinx with OpenAI Codex assistance is retained. + +The unchanged full source package of Rohan Arun's PR559, head `d858c0b2edcc704ef370b3c96dc51a75439b77b0`, is preserved at `vendor/pr559`. We credit its native exact-complex moment correction and source-scope argument; its original OpenAI Codex assistance notice, earlier rohanarun/Claude attribution and all source notices remain. Our transfer of that argument to the three-provider cover is documented separately. The original icekylinx Clifford and three-stage cover notes were independently checked at commit `12a4934d15006e8c10f9b2264f13f8f341be802b`. + +The new emitter, owner auditor and finite invoice adapt PR561's mixed-provider implementation, which in turn adapts the preserved PR531/PR514 implementation. PR561 is eumemic/Codex head `210dfa4896e77a8fb5e22ca5a970b0fb0ac984a6`; its notice is copied at `proof/PR561-NOTICE.md`. This package's providers use no cold kernel. The rational engines are retained unchanged; finite assembly follows the PR275 lineage. The unchanged PR543 bit supplier is cited at `2065fe4f72a914d907f1046603f5a36f17018535`; its complete pinned profile is repriced but its bit circuit is not rebuilt here. + +Source pins record exact copied bytes and derivations. All previously published PR heads and claims remain frozen. All inherited all-size/common-label/mutable-source, hosting, compiler, precision/tape, analytic and bit H1–H5 assumptions remain. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PROOF-ALLCOLD-NATIVE.txt b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PROOF-ALLCOLD-NATIVE.txt new file mode 100644 index 0000000000..86c0e641ef --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PROOF-ALLCOLD-NATIVE.txt @@ -0,0 +1,145 @@ +Independent native-complex transfer review: all 72 one-cold 0/4/8 providers +Prepared with OpenAI Codex assistance. Apache-2.0. + +Result and scope + +The independently checked exploratory controller with content SHA256 +639f2e6e9478c938e8579bf741cf0859c2114c09e172565ea9ee24b281059bfa +has the conditional exact-native-complex witness + b = 0.001595676284575998624254 + kappa = 0.001593134158181640. +Its separately admitted conservative-complex witness is + b = 0.001595676281828849775453 + kappa = 0.001593134155443237. +These statements retain the inherited all-size compiler, common-label and +mutable-source realization, whole-invocation hosting, precision/tape/exact +recovery, external-row, H1-H5 and analytic transfer assumptions. They do not +assert an unconditional multiplication theorem or a practical speedup. + +Source of the native correction + +This application uses the exact-complex versus exceptional-residue distinction +reviewed in rohanarun PR559, head 000ede8d8354bbf2e1f0f881d0a668dac979d953. +The earlier independent source review is PROOF-REVIEW.txt, SHA256 +0a807ea2c5fec29cbf994f94bd5a388914fb31de02dba03d18265040044c0dc6. +It checked the original note sources at commit 12a4934d15006e8c10f9b2264f13f8f341be802b: + general-clifford-frames.tex, Git blob 0367eeb005298601f28a673861d6f71bf1d0ebbb, + SHA256 c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54; + three-stage-cover-assembly.tex, Git blob 983ffb6ac8fb9117360cd0797c00c05dfa071c9d, + SHA256 ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d. +The present review consumes that preserved source analysis and freshly checks +its transfer hypotheses against the new literal controller and local receipts. +It does not claim a new download or proof of the inherited arbitrary-size +contracts. + +Why no complex exceptional-residue surcharge is present + +Every selected native complex word is an exact Gaussian-dyadic scalar and +Clifford construction. Its paid frame transitions, reflected orientations, +phase representatives and residual wrappers are operator identities. Its fixed +binary orthogonal owner chart acts on the complete retained finite orthogonal +cover by right translation, which is a bijection. Provider dispatch is fixed +for each complete schedule position; neither the selected provider nor its +schedule depends on a cover vertex or residue class. Thus this particular +three-provider composition introduces no exceptional subset of complex cover +vertices. The normalized complex moment is precisely + + sum_r H[r] * (r/73)^(1-b) / 7168. + +Only the extraneous bit-style complex fallback is removed. The unchanged PR543 +bit supplier retains its full bad-residue surcharge, its local-ring selector +conditions and separate compiler obligations. All complex paid children, +positive idle remainders, scalar/Horner work, wrappers, phases, finite group +stock and routers, precision, fixed tape and external rows remain charged. + +Fresh literal admission + +All 72 complete invocations use one of three actual one-cold providers: + rank5_zero_cold 15, rank5_four_cold 2, rank5_eight_cold 55. +Every helper index, ordered width and selected reflected program is bound to +its actual provider bytes. Helper 270 has width 8 in every provider; the width +inventories are {4:p,5:56-p,8:157,9:291} for p=0,4,8. Each provider has 504 helpers, +213 entering helpers and entrance rank 381+p. No width histogram substitutes +for an actual local word. + +The supplied local admission independently checks all 728 arbitrary columns in +both reflected orientations, including all 504 dirty helper columns and erased +private center/coefficient work, both native frame ledgers, all 2,929 literal +phase edges and 224 endpoints. The controller audit rebinds those canonical +words, emitted program hashes, paid profiles, exact phase recipes and normalized +residual adapters. Both orientations of each provider have 21,486 actual events +and 16,291 scalar macros. The complete selected primitive count is +11615712, including coefficient work +5751952. + +The independent serialized controller audit imports no emitter or optimizer. +It reconstructs all 36288 whole-helper owner roles, their +individual-bridge availability windows, per-replica event order, one whole +physical owner per helper during the complete invocation, disjoint residual +slots, spectator axes and all 2962 actual orthogonal +73-column chart types. It finds 29514 cross-replica roles, +15336 entering roles and 4204 positive idle +remainders. Every full cover invocation remains indivisible. The complete +literal paid profile is + + {'1': 166568, '2': 30928, '3': 35756, '4': 13696, '5': 4032, '6': 4032, '7': 172, '8': 576, '48': 1668}. + +Its rank mass is 520704, live stock 7168, physical stock 7682 and deficit 2560. +The positive idle profile is {3:2364,7:172,48:1668}. No bank or uncharged helper +family is added. Sixteen controller mutation controls are rejected, including +stale providers, program hashes, wrong owner windows/widths/charts and missing +cold-helper wrapper bindings. + +The fresh finite invoice sums all 72 selected provider/orientation programs and +normalization wrappers. It uses conservative shared compiler maxima and fully +charges the retained finite orthogonal group, family stock and routers. It also +retains the prior complete invoice allowance as an extra overcharge. All nine +finite checks pass. Prefix 225 is below 512; the physical row +coefficient 16467 is below 20161; the required +C0 bits 200012 are below 210000; the largest child obeys +73^2=5329 > 2*48^2=4608. + +Exact arithmetic and hardened admission + +Both independent rational power engines accept the conservative endpoint and +the native endpoint above, and reject each adjacent 10^-24 supplier endpoint. +The cited unchanged PR543 bit cap is 0.001653826988146798944268, with its surcharge retained. +Seven explicit bootstrap steps and all 47 strict outer inequalities produce +each stated 18-decimal kappa witness. Each next 10^-18 grid point is rejected by +that witness; zero eta/beta and unit beta controls are rejected. + +The assembler first checks the complete conservative admission, moments and +outer witness, then applies the native correction. It independently binds +ordered per-helper widths, each selected call and orientation, exact program +and source artifact hashes, scalar and wrapper counts, prefix envelopes, +finite compiler arithmetic, complete paid profiles and all physical counts. +The phase-review semantic hash removes only its seconds field; all substantive +phase data stay pinned. Fresh raw phase-review hashes still bind actual source +bytes in both controller and invoice. Six deterministic source artifacts retain +full byte pins, including the actual Clifford recipes. +All 54 rebound admission mutations are rejected. These +include synchronized forged recipe hashes, a cold width permutation preserving +the inventory, and self-consistent stale no-cold wrapper totals. A stale digest +is never used as the sole reason for rejection of an altered receipt. + +The old complex-surcharge model rejects the new native endpoint. Omitting the +bit surcharge invalidates its claimed adjacent-endpoint rejection. These two +model controls isolate exactly which recurrence changes and which remains. + +Remaining assumptions and attribution + +This finite audit does not enumerate the enormous full orthogonal group; the +actual finite charts and the exact translation-bijection argument are distinct. +It does not prove arbitrary-size realization, common-label synthesis, mutable +source/local-ring compiler contracts, precision-to-exact-recovery transfer, or +H1-H5. Those inherited obligations remain explicit. The changed local words, +controller, invoice and arithmetic are all separately evidenced. + +Provenance retains the icekylinx exact Clifford/complex-cover notes and prior +compiler/hosting work, PR558/PR552 rank-five provider lineage, the frozen PR561 +eight-plus-cold word, and eumemic PR543 for the unchanged bit supplier. The +native recurrence correction follows rohanarun PR559. This all 72 one-cold +application and independent review were prepared with OpenAI Codex assistance. +No previously published head or claim was changed. + +The packaged verifier reconstructs the same fixed words, call dispatch and owner assignment. Its final template/receipt hashes bind newly generated phase timing metadata; all deterministic artifact hashes and all phase semantics (excluding only elapsed seconds) remain frozen in the assembler. Final ASSEMBLY.json and RECEIPT.json identify that replay. The unchanged current PR559 head d858c0b2edcc704ef370b3c96dc51a75439b77b0 is vendored in full, with its source notices and the original exact-cover notes. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PROOF-REVIEW.txt b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PROOF-REVIEW.txt new file mode 100644 index 0000000000..ce86b29764 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/proof/PROOF-REVIEW.txt @@ -0,0 +1,133 @@ +Independent source-scope review of PR559 for the mixed PR558-derived complex cover +Prepared with OpenAI Codex assistance. 2026-10-12 UTC. + +Conclusion + +The native exact-complex moment is conditionally justified for mixed template +625590098a4c2bd3d0da9c78262a53c486a240477cb8348219bd4512f573edfc. +The PR559 reasoning applies to this actual two-provider controller, provided the +same inherited all-size exact-complex compiler and outer-transfer contracts are +retained. The bit bad-residue surcharge must remain. This is not a new proof of +those inherited contracts and is not an unconditional multiplication theorem. + +Source verification + +I downloaded PR559 at head 000ede8d8354bbf2e1f0f881d0a668dac979d953, +read its PROOF.md and complete arithmetic verifier, and reproduced its published +b = 0.001594507311629175685644 and kappa = 0.001591968905569359. +The manifest-bound replay passed. Independently fetched original notes at commit +12a4934d15006e8c10f9b2264f13f8f341be802b match the vendored note bytes and Git blob +identities: + + general-clifford-frames.tex: + blob 0367eeb005298601f28a673861d6f71bf1d0ebbb + SHA256 c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54 + three-stage-cover-assembly.tex: + blob 983ffb6ac8fb9117360cd0797c00c05dfa071c9d + SHA256 ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d + +I also read the original three-stage complex and bit cover notes, the retained +PR552 local emitter/auditor/controller invoice interfaces, the generic combined +assembly code, and the actual new mixed emitter, audit and invoice bindings. + +Why the two recurrence terms differ + +The original complex cover uses a finite binary orthogonal group. Exact +Gaussian-dyadic Clifford representatives exist for every selected binary frame; +each nested frame transition lowers to finite rank-zero adapters surrounding its +single paid coordinate Fourier child. Endpoint and dirty-tail identities are +operator equalities, including exact phases, rather than success statements on +a subset of residue classes. The full orthogonal-cover multiplicity cancels from +the normalized child moment, but remains fully charged in the finite invoice. + +The adjacent bit construction instead has width-dependent GL_m(R_w) selectors. +It proves good-class whole-rank execution and a real local-ring fallback on a +small exceptional residue fraction. The bound adds 32*m^2 rank-one fallback +children on a 10^-16 fraction of each ideal edge. This separate bit obligation +is not created merely because fixed binary GL matrices are used to choose exact +complex Clifford representatives. + +The conservative assembly used the same bad=True arithmetic helper for both +suppliers, thereby adding that bit fallback to the already exhaustive complex +profile. Under the exact-complex compiler contract, it is sufficient to charge + + sum_r H[r] * (r/73)^(1-b) / 7168. + +Only the extra complex fallback term is omitted. No paid child, idle remainder, +Clifford adapter, scalar/Horner primitive, wrapper, group router, precision, +tape, external-row or all-size obligation is omitted. + +Transfer to the actual mixed controller + +Both selected providers have been independently replayed on all 728 arbitrary +scalar columns in both reflected orientations, including all 504 dirty helper +columns and private-work erasure. Their native event lists, actual local paid +profiles, phase recipes and normalization adapters are bound into the emitted +provider registry. Exactly 71 calls use rank5_eight and only (stage 4, replica 6) +uses coldkernel000. The call, sweep, orientation and program hashes agree. +Provider selection does not depend on the cover group element or on a residue +class. Every cover vertex uses the same finite schedule and selected programs. + +The independent controller audit reconstructed all 36,288 helper owner roles, +including availability windows through individual bridges, one whole physical +owner per helper invocation, disjoint residual slots, actual spectator axes, +3,178 orthogonal 73-column chart types, and all 4,368 positive idle remainders. +Its complete profile is: + + {1:166881, 2:30530, 3:35777, 4:13824, 5:4032, 6:4032, + 7:208, 8:576, 40:1, 48:1660}. + +Each fixed orthogonal owner chart acts by right translation on the full retained +cover group; right translation is a bijection. This supplies the same complete +construction at every group vertex. Different fixed providers at different +schedule positions do not introduce an exceptional subset. No enumeration of +the enormous entire orthogonal group is claimed: the finite chart checks and +exact group-translation argument are distinct parts of the reasoning. + +The fresh mixed finite invoice recounts actual selected-provider scalar/Horner +work and wrappers, uses conservative shared compiler maxima, and retains the +full group stock and router charge. All nine finite checks pass; prefix 225 is +below payload 512, physical row coefficient 16,467 is below 20,161, and the +halving check is 73^2 = 5,329 > 2*48^2 = 4,608. Those guards are unchanged by the +recurrence correction. + +Independent exact arithmetic + +The two rational engines give the accepted supplier endpoint + b = 0.001595058893494095255548 +and reject b + 10^-24. The old contaminated complex model rejects the new +endpoint, demonstrating that the numerical difference is precisely a recurrence +choice and not a hidden change to source or owners. With the unchanged cited +PR543 bit cap c = 0.001653826988146798944268, including its fallback term, six +bootstrap levels and all 47 strict outer inequalities yield + kappa = 0.001592518732327041. +The next 10^-18 kappa grid point is rejected by that assembly witness. +The gain over the conservative mixed kappa 0.001592518729588709 is 2.738332e-12. +RESULT.json retains the exact rational intervals, inequalities and source hashes. + +Required conditions and limits + +1. Completed recursive children must implement the exact Gaussian-dyadic complex + operators on all roles under the inherited all-size compiler/common-label + interface; the finite replay does not prove arbitrary-size realization. +2. Selected providers must remain fixed per complete invocation and uniformly + transported across the complete finite orthogonal cover. A new provider with + actual exceptional residue classes would require a new fallback analysis. +3. Dirty restoration, both reflected scalar/frame ledgers, exact Clifford phases, + wrapper normalization, complete paid profiles, owner windows and residual + remainders remain admission requirements, all checked for this template. +4. Full finite group/router and literal scalar/Horner/adapter charges, completed + call precision, fixed tape/exact recovery and external-row contracts remain. +5. The PR543 bit compiler, mutable-source/local-ring selector and H1-H5 conditions, + including its complete bad-class fallback, remain separate assumptions. +6. The inherited analytic/outer transfer remains conditional. This review changes + no operator and proves no unconditional theorem, practical speedup or general + optimality claim. Published heads have not been edited. + +Attribution + +This recurrence correction follows rohanarun's PR559 source-scope review and +credits the original exact Clifford/complex-cover notes by icekylinx and prior +compiler/hosting authors. The mixed word and owner construction retain PR558, +Dugongue PR552 and eumemic PR543 provenance. This independent application and +arithmetic check were prepared with OpenAI Codex assistance. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/LICENSE b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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eight-pivot construction, its deterministic orchestration and its additional omission controls were prepared for eumemic with OpenAI Codex assistance. Apache-2.0 applies; the license is included. No claim of independent human authorship, Lean verification, or an unconditional all-size multiplication theorem is made. + +The unchanged reconstruction and admission dependencies are copied from [PR552](https://github.com/CrocSwap/integer-mult-bounds/pull/552), commit `33c33af0b7697155be1ea708e08cbd3f0707d94c`, package `research/filtration-wavefront`. Its complete 105-file source package is retained, including the historical notices, proofs, AI disclosures, source pins and license. The package credits earlier work by DreamingOfClouds with Claude Opus 5.5 through Claude Code, and work by icekylinx with OpenAI Codex assistance; those credits are not replaced by this notice. + +The complete phase compiler driver `code/phases_full.py` is copied unchanged from [PR551](https://github.com/CrocSwap/integer-mult-bounds/pull/551), commit `e7faafc4fec401d24080e5b2df12f964f1cfe123`, with its original attribution retained. Other phase and global admission sources remain the pinned PR552 vendored versions of the earlier PR531/PR535 lineage. + +The cited bit supplier is [PR543](https://github.com/CrocSwap/integer-mult-bounds/pull/543), commit `2065fe4f72a914d907f1046603f5a36f17018535`. Its published exact receipt is an explicit dependency. This package's verifier rebuilds the changed complex supplier; it does not claim a fresh bit replay. + +`SOURCE-PINS.json` records copied upstream paths, commits, SHA-256 digests and Git blob identifiers. Unmodified source files remain byte-for-byte copies. The final package manifest also covers the new construction, owner plan and scripts. Prior published PR heads and claims are preserved. + +The hardened assembly and admission controls are adapted from eumemic/Codex PR550, head `c7337040822978f1611ce9d9d44e7bb96d887e23`; the finite-parameter choice uses the retained PR275 finite-frontier method. Source hashes and changes are recorded in `proof/ASSEMBLY-PROVENANCE.json`. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/README.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/README.md new file mode 100644 index 0000000000..422d13cf25 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/README.md @@ -0,0 +1,21 @@ +κ = 0.001592517889315014 (conditional). + +This finite witness promotes eight post-center kernel pivots from entrance rank four to rank five in PR552's complex supplier and rebuilds their literal whole-owner assignment. It improves the tied PR551/PR552 value by 0.034484749%. The complex bound b = 0.001595058047790616770328 binds; the cited unchanged PR543 bit bound is c = 0.001653826988146798944268. + +The scalar instructions and coefficients remain unchanged. Two four-pivot groups acquire rank-five entrances and kernel frames, reducing eight helper widths from five to four. The complete local profile is `{1:2316,2:424,3:464,4:192,5:56,6:56,8:8}`; widths are `{4:8,5:48,8:156,9:292}`. Full promotion of all 48 eligible pivots loses after packing costs. The selected eight use a new chronological owner assignment, whose complete paid profile is `{1:166880,2:30528,3:35779,4:13824,5:4032,6:4032,7:208,8:576,39:1,48:1660}`. + +Run with Python 3.11+ and NumPy, assertions enabled, in a new output directory: + +```sh +python -B verify.py --work /absolute/new/output-directory +``` + +The offline verifier reconstructs pinned PR552 from primitive inputs, applies the deterministic promotion, checks all 728 columns in both orientations and every arbitrary dirty helper, 44 retained and eight new omitted-pivot controls, both reflected paid ledgers, 11 native controls and normalized wrappers. It compiles every one of 2,929 phase edges and 224 endpoint adapters, admits all 36,288 literal helper roles and seven owner corruptions, and derives a fresh finite invoice. Both rational moment engines certify the suppliers and reject their next grid points. Seven finite bootstrap steps satisfy all 47 strict outer constraints; four outer and 13 malformed-admission controls reject. The next κ grid point is excluded. No optimizer is needed for replay. + +Actual prefix 225 is below charged 512; row coefficient 16,467 is below charged 20,161. Every live stock, coefficient-work primitive, restoration field and artifact binding is checked before assembly. `--local-only` is an explicitly incomplete diagnostic. The full manifest binds all files; owner serialization follows asynchronous call time then helper so the emitted and independently audited chart streams agree. + +The selected helpers are 419,421,422,423 and 451,453,454,455 in the inherited helper indexing. Exact frames and the scalar argument are in `proof/CONSTRUCTION.md`; literal owners are `data/OWNERS.json.gz`. Clean replay evidence is retained beside this package; GitHub CI is separate and is not claimed green. + +The result remains conditional on the inherited all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic-transfer contracts. The retained bit interleaved source writes use their stated H1-H5 interface argument. This package cites and reprices PR543; it does not rebuild the unchanged bit circuit. No unconditional theorem or complete Lean proof is claimed. + +Prepared for eumemic with OpenAI Codex assistance. The complete pinned PR552 source and original authorship, AI disclosures, manifests and licenses remain in `vendor/pr552`; PR551 supplies the unchanged all-edge phase driver, and PR550 supplies the adapted hardened assembly. Earlier PR531/535, PR534, PR541/548, PR484 and their attributed ancestry remain credited. See `NOTICE.md`, `SOURCE-PINS.json` and `proof/ASSEMBLY-PROVENANCE.json`. 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"pr": 543, + "head": "2065fe4f72a914d907f1046603f5a36f17018535", + "scope": "Cited retained bit supplier; the current package does not rerun its C++ compiler or scalar programs." + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/assemble.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/assemble.py new file mode 100644 index 0000000000..c57a9805e7 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/assemble.py @@ -0,0 +1,103 @@ +"""Exact two-supplier assembly for the eight rank-five kernel pivots. + +Prepared with OpenAI Codex assistance. The rational engines and outer +constraints are retained from PR547/PR548 and their preserved ancestry. +The bit operator is the cited unchanged PR543 supplier. The complex owner +and invoice inputs must be freshly emitted by the packaged physical replay. +""" +from pathlib import Path +from fractions import Fraction as Q +from decimal import Decimal, localcontext +import argparse,json,hashlib,importlib.util +assert __debug__, 'Assertions required' +P=Path(__file__).resolve().parent.parent +read=lambda p:json.loads(p.read_text()) +sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +def load(n): + s=importlib.util.spec_from_file_location(n,P/'engines'/(n+'.py'));m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +M,B,A=[load(n)for n in ('moment','base_two_moment','outer')] +def dec(x): + with localcontext()as ctx:ctx.prec=70;return str(Decimal(x.numerator)/Decimal(x.denominator)) +def assemble(owner,invoice,owner_sha,invoice_sha): + # These are admission receipts, not optional collections of successful rows. + # Require both orientations and every finite check before pricing anything. + assert owner['status']=='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE' + assert invoice['status']=='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE' + assert all(isinstance(x,str) and len(x)==64 and all(t in '0123456789abcdef'for t in x)for x in (owner_sha,invoice_sha)) + checks={'local_primitive_bound','logical','router','literal','mass','precision','tape','row','halving'} + assert set(invoice['strict_checks'])==checks + assert all(invoice['strict_checks'][name] is True for name in checks) + assert set(invoice['local'])=={'forward','backward'} + assert owner['all_live_owners_per_call_distinct'] is True + assert owner['owners_per_call']==728 and owner['actual_helper_owner_charts']==36288 + assert owner['rank_mass']==520704 + assert invoice['complete_invocation_sweeps']==invoice['bridge_sweeps']==72 + assert invoice['live']==owner['live'] and invoice['physical']==owner['physical'] + assert invoice['helpers']==504 and invoice['centres']==8 + assert invoice['entering_helpers']==212 and invoice['entrance_rank']==388 + assert invoice['width_inventory']=={'4':8,'5':48,'8':156,'9':292} + assert invoice['physical_stock_identity']==dict(data_and_owner_families=7168,local_helpers=504,private_centres=8,coefficient_work=2) + assert sum(invoice['physical_stock_identity'].values())==invoice['physical'] + assert invoice['controller_audit_sha256']==owner['controller_audit_sha256'] + # The owner audit and fresh invoice must cite the same actual local artifacts. + links={'canonical_word_sha256':'split-centres/CANONICAL-WORD.json.gz', + 'local_programs_sha256':'split-centres/LOCAL-PROGRAMS.json.gz', + 'local_checks_sha256':'split-centres/LOCAL-CHECKS.json', + 'independent_local_replay_sha256':'split-centres/INDEPENDENT-LOCAL-REPLAY.json'} + for key,path in links.items():assert invoice[key]==owner['source_artifacts'][path] + for name,primitives,coefficient_work in [('forward',161308,79874),('backward',161356,79906)]: + z=invoice['local'][name] + assert z['all_dirty_helper_columns_restored'] is True and z['private_centres_and_coefficient_work_cleared'] is True + assert z['all_exact_columns']==728 and z['dirty_helper_columns']==504 + assert z['events']==21483 and z['macros']==16290 + assert z['real_component_primitives']==primitives and z['coefficient_work_primitive_count']==coefficient_work + assert z['pre_wrappers']==z['post_wrappers']==212 + assert 02*max(h)**2 + for z,accept in [(lower,True),(lower+Q(1,10**24),False)]: + l,u=M.moment(h,m,W,z,True);ll,uu=B.moment(m,W,list(h.items()),z) + fl,fu=B.moment(m,W,[(1,32*m*m*sum(h.values()))],z);ll+=fl/10**16;uu+=fu/10**16 + assert (u<1 and uu<1)if accept else(l>1 and ll>1) + moments.append(dict(side=side,endpoint=str(z),accept=accept,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)])) + assert bit['bit']['two_level_coefficient_bits']0 + ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512) + cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a) + q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18) + bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}} + outer=A.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta);assert len(outer['strict_constraints'])==47 and all(v>0 for v in outer['strict_constraints'].values()) + controls=[] + for name,kk,ee,bb in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]: + try:A.assembly(chain[-1],b,bridge,kk,eta=ee,beta=bb) + except AssertionError:controls.append(name) + else:raise AssertionError(name) + input_hashes={'owner_audit':owner_sha,'fresh_invoice':invoice_sha,'inputs/PR543-EXPECTED.json':sha(bit_path)} + input_hashes.update({'engines/'+name+'.py':sha(P/'engines'/(name+'.py'))for name in ('moment','base_two_moment','outer')}) + return dict(status='PASS_FRESH_EIGHT_PIVOT_EXACT_ASSEMBLY',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex',gain_over_pinned551_552_percent=dec(100*(k/Q('0.001591968902833346')-1)),complex_profile=H,template_sha256=owner['template_sha256'],input_sha256=input_hashes,bit_supplier=dict(pr=543,repository='eumemic/integer-mult-bounds',commit='2065fe4f72a914d907f1046603f5a36f17018535',path='research/e8-bit-r420/EXPECTED.json',git_blob_sha1='b61d859826246e0c3dabbe096e57ad7015eadfd5',replay_scope='Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit.'),moments=moments,bootstrap=cuts,outer={n:str(v)for n,v in outer['strict_constraints'].items()},controls=controls,scope='Conditional finite complex witness composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.') +if __name__=='__main__': + import sys + package,C,out=map(Path,sys.argv[1:4]);assert package.resolve()==P and not out.exists() + owner_path=C/'audit/OWNERS-AND-PROFILE.json';invoice_path=C/'audit/PREFIX-AND-INVOICE.json' + owner,invoice=read(owner_path),read(invoice_path) + assert owner['template_sha256']==read(C/'hosted/HOSTED.json')['template_sha256'] + r=assemble(owner,invoice,sha(owner_path),sha(invoice_path));out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],r['kappa_decimal']) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/assembly_controls.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/assembly_controls.py new file mode 100644 index 0000000000..4cb2fae937 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/assembly_controls.py @@ -0,0 +1,103 @@ +"""Admission-gate negative controls for the exact two-supplier assembly. + +Prepared with OpenAI Codex assistance; Apache-2.0. These use the fresh owner +and invoice receipts, never repeat the physical replay or change its artifacts. +""" +import argparse +import copy +import hashlib +import json +from pathlib import Path + +from assemble import assemble + +assert __debug__, 'Assertions required' +P = Path(__file__).resolve().parent +sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest() +digest = lambda x: hashlib.sha256(json.dumps(x, sort_keys=True, separators=(',', ':')).encode()).hexdigest() + + +def verify(owner_path, invoice_path): + owner = json.loads(owner_path.read_text()) + invoice = json.loads(invoice_path.read_text()) + baseline = assemble(owner, invoice, sha(owner_path), sha(invoice_path)) + + def empty_maps(o, i): + i['strict_checks'] = {} + i['local'] = {} + + def missing_backward(o, i): + del i['local']['backward'] + + def failed_status_zero_sweeps(o, i): + i['status'] = 'FAIL' + i['complete_invocation_sweeps'] = i['bridge_sweeps'] = 0 + + def understated_stock(o, i): + # Keep the two receipts mutually consistent, but remove a required role. + o['physical'] -= 1 + i['physical'] -= 1 + i['physical_stock_identity']['coefficient_work'] -= 1 + + def changed_profile(o, i): + # Keep the rank mass and deficit unchanged; pricing must bind the word. + o['paid_profile']['1'] += 2 + o['paid_profile']['2'] -= 1 + + controls = [ + ('empty_certification_maps', empty_maps), + ('missing_backward_orientation', missing_backward), + ('failed_status_zero_sweeps', failed_status_zero_sweeps), + ('nonboolean_precision_check', lambda o, i: i['strict_checks'].__setitem__('precision', 'true')), + ('wrong_owner_role_count', lambda o, i: o.__setitem__('actual_helper_owner_charts', 36287)), + ('understated_physical_stock', understated_stock), + ('changed_profile_same_rank_mass', changed_profile), + ('insufficient_finite_C0', lambda o, i: i['finite'].__setitem__('required_C0_bits', 210001)), + ('unpaid_scalar_primitive', lambda o, i: i['local']['forward'].__setitem__('real_component_primitives', i['local']['forward']['real_component_primitives']-8)), + ('wrong_local_artifact_binding', lambda o, i: i.__setitem__('local_programs_sha256', '0' * 64)), + ('false_dirty_restoration', lambda o, i: i['local']['backward'].__setitem__('all_dirty_helper_columns_restored', False)), + ('missing_finite_check', lambda o, i: i['strict_checks'].pop('halving')), + ] + rejected = [] + for name, mutate in controls: + o, i = copy.deepcopy(owner), copy.deepcopy(invoice) + mutate(o, i) + # Rebind each mutated owner to its mutated invoice so tests of roles and + # profiles cannot pass merely by tripping an unrelated stale-file hash. + oh = digest(o) + i['owner_audit_sha256'] = oh + try: + assemble(o, i, oh, digest(i)) + except (AssertionError, KeyError): + rejected.append(name) + else: + raise AssertionError('Invalid admission receipt accepted: ' + name) + try: + assemble(owner, invoice, '0' * 64, sha(invoice_path)) + except AssertionError: + rejected.append('wrong_owner_receipt_hash') + else: + raise AssertionError('Wrong owner digest accepted') + assert len(rejected) == 13 + assert baseline['controls'] == ['next_grid', 'zero_eta', 'zero_beta', 'unit_beta'] + return dict( + status='PASS_EXACT_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS', + valid_receipt_kappa=baseline['kappa'], + input_sha256=baseline['input_sha256'], + assembler_sha256=sha(P / 'assemble.py'), + rejected_controls=rejected, + exact_outer_controls=baseline['controls'], + scope='Mutation controls for receipt completeness, both orientations, literal work/stock, profile and hash binding. Does not replace the fresh physical replay.', + ) + + +if __name__ == '__main__': + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--owner', type=Path, required=True) + ap.add_argument('--invoice', type=Path, required=True) + ap.add_argument('--out', type=Path, required=True) + a = ap.parse_args() + assert not a.out.exists() + result = verify(a.owner, a.invoice) + a.out.write_text(json.dumps(result, indent=2) + '\n') + print(result['status'], len(result['rejected_controls'])) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/audit_promoted_scalar.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/audit_promoted_scalar.py new file mode 100644 index 0000000000..a532682863 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/audit_promoted_scalar.py @@ -0,0 +1,57 @@ +"""Independent exact scalar witness for a selected complex kernel word. +Uses immutable correct-word compensation for omission controls; no repaired +compensation is silently supplied to a mutant. No physical-hosting claim. +""" +import sys,json,gzip,hashlib,copy +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +p=Path(__file__).resolve().parent +path=Path(sys.argv[1]);selection=Path(sys.argv[2]);out=Path(sys.argv[3]);w=json.loads(gzip.decompress(path.read_bytes()));sel=json.loads(selection.read_text());v=len(w['ports']);n=2*v+w['report']['R'] +def ident():return[{r:Q(1)}for r in range(n)] +def apply(e,rows): + if e[0]=='scale': + _,t,a,b,*_=e;q=Q(a,b);rows[t]={j:q*x for j,x in rows[t].items()};return + _,t,s,a,b,*_=e;q=Q(a,b) + for j,x in list(rows[s].items()): + z=rows[t].get(j,Q(0))+q*x + if z:rows[t][j]=z + else:rows[t].pop(j,None) +def inv(e,dual=False): + e=copy.deepcopy(e) + if e[0]=='add': + e[3]*=-1 + if dual:e[1],e[2]=e[2],e[1] + else:e[2],e[3]=e[3],e[2] + return e +def replay(es): + rows=ident() + for e in es:apply(e,rows) + return rows +main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(n)] +for r in range(v,2*v):dirty[r]={j:x for j,x in mx[r].items()if j>=2*v} +for e in w['precondition']:apply(e,dirty) +comp=[] +for r in range(v,2*v): + for j,x in sorted(dirty[r].items()): + assert not w.get('start_extra',{}).get(str(j)),('nonzero-frame compensation',j) + comp.append(['add',r,j,-x.numerator,x.denominator,[]]) +cleanup=[inv(e)for e in reversed(w['A']+w['B'])if not v<=e[1]<2*v] +assert[e[:-1]for e in cleanup]==[e[:-1]for e in w['cleanup']] +program=w['precondition']+comp+main+cleanup;expected=ident() +for t in range(v):expected[v+t][t]=Q(1) +assert replay(program)==expected +back=ident() +for t in range(v):back[t][v+t]=Q(-1) +assert replay([inv(e,True)for e in program])==back +controls={} +recipe=json.loads((path.parent/'PROMOTION.json').read_text()) +for change in recipe['changes']: + for h in change['pivots']: + bb=[e for e in w['B']if not(e[0]=='add'and e[2]==2*v+h and e[1]>=2*v and e[-1]==change['new_E'])] + assert len(bb)==len(w['B'])-3 + cc=[inv(e)for e in reversed(w['A']+bb)if not v<=e[1]<2*v] + assert replay(w['precondition']+comp+w['A']+w['cut']+bb+cc)!=expected + controls[str(h)]='REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION' +r=dict(status='PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE',word_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),selection_sha256=hashlib.sha256(selection.read_bytes()).hexdigest(),columns_each_orientation=n,compensations=len(comp),program_operations=len(program),kernel_pivots=len(controls),controls=controls,scope='Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate.') +out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],n,len(controls)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/phases_full.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/phases_full.py new file mode 100644 index 0000000000..d68f097d5d --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/code/phases_full.py @@ -0,0 +1,39 @@ +# Adapted from PR425 for heterogeneous centres by icekylinx with Codex assistance. +"""Exact phase-aware lowering of every used edge of the new structural word.""" +import gzip,hashlib,json,sys,time +from collections import Counter +from pathlib import Path +sys.path.insert(0,str(Path(sys.argv[2]).resolve())) +from clifford_exact import * + +OUT=Path(sys.argv[1]);P=OUT/'CANONICAL-WORD.json.gz' +c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[] +for U in frames: + op=canonical_frame(n,U) + L=[u|(u<=18 + return raw[:9]+b'\xff'+raw[10:] +gzip.compress=compress_portable +script=Path(sys.argv[1]).resolve() +sys.argv=sys.argv[1:] +sys.path.insert(0,str(script.parent)) +runpy.run_path(str(script),run_name='__main__') diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/data/OWNERS.json.gz b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/data/OWNERS.json.gz new file mode 100644 index 0000000000..eeb01317d7 Binary files /dev/null and b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/data/OWNERS.json.gz differ diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/data/PLAN.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/data/PLAN.json new file mode 100644 index 0000000000..f48def86c4 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/data/PLAN.json @@ -0,0 +1,12546 @@ +{ + "status": "FRESH_INTEGER_MATCHED_RANK5_EIGHT_PIVOT_OWNER_PLAN", + "mode": "frozen-saturation-pattern-time-matching", + "K": 4, + "T": 8, + "M": 73, + "L": 9, + "live": 7168, + "deficit": 2560, + "profile": { + "1": 166880, + "2": 30528, + "3": 35779, + "4": 13824, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + 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421, + 422, + 423 + ], + "gates": 12 + }, + { + "group": 6, + "old_E": [ + 267, + 139, + 96, + 30 + ], + "new_E": [ + 267, + 139, + 96, + 25, + 7 + ], + "pivots": [ + 451, + 453, + 454, + 455 + ], + "gates": 12 + } + ], + "local_before": { + "1": 2300, + "4": 184, + "8": 8, + "3": 472, + "2": 440, + "6": 56, + "5": 56 + }, + "local_after": { + "1": 2316, + "4": 192, + "8": 8, + "3": 464, + "2": 424, + "6": 56, + "5": 56 + }, + "widths": { + "9": 292, + "8": 156, + "5": 48, + "4": 8 + }, + "exploratory_gzip_sha256": "59eb1a2356b764544be4aab0432df1b07710ca57f8fe32fe6c0788e83aded4aa", + "word_content_sha256": "2b67fd69853dfc28f30ab5bb928f573077ae9d2bfa12cc36254d018d56133a5d" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/engines/base_two_moment.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/engines/base_two_moment.py new file mode 100644 index 0000000000..14a90fa0e7 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/engines/base_two_moment.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Maintainer arithmetic cross-check of the pinned PR39 certificate. + +Uses no producer/checker imports. Counts are inputs, not proved by this script. +80-term rational logarithms and 12-term exponentials independently enclose +the two moments. The accompanying written review addresses their realization. +""" +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +GRID = 10**30 + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def log_unit(x): + require(1 <= x <= 2, "logarithm range") + z = (x-1)/(x+1) + lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0)) + return lo, lo+2*z**161/(161*(1-z*z)) + + +def log_bounds(x): + k = 0 + while x > 2: + x /= 2 + k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + # Outward rational rounding keeps later certificates compact. + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + + +def exp_bounds(x): + require(0 <= x < 1, "exponential range") + term = total = Q(1) + for j in range(1, 13): + term *= x/j + total += term + tail = term*x/13/(1-x/14) + return total, total+tail + + +def moment(m, W, entries, saving): + lo = hi = Q(0) + for t, count in entries: + t, count = int(t), int(count) + require(0 < t < m and count > 0, "improper child") + l, u = log_bounds(Q(m, t)) + lower = exp_bounds(saving*l)[0] + upper = exp_bounds(saving*u)[1] + lo += Q(t*count, m*W)*lower + hi += Q(t*count, m*W)*upper + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/engines/moment.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/engines/moment.py new file mode 100644 index 0000000000..7d697cb452 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/engines/moment.py @@ -0,0 +1,113 @@ +"""Independent prospective ordinary five-stage cost, never supplier admission. + +Consumes a raw one-invocation ledger made from the actual source/internal/target +paths. No packed profile is used as an input. Missing physical/finite/compiler +obligations must remain explicit in the accompanying report. +""" +from collections import Counter +from decimal import Decimal, localcontext, ROUND_FLOOR +from fractions import Fraction as F +from functools import lru_cache +from math import factorial +import hashlib, json, sys +from pathlib import Path + +DYAD = 1 << 224 + +def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) +def ceil(x): return -floor(-x) + +@lru_cache(None) +def logarithm(x): + """Mercator bounds after binary reduction; ln(2) via two Mercator sums. + + For 1 <= y < 2, log(y) is an alternating series in z=y-1. + We instead reduce to 1 <= y < 3/2, and bound log(3/2) and + log(2) by the same alternating series at z=1/2 and z=1/3, + using log(2)=log(3/2)+log(4/3). All sums are exact rationals. + """ + assert x >= 1 + k = 0 + while x >= 2: x /= 2; k += 1 + j = int(x >= F(3, 2)) + if j: x /= F(3, 2) + def mercator(y): + z=y-1 + assert 0 <= z <= F(1,2) + # An even partial sum is below log; the next term bounds its tail. + t=z; s=F(0) + for n in range(1, 225): + s += (t if n & 1 else -t)/n + t *= z + return s, s+t/225 + a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3)) + return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f) + +def exponential(l,u): + assert 0 <= l <= u < F(1,10) + def poly(x): + s=t=F(1) + for j in range(1,25): t=t*x/j; s+=t + return s,t + lo,_=poly(l);hi,last=poly(u) + return floor(lo),ceil(hi+last*u/25/(1-u/26)) + +def moment(H,m,W,a,bad=False): + lo=hi=F(0) + for r,n in H.items(): + assert 0 < r < m and n > 0 + l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u) + p=F(r*n,m*W);lo+=p*e;hi+=p*f + if bad: + # Existing envelope shape, only conditionally portable to the new cover. + l,u=logarithm(F(m));e,f=exponential(a*l,a*u) + p=F(32*m*sum(H.values()),10**16*W) + lo+=p*e;hi+=p*f + return floor(lo),ceil(hi) + +def decimal(x): + with localcontext() as c: + c.prec=70 + return str(Decimal(x.numerator)/Decimal(x.denominator)) + +def certify(H,m,W,bad=False): + with localcontext() as c: + c.prec=70 + terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()] + fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0) + lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003') + for _ in range(210): + a=(lo+hi)/2 + if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a + else:hi=a + q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR)) + lo=F(q,10**24);hi=lo+F(1,10**24) + lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad) + assert lv[1]<10 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2 + assert 1-eps*(1+c)==eta-eps*eta/4 + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/inputs/PR543-EXPECTED.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/inputs/PR543-EXPECTED.json new file mode 100644 index 0000000000..b61d859826 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/inputs/PR543-EXPECTED.json @@ -0,0 +1,239 @@ +{ + "word": { + "file": "data/bitE8mut-r420.json.gz", + "file_sha256": "9721a3819efd68307f66f00d84a952eb28eb7c3ad2ce79653ce295c98a764784", + "content_sha256": "e597e3885c0a8daa262afa5985ee2930443329126aece76d33159d81882bdcc2", + "plan_sha256": "d5c2494b4baae801143049e172db303b3c8e25a002e9d9715a1d79dcb2d74c58", + "R": 420, + "retained_totals": 9, + "gates": { + "D": 120, + "A": 2064, + "B": 837, + "C": 2661 + }, + "local_histogram": { + "1": 1320, + "2": 1440, + "4": 60, + "5": 120, + "8": 9 + }, + "legality": { + "records": 29874, + "common_frame_ADDs": 26916, + "rank_mass": 5112 + }, + "five_stage_columns": 900, + "five_stage_payload_bits": 100, + "nine_stage_columns": 1380, + "nine_stage_payload_bits": 100, + "eleven_stage_columns": 1620, + "eleven_stage_payload_bits": 100 + }, + "interface": { + "hypotheses": { + "H1_no_target_feeds_z": true, + "H2_D_frame0_targets_from_helpers": true, + "H3_A_z_only_scatter_targets_B_split": true, + "H4_C_literal_reverse_at_full": true, + "H5_V_identity": true + }, + "conclusion": { + "U_block_form": true, + "J_identity": true, + "K_equals_D": true, + "C_is_U_inverse": true + }, + "interleaving": { + "z_gates_A": 2064, + "source_writes_A": 0, + "z_gates_B": 597, + "source_writes_B": 597, + "helper_writes_B": 0, + "sources_rewritten_B": 120, + "B_z_write_frame_dims": { + "4": 477, + "6": 120 + }, + "B_z_operand_kinds": { + "source<-helper": 120, + "source<-source": 477 + }, + "B_z_operand_kinds_by_dim": { + "dim4:source<-source": 477, + "dim6:source<-helper": 120 + }, + "B_z_writes_after_a_target_read_of_the_same_register": 597, + "B_target_reads_of_registers_rewritten_earlier_in_B": 120, + "target_reads_of_targets": 0, + "cleanup_gates": 2661 + } + }, + "nine": { + "pipeline": "PR #510 (PR #463 nine-stage template, 32 replicas, PR #442 hosting, PR #493 outer assembly)", + "bit_lower": "413456747036699736067/250000000000000000000000", + "bit_lower_decimal": "0.001653826988146798944268", + "profile": { + "1": 380160, + "2": 426624, + "4": 32640, + "5": 34560, + "6": 15360, + "7": 23040, + "8": 2592, + "42": 3456 + }, + "bit": { + "live": 30720, + "physical": 30729, + "maxchild": 42, + "rank_mass": 1956096, + "hosted_residuals": 120960, + "bank_assignments": 0, + "prefix_bits": 189, + "charged_prefix_bits": 192, + "coefficient_bits": 189, + "two_level_coefficient_bits": 416, + "charged_two_level_coefficient_bits": 512, + "row_coefficient": 18355, + "halving_depth": 2 + }, + "kappa": { + "pr535": { + "kappa": "793733736881443/500000000000000000", + "kappa_decimal": "0.001587467473762886", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "binding_component": "complex" + }, + "pr531": { + "kappa": "1517760977820331/1000000000000000000", + "kappa_decimal": "0.001517760977820331", + "complex_lower": "304013615566499291631/200000000000000000000000", + "binding_component": "complex" + } + } + }, + "eleven": { + "pipeline": "PR #493 (PR #445 geometry, PR #472 emitter, audit and invoice, PR #442 hosting)", + "bit_lower": "82015816228313440961/50000000000000000000000", + "bit_lower_decimal": "0.00164031632456626881922", + "profile": { + "1": 116160, + "2": 130560, + "4": 9120, + "5": 10560, + "6": 3839, + "7": 7680, + "8": 792, + "14": 1, + "56": 3497 + }, + "bit": { + "live": 9600, + "physical": 9609, + "maxchild": 56, + "rank_mass": 745536, + "hosted_residuals": 36960, + "prefix_bits": 4710, + "charged_prefix_bits": 4736, + "coefficient_bits": 4710, + "three_level_coefficient_bits": 14185, + "charged_three_level_coefficient_bits": 14208, + "row_coefficient": 19431, + "halving_depth": 3 + }, + "emitted_program_sha256": "3de4325e0df33ca85116d05cbcc6810f025d6083e5134d128236769c97699f51", + "kappa": { + "pr535": { + "kappa": "793733736881443/500000000000000000", + "kappa_decimal": "0.001587467473762886", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "binding_component": "complex" + }, + "pr531": { + "kappa": "1517760977820331/1000000000000000000", + "kappa_decimal": "0.001517760977820331", + "complex_lower": "304013615566499291631/200000000000000000000000", + "binding_component": "complex" + } + } + }, + "controls": { + "pr510_r480_nine": { + "word": "vendor/pr510/e8-r480-dead-totals/data/bitE8mut-r480.json.gz", + "bit_lower": "396861776523137034277/250000000000000000000000", + "bit_lower_decimal": "0.001587447106092548137108", + "kappa": { + "pr535": { + "kappa": "1584931111785787/1000000000000000000", + "kappa_decimal": "0.001584931111785787", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "binding_component": "bit" + }, + "pr531": { + "kappa": "1517760977820331/1000000000000000000", + "kappa_decimal": "0.001517760977820331", + "complex_lower": "304013615566499291631/200000000000000000000000", + "binding_component": "complex" + }, + "pr484": { + "kappa": "662515748707749/500000000000000000", + "kappa_decimal": "0.001325031497415498", + "complex_lower": "663394767670133/500000000000000000", + "binding_component": "complex" + }, + "pr471": { + "kappa": "260706019542937/200000000000000000", + "kappa_decimal": "0.001303530097714685", + "complex_lower": "1305231506267591/1000000000000000000", + "binding_component": "complex" + }, + "pr458": { + "kappa": "323880830669511/250000000000000000", + "kappa_decimal": "0.001295523322678044", + "complex_lower": "1297203880559577927527/1000000000000000000000000", + "binding_component": "complex" + } + } + }, + "pr493_r489_eleven": { + "word": "../e8-bit-carrier-skeleton/data/bit/bitE8mut-r489.json.gz", + "bit_lower": "391360506745414227149/250000000000000000000000", + "bit_lower_decimal": "0.001565442026981656908596", + "emitted_program_sha256": "e37b52e4861c39154b5891460fb45df8651c92cd68961078f8f06596f057c822", + "kappa": { + "pr535": { + "kappa": "97687203033227/62500000000000000", + "kappa_decimal": "0.001562995248531632", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "binding_component": "bit" + }, + "pr531": { + "kappa": "1517760977820331/1000000000000000000", + "kappa_decimal": "0.001517760977820331", + "complex_lower": "304013615566499291631/200000000000000000000000", + "binding_component": "complex" + }, + "pr484": { + "kappa": "662515748707749/500000000000000000", + "kappa_decimal": "0.001325031497415498", + "complex_lower": "663394767670133/500000000000000000", + "binding_component": "complex" + }, + "pr471": { + "kappa": "260706019542937/200000000000000000", + "kappa_decimal": "0.001303530097714685", + "complex_lower": "1305231506267591/1000000000000000000", + "binding_component": "complex" + }, + "pr458": { + "kappa": "323880830669511/250000000000000000", + "kappa_decimal": "0.001295523322678044", + "complex_lower": "1297203880559577927527/1000000000000000000000000", + "binding_component": "complex" + } + } + } + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/ASSEMBLY-PROVENANCE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/ASSEMBLY-PROVENANCE.json new file mode 100644 index 0000000000..37f7dea7a9 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/ASSEMBLY-PROVENANCE.json @@ -0,0 +1,11 @@ +{ + "adapted_from_pr": 550, + "head": "c7337040822978f1611ce9d9d44e7bb96d887e23", + "original_assembler_sha256": "58ca07fd72c6ab605e94eb5dda44989cf48437f9fade913cccc192b14b4fc60e", + "changes": [ + "Bind new full paid profile and all actual invoice primitive counts.", + "Use seven finite bootstrap levels with eta=beta=1e-24 and seed backoff1e-27.", + "Retain all admission field checks, both exact rational engines,47outer constraints and13malformedreceipt controls." + ], + "ownership_serialization": "Literal allocation unchanged by sorting to async call time then helper; initial unsorted and stage-ordered inputs correctly rejected by stream digest. Unchanged auditor retained." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/CONSTRUCTION.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/CONSTRUCTION.md new file mode 100644 index 0000000000..c5d43a7591 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/CONSTRUCTION.md @@ -0,0 +1,18 @@ +# Literal rank-five kernel promotion + +Start with the exact raw PR552 word reconstructed from the pinned package. Immediately after the center, its B prefix contains 320 gauge compensation gates followed by 168 kernel shears. The latter use 14 disjoint groups with four donor helpers and four pivot helpers each. The four donor response columns span the four pivot response columns over dyadic rationals. Donors enter at the group's rank-one gauge line; pivots enter at a common rank-four frame E. + +For groups 10 and 6, all eight helpers' first downstream frames contain a common rank-five frame F containing E. The exact chosen frames are: + +| Group | E | F | Promoted pivots | +| --- | --- | --- | --- | +| 10 | 260,132,96,24 | 260,132,96,24,1 | 419,421,422,423 | +| 6 | 267,139,96,30 | 267,139,96,25,7 | 451,453,454,455 | + +These integer lists encode bases in the inherited nine-dimensional binary frame convention. `promote.py` checks both ranks and the actual span containment. It changes each pivot's entrance frame and its three outgoing kernel shear frames from E to F. Every scalar gate and coefficient is retained. Kernel gates commute because the set of donor destinations is disjoint from the set of pivot sources, so placing the retained rank-four kernel gates before the promoted rank-five gates leaves the scalar word unchanged. The cleanup is regenerated as the literal reversed inverse of the changed word. + +The original scalar dirty-response cancellation therefore still holds. It is nevertheless checked independently for every one of the 728 formal columns, including every arbitrary dirty helper, in forward and inverse-transpose orientations. The additional omission controls remove each promoted pivot's three corrections and recompute only literal cleanup; the correct word's compensation table is frozen and each resulting wrong operator must be rejected. + +Each selected group has downstream first-helper rank six. Its four donors previously climbed rank 1→4→6, paying four rank-three and four rank-two children. They now climb 1→5→6, paying four rank-four and four rank-one children. Its four pivots previously climbed 4→6 and now climb 5→6. Thus one complete four-pivot group has profile delta `{1:+8,2:-8,3:-4,4:+4}` and replaces four width-five helpers by four width-four helpers. Two groups produce the complete local profile and width inventory stated in the README. The actual full frame-chain calculation and both independently emitted reflected ledgers verify this count; it is not obtained by scaling an isolated pivot. + +Physical hosting is a separate obligation. The new width-four helper roles require a newly constructed literal owner map and plan. The final verifier must derive the globally paid profile from those actual owners, check stage and chart legality, compile every exact phase edge, compute the finite invoice, certify both moment engines including fallback, and satisfy every outer-assembly inequality. A positive local or relaxed packing calculation alone is not admission. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/EXPLORATORY-SCALAR-8-CONTROLS.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/EXPLORATORY-SCALAR-8-CONTROLS.json new file mode 100644 index 0000000000..9faee61b54 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/EXPLORATORY-SCALAR-8-CONTROLS.json @@ -0,0 +1,20 @@ +{ + "status": "PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE", + "word_sha256": "59eb1a2356b764544be4aab0432df1b07710ca57f8fe32fe6c0788e83aded4aa", + "selection_sha256": "16ecc4a5c08af6750ee8610b722f74eba82a9eeb9703f0f0e0ace08ce5c82ad3", + "columns_each_orientation": 728, + "compensations": 9132, + "program_operations": 16266, + "kernel_pivots": 8, + "controls": { + "419": "REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION", + "421": "REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION", + "422": "REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION", + "423": "REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION", + "451": "REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION", + "453": "REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION", + "454": "REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION", + "455": "REJECTED_OMITTED_PROMOTED_POSTCENTER_KERNEL_CORRECTION" + }, + "scope": "Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/RANK5-CAPS.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/RANK5-CAPS.json new file mode 100644 index 0000000000..d4b6dc0e6d --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/proof/RANK5-CAPS.json @@ -0,0 +1,636 @@ +{ + "status": "EXACT_POSTCENTER_RANK5_CAP_RESPONSE_SCREEN", + "source_word_sha256": "a30810b755cf80e1128c0b932728bd51ca8e0bb31225fc415675afb42a766c8f", + "source": "/private/tmp/pr552-full-independent/complex-local/weighted/FULL-WORD.json.gz", + "helper_count": 112, + "global_rank": 56, + "global_nullity": 56, + "distinct_rank5_caps": 5788, + "rows": [ + { + "E": [ + 260, + 132, + 96, + 24, + 1 + ], + "helpers": [ + 416, + 417, + 418, + 419, + 420, + 421, + 422, + 423 + ], + "groups": [ + 10 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 416, + 417, + 418, + 420 + ], + "relations": { + "419": { + "416": "1", + "418": "-1", + "417": "1" + }, + "421": { + "417": "-2", + "420": "1", + "416": "2" + }, + "422": { + "420": "1", + "416": "2", + "418": "-2" + }, + "423": { + "420": "1", + "418": "2", + "417": "-2" + } + } + }, + { + "E": [ + 267, + 139, + 96, + 25, + 7 + ], + "helpers": [ + 448, + 449, + 450, + 451, + 452, + 453, + 454, + 455 + ], + "groups": [ + 6 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 448, + 449, + 450, + 452 + ], + "relations": { + "451": { + "448": "1", + "450": "-1", + "449": "1" + }, + "453": { + "449": "1", + "452": "1", + "448": "-1" + }, + "454": { + "452": "1", + "448": "-1", + "450": "1" + }, + "455": { + "452": "1", + "450": "-1", + "449": "1" + } + } + }, + { + "E": [ + 272, + 144, + 96, + 6, + 1 + ], + "helpers": [ + 408, + 409, + 410, + 411, + 412, + 413, + 414, + 415 + ], + "groups": [ + 12 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 408, + 409, + 410, + 412 + ], + "relations": { + "411": { + "408": "1", + "410": "-1", + "409": "1" + }, + "413": { + "409": "1", + "412": "1", + "408": "-1" + }, + "414": { + "412": "1", + "408": "-1", + "410": "1" + }, + "415": { + "412": "1", + "410": "-1", + "409": "1" + } + } + }, + { + "E": [ + 291, + 163, + 97, + 24, + 7 + ], + "helpers": [ + 464, + 465, + 466, + 467, + 468, + 469, + 470, + 471 + ], + "groups": [ + 4 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 464, + 465, + 466, + 468 + ], + "relations": { + "467": { + "464": "1", + "466": "-1", + "465": "1" + }, + "469": { + "465": "1", + "468": "1", + "464": "-1" + }, + "470": { + "468": "1", + "464": "-1", + "466": "1" + }, + "471": { + "468": "1", + "466": "-1", + "465": "1" + } + } + }, + { + "E": [ + 297, + 169, + 97, + 25, + 6 + ], + "helpers": [ + 488, + 489, + 490, + 491, + 492, + 493, + 494, + 495 + ], + "groups": [ + 3 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 488, + 489, + 490, + 492 + ], + "relations": { + "491": { + "488": "1", + "490": "-1", + "489": "1" + }, + "493": { + "489": "1", + "492": "1", + "488": "-1" + }, + "494": { + "492": "1", + "488": "-1", + "490": "1" + }, + "495": { + "492": "1", + "490": "-1", + "489": "1" + } + } + }, + { + "E": [ + 298, + 170, + 102, + 30, + 1 + ], + "helpers": [ + 432, + 433, + 434, + 435, + 436, + 437, + 438, + 439 + ], + "groups": [ + 8 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 432, + 433, + 434, + 436 + ], + "relations": { + "435": { + "432": "1", + "434": "-1", + "433": "1" + }, + "437": { + "433": "-2", + "436": "1", + "432": "2" + }, + "438": { + "436": "1", + "432": "2", + "434": "-2" + }, + "439": { + "436": "1", + "434": "2", + "433": "-2" + } + } + }, + { + "E": [ + 385, + 75, + 42, + 25, + 7 + ], + "helpers": [ + 456, + 457, + 458, + 459, + 460, + 461, + 462, + 463 + ], + "groups": [ + 5 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 456, + 457, + 458, + 460 + ], + "relations": { + "459": { + "456": "1", + "458": "-1", + "457": "1" + }, + "461": { + "457": "1", + "460": "1", + "456": "-1" + }, + "462": { + "460": "1", + "456": "-1", + "458": "1" + }, + "463": { + "460": "1", + "458": "-1", + "457": "1" + } + } + }, + { + "E": [ + 385, + 96, + 16, + 9, + 6 + ], + "helpers": [ + 480, + 481, + 482, + 483, + 484, + 485, + 486, + 487 + ], + "groups": [ + 1 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 480, + 481, + 482, + 484 + ], + "relations": { + "483": { + "480": "1", + "482": "-1", + "481": "1" + }, + "485": { + "481": "1", + "484": "1", + "480": "-1" + }, + "486": { + "484": "1", + "480": "-1", + "482": "1" + }, + "487": { + "484": "1", + "482": "-1", + "481": "1" + } + } + }, + { + "E": [ + 385, + 96, + 24, + 4, + 3 + ], + "helpers": [ + 472, + 473, + 474, + 475, + 476, + 477, + 478, + 479 + ], + "groups": [ + 0 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 472, + 473, + 474, + 476 + ], + "relations": { + "475": { + "472": "1", + "474": "-1", + "473": "1" + }, + "477": { + "473": "1", + "476": "1", + "472": "-1" + }, + "478": { + "476": "1", + "472": "-1", + "474": "1" + }, + "479": { + "476": "1", + "474": "-1", + "473": "1" + } + } + }, + { + "E": [ + 390, + 68, + 34, + 24, + 1 + ], + "helpers": [ + 424, + 425, + 426, + 427, + 428, + 429, + 430, + 431 + ], + "groups": [ + 9 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 424, + 425, + 426, + 428 + ], + "relations": { + "427": { + "424": "1", + "426": "-1", + "425": "1" + }, + "429": { + "425": "-2", + "428": "1", + "424": "2" + }, + "430": { + "428": "1", + "424": "2", + "426": "-2" + }, + "431": { + "428": "1", + "426": "2", + "425": "-2" + } + } + }, + { + "E": [ + 390, + 96, + 20, + 10, + 1 + ], + "helpers": [ + 440, + 441, + 442, + 443, + 444, + 445, + 446, + 447 + ], + "groups": [ + 7 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 440, + 441, + 442, + 444 + ], + "relations": { + "443": { + "440": "1", + "442": "-1", + "441": "1" + }, + "445": { + "441": "-2", + "444": "1", + "440": "2" + }, + "446": { + "444": "1", + "440": "2", + "442": "-2" + }, + "447": { + "444": "1", + "442": "2", + "441": "-2" + } + } + }, + { + "E": [ + 408, + 80, + 40, + 6, + 1 + ], + "helpers": [ + 400, + 401, + 402, + 403, + 404, + 405, + 406, + 407 + ], + "groups": [ + 11 + ], + "rank": 4, + "nullity": 4, + "donors": [ + 400, + 401, + 402, + 404 + ], + "relations": { + "403": { + "400": "1", + "402": "-1", + "401": "1" + }, + "405": { + "401": "1", + "404": "1", + "400": "-1" + }, + "406": { + "404": "1", + "400": "-1", + "402": "1" + }, + "407": { + "404": "1", + "402": "-1", + "401": "1" + } + } + } + ], + "scope": "Exact suffix responses of112postcenter rank4-group helpers at current cut on552. Complete rank5subspaces of each current first-use frame, restricted to each groups existing rank1gauge line. No downstream-frame restructuring or physical claim." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/EXPECTED.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/EXPECTED.json new file mode 100644 index 0000000000..7ee2fb720a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/EXPECTED.json @@ -0,0 +1,30 @@ +{ + "status": "PASS_FILTRATION_WAVEFRONT", + "kappa": "795984451416673/500000000000000000", + "kappa_decimal": "0.001591968902833346", + "bit_lower": "413456747036699736067/250000000000000000000000", + "complex_lower": "1594507308884431019637/1000000000000000000000000", + "complex_template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "complex_canonical_word_sha256": "995e46ed6dc8377f02bf05a3370171796364cedefdfeaeae47c2a207b5a8b173", + "complex_global_profile": { + "1": 165600, + "2": 32128, + "3": 35907, + "4": 13248, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "complex_prefix_bits": 225, + "forward_events": 21483, + "backward_events": 21483, + "waves": 8, + "wave_omission_controls": 8, + "coset_rewrites": 12, + "compensation_additions_saved": 624, + "outer_constraints": 47, + "bit_operator": "Pinned PR543 cited dependency, not physically replayed here" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/LICENSE b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. Definitions. + + "License" shall mean the terms and conditions for use, reproduction, + and distribution as defined by Sections 1 through 9 of this document. + + "Licensor" shall mean the copyright owner or entity authorized by + the copyright owner that is granting the License. + + "Legal Entity" shall mean the union of the acting entity and all + other entities that control, are controlled by, or are under common + control with that entity. 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"verify.py": { + "mode": "lf-text", + "sha256": "eb4bb8d1c6eaf5327c7d13fc20ebcf2ae2ecebff5b008d44fc1713a7b162084d" + } + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/README.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/README.md new file mode 100644 index 0000000000..f4c470edd1 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/README.md @@ -0,0 +1,62 @@ +# Collective frame contraction and weighted response decoding + +Conditional **kappa = 0.001591968902833346** = 795984451416673 / 500000000000000000. +This is **0.07906544% above PR547**, and improves the previous delivered0.001590591090759927. The public snapshot is frozen through PR547. The new contribution is a physically admitted collective frame transformation and a sparse-response rewrite family, composed with PR543's stronger bit supplier. + +## Concrete improvement + +The old construction was locally stuck under single-event frame choices and whole equal-frame plateaus. Interpret its frame histories as coupled persistence flags. Intersect a predecessor-closed collection of events with a hyperplane, leaving all observation and boundary frames fixed. Eight such collective waves change8 to10 event frames at a time. They preserve the scalar program but alter the paid rank distribution. + +Every wave replaces two copies of the pair of child ranks(2,3) by(1,4). Across all eight, the exact local delta is + + 16(e1 - e2 - e3 + e4). + +Strict concavity proves a better moment for every exponent in(0,1), with unchanged rank mass and child count. No floating optimization score is accepted as evidence. The new phases, local programs, global physical charts and scalar invoice are all reconstructed. + +Next, twelve exact weighted-coset source rewrites reduce the cold-dirt compensation table from9,756 to9,132 additions, saving624. The complete emitted local program shrinks from22,107 to21,483 events in each orientation. This second change preserves the paid histogram: its saving is scalar complexity, not an additional kappa increase. + +The exact final complex saving is b=0.001594507308884431019637. The cited PR543 bit saving is c=0.001653826988146798944268, so the complex side binds. Complete profiles, not separately estimated gains, enter both rational moment engines and all47 strict outer inequalities. + +## Eight cross-field structures, with their actual roles + +| Worker | Connection | What transfers here | +|---|---|---| +| Root | Persistent vector-space flags <-> register-frame histories | A birth-time picture exposes collective changes missed by isolated event edits; the selected eight waves improve the paid moment. | +| Root | Galois adjunctions/subspace-lattice geometry <-> compiler legality closure | Meet with a hyperplane gives an exact predecessor-closure theorem with fixed boundaries; no global common-basis assumption. | +| Elimination | Electrical Kron/Schur elimination <-> eliminating internal register versions | A sufficient paid-elimination theorem and independent exact boundary-transfer audit; direct helper-removal screens found no new gain. | +| Elimination | Quiver path algebra <-> linear circuit transfer | Finite path sums verify the protected endpoint and all twelve source-error witnesses using an independent exact-dyadic C++ implementation. | +| Response | State-space impulse response <-> prefix/suffix rank-one transfer updates | Supplies exact response updates for source changes; the separate minimal-realization search found no additional merge. | +| Response | Coding-theory coset representatives <-> sparse cold-dirt compensation | Twelve checked rewrites save624 scalar additions, with all protected columns preserved. | +| Resource | Integral space-time circulation <-> physical whole-owner schedules | Reuses the explicit feasible owner map and rebuilds its charts for the new provider; stage/mixed-provider searches yielded no extra gain. | +| Resource | Majorization/thermomajorization <-> paid child-rank transport | An explicit doubly stochastic2x2 certificate proves the selected(2,3)->(1,4) change improves every relevant moment. | + +These are precise structural transfers with constructive hypotheses, not a claim that everything in one subject transfers automatically. The underlying mathematics is established; the new result is this compatible construction and application. Negative searches and their finite scope are retained. Detailed proofs and exact source hashes are in docs/, response/ and complex-global/. + +## Replay + +Requirements: Python3.11+ and NumPy. No network, Lean, optimizer, GPU or C++ compiler is needed for the mandatory replay. Run with assertions enabled: + + python -B verify.py --work ../fresh-wavefront-run + +The output directory must be new and outside this package. The verifier validates the LF-aware manifest, normalizes a scratch copy, reconstructs the complex word from primitive inputs through the complete static44/frame/syndrome/wave/coset chain, runs the actual local phase and all-column checks, rebuilds the complete physical owner controller, recounts the invoice, and certifies both moment endpoints plus the outer assembly. EXPECTED.json pins the identities and result. The unchanged PR543 bit operator is a cited dependency; this package checks its numerical profile and invoice conditions without duplicating its cold physical replay. + +Checks include728 complex columns in both orientations,44 static-response omission controls,23 adapter recipes,all2,929 directed phase edges (199 fresh for the changed wave frames),11 local mutations,2,972 full73-column owner charts,seven controller mutations,eight new wave-omission controls and47 outer constraints with four invalid-parameter/grid controls. A separate independent exact-dyadic C++ path/Schur audit checks48,832 protected transfer entries and8,736 entries in the twelve source-error witnesses; its source, input and receipt are supplied as an optional audit artifact. + +Generated new word constructors and the complex launcher fix gzip level,timestamp and OS byte. Text files, including headers and hashes, are LF-normalized in the manifest. The release is tested from an all-text CRLF copy; the upload batches are checked by byte-for-byte reassembly. + +## Numerical and physical data + +- Local histogram: {1:2300,2:440,3:472,4:184,5:56,6:56,8:8}. +- Global histogram: {1:165600,2:32128,3:35907,4:13248,5:4032,6:4032,7:208,8:576,39:1,48:1660}. +- Complex live stock7168;physical7682;deficit2560;36,288 helper roles across72 calls. +- Measured complex prefix225 is below charged512;row16467 is below retained20161. +- Final canonical complex word hash371638c4f444515caa0586fa7bac838fc7a7c01c4f6110caccf1d4c4f90453b1. +- Complete template hash1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0. + +## Scope and direct lineage + +This is a conditional finite witness under retained all-size realization,common-label/mutable-basis,complete-call hosting,precision/tape and analytic-transfer interfaces. PR543's interleaved phase-B source updates retain its explicit H1-H5 interface argument. No unconditional multiplication theorem, fresh Lean certification, global optimizer guarantee or measured end-to-end multiplication speedup is claimed. Restoring scalar helper dirt does not erase the complete helper's residual Q action. + +PR543 supplies the unchanged R420 bit supplier;PR547 supplies the latest two-supplier arithmetic composition pattern. PR544/546 supply current comparison compositions;PR545's larger draft bit bound was inspected but would not increase this complex-bound kappa. PR541 published the preceding preload/static44 work. PR534 supplies the earlier frame assignment;PR535 and531 supply the complex construction,transport,phase,owner and invoice machinery. The inherited bit lineage includes PR510/503/493, and the compiler/physical lineage includes PR484/463/444/442/386. Detailed attribution and source links are in docs/PR-LINEAGE.md; upstream notices and licenses are preserved. + +No files are published by these scripts. All submission actions remain manual. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/code/alien-avalanche80.cpp b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/code/alien-avalanche80.cpp new file mode 100644 index 0000000000..568feafc63 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/code/alien-avalanche80.cpp @@ -0,0 +1,7 @@ +#include +using namespace std;using B=bitset<512>;struct N{bool fixed;B s;int d;vector pre,nxt,regs;};vectora;vectorhyper(512);long double pc[11]; +int main(int argc,char**argv){ifstream in(argv[1]);int nf,nn,nr;in>>nf>>nn>>nr;vectorfs(nf);vectordims(nf);for(int f=0;f>n;dims[f]=round(log2(n));while(n--){in>>x;fs[f][x]=1;}}a.resize(nn);vectorlast(nr,-1);for(int i=0;i>fixed>>f>>k;auto &n=a[i];n.fixed=fixed;n.s=fs[f];n.d=dims[f];while(k--){int r;in>>r;n.regs.push_back(r);n.pre.push_back(last[r]);n.nxt.push_back(-1);if(last[r]>=0){auto&p=a[last[r]];int j=find(p.regs.begin(),p.regs.end(),r)-p.regs.begin();p.nxt[j]=i;}last[r]=i;}} +for(int v=1;v<512;v++)for(int x=0;x<512;x++)if(!(__builtin_popcount(v&x)%2))hyper[v][x]=1;for(int d=1;d<11;d++)pc[d]=powl(d,1-.001594L);vectormark(nn,0);int stamp=0;long long cases=0,feasible=0;ofstream out(argv[2]);out<<"{\"passes\":[";bool first=true; +for(int round=0;round<80;round++){long double best=-1e-13;vectorbst;int bv=0,bs=0;for(int sign:{1,-1})for(int v=1;v<512;v++){vectoractive(nn);for(int i=0;iq{seed};mark[seed]=stamp;bool bad=false;for(int pos=0;pos<(int)q.size();pos++){int i=q[pos];const auto &adj=sign==1?a[i].nxt:a[i].pre;for(int j:adj)if(j>=0&&active[j]&&mark[j]!=stamp){if(a[j].fixed){bad=true;break;}mark[j]=stamp;q.push_back(j);}if(bad)break;}if(bad)continue;feasible++;long double d=0;for(int i:q){for(int j:a[i].pre)if(j>=0&&mark[j]!=stamp){int r=a[i].d-a[j].d;assert(r+sign>=0);d+=pc[r+sign]-pc[r];}for(int j:a[i].nxt)if(j>=0&&mark[j]!=stamp){int r=a[j].d-a[i].d;assert(r-sign>=0);d+=pc[r-sign]-pc[r];}}if(d +using namespace std; using B=bitset<512>; +struct F{B s;int d;};struct N{bool fixed;int f;vector regs,pre,nxt;}; +vector fs;vector ns;long double pc[10]; +bool sub(int a,int b){return (fs[a].s & ~fs[b].s).none();} +long double change(const vector&v,int f){unordered_setS(v.begin(),v.end());long double z=0;for(int i:v){auto &n=ns[i];for(int j:n.pre)if(j>=0&&!S.count(j)){z+=pc[fs[f].d-fs[ns[j].f].d]-pc[fs[n.f].d-fs[ns[j].f].d];}for(int j:n.nxt)if(j>=0&&!S.count(j)){z+=pc[fs[ns[j].f].d-fs[f].d]-pc[fs[ns[j].f].d-fs[n.f].d];}}return z;} +int main(int argc,char**argv){ifstream in(argv[1]);int nf,nn,nr;in>>nf>>nn>>nr;fs.resize(nf);ns.resize(nn);for(auto &f:fs){int n,x;in>>n;f.d=round(log2(n));while(n--){in>>x;f.s[x]=1;}}vectorlast(nr,-1);for(int i=0;i>fixed>>n.f>>k;n.fixed=fixed;while(k--){int r;in>>r;n.regs.push_back(r);n.pre.push_back(last[r]);n.nxt.push_back(-1);if(last[r]>=0){auto &p=ns[last[r]];int j=find(p.regs.begin(),p.regs.end(),r)-p.regs.begin();p.nxt[j]=i;}last[r]=i;}} +for(int d=1;d<10;d++)pc[d]=powl(d,1-.001594L);vectororig;for(auto &n:ns)orig.push_back(n.f);mt19937 rng(20261011);int accepted=0;long double gain=0; +auto trygroup=[&](vectorv){unordered_setS(v.begin(),v.end());vectorlo,hi;for(int i:v){for(int j:ns[i].pre)if(j>=0&&!S.count(j))lo.push_back(ns[j].f);for(int j:ns[i].nxt)if(j>=0&&!S.count(j))hi.push_back(ns[j].f);}int best=-1;long double bestdelta=-1e-13L;for(int f=0;ford(nn);iota(ord.begin(),ord.end(),0);shuffle(ord.begin(),ord.end(),rng);for(int i:ord)if(!ns[i].fixed)trygroup({i});vectorseen(nn);for(int i:ord)if(!seen[i]&&!ns[i].fixed){vectorv{i};seen[i]=1;for(int k=0;k<(int)v.size();k++){int t=v[k];vectoradj=ns[t].pre;adj.insert(adj.end(),ns[t].nxt.begin(),ns[t].nxt.end());for(int j:adj)if(j>=0&&!seen[j]&&!ns[j].fixed&&ns[j].f==ns[i].f){seen[j]=1;v.push_back(j);}}if(v.size()>1)trygroup(v);}cerr<oldh,newh;for(int i=0;i=0){int o=fs[orig[i]].d-fs[orig[j]].d,n=fs[ns[i].f].d-fs[ns[j].f].d;assert(sub(ns[j].f,ns[i].f));if(o)oldh[o]++;if(n)newh[n]++;}ofstream out(argv[2]);out<<"{\"changes\":[";bool first=true;for(int i=0;i2*max(H)**2 + for z,ok in [(lower,True),(lower+Q(1,10**24),False)]: + l,u=M.moment(H,m,W,z,True);ll,uu=B.moment(m,W,list(H.items()),z);fl,fu=B.moment(m,W,[(1,32*m*m*sum(H.values()))],z);ll+=fl/10**16;uu+=fu/10**16 + assert(u<1 and uu<1)if ok else(l>1 and ll>1) + receipts.append(dict(side=side,endpoint=str(z),accept=ok,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)])) +assert bit['bit']['two_level_coefficient_bits']0;ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512);cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a) +q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18) +bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}};assembly=A.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta);assert len(assembly['strict_constraints'])==47 and all(v>0 for v in assembly['strict_constraints'].values()) +controls=[] +for name,kk,ee,bb in [('next_grid',k+Q(1,10**18),eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]: + try:A.assembly(chain[-1],b,bridge,kk,eta=ee,beta=bb) + except AssertionError:controls.append(name) + else:raise AssertionError(name) +def dec(a): + with localcontext()as ctx:ctx.prec=60;return str(Decimal(a.numerator)/Decimal(a.denominator)) +r=dict(status='PASS_FRESH_WAVE_COMPLEX_AND_CITED_R420_COMPOSITION',kappa=str(k),kappa_decimal=dec(k),complex_lower=str(b),complex_decimal=dec(b),bit_lower=str(c),bit_decimal=dec(c),binding='complex'if (1-beta)*b= sum_j P_ij*s_j^a. Sum the rows and use column sums one to obtain sum_i r_i^a >= sum_j s_j^a. Thus replacement r→s weakly improves every relevant recurrence moment. It is strict whenever a row mixes two unequal positive/zero ranks nontrivially. The total rank is unchanged. Dividing by common ambient m^a preserves the inequality, so any old strict recurrence certificate remains strict. + +This alone is not a new algorithm: s must be produced by the preceding legal physical exchange theorem, or another explicit normalized-call construction. The matrix proves the pricing statement; the literal owner witness proves feasibility. This separation prevents an abstract majorization claim from hiding impossible time transport. + +A basic exact certificate replaces (u,v), with 0 < u <= v, by(u-d,v+d), where 0 < d <= u. Set theta=(v-u+d)/(v-u+2d). The symmetric doubly stochastic matrix with diagonal theta and off-diagonal1-theta sends the new ordered pair to the old pair. Consequently this physically realizable concentration strictly decreases the paid power sum. Chains of such rational witnesses multiply to another doubly stochastic matrix. + +The read Mathlib source Analysis/Convex/DoublyStochasticMatrix.lean defines both stochastic marginal conditions, proves their row/column-sum equivalence and convex closure, and includes permutation matrices. Jensen's inequality and the specialization to the paid moment are proved directly above; no new Lean compilation or global novelty is claimed. + +## Bounded outcomes so far + +An all-pattern integer capacity screen enumerated every 5/8/9 pattern fitting ranks 8, 16, 32, 48 at the baseline inventory. Its optimal floating linear objective returned exactly the already realized saturation profile. This is a bounded numerical optimization result, not an exact universal optimality theorem. Alternative stage geometries K = 5 and K = 6 gave optimistic nominal savings 0.00156922111 and 0.00152941033, both below the selected 0.00159351942. K = 3 could not fit the total helper width. None is asserted as a new improvement. Search therefore turns to changed provider signatures and heterogeneous complete-call choices rather than repeatedly moving a fixed optimal-looking stock. + +## Actual parent contraction application + +The parent discovered a source-level waveflag contraction with paid change rank 2 + rank 3 to rank 1 + rank 4. Its price certificate is exact and uniform in the recurrence exponent: + + (2,3)^T = [[2/3,1/3],[1/3,2/3]] (1,4)^T. + +Both rows mix unequal endpoints, so strict concavity gives 1^a + 4^a < 2^a + 3^a for every 0 < a < 1. Multiplying this two-by-two certificate by the number of actual contractions proves the complete local paid improvement. Ordered helper widths remain unchanged, so the selected whole-owner slot map is reusable after fresh source-bound physical charts and local phase verification. This is a concrete application of the sufficient majorization theorem. The parent supplies the physical waveflag proof and its exact scalar replay; this file does not replace either. + +## Completed finite application + +The frozen parent construction performs 16 such local rank transfers in each of 72 complete calls. The unchanged ordered 504-helper widths permit the same literal 36,288-role owner map. Fresh global emission rebuilds all 2,972 actual 73-column charts from the changed local source; independent chronology, full-owner uniqueness, pending intervals, residual and spectator axes, seven mutation controls and the complete finite scalar invoice all pass. Reusing slot identities is justified by the exact incidence equalities and source-bound chart reconstruction, not by assuming old charts certify a new source. + +The new global profile is + + {1:165600,2:32128,3:35907,4:13248, + 5:4032,6:4032,7:208,8:576,39:1,48:1660}. + +Its exact certified complex saving is 1594507308884431019637/10^24, or 0.001594507308884431019637. This is the supplier saving; the top-level package computes final kappa from both admitted suppliers and all 47 constraints. The retained all-size interfaces remain explicit. No numerical gain is attributed to reusing the same optimal-looking resource layout: the genuine new paid gain is the parent's physical frame contraction, whose uniform improvement is proved by the exact majorization certificate above. + +The final weighted-coset local refinement preserves that exact paid profile and all helper widths while removing 624 scalar additions per local orientation. The complete global replay was repeated on this final source; the certified complex saving is unchanged. Its actual prefix and invoice are stored in FINAL-RESOURCE-REVIEW.json. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SAT-OWNERS.json.gz b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SAT-OWNERS.json.gz new file mode 100644 index 0000000000..243bc54840 Binary files /dev/null and b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SAT-OWNERS.json.gz differ diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SAT534-PLAN.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SAT534-PLAN.json new file mode 100644 index 0000000000..bfa9e846a0 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SAT534-PLAN.json @@ -0,0 +1,11389 @@ +{ 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"solver_status": 1, + "gap": 1.1667391998196086e-07, + "local_profile": { + "1": 2284, + "2": 456, + "3": 488, + "4": 168, + "5": 56, + "6": 56, + "8": 8 + }, + "numeric_saving_scope": "Discovery metadata only; fresh exact global certificate supersedes." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SCREEN-RECEIPT.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SCREEN-RECEIPT.json new file mode 100644 index 0000000000..5509841f55 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SCREEN-RECEIPT.json @@ -0,0 +1,16 @@ +{ + "fixed_inventory": { + "scope": "All width5/8/9 patterns at fixed K4,T8; floating objective with exact integer row check", + "same_histogram": true, + "solver_status": "Optimization terminated successfully. (HiGHS Status 7: Optimal)" + }, + "alternative_stages": { + "5": 0.0015692211099619933, + "6": 0.0015294103291623729 + }, + "K3": { + "scope": "Necessary total-capacity check only", + "demand": 232736, + "pending_capacity": 200704 + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SOURCE-TRANSFERS.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SOURCE-TRANSFERS.json new file mode 100644 index 0000000000..571c31eb3f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SOURCE-TRANSFERS.json @@ -0,0 +1,21 @@ +[ + { + "path": "OAI/Combinatorics/Hamiltonian/Circulation.lean", + "sha256": "e369fc93872bb65a36a48c1b7997540e74e279eab3a7bf31000e8ce3c20c4e26", + "declarations": [ + "FlowCircuit.proportional", + "oriented_face" + ], + "scope": "Read source only; no new Lean compilation" + }, + { + "path": "Mathlib/Analysis/Convex/DoublyStochasticMatrix.lean", + "sha256": "02ab3084bf1c107203989593ed23c4654f308aa5b26161295c38bfdd294e6120", + "declarations": [ + "mem_doublyStochastic_iff_sum", + "convex_doublyStochastic", + "permMatrix_mem_doublyStochastic" + ], + "scope": "Read source only; no new Lean compilation" + } +] diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SOURCES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SOURCES.json new file mode 100644 index 0000000000..bfc6fabd0a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/SOURCES.json @@ -0,0 +1,21 @@ +{ + "scope": "Source-read adaptation; no Lean compilation or global novelty claim", + "sources": [ + { + "path": "OAI/Probability/SwitchChain/SwitchInFiber.lean", + "sha256": "53d03b1ddef801b54474f0f0c56b3bf00dcab902b08093ea0f6eeacd2bfdd38b", + "declarations": [ + "sameFiber_of_same_side", + "switchStep_sameFiber" + ] + }, + { + "path": "OAI/Computability/MatchingCount/CutAlgebra.lean", + "sha256": "048e26d6eaabd92329acad1b9c57f740a23cfdafa2a3e1cb6113e1477c84af68", + "declarations": [ + "cut_submodular", + "cut_push" + ] + } + ] +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/TWO-RESOURCE-TECHNIQUES.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/TWO-RESOURCE-TECHNIQUES.md new file mode 100644 index 0000000000..6c9da1f090 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/TWO-RESOURCE-TECHNIQUES.md @@ -0,0 +1,67 @@ +# Two source-derived resource constructions + +These are sufficient constructions for complete-owner schedules. They preserve each complete invocation's physical endpoint: Q on the assigned residual coordinates, identity on spectators, with scalar-body arbitrary-dirt restoration certified separately. They do not replace the retained all-size multiplication hypotheses. + +## 1. Exchange paths inside a fixed physical owner fiber + +Start with a source-bound legal schedule and its complete physical slots. For each call c, let E_c be its available occurrences of width-nine slots. A selected subset S must contain exactly four elements of every E_c. Shrink selected slots from width nine to width eight. Reassign the new provider's width-five, width-eight, and width-nine helpers bijectively to the matching-width slots of that same call, and repack each pending bin contiguously in its original occurrence order. + +Sufficient conclusion: the resulting assignment is legal at the resource level. Each call retains its exact set of physical owner families and times; no active data owner is added, no owner is aliased, and every occurrence remains in its original legal idle interval. Packing only shrinks widths, so the concatenated intervals fit their pending child. The final chart must be rebuilt from the assigned helper's actual frame; matching widths alone never proves chart equality. With this chart check and the new provider's endpoint certificate, the whole physical schedule is admitted under the same interface. + +A same-call exchange S -> S - {e} + {f}, where e is selected and f is unselected in E_c, preserves the call quota. It is a two-edge exchange path. Adding an auxiliary complement assignment makes it a standard four-edge bipartite switch: selected and unselected degrees are preserved in the extended fiber. Any finite sequence of these exchanges is safe, irrespective of intermediate changes in the remainder histogram. Acceptance is based on the full paid moment, not a local entropy heuristic. + +Source read: OAI/Probability/SwitchChain/SwitchInFiber.lean, in particular sameFiber_of_same_side and switchStep_sameFiber. The source proves a degree-constrained graph switch stays in a resampling fiber; it does not itself prove this multiplication admission theorem. The physical proof above supplies that missing specialization. + +## 2. Concave remainder costs as an explicit cut network + +Let a be fixed with 0 z of capacity lambda, and add z -> sink of capacity lambda*k. With selected event vertices on the source side, minimizing over the auxiliary vertex z gives precisely lambda*min(x,k). The linear term uses event-to-sink arcs. This represents the whole remainder objective as a cut potential, with no unknown optimization oracle. + +Source read: OAI/Computability/MatchingCount/CutAlgebra.lean, cut_submodular and cut_push. Its pointwise cut submodularity and exact contraction/lift identity justify graph-level aggregation. Here the discrete-concavity identity supplies the explicit gadget representation. Exact quotas |S intersect E_c|=4 remain additional constraints; unconstrained minimum cut does NOT solve that constrained problem automatically. Our bounded native search uses the potential to accept legal exchanges, and the literal endpoint witness is independently checked. There is no global optimality claim. + +## 3. Constructive lift from pattern counts to literal owners + +A bin group consists of 112 physical ports sharing one owner replica, pending child, rank and legal time set. For each pattern p, choose n_p ports and a list of helper widths w_1,...,w_d with sum at most the pending rank. Let x_(p,t,w) be nonnegative integers. Require: + +- sum_t x_(p,t,w) equals n_p times the multiplicity of w in p; +- sum_w x_(p,t,w) is at most n_p for each pattern and time; +- across all groups and patterns, each call t receives its exact provider width inventory; +- only times in the actual group's legal idle interval occur. + +These conditions construct a complete-owner assignment. Split each width's incidences among its distinct positions in the pattern, each position having degree n_p. Form the bipartite multigraph whose left vertices are times and right vertices are pattern positions. Its maximum degree is n_p; add dummy vertices and edges until it is n_p-regular. For every subset S of left vertices, n_p|S| edges enter at most n_p|N(S)| slots, so Hall's condition holds. Remove a perfect matching and repeat. The n_p matchings are literal ports. Every port receives one incidence for each pattern position, never two incidences at the same time. Deleting dummy edges therefore yields the exact desired complete-owner slots. Assign each call's actual helpers bijectively to its matching-width slots. Offsets are contiguous partial sums of the pattern widths. + +This is an explicit sufficient lifting theorem, not an assertion that aggregate counts alone imply physical feasibility. The integer time rows, matching decomposition and final independently reconstructed physical chart are all checked. It also explains the exchange-fiber structure: different matching decompositions preserve the same exact time and pattern margins. The earlier cut potential supplies remainder costs before this constructive lift; the final broader integer pattern search additionally permits changes to pattern counts. No theorem about globally optimal constrained cuts is claimed. + +## Frozen concrete result + +The final provider combines the static44 response selection, PR534 frame lift and one cold-dirt quotient simplification. The final local histogram is + + {1:2284,2:456,3:488,4:168,5:56,6:56,8:8}. + +Its 504 helpers have widths 56x5,156x8,292x9. A bounded finite pattern/time search selected these counts across all owner replicas: + + rank8: 5376*[8] + rank16: 2928*[8,8],448*[5,9],208*[9] + rank32: 3584*[5,9,9,9] + rank48: 1923*[9,9,9,9,9],1*[9],1660*[] + +The literal matching lift produces 36,288 helper roles across 72 complete calls and 16,128 pending bins. All actual 2,972 full 73-column charts, per-replica event orders, whole-owner uniqueness, spectator axes and residual endpoints pass the independent physical audit; seven genuine corruptions reject. The resulting paid global histogram is + + {1:164448,2:33280,3:37059,4:12096, + 5:4032,6:4032,7:208,8:576,39:1,48:1660}. + +The exact deficit is 2,560 at m=73, live stock 7,168 and physical stock 7,682. The fresh scalar invoice charges prefix512 for measured225, and row20161 for measured16467. The certified complex saving is + + b = 796759709641153381751 / 500000000000000000000000 + = 0.001593519419282306763502. + +This is a complex supplier saving, not final kappa. The outer assembly must combine it with the independently admitted bit supplier through all strict constraints. All-size compiler, precision/tape and analytic-transfer hypotheses remain the retained interfaces. + +The earlier fixed-slot C++ exchange search gave b=0.001590643179579185038482 with the static44 provider and is preserved as a passed intermediate. The final broader pattern search stopped at its finite time limit with a feasible integer witness; no global optimum is asserted. Replaying the final witness needs Python's standard library only, not SciPy, HiGHS, or the optimizer. Both OpenAI sources were read and adapted; neither was newly Lean-compiled. These sources informed the two resource constructions, rather than establishing a claim of two independently additive numerical gains. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/WAVE-MAJORISATION.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/WAVE-MAJORISATION.json new file mode 100644 index 0000000000..b3b738d77d --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/WAVE-MAJORISATION.json @@ -0,0 +1,32 @@ +{ + "status": "EXACT_SUFFICIENT_MAJORISATION_CERTIFICATE", + "old": [ + 2, + 3 + ], + "new": [ + 1, + 4 + ], + "matrix": [ + [ + "2/3", + "1/3" + ], + [ + "1/3", + "2/3" + ] + ], + "row_sums": [ + "1", + "1" + ], + "column_sums": [ + "1", + "1" + ], + "interval": "0=18 + return raw[:9]+b'\xff'+raw[10:] +gzip.compress=compress_portable +script=Path(sys.argv[1]).resolve() +sys.argv=sys.argv[1:] +sys.path.insert(0,str(script.parent)) +runpy.run_path(str(script),run_name='__main__') diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/LICENSE b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/NOTICE.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/NOTICE.md new file mode 100644 index 0000000000..f3833c1cb2 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/NOTICE.md @@ -0,0 +1,24 @@ +# Attribution and derivative scope + +Prepared for icekylinx with OpenAI GPT-6 Astra assistance; Apache-2.0. +Copyright 2026 icekylinx. Local review and submission packaging used OpenAI Codex. +The new work is the same-partition 504-helper scalar architecture, its frozen +entrance selection, delivery-frame coalescing, literal global allocation, +targeted certificate reuse and complete new finite recount. + +The included Hamming inputs, Gaussian-dyadic Clifford compiler, primitive +scalar routines, rational moment engines and outer assembly descend from the +authors recorded in `SOURCES.json` and `inputs/PR523-ANCESTRY.json`. Original +source notices are retained. In particular, DreamingOfClouds' gauge/kernel +and paid-wrapper files retain their notice crediting Claude Opus 5.5 assistance; +those files are not presented as newly authored work. + +contributor (handle omitted)'s PR522 rank-sector coordinate-total principle was inspected and is +credited as a related idea. This increment does not import its ranksector99 +patch or add its reported gain arithmetically. Higherbeing's PR520 face-packet +geometry helped direct the structural investigation; its code is not copied. +The latest numerical comparison, Rohan Arun's PR527, is a comparison source. + +The reproduction wrapper deliberately separates fresh changed-word/global +checks from reuse of the byte-pinned completed baseline and unchanged bit +operator. Old finite receipts never stand in for the changed local word. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/SOURCES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/SOURCES.json new file mode 100644 index 0000000000..6991a2a9c6 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/SOURCES.json @@ -0,0 +1,63 @@ +{ + "repository": "https://github.com/CrocSwap/integer-mult-bounds", + "prepared_for": "icekylinx", + "assistance": "OpenAI GPT-6 Astra", + "license": "Apache-2.0", + "baseline": { + "pr": 523, + "author": "icekylinx", + "head": "a900f98be8ff2c09d3292b5112d4731dbd0c8438", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/523", + "role": "112 ordered ports, fixed data controller, completed phase cache and finite baseline allowances." + }, + "retained": [ + { + "pr": 514, + "author": "contributor (handle omitted)", + "head": "246bfacd4cb4072836ae3147099f548bb728229f", + "role": "Pinned Hamming modules and scalar constructor ancestry; derived from PR507 and PR425/433." + }, + { + "pr": 493, + "author": "eumemic", + "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7", + "role": "Unchanged bit supplier; published histogram repriced, operator not reconstructed." + }, + { + "pr": 484, + "author": "DreamingOfClouds", + "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f", + "role": "Attributed shared-donor kernel, entrance-gauge, paid-wrapper and hosting lineage; original Claude Opus assistance notices retained." + } + ], + "related_ideas": [ + { + "pr": 522, + "author": "contributor (handle omitted)", + "head": "e9f8075b5212e9bddf361097dbb022dcd052e0bb", + "role": "Rank-sector coordinate-total principle inspected and credited. Its ranksector99 patch is not imported; this word completes eight independent retired carriers before the center cut." + }, + { + "pr": 520, + "author": "higherbeing", + "head": "6077fa76950facbce11ec2f04dfbc93493114a44", + "role": "Face-packet delivery geometry and open allocation framing informed the bottleneck investigation; no PR520 implementation is copied." + } + ], + "comparison": { + "pr": 527, + "author": "rohanarun", + "head": "2080903b9e6bd01e3f64cc4c7c62ea1b3af0aa6a", + "kappa": "0.001467289440740487", + "role": "Latest comparable numerical PR in the recorded snapshot; comparison only." + }, + "new_contribution": "Same-partition direct output loading and two-half face delivery with 504 helpers; 72 compatible gauges and 80 exact kernel pivots; body frame coalescing; literal pure-pattern whole-owner allocation; fresh finite global invoice and exact kappa.", + "ancestry_file": "inputs/PR523-ANCESTRY.json", + "comparison_at_submission": { + "pr": 529, + "author": "chafreaky", + "head": "05fc7e332651a41860add3c217cd6f6e88758003", + "kappa": "0.001469603966017302", + "role": "Comparison only; no code or proof imported." + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/adapters_local.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/adapters_local.py new file mode 100644 index 0000000000..787416e4dd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/adapters_local.py @@ -0,0 +1,60 @@ +"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding. Apache-2.0. +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. The wrapper construction follows PR #458 +(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first); +S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers R_E^-1 before the whole local invocation and L_E^-1 after its +full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically. +usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json +Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive +constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that L_E^-1 S_E R_E^-1 has exactly the +tableau and zero-state vector (global phase included) of fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong +translation, wrong width) must be rejected.""" +import copy, gzip, json, sys +from pathlib import Path +# Package-path adaptation only; the exact wrapper mathematics is unchanged. +R = Path(__file__).resolve().parents[1] +sys.path.insert(0, str(R / 'vendor/clifford')) +from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity +n = 9; FULL = tuple(1 << i for i in range(n)) +def monomial_op(rec): + """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)""" + out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset'])) + return out.then(Op(n, identity(n), [('phase', rec['phase'])])) +def S_of(U): + return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, FULL)) +def wrapped_ok(U, rec): + """exactly: L^-1 S R^-1 = C_[w] x I (apply order: R^-1, S, L^-1)""" + w = n - len(U); S = S_of(U); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left']) + net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w)) + return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state() +def main(): + c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v'] + starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0}) + recipes = {} + for f in starts: + U = frames[f]; rec, compiled = lower_child(S_of(U)) + recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right']) + Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes), sort_keys=True, separators=(',', ':')) + '\n') + # ---- independent decode of the serialized file + data = json.loads(Path(sys.argv[2]).read_text())['recipes'] + dot = lambda a, b: bin(a & b).count('1') & 1 + detail = [] + for f in starts: + rec = data[str(f)]; U = frames[f] + assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f) + detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U), + totally_isotropic=all(dot(a, b) == 0 for a in U for b in U))) + controls = [] + def reject(name, fn): + f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec) + if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name) + controls.append(name) + reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4)) + reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1)) + reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4)) + reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left']))) + reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1)) + res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail), + all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail) + Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n') + print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight']) +if __name__ == '__main__': main() diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/audit_and_transport.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/audit_and_transport.py new file mode 100644 index 0000000000..95ae517f2e --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/audit_and_transport.py @@ -0,0 +1,222 @@ +"""Rebuild arbitrary-dirt compensation and transport a changed local word. + +Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0. +Adapted from PR425/433 (icekylinx), PR484's audit_gk.py +(DreamingOfClouds), and Round19's 112-port transport. This auditor does not +import a constructor, a nominated compensation table, or a global price. +Only the changed scalar word and its actual frame chains are checked here. +""" +import argparse +import copy +import gzip +import hashlib +import json +import time +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def content_hash(path): + data = path.read_bytes() + return hashlib.sha256(gzip.decompress(data) if path.suffix == '.gz' else data).hexdigest() + + +def basis(vs): + pivots = {} + for x in vs: + for k in sorted(pivots, reverse=True): + if x >> k & 1: + x ^= pivots[k] + if x: + k = x.bit_length() - 1 + for j in pivots: + if pivots[j] >> k & 1: + pivots[j] ^= x + pivots[k] = x + return tuple(pivots[k] for k in sorted(pivots, reverse=True)) + + +def apply(e, rows): + if e[0] == 'scale': + _, target, a, b, *_ = e + q = Q(a, b) + assert q + rows[target] = {j: q*x for j, x in rows[target].items()} + else: + _, target, source, a, b, *_ = e + assert target != source + q = Q(a, b) + for j, x in list(rows[source].items()): + value = rows[target].get(j, Q(0)) + q*x + if value: + rows[target][j] = value + else: + rows[target].pop(j, None) + + +def inverse(e): + e = copy.deepcopy(e) + if e[0] == 'add': + e[3] *= -1 + else: + e[2], e[3] = e[3], e[2] + return e + + +def dual(e): + e = inverse(e) + if e[0] == 'add': + e[1], e[2] = e[2], e[1] + return e + + +def run(raw_path, routing_path, out): + start_time = time.monotonic() + word, routing = read(raw_path), read(routing_path) + v, h, helpers = word['report']['v'], word['report']['h'], word['report']['R'] + assert h == 9 and v == 112 and routing['v'] == v + n = 2*v + helpers + ident = lambda: [{r: Q(1)} for r in range(n)] + main = word['A'] + word['cut'] + word['B'] + assert all(not v <= e[2] < 2*v for e in word['A'] + word['B'] + if e[0] == 'add' and not v <= e[1] < 2*v) + matrix = ident() + for e in main: + apply(e, matrix) + dirty = [{} for _ in range(n)] + for r in range(v, 2*v): + dirty[r] = {j: x for j, x in matrix[r].items() if j >= 2*v} + for e in word['precondition']: + apply(e, dirty) + compensation = [['add', r, j, -q.numerator, q.denominator, []] + for r in range(v, 2*v) for j, q in sorted(dirty[r].items())] + entering = set(map(int, word.get('start_extra', {}))) + assert all(e[2] not in entering for e in compensation) + cleanup = [inverse(e) for e in reversed(word['A'] + word['B']) + if not v <= e[1] < 2*v] + assert [e[:-1] for e in cleanup] == [e[:-1] for e in word['cleanup']] + program = word['precondition'] + compensation + main + cleanup + for backward in (False, True): + actual = ident() + for e in program: + apply(dual(e) if backward else e, actual) + expected = ident() + for t in range(v): + expected[t if backward else v+t][v+t if backward else t] = Q(-1 if backward else 1) + assert actual == expected, ('arbitrary-dirt endpoint', backward) + # The native scalar compiler allows dyadic additions and signed binary scales. + for e in program: + q = Q(e[3], e[4]) if e[0] == 'add' else Q(e[2], e[3]) + assert q.denominator & (q.denominator-1) == 0 + if e[0] == 'scale': + a = abs(q.numerator) + assert a and a & (a-1) == 0 + + tau = lambda x: x ^ (43 if (x & 43).bit_count() % 2 else 0) + ports = routing['ports'] + assert len(set(ports)) == v and set(map(tau, word['ports'])) == set(ports) + mapping = {i: ports.index(tau(p)) for i, p in enumerate(word['ports'])} + mapping.update({v+i: v+mapping[i] for i in range(v)}) + mapping.update({r: r for r in range(2*v, n)}) + full = tuple(1 << i for i in range(h-1, -1, -1)) + frames, frame_ids = [(), full], {(): 0, full: 1} + + def fid(vectors): + frame = basis(vectors) + if frame not in frame_ids: + frame_ids[frame] = len(frames) + frames.append(frame) + return frame_ids[frame] + + def transform(e): + e = copy.deepcopy(e) + e[1] = mapping[e[1]] + if e[0] == 'add': + e[2] = mapping[e[2]] + if e[-1] is not None: + e[-1] = fid([tau(x) for x in e[-1]]) + return e + + canonical = {key: [transform(e) for e in word[key]] + for key in ('A', 'B', 'cut', 'cleanup', 'precondition')} + canonical['compensation'] = [transform(e) for e in compensation] + canonical['start'] = [fid([p]) for p in ports] + [0]*(v+helpers) + for r, frame in word.get('start_extra', {}).items(): + assert 2*v <= int(r) < n + canonical['start'][int(r)] = fid([tau(x) for x in frame]) + canonical['final'] = ([1]*v + + [fid(x for x in range(1, 1 << h) if (x & p).bit_count() % 2 == 0) for p in ports] + + [1]*helpers) + canonical.update(h=h, v=v, R=helpers, ports=ports, frames=frames, + centers=[mapping[r] for r in word['centers']], + center_frames=[fid(tau(x) for x in frame) for frame in word['center_frames']]) + levels = {mapping[v+int(t)]-v: fid(tau(x) for x in frame) + for t, frame in word.get('target_levels', {}).items()} + canonical['target_levels'] = {str(t): f for t, f in levels.items()} + current, paid, edges = canonical['start'].copy(), Counter(), set() + + def climb(r, f): + old = current[r] + assert basis(frames[old] + frames[f]) == frames[f], ('nonmonotone', r, old, f) + if old != f: + degree = len(frames[f]) - len(frames[old]) + assert degree > 0 + paid[degree] += 1 + edges.add((old, f)) + current[r] = f + + for part in ('A', 'B'): + if part == 'B': + assert all(current[r] == f for r, f in zip(canonical['centers'], canonical['center_frames'])) + assert all(current[v+t] == levels.get(t, 0) for t in range(v)) + for r, frame in zip(canonical['centers'], canonical['center_frames']): + served = {levels.get(e[1]-v, 0) for e in canonical['cut'] if e[2] == r} + old = frame + for f in sorted(served, key=lambda f: -len(frames[f])): + assert basis(frames[old] + frames[f]) == frames[old] + if old != f: + paid[len(frames[old])-len(frames[f])] += 1 + edges.add((old, f)) + edges.add((f, old)) + old = f + for e in canonical[part]: + for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): + climb(r, e[-1]) + for r, f in enumerate(canonical['final']): + climb(r, f) + assert dict(paid) == {int(r): count for r, count in word['report']['local_profile'].items()} + canonical['local_profile'] = dict(sorted(paid.items())) + canonical['edges'] = sorted(edges) + out.mkdir(parents=True, exist_ok=False) + payload = json.dumps(canonical, sort_keys=True, separators=(',', ':')).encode() + (out/'CANONICAL-WORD.json.gz').write_bytes(gzip.compress(payload, mtime=0)) + (out/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(word, sort_keys=True, separators=(',', ':')).encode(), mtime=0)) + receipt = dict(status='PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES', + input_content_sha256=content_hash(raw_path), routing_content_sha256=content_hash(routing_path), + canonical_content_sha256=hashlib.sha256(payload).hexdigest(), + live_columns_each_orientation=n, helpers=helpers, + compensation_additions=len(compensation), scalar_operations=len(program), + center_rank_sum=sum(map(len, word['center_frames'])), + local_profile=dict(sorted(paid.items())), local_rank_mass=sum(r*z for r, z in paid.items()), + widths=[h-len(frames[f]) for f in canonical['start'][2*v:]], + frames=len(frames), directed_edges=len(edges), + tau=43, target_port_order_matches_baseline=True, + seconds=time.monotonic()-start_time, + scope='Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. Phase lowering, wrappers, global owners and global assembly are separate.') + (out/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(receipt, indent=2)+'\n') + print(json.dumps({k: value for k, value in receipt.items() if k != 'widths'}, indent=2), flush=True) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--raw', type=Path, required=True) + parser.add_argument('--routing', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + run(args.raw, args.routing, args.out) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/audit_local.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/audit_local.py new file mode 100644 index 0000000000..a09611844a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/audit_local.py @@ -0,0 +1,144 @@ +# Local-only extraction of the attributed PR514 / PR433 independent replay. +# Prepared for icekylinx with OpenAI Codex assistance. Apache-2.0. +# The complete local checker and its negative controls are retained verbatim. +# Global hosting is verified separately for the changed 112-port geometry. +import copy,gzip,hashlib,json,sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +OUT=Path(sys.argv[1]) +c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz')) +ir={'local_programs':json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'))} +v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames'] +levels={int(t):f for t,f in c.get('target_levels',{}).items()} +entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0] +plain={r for r in range(n) if r not in set(entering)} +def contains(a,b): + for x in a: + for y in b: + if x>>(y.bit_length()-1)&1:x^=y + if x:return False + return True +def local(events,back): + rows={('L',r):{r:Q(1)} for r in range(n)} + norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={} + hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256();chain={};wrappers=[] + allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done'] + for event in events: + tag=event[0] + if tag=='phase': + phases.append(event[1]);assert phases==allowed[:len(phases)] + if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==entering # GK + if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v)) # GK + if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final'])) + assert not private + elif tag=='residual_adapter': # GK: paid wrappers of entering helpers: R_E^-1 before the invocation, L_E^-1 after the full-frame cleanup + _,kind,r,f=event;assert r in entering and f==c['start'][r] and kind in ('pre','post') + assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup') + assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f)) + elif tag=='adapter': + assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]] + (entry if event[1]=='old_to_new' else exit).append((event[2],event[3])) + elif tag=='climb': + _,part,r,a,b,rank=event + assert not private and phases[-1]==part and cur[r]==a + assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0 + hist[rank]+=1;cur[r]=b + elif tag=='center': + _,k,a,b,rank=event + assert phases[-1]=='centers' and private=={('C',k):a} + cf=c['center_frames'][k];cr=len(frames[cf]) + # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child + assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a]) + assert rank==abs(len(frames[a])-len(frames[b]))>0 + chain.setdefault(k,[]).append((a,b)) + private['C',k]=b;hist[rank]+=1;centers.append(k) + elif tag=='scalar': + _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None + if target[0]=='C' and op=='clear': + assert private.get(target,f)==f + private.pop(target,None) + else: + for r in (target,source): + if r is None:continue + if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f) + else: + if r==target and r not in private:private[r]=f + assert private[r]==f + if op=='clear':rows[target]={};norm[target]=Q(0) + elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source] + elif op=='scale': + q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator + assert a&(a-1)==0 and b&(b-1)==0 + rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q) + else: + q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator + assert source!=target and b&(b-1)==0 + # Independent symbolic replay of the cleared coefficient work. + w=0 + for bit in bin(a)[2:]:w=2*w+int(bit) + assert Q(w,b)*(1 if q>0 else -1)==q + prefix=max(prefix,Q(a)*norm[source]) + norm[target]=norm.get(target,Q(0))+abs(q)*norm[source] + row=rows.setdefault(target,{}) + for j,x in list(rows[source].items()): + z=row.get(j,Q(0))+q*x + if z:row[j]=z + else:row.pop(j,None) + prefix=max(prefix,norm[target]) + else:raise AssertionError(tag) + assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private + assert sorted(r for k,r,_ in wrappers if k=='pre')==entering and sorted(r for k,r,_ in wrappers if k=='post')==entering # GK + for k,st in chain.items(): # GK: the steps of each centre chain link up and end at the centre frame + cf=c['center_frames'][k] + if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1)) + else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1)) + assert all(not row for reg,row in rows.items() if reg[0]=='C') + for r in range(n): + expected={r:Q(1)} + if back and r>i)&1==0);a=q^(1<>i&1 else 0)for i in order]+[1<2*max(paid)**2 + return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72) + +r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256'] +assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items()) +controls=[] +def reject(name,mut): + if '--mutation-controls' not in sys.argv[4:]:return + q=copy.deepcopy(ct);mut(q) + try:audit(q) + except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name) + else:raise AssertionError('ACCEPTED '+name) +enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4) +reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)])) +reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0])) +reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA)) +reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1)) +reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72)) +reject('omit idle remainder',lambda q:q['idle_children'].pop()) +reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1)) +report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,mutation_controls_run='--mutation-controls' in sys.argv[4:],widths=dict(sorted(Counter(width).items())),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses the new selected local program bound by fresh scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations.') +REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2)) + +owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,hosted_residuals=HOSTED,banked_residuals=0,all_live_owners_per_call_distinct=True,owners_per_call=N,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest()) +(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n') + +# Literal residual frames are a compact export of the already checked offsets, +# not another global replay. Every row names its actual inherited axes. +frames=[] +for z in ct['idle_children']: + axes=list(map(int,ph['recipes'][z['port']]['idle_children'][z['child']]['orthogonal_axes'])) + tail=axes[z['pending_offset']:] + assert len(tail)==z['rank'] + frames.append(dict(z,orthogonal_axes=tail)) +frame_raw=json.dumps(frames,sort_keys=True,separators=(',',':')).encode() +(OUT/'IDLE-REMAINDER-FRAMES.json.gz').write_bytes(gzip.compress(frame_raw,mtime=0)) +frame_receipt=dict(status='PASS_LITERAL_IDLE_REMAINDER_FRAMES',template_sha256=summary['template_sha256'], + uncompressed_frames_sha256=hashlib.sha256(frame_raw).hexdigest(),children=len(frames), + rank_profile=dict(sorted(Counter(z['rank']for z in frames).items())), + source_data_phase_sha256=hashlib.sha256((BASE/'work/complex-nine-native/DATA-PHASES.json').read_bytes()).hexdigest(), + scope='Actual orthogonal axes after the independently checked whole-owner prefix in each inherited pending child.') +(REPORT.parent/'IDLE-REMAINDER-FRAMES.json').write_text(json.dumps(frame_receipt,indent=2)+'\n') + diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/emit_local.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/emit_local.py new file mode 100644 index 0000000000..a54170b002 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/emit_local.py @@ -0,0 +1,156 @@ +# GK: modified copy of PR #433's complex_emit.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5 +# (Anthropic), via Claude Code. Every change is marked "GK:". On a word without start_extra / target_levels the behaviour +# and every written file equal PR #433's (regression anchor in verify.py). +import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__))) +# Adapted from PR425 by icekylinx with Codex assistance. +"""Emit both local programs, integrate the fixed nine-stage geometry, and bill. + +The expanded scalar interface is justified in PROOF.txt. This script does not +claim a Lean proof or discharge the inherited all-size/analytic interfaces. +""" +import copy,gzip,hashlib,importlib.util,json,math +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +OUT=Path(_sys.argv[1]);cp=OUT/'CANONICAL-WORD.json.gz' +c=json.load(gzip.open(cp)) +frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R +def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest() +def basis(vs): + b={} + for x in vs: + for p in sorted(b,reverse=True): + if x>>p&1:x^=b[p] + if x: + p=x.bit_length()-1 + for q in b: + if b[q]>>p&1:b[q]^=x + b[p]=x + return tuple(b[p] for p in sorted(b,reverse=True)) +def dual(e): + e=list(e) + if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1 + else:e[2],e[3]=e[3],e[2] + return e +def scalar(e,back): + e=dual(e) if back else list(e) + if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]] + return ['scale',['L',e[1]],e[2],e[3]] +def primitive_bound(e): + if e[0] in ('clear','copy'):return 1 + q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3]) + a,b=abs(q.numerator),q.denominator + assert b&(b-1)==0 + if e[0]=='scale': + assert a&(a-1)==0 + return abs(a.bit_length()-b.bit_length())+int(q<0) + # Exact binary Horner multiplication on a cleared private stream, repeated + # halving, signed accumulation into the target, then clear the private stream. + return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1) + +def emit(back): + out=[];cur=c['start'].copy() + def event(e):out.append(e) + def scal(e,f):event(['scalar',e,f]) + event(['phase','zero_frame_precondition']) + for e in c['precondition']+c['compensation']: + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + assert all(c['start'][r]==0 for r in regs) + scal(scalar(e,back),0) + event(['phase','entry_adapters']) + # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate + # that touches it and L_E^-1 follows the full-frame cleanup. Words without entrances emit PR #433's events. + entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0] + for r,f in enumerate(c['start']): + if r in entering:event(['residual_adapter','pre',r,f]) + else:event(['adapter','old_to_new',r,f]) + def climb(r,f,part): + old=cur[r] + if old==f:return + assert basis(frames[old]+frames[f])==tuple(frames[f]) + rank=len(frames[f])-len(frames[old]);assert rank>0 + event(['climb',part,r,old,f,rank]);cur[r]=f + for part in ('A','centers','B','final'): + event(['phase',part]) + if part in ('A','B'): + for e in c[part]: + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + for r in regs:climb(r,e[-1],part) + scal(scalar(e,back),e[-1]) + elif part=='centers': + # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends + # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level + lv=lambda r:c.get('target_levels',{}).get(str(r-v),0) + assert all(cur[r]==lv(r) for r in range(v,2*v)) + for k,r in enumerate(c['centers']): + cf=c['center_frames'][k];assert cur[r]==cf + terms=[e for e in c['cut'] if e[2]==r] + path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x])) + C=['C',k] + if not back: + scal(['clear',C],cf);scal(['copy',C,['L',r]],cf) + for a in range(len(path)): + if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])]) + for e in terms: + if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a]) + scal(['clear',C],path[-1]) + else: + scal(['clear',C],path[-1]) + for a in range(len(path)-1,-1,-1): + for e in terms: + if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a]) + if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])]) + scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf) + else: + for r,f in enumerate(c['final']):climb(r,f,part) + event(['phase','exit_adapters']) + for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f]) + event(['phase','full_frame_cleanup']) + for e in c['cleanup']: + regs=[e[1]]+([e[2]] if e[0]=='add' else []) + assert all(c['final'][r]==1 for r in regs) + scal(scalar(e,back),1) + for r in entering:event(['residual_adapter','post',r,c['start'][r]]) # GK: L_E^-1 after the full-frame cleanup + event(['phase','done']) + return out + +def check_local(events,back): + # Literal scalar replay of the emitted stream, including center lifetimes. + state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0 + for e in events: + if e[0]=='climb':assert not live;paid[e[5]]+=1 + elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1 + elif e[0]=='scalar': + op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op) + if tag=='clear': + state[t]={} + if t[0]=='C' and t[1] in live:live.remove(t[1]) + elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1]) + elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()} + else: + s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{}) + if t[0]=='C' and t[1] not in live:live.append(t[1]) + for j,x in list(state.get(s,{}).items()): + z=row.get(j,Q(0))+q*x + if z:row[j]=z + else:row.pop(j,None) + assert not live and all(not row for r,row in state.items() if r[0]=='C') + for r in range(n): + expected={r:Q(1)} + if back and r>i)&1);u=q^(1<>i&1 else 0)for i in order]+[1<=0 and off+w<=rank[i] + assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1] + B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i] + occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[] + order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M + sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma + route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9 + cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells + digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n') +for c in t['calls']: + k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R)) + c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f2*max(paid)**2 + +assert t['local_programs']==parent['local_programs'] +raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0)) +res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=2560,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'split-centres/CLIFFORD-RECIPES.json',BASE/'split-centres/CLIFFORD-REVIEW.json',BASE/'split-centres/INDEPENDENT-LOCAL-REPLAY.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.') +(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/invoice_final.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/invoice_final.py new file mode 100644 index 0000000000..abefcee47b --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/invoice_final.py @@ -0,0 +1,299 @@ +"""Recount a changed local word and its actual asynchronous finite invoice. + +Prepared for icekylinx with OpenAI Codex assistance. Apache-2.0. +Adapted from the attributed Round19 audit_async_invoice.py and its PR484/514 +ancestry. Uses the fresh hash-bound independent local replay for exact scalar +endpoints; independently recounts emitted Horner work, prefix envelopes, +paid local calls, wrappers and finite charges. Does not rerun the old baseline +or read an old INTEGRATION.json as evidence for the changed word. +""" +import argparse +import gzip +import hashlib +import json +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def filehash(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def contenthash(path): + data = path.read_bytes() + return hashlib.sha256(gzip.decompress(data) if path.suffix == '.gz' else data).hexdigest() + + +def run(base, hosted, audit, out, retained_invoice=None): + local_dir = base / 'split-centres' + cp = local_dir / 'CANONICAL-WORD.json.gz' + pp = local_dir / 'LOCAL-PROGRAMS.json.gz' + rp = local_dir / 'INDEPENDENT-LOCAL-REPLAY.json' + w, programs, replay = read(cp), read(pp), read(rp) + checks = read(local_dir / 'LOCAL-CHECKS.json') + parent = read(local_dir / 'GLOBAL-TEMPLATE.json.gz') + template_path = hosted / 'GLOBAL-TEMPLATE.json.gz' + template = read(template_path) + owners = read(audit / 'OWNERS-AND-PROFILE.json') + control = read(audit / 'ASYNC-AUDIT.json') + template_hash = contenthash(template_path) + assert template_hash == control['complex_template_sha256'] == owners['template_sha256'] + assert owners['status'] == 'PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE' + assert replay['status'] == 'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY' + assert replay['canonical_word_sha256'] == filehash(cp) + assert replay['local_programs_sha256'] == filehash(pp) + assert template['local_programs'] == parent['local_programs'] == programs + assert template['recipe'] == parent['recipe'] + assert Counter(c['orientation'] for c in template['calls']) == Counter(c['orientation'] for c in parent['calls']) + + v, helpers, h, m = w['v'], w['R'], w['h'], template['m'] + assert v == 112 and h == 9 and m == 73 + assert replay['v'] == v and replay['helpers'] == helpers + n = 2*v + helpers + stages, replicas, blocks_per_stream = 9, 8, 4 + call_count = len(template['calls']) + assert call_count == stages*replicas == control['complete_invocations'] + assert control['one_owner_per_complete_invocation'] + payload = 512 + + widths = [h-len(w['frames'][f]) for f in w['start'][2*v:]] + assert len(widths) == helpers + entrances = {r: f for r, f in enumerate(w['start']) if r >= 2*v and f != 0} + entering = len(entrances) + assert entering == replay['entering_helpers'] + local = {} + for orientation, events in programs.items(): + # Endpoint equality and native frames were already independently + # replayed on all n columns in the hash-bound receipt above. + env = {('L', r): Q(1) for r in range(n)} + peak = Q(1) + real = macros = workops = 0 + paid = Counter() + wrappers = {'pre': set(), 'post': set()} + for event in events: + tag = event[0] + if tag == 'climb': + paid[event[5]] += 1 + elif tag == 'center': + paid[event[4]] += 1 + elif tag == 'residual_adapter': + _, kind, register, frame = event + assert kind in wrappers and entrances.get(register) == frame + assert register not in wrappers[kind] + wrappers[kind].add(register) + elif tag == 'scalar': + macros += 1 + scalar = event[1] + op, target = scalar[0], tuple(scalar[1]) + if op == 'clear': + env[target] = Q(0) + count = 1 + elif op == 'copy': + env[target] = env[tuple(scalar[2])] + count = 1 + elif op == 'scale': + q = Q(scalar[2], scalar[3]) + numerator, denominator = abs(q.numerator), q.denominator + assert numerator and numerator & (numerator-1) == 0 + assert denominator & (denominator-1) == 0 + env[target] *= abs(q) + count = abs(numerator.bit_length()-denominator.bit_length()) + int(q < 0) + elif op == 'add': + source = tuple(scalar[2]) + q = Q(scalar[3], scalar[4]) + numerator, denominator = abs(q.numerator), q.denominator + assert source != target and numerator > 0 + assert denominator & (denominator-1) == 0 + acc, count = 0, 1 # clear coefficient work + for i, bit in enumerate(bin(numerator)[2:]): + if i: + acc *= 2 + count += 1 + peak = max(peak, acc*env[source]) + if bit == '1': + acc += 1 + count += 1 + peak = max(peak, acc*env[source]) + value = Q(acc) + for _ in range(denominator.bit_length()-1): + value /= 2 + count += 1 + peak = max(peak, value*env[source]) + assert value == abs(q) + count += 2 # signed accumulation and work clear + env[target] = env.get(target, Q(0)) + abs(q)*env[source] + workops += count + else: + raise AssertionError(op) + real += 2*count + peak = max(peak, env[target]) + else: + assert tag in ('adapter', 'phase') + assert wrappers['pre'] == wrappers['post'] == set(entrances) + assert all(value == 0 for register, value in env.items() if register[0] == 'C') + prior = replay['local'][orientation] + assert prior['all_exact_columns'] == n and prior['private_work_erased'] + assert peak == Q(prior['prefix_l1_upper']) and peak < 2**prior['charged_payload_bits'] + bits = peak.numerator.bit_length()-peak.denominator.bit_length()+1 + assert bits == prior['prefix_bits_upper'] + assert real == checks[orientation]['real_component_primitive_bound'] + assert macros == checks[orientation]['scalar_macros'] + assert dict(paid) == {int(r): count for r, count in checks[orientation]['paid_profile'].items()} + assert dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()} + local[orientation] = dict( + events=len(events), macros=macros, real_component_primitives=real, + prefix_l1=str(peak), prefix_bits=bits, + coefficient_work_primitive_count=workops, all_exact_columns=n, + dirty_helper_columns=helpers, all_dirty_helper_columns_restored=True, + private_centres_and_coefficient_work_cleared=True, + pre_wrappers=len(wrappers['pre']), post_wrappers=len(wrappers['post']), + endpoint_evidence='Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json') + + centres = len(w['centers']) + children = sum(checks['forward']['paid_profile'].values()) + assert checks['forward']['paid_profile'] == checks['backward']['paid_profile'] + macro_bound = max(row['macros'] for row in local.values()) + compiler = 64*(m+1)**3 + adapters = 16*(macro_bound+children+n+centres)+64*m + primitive_bound = max(row['real_component_primitives'] for row in local.values())+adapters*compiler + + bridge_steps = sum(event['kind'] == 'bridge' for event in parent['recipe']) + bridge_sweeps = sum(event['kind'] == 'bridge' for event in template['execution_schedule']) + assert bridge_sweeps == replicas*bridge_steps + bridge_additions = 2*v*bridge_sweeps + shifts = blocks_per_stream*v*replicas + moves = 2*shifts + parent_live, parent_physical = parent['live'], parent['physical'] + data_stock = 2*v*blocks_per_stream*replicas + assert (parent_live-data_stock) % stages == 0 + parent_banks = (parent_live-data_stock)//stages + assert parent_banks >= 0 + assert parent_physical == parent_live+helpers+centres+2 + scalar = sum(local[call['orientation']]['real_component_primitives'] for call in template['calls']) + factors_per_wrapper = 2*(m-1) + wrapper_factors = 2*call_count*entering*factors_per_wrapper + nonlocal_items = ( + 4*v*replicas*stages + 2*v*replicas*stages + + 2*call_count*helpers + + sum(child['replicas'] for child in parent['idle_children']) + + stages*parent_banks + bridge_additions + shifts + moves + + parent_live + parent_physical + wrapper_factors) + outside = 8*nonlocal_items+64*m + parent_pervertex = ( + scalar+bridge_additions+shifts+moves+parent_live + +(call_count*adapters+outside)*compiler+64*parent_physical) + + live, physical = template['live'], template['physical'] + mass, profile = owners['rank_mass'], owners['paid_profile'] + assert m*live-mass == owners['deficit'] == 2560 + assert mass == sum(int(r)*count for r, count in profile.items()) + assert physical == live+helpers+centres+2 + assert live == owners['live'] and physical == owners['physical'] + assert live <= parent_live and physical <= parent_physical + assert not template['bank_padding']['families'] + assert owners['explicit_idle_remainder_children'] <= owners['source_idle_children_charged'] + rebased = parent_pervertex+65*(physical-parent_physical)+(live-parent_live) + used = max(rebased, parent_pervertex) + retained = None + if retained_invoice is not None: + previous = read(retained_invoice) + assert previous['compiler'] == compiler + assert previous['charged_prefix_bits'] == payload + previous_bound = previous['conservative_pervertex_used'] + # The entire newly reconstructed charge is added to the retained old + # allowance. This is intentionally stronger than only paying positive + # deltas and makes no claim that the old integration certifies this word. + used = max(used, previous_bound+parent_pervertex) + retained = dict(sha256=filehash(retained_invoice), + previous_pervertex_allowance=previous_bound, + added_complete_new_pervertex=parent_pervertex, + policy='Retain old allowance and add the entire fresh recount.') + + half = m//2 + group = 2**(half*half) + for i in range(1, half+1): + group *= 2**(2*i)-1 + stock, streamed_mass = group*physical, group*mass + logical = group*used+64 + router = compiler*(logical+1)*(stock+1)**2 + g_bound, e_bound, c0 = 2**30000, 2**100000, 2**210000 + total_mass = streamed_mass+e_bound + literal = 2*g_bound*stock**2+8*streamed_mass+4*stock+4+32*m + row = 2*stock.bit_length()+9909+252+2*payload + maxchild = max(map(int, profile)) + inequalities = dict( + local_primitive_bound=primitive_bound < 2**48, + logical=logical < 2**6050, router=router < g_bound, + literal=literal < e_bound, mass=total_mass < 2**100001, + precision=32*m*total_mass*total_mass < c0, + tape=2*total_mass+18 < c0, row=row < 20161, + halving=m*m > 2*maxchild*maxchild) + assert all(inequalities.values()) + localbits = max(row['prefix_bits'] for row in local.values()) + input_l2_bits = (m+1)//2 + required_prefix = localbits+input_l2_bits+call_count+bridge_sweeps+4 + assert required_prefix < payload + + receipt = dict( + status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE', + template_sha256=template_hash, + parent_template_sha256=contenthash(local_dir/'GLOBAL-TEMPLATE.json.gz'), + owner_audit_sha256=filehash(audit/'OWNERS-AND-PROFILE.json'), + controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'), + independent_local_replay_sha256=filehash(rp), + canonical_word_sha256=filehash(cp), local_programs_sha256=filehash(pp), + local_checks_sha256=filehash(local_dir/'LOCAL-CHECKS.json'), + global_prefix_bits=required_prefix, charged_prefix_bits=payload, + complete_invocation_sweeps=call_count, bridge_sweeps=bridge_sweeps, + row_prefix_extra=2*payload, local=local, helpers=helpers, + centres=centres, live=live, physical=physical, + physical_stock_identity=dict(data_and_owner_families=live, + local_helpers=helpers, private_centres=centres, + coefficient_work=2), + entering_helpers=entering, entrance_rank=sum(h-width for width in widths), + width_inventory=dict(sorted(Counter(widths).items())), + local_adapters=adapters, local_primitive_bound=primitive_bound, + wrapper_elementary_factors_charged=wrapper_factors, + factors_per_wrapper=factors_per_wrapper, compiler=compiler, + unhosted_pervertex=parent_pervertex, hosted_rebased_pervertex=rebased, + conservative_pervertex_used=used, retained_prior_overcharge=retained, + finite=dict(physical_stock_bits=stock.bit_length(), router_bits=router.bit_length(), + literal_bits=literal.bit_length(), physical_row_coefficient=row, + retained_row_coefficient=20161, + required_C0_bits=(32*m*total_mass*total_mass).bit_length(), + halving_integer_inequality=[m*m, 2*maxchild*maxchild], + G_exponent=30000, E_exponent=100000, C0_exponent=210000), + strict_checks=inequalities, + scope='Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged.') + prefix = dict( + status='PASS_ASYNC_GLOBAL_PREFIX', template_sha256=template_hash, + global_prefix_bits=required_prefix, retained_payload_bits=payload, + complete_invocation_cover_sweeps=call_count, + bridge_factor_two_sweeps=bridge_sweeps, + local_scalar_coefficient_work_prefix_bits=localbits, + stream_input_sup_to_l2_bits=input_l2_bits, + primitive_arithmetic_margin_bits=4, + controller_audit_sha256=filehash(audit/'ASYNC-AUDIT.json'), + independent_local_replay_sha256=filehash(rp), + proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Actual full orthogonal owner charts act by right-translation bijections on the retained cover group. Count all {call_count} complete local sweeps and {bridge_sweeps} individual bridge sweeps. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently recounted scalar/Horner envelope uses {localbits} bits; input sup-to-L2 uses {input_l2_bits}; arithmetic margin is 4. Total {required_prefix} < {payload}. All-size child/compiler and precision/tape interfaces remain inherited.') + out.mkdir(parents=True, exist_ok=True) + (out/'PREFIX-AND-INVOICE.json').write_text(json.dumps(receipt, indent=2)+'\n') + (out/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix, indent=2)+'\n') + print(json.dumps(receipt, indent=2), flush=True) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--base', type=Path, required=True) + parser.add_argument('--hosted', type=Path, required=True) + parser.add_argument('--audit', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + parser.add_argument('--retained-invoice', type=Path) + args = parser.parse_args() + run(args.base, args.hosted, args.audit, args.out, args.retained_invoice) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/phases_delta.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/phases_delta.py new file mode 100644 index 0000000000..8d78d26b3b --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/phases_delta.py @@ -0,0 +1,158 @@ +"""Reuse the pinned PR523 phase certificates and lower only changed edges. + +The inherited Gaussian-dyadic compiler still checks every fresh tableau and +global phase. Its zero-state interpreter is accelerated with cached exact +integer permutations and Z4 phases. Overflow is checked before every sum; +there is no floating-point arithmetic in a phase equality. + +Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0. +Compiler and certificate format: PR425/433, icekylinx with Codex assistance. +""" +import argparse +import copy +import gzip +import hashlib +import json +import sys +import time +from collections import Counter +from functools import lru_cache +from pathlib import Path + +import numpy as np + + +def sha(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def frozen(x): + return tuple(map(frozen, x)) if isinstance(x, (list, tuple)) else x + + +def main(): + p = argparse.ArgumentParser() + p.add_argument('--local', type=Path, required=True) + p.add_argument('--baseline', type=Path, required=True) + p.add_argument('--compiler', type=Path, required=True) + a = p.parse_args() + sys.path.insert(0, str(a.compiler.resolve())) + import clifford_exact as ce + started = time.monotonic() + assert sha(a.compiler/'clifford_exact.py') == '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962', 'baseline canonical-frame and phase convention must remain pinned' + c = json.load(gzip.open(a.local/'CANONICAL-WORD.json.gz')) + b = json.load(gzip.open(a.baseline/'CANONICAL-WORD.json.gz')) + old = json.loads((a.baseline/'CLIFFORD-RECIPES.json').read_text()) + prior = json.loads((a.baseline/'CLIFFORD-REVIEW.json').read_text()) + assert prior['all_child_equalities_include_global_phase'] + assert prior['recipe_sha256'] == sha(a.baseline/'CLIFFORD-RECIPES.json') + assert prior['canonical_word_sha256'] == sha(a.baseline/'CANONICAL-WORD.json.gz') + assert c['h'] == b['h'] == 9 and c['ports'] == b['ports'] + n = c['h']; N = 1 << n + xs = np.arange(N, dtype=np.int64) + parity = np.array([x.bit_count() & 1 for x in range(N)], dtype=np.int64) + + @lru_cache(None) + def action(e): + if e[0] == 'P': + return sum(parity[xs & row] << i for i, row in enumerate(e[1])) + if e[0] == 'D': + Q, alpha = e[1:] + phase = np.zeros(N, dtype=np.int64) + for i in range(n): + phase += ((xs >> i) & 1) * alpha[i] + for j in range(i+1, n): + if (Q[i] >> j) & 1: + phase += 2*((xs >> i) & (xs >> j) & 1) + return phase % 4 + if e[0] in ('C', 'X'): + return xs ^ e[1] + return e[1] + + @lru_cache(maxsize=4096) + def state(circuit, basis): + re = np.zeros(N, dtype=np.int64); im = np.zeros(N, dtype=np.int64) + re[basis] = 1; den = 0 + for e in circuit: + z = action(e) + if e[0] == 'P': + rr = np.empty_like(re); ii = np.empty_like(im) + rr[z] = re; ii[z] = im; re, im = rr, ii + elif e[0] == 'X': + re, im = re[z], im[z] + elif e[0] in ('D', 'phase'): + sign = 1 - 2*(z//2) + odd = z % 2 + re, im = sign*np.where(odd, -im, re), sign*np.where(odd, re, im) + elif e[0] == 'C': + assert max(int(np.max(np.abs(re))), int(np.max(np.abs(im)))) < 2**60 + s = e[2]; rr, ii = re[z], im[z] + re, im = re-s*im+rr+s*ii, im+s*re+ii-s*rr + den += 1 + else: + raise AssertionError(e) + while den and not bool(np.any((re & 1) | (im & 1))): + re //= 2; im //= 2; den -= 1 + return tuple(zip(map(int, re), map(int, im))), den + + original = ce.Op.zero_state + # Check the independent vectorized interpreter against the inherited + # literal one on one nontrivial changed edge and its adjoint, once. + probe = ce.canonical_frame(n, c['frames'][c['center_frames'][0]]) + probes = (probe, probe.adjoint().then(ce.fourier(n))) + for op in probes: + expected, den = original(op) + got, d = state(frozen(op.circuit), 0) + assert tuple(expected) == got and den == d + ce.Op.zero_state = lambda self, basis=0: state(frozen(self.circuit), basis) + + @lru_cache(None) + def frame(U): + op = ce.canonical_frame(n, U) + L = [u | (u << n) for u in U] + [v << n for v in ce.nullspace(U, n)] + pre = [x | (z << n) for x, z, _ in ce.inverse(op.tab)[n:]] + assert ce.rank(L) == ce.rank(L+pre) == n + assert ce.rank([x for x, _, _ in op.tab[n:]]) == len(U) + return op + + key = lambda frames, x, y: (tuple(frames[x]), tuple(frames[y])) + known = {key(b['frames'], r['old'], r['new']): r for r in old['children']} + edges = set(map(tuple, c['edges'])) | {(x,y) for f in c['center_frames'] for x,y in ((f,0),(0,f))} + recipes = []; hist = Counter(); fresh = []; reused = [] + for i, (x, y) in enumerate(sorted(edges)): + U, V = key(c['frames'], x, y) + if (U,V) in known: + rec = copy.deepcopy(known[U,V]); rec.update(old=x, new=y); reused.append([x,y]) + else: + rec, _ = ce.lower_child(frame(U).adjoint().then(frame(V))) + rec = dict(old=x, new=y, **rec); fresh.append([x,y]) + assert rec['rank'] == abs(len(U)-len(V)) + hist[rec['rank']] += 1; recipes.append(rec) + if i and i % 600 == 0: + print('delta phases', i, '/', len(edges), 'fresh', len(fresh), 'seconds', round(time.monotonic()-started, 2), flush=True) + adapters = [] + for r in old['endpoint_adapters']: + rec = copy.deepcopy(r); port = r['port'] + f = c['start'][port] if r['role'] == 'source' else c['final'][c['v']+port] + assert tuple(c['frames'][f]) == tuple(b['frames'][r['frame']]) and rec['rank'] == 0 + rec['frame'] = f; adapters.append(rec) + assert len(adapters) == 2*c['v'] + assert {(r['role'], r['port']) for r in adapters} == {(role, port) for role in ('source', 'target') for port in range(c['v'])} + payload = json.dumps(dict(children=recipes, endpoint_adapters=adapters), sort_keys=True, separators=(',',':')).encode() + (a.local/'CLIFFORD-RECIPES.json').write_bytes(payload) + report = dict(status='PASS_REUSED_AND_FRESH_EXACT_LOCAL_PHASE_RECIPES', + canonical_word_sha256=sha(a.local/'CANONICAL-WORD.json.gz'), frames=len(c['frames']), + directed_edges=len(edges), reused_edges=len(reused), fresh_edges=len(fresh), + ranks=dict(hist), endpoint_adapters=len(adapters), reused_endpoint_adapters=len(adapters), + all_child_equalities_include_global_phase=True, recipe_sha256=hashlib.sha256(payload).hexdigest(), + baseline_recipe_sha256=prior['recipe_sha256'], baseline_review_sha256=sha(a.baseline/'CLIFFORD-REVIEW.json'), + compiler_sha256=sha(a.compiler/'clifford_exact.py'), seconds=time.monotonic()-started, + vector_arithmetic='Exact checked int64 Gaussian dyadics; cached permutations and Z4 phase actions. No floating-point equality.', + fresh_edge_ids=fresh, + scope='Only previously unseen ordered pairs of actual canonical subspaces were freshly lowered. Identical baseline pairs and all endpoint adapters reuse the pinned phase certificates; no full cold replay was performed.') + (a.local/'CLIFFORD-REVIEW.json').write_text(json.dumps(report,indent=2)+'\n') + print(json.dumps({k:report[k] for k in ('status','directed_edges','reused_edges','fresh_edges','seconds')},sort_keys=True),flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py new file mode 100644 index 0000000000..650fc9fd77 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py @@ -0,0 +1,95 @@ +"""Bind the new supplier to the unchanged verified 112-port data controller. + +The parent uses one dedicated bank per helper and stage. Each of its eight +complete invocations uses a disjoint width-w block; the residual bank frame is +listed literally. The final whole-owner derivative removes every such bank. +All inherited data routes and exact data phase recipes remain byte-identical. +""" +import argparse +import copy +import gzip +import hashlib +import json +import shutil +from collections import Counter +from pathlib import Path + +ap=argparse.ArgumentParser(description=__doc__) +ap.add_argument('--data-base',type=Path,required=True) +ap.add_argument('--local',type=Path,required=True) +ap.add_argument('--out',type=Path,required=True) +a=ap.parse_args() +def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +def dump(p,obj): + b=json.dumps(obj,sort_keys=True,separators=(',',':')).encode();p.parent.mkdir(parents=True,exist_ok=True) + p.write_bytes(gzip.compress(b,mtime=0)if p.suffix=='.gz'else b+b'\n') + return hashlib.sha256(b).hexdigest() +assert not a.out.exists(),'Output must be new' +old=read(a.data_base/'split-centres/GLOBAL-TEMPLATE.json.gz') +oldcan=read(a.data_base/'split-centres/CANONICAL-WORD.json.gz') +can=read(a.local/'CANONICAL-WORD.json.gz');checks=read(a.local/'LOCAL-CHECKS.json');programs=read(a.local/'LOCAL-PROGRAMS.json.gz') +V,H,R=can['v'],can['h'],can['R'];C=len(can['centers']);M,T,L,K=73,8,9,4 +assert(V,H,C)==(112,9,8)and can['ports']==oldcan['ports'] +widths=[H-len(can['frames'][f])for f in can['start'][2*V:]];assert len(widths)==R +local_H={int(r):n for r,n in checks['forward']['paid_profile'].items()} +assert all({int(r):n for r,n in z['paid_profile'].items()}==local_H for z in checks.values()) +assert sum(r*n for r,n in local_H.items())==2*V*(H-1)+64+sum(widths) +D=a.out/'split-centres';D.mkdir(parents=True) +required=('CANONICAL-WORD.json.gz','FULL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','RESIDUAL-ADAPTERS.json','CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','INDEPENDENT-LOCAL-REPLAY.json') +for name in required:assert(a.local/name).is_file() +for p in a.local.iterdir(): + if p.is_file():shutil.copyfile(p,D/p.name) +shutil.copyfile(a.local/'INDEPENDENT-LOCAL-REPLAY.json',D/'INDEPENDENT-REPLAY.json') +for rel in('work/complex-nine-native/DATA-PHASES.json',*[f'work/pr361/code/engines/{n}'for n in('moment.py','base_two_moment.py','outer.py')]): + dst=a.out/rel;dst.parent.mkdir(parents=True,exist_ok=True);shutil.copyfile(a.data_base/rel,dst) +DATA=2*K*T*V;W=DATA+L*R;P=W+R+C+2 +t=copy.deepcopy(old);t.update(version='round20-new-supplier-dedicated-bank-parent-v1',live=W,physical=P,local_programs=programs) +t['private_namespace']={'centers':[W,W+C],'reserved_tableau':[W+C,W+C+R],'coefficient':[P-2,P]} +for c in t['calls']: + s,rep=c['stage'],c['replica'];owners=copy.deepcopy(c['owners'][:2*V]) + for helper,w in enumerate(widths): + family=DATA+s*R+helper + route=[2,rep]if w==9 else[2,rep*w,w,list(range(T*w,T*w+9-w))] + owners.append([family,route]) + assert len(owners)==len({f for f,_ in owners})==2*V+R + c['owners']=owners;c['local_program_sha256']=checks[c['orientation']]['sha256'] +bank_children=[];pad=Counter() +for s in range(L): + for helper,w in enumerate(widths): + f=DATA+s*R+helper;axes=list(range(T*w,M));rank=len(axes) + assert 02*max(paid)**2 +assert t['recipe']==old['recipe'] and t['idle_children']==old['idle_children'] +assert t['execution_schedule'][:30]==old['execution_schedule'][:30] +assert all(c['owners'][:2*V]==oc['owners'][:2*V]for c,oc in zip(t['calls'],old['calls'])) +th=dump(D/'GLOBAL-TEMPLATE.json.gz',t) +report=dict(status='BOUND_NEW_LOCAL_SUPPLIER_TO_UNCHANGED_DATA_CONTROLLER',R=R,v=V,m=M, + live=W,physical=P,rank_mass=mass,deficit=2560,global_profile=dict(sorted(paid.items())), + bank_remainder_profile=dict(sorted(pad.items())),bank_assignments=L*T*R, + global_template_sha256=th,local_program_checks=checks, + canonical_word_sha256=sha(D/'CANONICAL-WORD.json.gz'),exact_phase_receipt_sha256=sha(D/'CLIFFORD-REVIEW.json'), + scope='The new local programs and phase/normalization artifacts are hash-bound to the unchanged data controller. Every dedicated bank and complement frame is explicit. The final whole-owner placement and independent scalar/finite recount are supplied separately; this file does not assert an old finite invoice.') +dump(D/'INTEGRATION.json',report) +print(json.dumps({k:report[k]for k in('status','R','live','physical','global_profile','bank_remainder_profile')},indent=2),flush=True) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json new file mode 100644 index 0000000000..a16bf40bcc --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json @@ -0,0 +1,105 @@ +{ + "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE", + "template_sha256": "ed47b5454779f7ad6b32ae492a13f8b5172b11c94c3877cbc5cc5d7a4c357738", + "parent_template_sha256": "9bebafae2c7e21a8a134cc9f2d4709c075b1641abafc33825d116b2508253ceb", + "owner_audit_sha256": "e5f11e7b920f9985f085546c641dbac5b8d98231d562e1e030ab2566ccea4bd6", + "controller_audit_sha256": "01ea0015d4e08170ac65f1cdd051be64e07f622eba62eadbf39524317388cba7", + "independent_local_replay_sha256": "4149f3d2ec3041965c5d72869748090d9aeed422f36d753550c543bb7808b30b", + "canonical_word_sha256": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667", + "local_programs_sha256": "755a5c4ebe958fd9f7b5d4a6e7a506d2c802e31c4d9da46b63db1994c4d8ffa6", + "local_checks_sha256": "c6807681d40cb46c21a50edc1058044ddc758f2dd3e6b0bab16d7cb28d41732f", + "global_prefix_bits": 225, + "charged_prefix_bits": 512, + "complete_invocation_sweeps": 72, + "bridge_sweeps": 72, + "row_prefix_extra": 1024, + "local": { + "backward": { + "events": 22937, + "macros": 17872, + "real_component_primitives": 177740, + "prefix_l1": "1014379823310", + "prefix_bits": 40, + "coefficient_work_primitive_count": 88098, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 152, + "post_wrappers": 152, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + }, + "forward": { + "events": 22937, + "macros": 17872, + "real_component_primitives": 177692, + "prefix_l1": "86491024246", + "prefix_bits": 37, + "coefficient_work_primitive_count": 88066, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 152, + "post_wrappers": 152, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + } + }, + "helpers": 504, + "centres": 8, + "live": 7168, + "physical": 7682, + "physical_stock_identity": { + "data_and_owner_families": 7168, + "local_helpers": 504, + "private_centres": 8, + "coefficient_work": 2 + }, + "entering_helpers": 152, + "entrance_rank": 152, + "width_inventory": { + "8": 152, + "9": 352 + }, + "local_adapters": 357568, + "local_primitive_bound": 9273288832588, + "wrapper_elementary_factors_charged": 3151872, + "factors_per_wrapper": 144, + "compiler": 25934336, + "unhosted_pervertex": 1361655146111768, + "hosted_rebased_pervertex": 1361655145812392, + "conservative_pervertex_used": 2877946989724568, + "retained_prior_overcharge": { + "sha256": "bb43ef04791037a37d2596c395e81191991fde6581326118995cf4318ee472a3", + "previous_pervertex_allowance": 1516291843612800, + "added_complete_new_pervertex": 1361655146111768, + "policy": "Retain old allowance and add the entire fresh recount." + }, + "finite": { + "physical_stock_bits": 2641, + "router_bits": 7985, + "literal_bits": 35282, + "physical_row_coefficient": 16467, + "retained_row_coefficient": 20161, + "required_C0_bits": 200012, + "halving_integer_inequality": [ + 5329, + 4608 + ], + "G_exponent": 30000, + "E_exponent": 100000, + "C0_exponent": 210000 + }, + "strict_checks": { + "local_primitive_bound": true, + "logical": true, + "router": true, + "literal": true, + "mass": true, + "precision": true, + "tape": true, + "row": true, + "halving": true + }, + "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/local/CANONICAL-WORD.json.gz b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/local/CANONICAL-WORD.json.gz new file mode 100644 index 0000000000..3b0a475178 Binary files /dev/null and b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/local/CANONICAL-WORD.json.gz differ diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/PR523-ANCESTRY.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/PR523-ANCESTRY.json new file mode 100644 index 0000000000..4af8dd0d34 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/PR523-ANCESTRY.json @@ -0,0 +1,118 @@ +{ + "prepared_at_utc": "2026-10-12T00:00:25Z", + "repository": "https://github.com/CrocSwap/integer-mult-bounds", + "new_contribution": "Exact 112-port direct-sum restriction, new complete physical whole-owner allocation, independent raw geometric/chronological audit and exact global assembly.", + "baseline": { + "pr": 514, + "author": "contributor (handle omitted)", + "head_repository": "contributor (handle omitted)/integer-mult-bounds", + "head": "246bfacd4cb4072836ae3147099f548bb728229f", + "source_path": "research/partial-kernel92-async", + "local_path": "vendor/pr514", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/514", + "kappa": "1391523459591829/1000000000000000000", + "manifest_sha256": "4e6ffc149df6515f330d984e99b86e7d1deef01ed2bbac24bba3f19708f36c02" + }, + "pinned_bit_supplier": { + "pr": 493, + "author": "eumemic", + "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/493", + "scope": "Published profile repriced; unchanged operator cited, not freshly rebuilt." + }, + "comparison_only": [ + { + "pr": 518, + "author": "contributor (handle omitted)", + "head": "e0a071dce251eeca96d446f73147048cfebbd5c7", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/518", + "kappa": "1393662920776407/1000000000000000000", + "created_at": "2026-10-11T23:50:50Z", + "role": "Newer comparable numerical report observed during packaging; no added pair choices, 99-pivot word, or owner transport copied." + }, + { + "pr": 519, + "head": "ffd3c48a80ba8b579dc300e785e387fe8acddfef", + "role": "Automatic-width binary counting formalization; public context only." + }, + { + "pr": 517, + "head": "65518fcff5a7bd490365273ae5469a82aac14853", + "kappa": "0.001389125582984265", + "role": "Smaller asynchronous result and fixed-word packing ceiling; no code adopted." + }, + { + "pr": 516, + "head": "1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814", + "role": "Lemma A Lean realization, updated during work; formal context only, not recompiled or used as a newly discharged interface.", + "first_observed_head": "871b1c51e53918c5e6c945dfe8ef45546c17da56" + }, + { + "pr": 510, + "head": "64edee18af02aab0c1696b677a0287dd0146381b", + "role": "Larger nonbinding bit rate; not adopted." + }, + { + "pr": 520, + "head": "6077fa76950facbce11ec2f04dfbc93493114a44", + "author": "higherbeing", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/520", + "role": "Open asynchronous allocator and delivery map. Viewed only during the final comparison refresh; no code or claimed gain adopted. No larger global kappa stated." + } + ], + "retained_ancestry": [ + { + "pr": 496, + "head": "00cf70efd6a8637531deafef698157ca83e249ee", + "role": "whole-owner parent, invoice and assembly ancestry" + }, + { + "pr": 484, + "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f", + "role": "PR496 pinned gauge80-kernel42 parent, not newer moving head" + }, + { + "pr": 493, + "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7", + "role": "unchanged cited R489 bit supplier" + }, + { + "pr": 502, + "head": "4d30b8322184598e65e90a92389e17e1baedd9eb", + "role": "retiming transfer constructor and PR495 schedule fixture" + }, + { + "pr": 501, + "head": "1dc056496fdbbc74073ed26d948a2dc235dbf356", + "role": "parallel retiming integration; credited, no duplicated gain" + }, + { + "pr": 473, + "head": "628b454d3df00367d2d4f78de7d4eb9cbcbd47ca", + "role": "single-helper gauge withdrawal inspiration" + }, + { + "pr": 507, + "head": "8d4444cf8a16d500cbb94add6e4fa8bcfb9c7d5e", + "role": "partial-own factory, 84-pivot reference and retiming map" + }, + { + "pr": 505, + "head": "4ee769c8e28837482272b5f4742497da8e2fc9d4", + "role": "Complete-invocation asynchronous scheduling", + "author": "contributor (handle omitted)" + }, + { + "pr": 506, + "head": "a4948baee6c7ea35323db74ff636620c6af2925a", + "role": "public asynchronous retiming comparison and portability feedback" + } + ], + "original_additional_credits_file": "vendor/pr514/NOTICE.md", + "excluded_interfaces": { + "494": "Disputed residual splitting is not used.", + "499": "Larger claimed number using the disputed split-residual interface is not a proof ingredient." + }, + "last_public_comparison_utc": "2026-10-12T00:09:14Z", + "public_snapshot": "evidence/PUBLIC-SNAPSHOT.json" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/complex-nine-native/DATA-PHASES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/complex-nine-native/DATA-PHASES.json new file mode 100644 index 0000000000..d9a4f84211 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/complex-nine-native/DATA-PHASES.json @@ -0,0 +1 @@ +{"cover_correction":{"complete_small_cover_checks":[{"n":1,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":1},{"n":2,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":2},{"n":3,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":6},{"n":4,"nonzero_full_kernel_corrections":24,"orthogonal_matrices":48},{"n":5,"nonzero_full_kernel_corrections":600,"orthogonal_matrices":720}],"formula":"delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.","mandatory":true,"reason":"P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector."},"global_phase_argument":"Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as 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complete recipe is unchanged except its port index; the retained parent polynomial checks establish every selected equality.","scope":"All compressed data boundary operators, idle children, terminal X_q and all-live cover correction. Internal arbitrary-subspace canonical labels are checked separately.","source_parent_sha256":"f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a","status":"PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES","terminal_omission_controls_rejected":112} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/base_two_moment.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/base_two_moment.py new file mode 100644 index 0000000000..14a90fa0e7 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/base_two_moment.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Maintainer arithmetic cross-check of the pinned PR39 certificate. + +Uses no producer/checker imports. Counts are inputs, not proved by this script. +80-term rational logarithms and 12-term exponentials independently enclose +the two moments. The accompanying written review addresses their realization. +""" +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +GRID = 10**30 + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def log_unit(x): + require(1 <= x <= 2, "logarithm range") + z = (x-1)/(x+1) + lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0)) + return lo, lo+2*z**161/(161*(1-z*z)) + + +def log_bounds(x): + k = 0 + while x > 2: + x /= 2 + k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + # Outward rational rounding keeps later certificates compact. + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + + +def exp_bounds(x): + require(0 <= x < 1, "exponential range") + term = total = Q(1) + for j in range(1, 13): + term *= x/j + total += term + tail = term*x/13/(1-x/14) + return total, total+tail + + +def moment(m, W, entries, saving): + lo = hi = Q(0) + for t, count in entries: + t, count = int(t), int(count) + require(0 < t < m and count > 0, "improper child") + l, u = log_bounds(Q(m, t)) + lower = exp_bounds(saving*l)[0] + upper = exp_bounds(saving*u)[1] + lo += Q(t*count, m*W)*lower + hi += Q(t*count, m*W)*upper + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/moment.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/moment.py new file mode 100644 index 0000000000..7d697cb452 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/inputs/data-base/work/pr361/code/engines/moment.py @@ -0,0 +1,113 @@ +"""Independent prospective ordinary five-stage cost, never supplier admission. + +Consumes a raw one-invocation ledger made from the actual source/internal/target +paths. No packed profile is used as an input. Missing physical/finite/compiler +obligations must remain explicit in the accompanying report. +""" +from collections import Counter +from decimal import Decimal, localcontext, ROUND_FLOOR +from fractions import Fraction as F +from functools import lru_cache +from math import factorial +import hashlib, json, sys +from pathlib import Path + +DYAD = 1 << 224 + +def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) +def ceil(x): return -floor(-x) + +@lru_cache(None) +def logarithm(x): + """Mercator bounds after binary reduction; ln(2) via two Mercator sums. + + For 1 <= y < 2, log(y) is an alternating series in z=y-1. + We instead reduce to 1 <= y < 3/2, and bound log(3/2) and + log(2) by the same alternating series at z=1/2 and z=1/3, + using log(2)=log(3/2)+log(4/3). All sums are exact rationals. + """ + assert x >= 1 + k = 0 + while x >= 2: x /= 2; k += 1 + j = int(x >= F(3, 2)) + if j: x /= F(3, 2) + def mercator(y): + z=y-1 + assert 0 <= z <= F(1,2) + # An even partial sum is below log; the next term bounds its tail. + t=z; s=F(0) + for n in range(1, 225): + s += (t if n & 1 else -t)/n + t *= z + return s, s+t/225 + a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3)) + return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f) + +def exponential(l,u): + assert 0 <= l <= u < F(1,10) + def poly(x): + s=t=F(1) + for j in range(1,25): t=t*x/j; s+=t + return s,t + lo,_=poly(l);hi,last=poly(u) + return floor(lo),ceil(hi+last*u/25/(1-u/26)) + +def moment(H,m,W,a,bad=False): + lo=hi=F(0) + for r,n in H.items(): + assert 0 < r < m and n > 0 + l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u) + p=F(r*n,m*W);lo+=p*e;hi+=p*f + if bad: + # Existing envelope shape, only conditionally portable to the new cover. + l,u=logarithm(F(m));e,f=exponential(a*l,a*u) + p=F(32*m*sum(H.values()),10**16*W) + lo+=p*e;hi+=p*f + return floor(lo),ceil(hi) + +def decimal(x): + with localcontext() as c: + c.prec=70 + return str(Decimal(x.numerator)/Decimal(x.denominator)) + +def certify(H,m,W,bad=False): + with localcontext() as c: + c.prec=70 + terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()] + fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0) + lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003') + for _ in range(210): + a=(lo+hi)/2 + if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a + else:hi=a + q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR)) + lo=F(q,10**24);hi=lo+F(1,10**24) + lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad) + assert lv[1]<10 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2 + assert 1-eps*(1+c)==eta-eps*eta/4 + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford/clifford_exact.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1< 1 and a > 1) + receipts.append(dict(endpoint=str(endpoint), accept=accept, + mercator=[str(lo - 1), str(hi - 1)], + base_two=[str(a - 1), str(b - 1)])) + return receipts + + +cert = M.certify(P, m, W, True) +b, bp = Q(cert['lower']), Q(cert['upper']) +assert bp - b == Q(1, 10**24) +complex_receipts = two_moments(P, m, W, b) + +# These checks bind and reprice published bit data. They do not stand in for +# the physical-operator and mutable-source realization dependency. +assert sha(B) == BIT_EXPECTED_SHA256 +bit = json.loads(B.read_text())['nine'] +bitP = {int(rank): count for rank, count in bit['profile'].items()} +bit_inv = bit['bit'] +bm, bW = bit['m'], bit_inv['live'] +assert (bm, bW, bit['stages'], bit['replicas']) == (64, 30720, 9, 32) +assert sum(rank * count for rank, count in bitP.items()) == bit_inv['rank_mass'] +assert bm * bW - bit_inv['rank_mass'] == 9984 +assert max(bitP) == bit_inv['maxchild'] == 8 +assert bm * bm > 2 * 64 * max(bitP) +assert bit_inv['physical'] == bW + 9 == 30729 +assert bit_inv['hosted_residuals'] == 480 * 9 * 32 +assert bit_inv['bank_assignments'] == 0 +assert bit['nine_stage_payload_bits'] < 104 +assert bit_inv['prefix_bits'] < bit_inv['charged_prefix_bits'] == 256 +assert bit_inv['two_level_coefficient_bits'] < bit_inv['charged_two_level_coefficient_bits'] == 512 +assert bit_inv['row_coefficient'] < 20161 +c = Q(bit['bit_lower']) +assert c == Q(bit['bit_lower_decimal']) +bit_receipts = two_moments(bitP, bm, bW, c) + +eta = beta = grid = Q(1, 10**18) +s = min(c, (1 - beta) * b) - Q(1, 10**24) +assert 0 < s < c and s < (1 - beta) * b +coeff = bit_inv['charged_two_level_coefficient_bits'] +row = max(20161, bit_inv['row_coefficient'], inv['finite']['physical_row_coefficient']) +chain, cuts = [Q(384599, 10**10)], [] + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +for _ in range(6): + old = chain[-1] + a = (1 - s) * s + s * old + gap = min(s - a, 1 - a - s, 1 - a - s * (1 - old), 1 - s) + assert old < a < s < 1 - a and gap > 0 + cut = max(ceil(36 / gap**2), ceil(2 * (4 + coeff) / gap)) + assert cut * gap**2 >= 36 and cut * gap >= 2 * (4 + coeff) + cuts.append(dict(gap=str(gap), cutoff_log2=str(cut))) + chain.append(a) +q = chain[-1] * (1 - 2 * eta) +margin = (1 - eta) * q / (1 + q) +ticks = margin / grid +kap = grid * ((ticks.numerator - 1) // ticks.denominator) +bridge = {'semantic': {'C0': {'base': 2, 'exponent': 210000}, 'strict_literal_gap': 1}, + 'rows': {'degree_gap': Q(10**6) - Q(51 * row, 25)}} +assembly = Outer.assembly(chain[-1], b, bridge, kap, eta=eta, beta=beta) +assert len(assembly['strict_constraints']) == 47 +assert all(value > 0 for value in assembly['strict_constraints'].values()) +controls = [] +for name, k, e, be in [('next_grid', kap + grid, eta, beta), + ('zero_eta', kap, Q(0), beta), + ('zero_beta', kap, eta, Q(0)), + ('unit_beta', kap, eta, Q(1))]: + try: + Outer.assembly(chain[-1], b, bridge, k, eta=e, beta=be) + except AssertionError: + controls.append(name) + else: + raise AssertionError(name) + +baselines = {'PR531': Q('0.001517760977820331'), + 'rejected_POST208_checkpoint': Q('0.001543640781718742'), + 'PR533': Q('0.001524207950793244')} +res = dict( + status='PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY', + complex_lower=str(b), complex_decimal=decimal(b, 24), + next_b_rejected=str(bp), exact_moment_receipts=complex_receipts, + bit_lower=str(c), bit_decimal=decimal(c, 24), + bit_exact_moment_receipts=bit_receipts, + bit_result_sha256=sha(B), + bit_dependency={'pull_request': 510, 'commit': BIT_COMMIT, + 'path': 'research/e8-r480-nine-stage', + 'expected_sha256': BIT_EXPECTED_SHA256}, + bit_prefix_bits=bit_inv['charged_prefix_bits'], + bit_charged_two_level_coefficient_bits=coeff, + external_row_allowance=row, + kappa=str(kap), kappa_decimal=decimal(kap, 18), + binding_component='bit' if c < (1 - beta) * b else 'complex', + improvements={name: {'baseline': str(value), + 'relative_gain': str(kap / value - 1), + 'percent_display': f'{float(100 * (kap / value - 1)):.8f}'} + for name, value in baselines.items()}, + strict_outer_constraints={k: str(v) for k, v in assembly['strict_constraints'].items()}, + outer_controls=controls, bootstrap=cuts, + complex_template_sha256=host['template_sha256'], + owner_audit_sha256=sha(O / 'OWNERS-AND-PROFILE.json'), + invoice_sha256=sha(O / 'PREFIX-AND-INVOICE.json'), + bit_scope='Pinned PR510 published profile and operator are cited dependencies. ' + 'Both exact moments are freshly repriced here; the unchanged physical ' + 'bit operator is not cold-reconstructed. See PR510-MUTABLE-SOURCE-CARRYOVER.md.', + scope='Conditional finite witness under the retained all-size compiler, ' + 'common-label/mutable-basis, whole-call hosting, restored-work, ' + 'precision/tape and analytic-transfer contracts. Fresh complex admission ' + 'and finite invoice are separately hash-bound; no unconditional theorem is claimed.') +(O / 'EXACT-ASSEMBLY.json').write_text(json.dumps(res, indent=2) + '\n') +print(res['status'], 'b', res['complex_decimal'], 'kappa', res['kappa_decimal']) +print(json.dumps(res['improvements'], sort_keys=True)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/PR510-EXPECTED.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/PR510-EXPECTED.json new file mode 100644 index 0000000000..9e5d366963 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/PR510-EXPECTED.json @@ -0,0 +1,102 @@ +{ + "nine": { + "bit_lower": "396861776523137034277/250000000000000000000000", + "bit_lower_decimal": "0.001587447106092548137108", + "profile": { + "1": 345600, + "2": 430080, + "4": 67200, + "6": 49920, + "7": 23040, + "8": 2592 + }, + "bit": { + "live": 30720, + "physical": 30729, + "maxchild": 8, + "rank_mass": 1956096, + "hosted_residuals": 138240, + "bank_assignments": 0, + "prefix_bits": 193, + "charged_prefix_bits": 256, + "coefficient_bits": 193, + "two_level_coefficient_bits": 425, + "charged_two_level_coefficient_bits": 512, + "row_coefficient": 18355, + "halving_depth": 2 + }, + "kappa": { + "pr484": { + "kappa": "662515748707749/500000000000000000", + "kappa_decimal": "0.001325031497415498", + "binding_component": "complex", + "complex_lower": "663394767670133/500000000000000000" + }, + "pr471": { + "kappa": "260706019542937/200000000000000000", + "kappa_decimal": "0.001303530097714685", + "binding_component": "complex", + "complex_lower": "1305231506267591/1000000000000000000" + }, + "pr458": { + "kappa": "323880830669511/250000000000000000", + "kappa_decimal": "0.001295523322678044", + "binding_component": "complex", + "complex_lower": "1297203880559577927527/1000000000000000000000000" + } + }, + "nine_stage_payload_bits": 102, + "stages": 9, + "replicas": 32, + "m": 64 + }, + "parent_r480": { + "pr": 503, + "bit_lower": "393688338238452162729/250000000000000000000000", + "bit_lower_decimal": "0.001574753352953808650916", + "stages": 11 + }, + "parent_r489": { + "pr": 493, + "bit_lower": "391360506745414227149/250000000000000000000000", + "bit_lower_decimal": "0.001565442026981656908596", + "stages": 11 + }, + "findings": { + "lp_helpers_per_4frame": 16, + "lp_total": 480, + "levels": { + "1": { + "frames": 120, + "helper_visits": 240 + }, + "2": { + "frames": 180, + "helper_visits": 480 + }, + "4": { + "frames": 60, + "helper_visits": 360 + }, + "6": { + "frames": 180, + "helper_visits": 480 + }, + "7": { + "frames": 120, + "helper_visits": 240 + } + }, + "cells": { + "2,2,0": 60, + "3,0,0": 120 + }, + "d6": { + "2,1,2": 60, + "3,0,0": 120 + }, + "pivots_max": 0, + "line_classes": 120, + "class_nullity": 0 + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz new file mode 100644 index 0000000000..3e28a9b59f Binary files /dev/null and b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz differ diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/README.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/README.md new file mode 100644 index 0000000000..840555bd17 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/README.md @@ -0,0 +1 @@ +Run python -B run_local.py --out NEW_DIRECTORY --vendor PATH_TO_COMPLEX_GLOBAL_VENDOR531. This rebuilds primitive inputs, static44, PR534 frame lifts, the earlier syndrome substitution, eight collective hyperplane waves and twelve weighted coset rewrites, then checks the full emitted local program. Final canonical SHA-256:371638c4f444515caa0586fa7bac838fc7a7c01c4f6110caccf1d4c4f90453b1. Use the enclosing top-level verifier for the complete global and numerical result. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/SOURCE-MANIFEST.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..0f3ff6125b --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/SOURCE-MANIFEST.json @@ -0,0 +1,29 @@ +{ + "README.md": "1018ca8cbd77cb7b2bd52b77859613724d9ddedb61908e9f103db23c203aa65e", + "run_local.py": "607d144221726b69d8e9da8a1438c83264154bba0fc4a010281962143f40bd35", + "code/apply_syndrome.py": "e2e88b38f6b0a087814c54f65cdf8439fc10e6377ca13e356eb39fdbca6ef99c", + "code/port_frames.py": "7f86660cfbf7a9123347587f467a5775118f5842ccf03bf9837daf8cb0bbd376", + "code/run_portable.py": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955", + "docs/OPENAI-SOURCES.json": "46c3a475a4c58f4137373fdf0705690b7f085536671d7be75cc3863895190062", + "docs/SEARCH-RECORD.md": "7b09479215c407e4258ef6af64c34dc865e3b9a60c845040258413a2a960f5b8", + "docs/TWO-SOURCE-PROOF.md": "4d6423f773ec47d2eea984e02f11f2d636e02ad3e6f3eb3e640a3768fa04fe75", + "inputs/PR534-WORD.json.gz": "a275792cb9f5729fac295cb04c556afbaa4513945c517190219fd0e44ab90095", + "inputs/phase-baseline/CANONICAL-WORD.json.gz": "e070ae2c78b4a1b644b418774af62b40d8d16e6ba89602f0474afb557d507c37", + "inputs/phase-baseline/CLIFFORD-RECIPES.json": "577a1be13f5140d9c3997637784b2f812f46b24c61877699430b02de4f662102", + "inputs/phase-baseline/CLIFFORD-REVIEW.json": "cd48fe6882a39c57021c4614747cc5c2c88ec07e806cebb914cf533997b73d9b", + "static44/audit_scalar.py": "d22159087c1d0df0edf452aae3a1a7a45bf2cde4ce6e177850e415f9620151e1", + "static44/build.py": "31d68795916985e2abb3207b07c1d3e39ed3560f1b46f18ade0a509278c710dc", + "static44/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "static44/META-SOURCES.json": "b30c82ad1d707b68e84af85e90b1bab0e41e49ccacda3069b952c790092be920", + "static44/NOTICE-upstream.md": "1547136e6d269fdcef2b68c10a97a786a79a4732a12738363f679bfb282430cd", + "static44/PROOF.md": "d1dafe41a1698d6df575ec86f796bcba08c54fe14b6d69e78f5f6cff8b55de4a", + "static44/README.md": "c4b3ce02012fe97598e76a77877541a8f3387ba4305cee600ee557a48b3493e8", + "static44/RECIPE.json": "973f1975213398f2b711e8ce4eddece181d4cbea83be5b6b650115b9bc43f2eb", + "static44/replay.py": "5b12ea184b3afde41b1028d1926a0d158f2f05585dae6d9024e31424c290bccf", + "static44/SOURCE-MANIFEST.json": "9c64b98a2c7771e77eccc476910a91c17eefc0ee95fb638b058c598c96bbdaf3", + "static44/gk/gk_common.py": "e68d190fd436b2f3955decb590adb53344d5d4ea0a19d62d86df1e4b55ecd198", + "static44/gk/gk_word.py": "f027a9273bcf4e0971258c160b7d3b3c196366b32a529cff6e6a0e666b03826b", + "static44/inputs/BASE535.json.gz": "edfffb8e8735e0d1f07c81d818022b705ef0889c2bccc193a2f7a661b9f7d390", + "static44/inputs/OLD-RECIPE.json": "7e5c179246261edd9e1019e81e6e979537f02559da773b993a318f771cb7d763", + "static44/inputs/RAW504.json.gz": "1c6144791dbedf6427e3ee7b4c24fb05b5bf407f6346592f50f8dd8d9638108d" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/apply_syndrome.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/apply_syndrome.py new file mode 100644 index 0000000000..6fd085c5ed --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/apply_syndrome.py @@ -0,0 +1,23 @@ +from pathlib import Path +from fractions import Fraction as Q +import json,gzip,sys,copy,hashlib,argparse +ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--gk',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);args=ap.parse_args();sys.path.insert(0,str(args.gk)) +import gk_word as g,gk_common as c +g.V=c.V=112;g.DATA=c.DATA=7168 +p=Path(__file__).resolve().parent;w=json.load(gzip.open(args.input));old=copy.deepcopy(w) +N=728;V=112;protected=set(range(V))|set(map(int,w['start_extra'])) +rows=[{i:Q(1)}for i in range(N)] +e=w['A'][33];assert e[1:3]==[513,523] +for op in w['A'][:33]:g.apply_op(op,rows) +a=Q(-1);err=rows[523].copy() +for j,x in rows[512].items(): + err[j]=err.get(j,Q(0))-a*x + if not err[j]:err.pop(j) +assert err and not protected&set(err) and all(j>=224 for j in err) +e[2]=512;e[3]*=-1 +w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not V<=e[1]<2*V] +before=g.profile(old);after=g.profile(w);assert before==after +out=args.out;out.mkdir(exist_ok=False) +raw=json.dumps(w,sort_keys=True,separators=(',',':')).encode();(out/'FULL-WORD.json.gz').write_bytes(gzip.compress(raw,mtime=0)) +r=dict(status='PASS_EXACT_COLD_DIRT_QUOTIENT_SUBSTITUTION',section='A',index=33,old_operation=old['A'][33],new_operation=e,source_relation_multiplier=str(a),cold_initial_error={str(j):str(x)for j,x in err.items()},protected_columns=len(protected),source_rows_computed_by_finite_triangular_forward_elimination=True,local_profile=dict(after),profile_unchanged=True,requires_regenerated_frame_zero_compensation=True,source_content_sha256=hashlib.sha256(json.dumps(old,sort_keys=True,separators=(',',':')).encode()).hexdigest(),output_content_sha256=hashlib.sha256(raw).hexdigest()) +(out/'SYNDROME-CERTIFICATE.json').write_text(json.dumps(r,indent=2)+'\n');print(json.dumps(r)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/port_frames.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/port_frames.py new file mode 100644 index 0000000000..bd9187bd06 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/port_frames.py @@ -0,0 +1,50 @@ +from pathlib import Path +from collections import defaultdict,Counter,deque +import json,gzip,sys,copy,math,argparse +ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--source',type=Path,required=True);ap.add_argument('--gk',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);args=ap.parse_args();sys.path.insert(0,str(args.gk)) +import gk_word as g, gk_common as c +g.V=c.V=112;g.DATA=c.DATA=7168 +p=Path(__file__).resolve().parent +src=args.input +a=json.load(gzip.open(src));b=json.load(gzip.open(args.source)) +old=copy.deepcopy(a);before=g.profile(a);sp={} +def span(E): + E=g.basis(E) + if E not in sp:sp[E]=g.span(E) + return sp[E] +def meet(A,B):return g.basis(span(A)&span(B)) +def join(A,B):return g.basis(tuple(A)+tuple(B)) +N=728;V=112 +changes=[] +for sec in ('B','A'): + mapping=defaultdict(deque) + for e in b[sec]:mapping[tuple(e[:-1])].append(e[-1]) + desired=[] + for e in a[sec]: + d=mapping[tuple(e[:-1])];desired.append(d.popleft()if d else e[-1]) + nxt=[g.FULL]*N + for r in range(V,2*V):nxt[r]=g.perp(a['ports'][r-V]) + if sec=='A': + for e in reversed(a['B']): + for r in (e[1:3]if e[0]=='add'else e[1:2]):nxt[r]=g.basis(e[-1]) + for r,F in zip(a['centers'],a['center_frames']):nxt[r]=g.basis(F) + for r in range(V,2*V):nxt[r]=g.basis(a.get('target_levels',{}).get(str(r-V),[])) + for i in reversed(range(len(a[sec]))): + e=a[sec][i];rs=e[1:3]if e[0]=='add'else e[1:2] + upper=nxt[rs[0]] + for r in rs[1:]:upper=meet(upper,nxt[r]) + E=join(e[-1],meet(desired[i],upper)) + assert span(E)<=span(upper) + if E!=g.basis(e[-1]):changes.append([sec,i,e[-1],list(E)]);e[-1]=list(E) + for r in rs:nxt[r]=E +prof=g.profile(a);gain=sum((prof[r]-before[r])*r*math.log(r)for r in set(prof)|set(before)) +a['report']['local_profile']={str(k):v for k,v in sorted(prof.items())} +a['cleanup']=[g.inverse(e,g.FULL)for e in reversed(a['A']+a['B'])if not V<=e[1]<2*V] +out=args.out;out.mkdir(exist_ok=False);(out/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(a,sort_keys=True,separators=(',',':')).encode(),mtime=0)) +r=dict(before=dict(before),after=dict(prof),delta={r:prof[r]-before[r]for r in set(prof)|set(before)if prof[r]!=before[r]},changes=changes,entropy_gain=gain) +(out/'PORT.json').write_text(json.dumps(r,indent=2)+'\n');print(json.dumps({k:v for k,v in r.items()if k!='changes'}));print('changes',len(changes)) + +assert len(changes)==477 and dict(prof)=={1:2284,2:456,3:488,4:168,5:56,6:56,8:8} +assert all(old[k]==a[k] for k in ('cut','precondition','centers','center_frames','start_extra','target_levels')) +assert all(x[:-1]==y[:-1] for sec in ('A','B') for x,y in zip(old[sec],a[sec])) +assert all(span(x[-1])<=span(y[-1]) for sec in ('A','B') for x,y in zip(old[sec],a[sec])) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/run_portable.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/run_portable.py new file mode 100644 index 0000000000..2fed13f432 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/code/run_portable.py @@ -0,0 +1,24 @@ +"""Run one retained verifier with UTF-8/LF text outputs on every platform. +This changes output serialization only; no mathematical operation is replaced. +""" +from pathlib import Path +import runpy,sys,gzip +if not __debug__: + raise RuntimeError('Assertions must remain enabled') +original_write_text=Path.write_text +def write_text_lf(self,data,encoding=None,errors=None,newline=None): + return original_write_text(self,data,encoding=encoding or 'utf-8',errors=errors,newline='\n') +Path.write_text=write_text_lf +# Pin generated gzip serialization. Python3.11 may expose zlib's platform OS +# byte, Python3.13 normalizes it, and Python3.15 changes the default level. +# Immutable input files are never rewritten by this wrapper. +original_gzip_compress=gzip.compress +def compress_portable(data,compresslevel=9,*,mtime=0): + raw=original_gzip_compress(data,compresslevel=compresslevel,mtime=mtime) + assert raw[:3]==b'\x1f\x8b\x08' and len(raw)>=18 + return raw[:9]+b'\xff'+raw[10:] +gzip.compress=compress_portable +script=Path(sys.argv[1]).resolve() +sys.argv=sys.argv[1:] +sys.path.insert(0,str(script.parent)) +runpy.run_path(str(script),run_name='__main__') diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/OPENAI-SOURCES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/OPENAI-SOURCES.json new file mode 100644 index 0000000000..9d480f5d1c --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/OPENAI-SOURCES.json @@ -0,0 +1,22 @@ +[ + { + "technique": "finite_inverse", + "path": "lean/OAI/Algebra/OddKaplansky/FiniteInverse.lean", + "sha256": "451f40d08deec33d91ceb4e3f03b1366933c48220bce5d230ca2fe395ea78118", + "declarations": [ + "series_mul", + "inverse_formula" + ], + "scope": "Source inspected; no Lean compilation in this campaign" + }, + { + "technique": "dual_syndrome", + "path": "lean/OAI/Algebra/AuslanderReiten/Duality/LinearHomologyDuality.lean", + "sha256": "842a26ea92d7687bb607b331dd4f8e9fb4a47f024b9def1c2c48a7767d3e6459", + "declarations": [ + "dualCyclesToDualHomology_kernel", + "dualHomologyEquiv" + ], + "scope": "Source inspected; no Lean compilation in this campaign" + } +] diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/SEARCH-RECORD.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/SEARCH-RECORD.md new file mode 100644 index 0000000000..5fd16a03a4 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/SEARCH-RECORD.md @@ -0,0 +1,9 @@ +# Bounded discovery record + +1. Bit finite-inverse prefix expansion: 480 first-helper packets screened. 300 replacements passed the fixed frame-chain gate; all were neutral direct loads. The remaining 180 were blocked by this specific early-source frame schedule. This is not a general impossibility result. +2. Complex protected-syndrome screen: 324 protected columns, modulus 1000000007, 130 legal proportional-source nominations; none had strict immediate paid-profile gain. These modular results are discovery filters, not rational certificates. +3. Zero-incremental-frame-cost basis factoring and greedy frame-fee weighted factoring found no positive nomination in the bounded scan. No optimality claim follows. +4. One modular nomination was reconstructed over the rationals and passed the full native pipeline: A[33] source523 becomes minus source512. This changes the cold-dirt response and removes four compensation operations, while preserving all paid ranks. +5. PR534 frame assignment transfers constructively to static44 through exact successor intersections and frame joins. The resulting positive paid-profile change was fully replayed. It is public-mechanism composition, not a newly invented numerical technique. + +Native discovery sources and complete negative results remain in the research lane. Shipping replay uses only frozen constructors; it does not perform search. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/TWO-SOURCE-PROOF.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/TWO-SOURCE-PROOF.md new file mode 100644 index 0000000000..7ab57778a1 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/docs/TWO-SOURCE-PROOF.md @@ -0,0 +1,64 @@ +# Finite inverse and cold-dirt syndrome substitution + +The two OpenAI sources are listed with exact source hashes in OPENAI-SOURCES.json. They were inspected as mathematical sources. No Lean execution or new Lean certificate is claimed. + +## 1. Finite version-DAG expansion + +Let v be the vector of all assigned register versions in a finite linear straight-line program, ordered chronologically. Every version has an equation using earlier versions and initial registers x. Thus v = N v + B x with N strictly triangular. If there are n versions then N^n = 0, and + +v = (I + N + ... + N^(n-1)) B x. + +Multiplying by I-N proves this identity; the two products telescope to I-N^n = I. Conversely these equations have a unique solution, by forward substitution. This remains true when mutable physical registers are reused: distinct versions, rather than register names, are the vertices. Every scalar coefficient remains exact. + +This is the constructive specialization of OAI.OddKaplansky.FiniteMatrixInverse.series_mul and inverse_formula in Algebra/OddKaplansky/FiniteInverse.lean. We use the identity to derive actual register functionals at a chosen cut. It does not itself permit moving a gate or changing its frame. + +## 2. Exact syndrome factorization + +Let S: X -> Z be a linear map over a field and f: X -> K a linear functional. Then the following are equivalent: + +- f vanishes on ker S; +- there is a functional a on Z with f = a S. + +For sufficiency of the first condition, define a on im S by a(Sx)=f(x). This is well defined because two preimages differ by ker S. Extend a from a basis of im S to a basis of Z. Necessity follows by evaluation on ker S. Finite Gaussian elimination constructs the extension and checks the complete identity. + +The relevant OpenAI source is Algebra/AuslanderReiten/Duality/LinearHomologyDuality.lean, particularly dualCyclesToDualHomology_kernel and its use of LinearMap.range_dualMap_eq_dualAnnihilator_ker. The present finite matrix statement is proved above independently; the larger homology theorem is not assumed as a circuit compiler. + +## 3. Sufficient circuit replacement theorem + +Partition initial coordinates into protected coordinates P and cold helper dirt D. Cold helpers have entrance frame zero. At a program cut let f be the current source value and g_j other available register values. Suppose exact version expansion proves + +f - sum_j a_j g_j = q(D), + +where q is an explicitly known linear functional of cold initial dirt only. Replace a background shear t += c f by the sequence t += c a_j g_j. The destination is excluded from all g_j. Every replacement coefficient is admitted by the native dyadic primitive contract, and its actual register-frame chains must be legal. + +For every initial vector with D=0 the programs agree at this cut and therefore at every later point. Their full output difference is a linear function of D only. In particular the data map, action on initial targets, and responses to every warm helper are identical. This argument applies to any number of subsequent target deliveries. + +Assume, as in the emitted program, that the background subsystem never reads target registers, that all changed background operations are invertible elementary gates, and that cleanup is regenerated as their literal reverse inverse. Background registers then return to their arbitrary initial values. Write the target action of the main program as A y + B x + C D after separating the protected coordinates. Its fixed initial target preconditioner is L=A^-1. Insert the explicit frame-zero target compensation -L C D after that preconditioner. Then the final target map is y+B x, with all cold dirt canceled. This compensation is sufficient only after checking its coefficients and that every referenced helper is indeed cold. The independent native auditor computes C from the entire changed main program; it does not trust a supplied compensation table. + +The theorem has no free storage or routing assumption. The replacement gate sequence, changed cleanup, compensations, frame edges, exact Clifford phases, wrappers, full owner program and finite toll are separately charged by the enclosing verifier. + +## Concrete application + +On the pinned static44 plus PR534 frame-lift word, immediately before A[33], exact rational version expansion proves + +value(z523) + value(z512) = initial(z512). + +Register 512 is cold. The 324 protected columns are 112 original data columns and 212 warm helper columns. Therefore the operation z513 -= z523 at frame [480] can be replaced by z513 += z512 at the same frame. The difference is exactly one known cold initial coordinate, not an approximate or clean-only equality. + +The frozen constructor checks this exact identity and all frame chains. Regenerated compensation has 9,756 additions instead of 9,760. Both oriented emitted programs have 22,107 events instead of 22,111. All 728 formal columns pass in both orientations, including arbitrary dirty helpers; 11 independent local mutation controls are rejected. All 2,929 directed phase edges and 23 residual adapter recipes are checked. The paid child profile is unchanged by this substitution, so it contributes a scalar-program simplification, not a new paid-rank saving. + +## Positive paid-rank composition and attribution + +The numerical paid-rank improvement in this lane comes from composing the previously proved static44 response presentation with PR534's supplied frame assignment. Matching unchanged scalar operations, the constructor transports desired frames and clips each lift to the exact common successor frame while processing events in reverse dependency order. Each chosen frame contains the old frame and lies below every next use. The existing coalescing realization therefore applies gate by gate; all register chains stay nested. + +There are 477 changed frames. The local profile changes from + +{1:2204, 2:728, 3:184, 4:280, 5:56, 6:56, 8:8} + +to + +{1:2284, 2:456, 3:488, 4:168, 5:56, 6:56, 8:8}. + +The exact delta is 80 e1 - 272 e2 + 304 e3 - 112 e4. Rank mass and ordered helper widths remain unchanged. Its entropy gain is approximately 3.802467258994966 per invocation; the enclosing package uses exact moment bounds, not this approximation, for its final claim. PR534 supplies the new frame assignment, PR535 supplies the post-center rank-four construction, and the retained PR531/PR484 code supplies transport, response compilation and native audits. Earlier attribution and licenses are preserved in static44/NOTICE-upstream.md and the shared vendor tree. + +The OpenAI-inspired syndrome rewrite is composed after these frame lifts. We do not attribute PR534's numerical gain to the two OpenAI lemmas. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/PR534-WORD.json.gz b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/PR534-WORD.json.gz new file mode 100644 index 0000000000..965888339a Binary files /dev/null and b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/PR534-WORD.json.gz differ diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz new file mode 100644 index 0000000000..cbb49a6277 Binary files /dev/null and b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz differ diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CLIFFORD-RECIPES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CLIFFORD-RECIPES.json new file mode 100644 index 0000000000..e791d26d89 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CLIFFORD-RECIPES.json @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CLIFFORD-REVIEW.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CLIFFORD-REVIEW.json new file mode 100644 index 0000000000..9438efb75e --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CLIFFORD-REVIEW.json @@ -0,0 +1,533 @@ +{ + "status": "PASS_REUSED_AND_FRESH_EXACT_LOCAL_PHASE_RECIPES", + "canonical_word_sha256": "e070ae2c78b4a1b644b418774af62b40d8d16e6ba89602f0474afb557d507c37", + "frames": 997, + "directed_edges": 2927, + "reused_edges": 2801, + "fresh_edges": 126, + "ranks": { + "1": 1749, + "2": 670, + "8": 16, + "3": 142, + "4": 280, + "5": 14, + "6": 56 + }, + "endpoint_adapters": 224, + "reused_endpoint_adapters": 224, + 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Identical baseline pairs and all endpoint adapters reuse the pinned phase certificates; no full cold replay was performed." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/run_local.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/run_local.py new file mode 100644 index 0000000000..b18de2591a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/run_local.py @@ -0,0 +1,26 @@ +"""Rebuild the chosen complex word from primitive inputs and independently audit it.""" +from pathlib import Path +import argparse,subprocess,sys,json,gzip,hashlib +if not __debug__:raise SystemExit('Assertions must remain enabled.') +p=Path(__file__).resolve().parent +ap=argparse.ArgumentParser();ap.add_argument('--out',type=Path,required=True);ap.add_argument('--vendor',type=Path,required=True);a=ap.parse_args() +out=a.out.resolve();assert not out.exists();out.mkdir(parents=True) +v=a.vendor.resolve();launcher=p/'code/run_portable.py' +def run(script,*args): + subprocess.run([sys.executable,'-B',str(launcher),str(script),*map(str,args)],check=True) +s=p/'static44';g=s/'gk' +run(s/'build.py','--raw',s/'inputs/RAW504.json.gz','--base',s/'inputs/BASE535.json.gz','--old-recipe',s/'inputs/OLD-RECIPE.json','--recipe',s/'RECIPE.json','--gk-dir',g,'--out',out/'static44') +run(s/'audit_scalar.py',out/'static44/FULL-WORD.json.gz',out/'static44/SELECTION.json',out/'static44/SCALAR-AUDIT.json') +run(p/'code/port_frames.py','--input',out/'static44/FULL-WORD.json.gz','--source',p/'inputs/PR534-WORD.json.gz','--gk',g,'--out',out/'lifted') +run(p/'code/apply_syndrome.py','--input',out/'lifted/FULL-WORD.json.gz','--gk',g,'--out',out/'syndrome') +run(p.parent/'code/build_wave.py','--input',out/'syndrome/FULL-WORD.json.gz','--recipe',p.parent/'inputs/WAVES.json','--gk',g,'--out',out/'wave') +run(p.parent/'response/build_weighted_coset.py','--input',out/'wave/FULL-WORD.json.gz','--selection',p.parent/'response/WEIGHTED-COSET-SELECTION.json','--gk-dir',g,'--out',out/'weighted') +local=out/'local';base=p/'inputs/phase-baseline' +run(v/'code/audit_and_transport.py','--raw',out/'weighted/FULL-WORD.json.gz','--routing',base/'CANONICAL-WORD.json.gz','--out',local) +run(v/'code/phases_delta.py','--local',local,'--baseline',base,'--compiler',v/'vendor/clifford') +run(v/'code/adapters_local.py',local/'CANONICAL-WORD.json.gz',local/'RESIDUAL-ADAPTERS.json',local/'WRAPPER-CHECKS.json') +run(v/'code/emit_local.py',local) +run(v/'code/audit_local.py',local) +actual=hashlib.sha256(gzip.decompress((local/'CANONICAL-WORD.json.gz').read_bytes())).hexdigest() +assert actual=='371638c4f444515caa0586fa7bac838fc7a7c01c4f6110caccf1d4c4f90453b1',actual +print('PASS complete local reconstruction, all columns and controls, final canonical hash',actual) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/LICENSE b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/META-SOURCES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/META-SOURCES.json new file mode 100644 index 0000000000..8cbd32f8bd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/META-SOURCES.json @@ -0,0 +1,24 @@ +{ + "scope": "Actual source statements inspected as structural analogues; no Lean compilation or source theorem directly certifies the new circuit.", + "sources": [ + { + "relative_source": "Mathlib/LinearAlgebra/Matrix/Transvection.lean", + "sha256": "c8c60dfbda7a09877a884aa2c7ce385f24f5370bb2a456cc20aae872c7dd41ef", + "statements": [ + "mul_transvection_apply_same", + "mul_transvection_apply_of_ne", + "TransvectionStruct.reverse_inv_prod_mul_prod", + "TransvectionStruct.prod_mul_reverse_inv_prod" + ] + }, + { + "relative_source": "OAI/GroupTheory/Congruence/Elementary.lean", + "sha256": "dde2c70e97566d678e96c126476314c994ce4b68858b9aa6c484b9820e950bd8", + "statements": [ + "OAI.CoboundaryExpanders.Elementary.E_mul_apply", + "OAI.CoboundaryExpanders.Elementary.upper_E_mul", + "OAI.CoboundaryExpanders.Elementary.clear_step" + ] + } + ] +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/NOTICE-upstream.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/NOTICE-upstream.md new file mode 100644 index 0000000000..f42e0eed85 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/NOTICE-upstream.md @@ -0,0 +1,70 @@ +# Attribution and dependency notice + +Package: **`integer_mult_round21_rank4_delta`**. + +Copyright 2026 icekylinx. Local review and packaging used OpenAI Codex. + +## New work + +Prepared by **icekylinx with GPT-6 Astra assistance**. The new contribution is +the post-center timing and ordered composition of dirty gauges with rank-four +response kernels, including the 14 disjoint M-helper groups, explicit scalar +word, frame and cleanup treatment, independent local argument, physical global +integration, paid accounting, and combined conditional κ assembly. + +The same helper can first serve its own gauge and then donate to a larger +kernel because compensation occurs before the new pivot dirt is injected. +This ordering, its actual frame nesting, and its global use are the substantive +delta. Earlier gauge/kernel primitives and the SAME504 scalar construction +retain their original authorship. + +## Baseline + +[PR531](https://github.com/CrocSwap/integer-mult-bounds/pull/531), by icekylinx +with the disclosed GPT-6 Astra assistance, supplies the SAME504 construction +and the baseline package `research/direct-delivery504-global`. The final +baseline head is `e07a8a3f9f79c22113398a0c5dbbc7601f489b3e`; the scientific +files used here match the original Round20 pins. + +**The original PR531 NOTICE is retained separately and remains applicable.** +That notice records the scalar, geometry, controller, phase, wrapper, hosting, +and analytic ancestry. This short incremental notice does not replace it. + +In particular, DreamingOfClouds's PR484 response/kernel implementation and its +predecessors retain their source notices. Zhihao Chen's PR425 mutable-basis +lemma, the PR425/433/514 scalar lineage, and the previously credited source +and delivery contributions remain attributed through PR531's notice. + +## Adopted bit supplier + +[PR510](https://github.com/CrocSwap/integer-mult-bounds/pull/510), pinned to +`64edee18af02aab0c1696b677a0287dd0146381b`, is by **DreamingOfClouds with +Claude Opus 5.5 assistance via Claude Code**, as disclosed by that package. +Its R480 nine-stage bit endpoint is adopted as a cited conditional dependency. +It is not a new bit-side research result of this delta, and no cold replay +of that full bit pipeline was performed here. + +**The original PR510 NOTICE is retained separately and remains applicable.** +Its ancestry includes eumemic's PR493 carrier-skeleton word; PR503's R480 +dead-total change; chafreaky's PR443/444 replication pipeline; DaysSky's PR442 +whole-residual hosting and PR381 column checker; Zhihao Chen's PR386 geometry; +DreamingOfClouds's PR315 moment engines and pipeline adaptations; and Dylan +Crow's PR370 framework, with the assistance disclosures in those sources. + +The present PR510 mutable-source carryover exposition is by icekylinx with +GPT-6 Astra assistance. It expands the role-independent common-label argument +already present in PR472 and the mutable-basis lemma of PR425; it does not +claim those underlying ideas as new. + +## Comparison, evidence, and licenses + +PR493 is also retained as the former-bit-supplier control. PR533 is used only +for numerical comparison. A cited rate, reused certificate, or prior notice +does not imply a fresh replay in this package; the README states the completed +validation scope. + +Original source headers, notices, licenses, and pinned provenance remain in +force. This incremental notice does not relicense upstream material. New +Python research/audit files carry the Apache-2.0 notice stated in their source +headers. All reported bounds remain conditional on the listed inherited +interfaces. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/PROOF.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/PROOF.md new file mode 100644 index 0000000000..1d43cf78f4 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/PROOF.md @@ -0,0 +1,61 @@ +# Filtered elimination and state-version transport + +These are sufficient compilation theorems. They do not assert that a desired low-cost factorization exists, that the searched family is complete, or that scalar rank alone determines the recurrence exponent. Every elementary operation and changed frame transition remains part of the actual invoice. + +## Theorem 1: elimination with reusable donors and reversed execution + +Let C be the observed target-response matrix on helper coordinates over a field. Suppose we have stages j=1,...,k. At stage j choose new pivots P_j, donor indices D_j disjoint from P_j, and relations between the current response columns + + C_j[:,p] = sum_{d in D_j} q[d,p] C_j[:,d]. + +No previously eliminated pivot may be used again as a new pivot or a donor. A donor may become a pivot at a later stage. Form U_j from the commuting shears d <- d-q[d,p]p. Then right multiplication by U_j changes only the pivot columns, setting them to zero, and leaves all other columns unchanged. Thus, by induction, C U_1 ... U_k has zero columns at every selected pivot, including pivots which previously served as donors. The products are invertible, with explicit inverse obtained by reversing the elementary operations and their signs. + +The actual physical prefix must execute the stage blocks in order k,...,1, since column states are multiplied on the left while the response map is on the right. This reversal is essential: merely concatenating algebraic discovery order is generally wrong. The numerical relations at later stages can be evaluated on the original remaining columns because only already-eliminated columns changed. + +For each helper, collect the frames of every stage touching it in physical execution order, followed by its original first-touch frame. Require this list to be nested. A pivot starts at its own elimination frame; other helpers start at their specified old entrance. Require all initial frames to be contained in their first physical touch. These are finite sufficient geometric tests. Regenerate the inverse background cleanup. If the background subsystem never reads output target registers, this cleanup restores every background coordinate for arbitrary initial dirt. Zero response of every warm pivot ensures its dirt never needs a forbidden zero-frame output compensation. Existing gauges may be retained only under explicitly checked separation or a proved read-before-injection order, not by ignoring overlap. + +The exact local resource signature is obtained register by register from the successive dimension differences in this list. Repeated equal frames cost zero; every positive difference contributes one child of that rank. A pivot's residual width decreases by its entrance dimension. This chain invoice is valid even when supports overlap and the simple sum of disjoint component invoices is not. Full wrapper and physical owner costs remain separate. + +Proof of the response assertion is the elementary column-update identity above and induction. Proof of geometric legality is exactly the nested-chain test at every instruction. Proof of restoration is inversion of the explicitly changed background product. There is no existential oracle in the construction. + +## Concrete application: the PR535 static quotient presentation + +The frozen PR535 construction has 40 static rank-one pivots, 112 post-center gauges and 56 rank-four post-center pivots. We leave its post-center construction unchanged and replace only the static response presentation. The new selection uses six line classes: + +| Frame | Pivots | Active donor list size | +| --- | ---: | ---: | +| 96 | 8 | 8 | +| 102 | 8 | 8 | +| 120 | 8 | 8 | +| 126 | 8 | 8 | +| 480 | 10 | 14 | +| 486 | 2 | 6 | + +This gives 44 static pivots. The actual scalar word loses exactly four rank-one children; all other local rank multiplicities remain identical. Residual inventory changes from 56 width-five, 152 width-eight, 296 width-nine to 56 width-five, 156 width-eight, 292 width-nine. + +This witness is a depth-one special case of the staged theorem: its selected supports do not need donor-to-pivot reuse. The broader nested search generated it, but we do not attribute its numerical change to deeper nesting. The gain here comes from choosing a different joint response presentation across line classes, rather than maximizing each public component in isolation. + +`build_static44_portable.py` recomputes every selected rational relation, retains the original downstream scalar operations and frame labels, regenerates cleanup, and checks source/result semantic hashes. It checks the actual nested frames, complete local histogram and dyadic scalar contract. `STATIC44-SCALAR-AUDIT.json` independently checks every one of the 728 formal columns in both orientations and rejects all 44 omitted-static-correction controls with the correct compensation held fixed. Arbitrary helper dirt is included among these columns. This is a checked local construction, not a claimed globally hosted bound. The final package may continue to use unchanged PR535 if the bit supplier still binds. + +## Theorem 2: compensation transport along exact register versions + +Split state into background X and outputs Y. Let an invertible background prefix act by X -> A X and leave Y unchanged. The old compensation is Y -> Y+D X. Then the exact identity + + [A on X] after [add D X to Y] + = [add (D A^{-1}) X to Y] after [A on X] + +holds on every input, including arbitrary helper dirt. Therefore compensation may be moved to another program cut by computing the inverse-version response D A^{-1}. One must factor the transported map into actual allowed scalar gates and check that every source and target frame can reach the chosen common frame and still reach their next uses. If those finite checks pass, the transformed program has precisely the same full scalar endpoint. It is not enough to compare clean-input columns or to reuse D without the inverse-version factor. + +For a sequence of elementary background gates, D A^{-1} is computed by the opposite column update, in the original prefix order. Thus this theorem supplies a constructive compiler pass with an exact rejection test. The untouched-register case gives a useful safe normal form: each dirty compensation read can be delayed up to the first instruction that touches its helper, while the target remains at frame zero. This special case needs no extra storage and preserves the frame-chain invoice. It is not claimed as an exponent improvement. `transport_compensation.py` implements this normal form on R480: all 480 helper dirt reads move to their last untouched versions, all 720 scalar columns agree exactly, and every deduplicated register frame chain is unchanged. The exact receipt is `transport-bit510/TRANSPORT.json`. This appendix does not claim a new native phase or global-program replay. + +## Bounded screens and scope + +On the original filtered504 source, 100 native nested-elimination trials were preserved; they reached up to 92 pivots and rank188, but became secondary when PR535 moved the frontier. No whole-profile gain is inferred from those counts. + +On the new binding R480 bit source, the exact post-center compensation screen rejected every individual helper under its specified first-B-frame schedule: 448 failed because a transported source frame was already above the target frame, and 23 failed the next-use containment test. The full transported compensator had 1273 incompatible support entries in that schedule. A separate exact screen of 120 additional non-root sum/difference lines, together with all 120 root lines, found no entry response circuit. These are bounded family failures, not a theorem excluding other cuts, joint cancellation, general frames, or other schedules. + +On PR535, all 112 post-center gauges already attain rank one in the intersection of their actual first frames, target first-use caps and donor-kernel caps. The remaining static census examined 27195 first-frame subspaces and found 12 nonzero-nullity line classes and no higher-rank candidate in that restricted interface. A bounded 100-seed presentation search yielded the checked 44-pivot witness above. No optimality claim follows. + +## Structural source references + +Mathlib's matrix transvection file supplies explicit left/right elementary update identities and reverse-inverse product identities. OpenAI's congruence elementary-matrix development supplies `clear_step`: an elementary update clears another entry while preserving an already-cleared prefix. We inspected these actual statements as structural models for the inductive invariant and product order. The new geometric compilation theorem and its changed provider were proved and checked here; they are not asserted to be direct imports or newly Lean-certified theorems. Exact source hashes are in META-SOURCES.json. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/README.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/README.md new file mode 100644 index 0000000000..6aed83ec92 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/README.md @@ -0,0 +1,7 @@ +# Static44 local construction appendix + +Run `python -B replay.py --out NEW_DIRECTORY` from any working directory. This reconstructs the exact new static response presentation and checks all 728 scalar columns in both orientations, including arbitrary helper dirt, plus44 omitted-correction controls. Python standard library only. The output directory must not exist. + +The local profile changes by -4 rank-one children relative to PR535. The residual inventory becomes56 width-five,156 width-eight,292 width-nine. The global controller, owner charts, phase recipes and outer assembly are NOT replayed here. This appendix does not contribute a claimed final kappa gain. + +The attributed raw and baseline words and old recipe come from PR535 post-center-rank4-global. The gauge/kernel primitives come from PR531's attributed PR484 lineage; their original copyright/assistance notices are preserved. The new selection, replacement proof and constructor are our contribution. No new all-size or analytic interfaces are claimed discharged. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/RECIPE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/RECIPE.json new file mode 100644 index 0000000000..68c751bb56 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/RECIPE.json @@ -0,0 +1,168 @@ +{ + "selection": { + "kernel": [ + { + "E": [ + 96 + ], + "donors": [ + 250, + 251, + 256, + 257, + 266, + 267, + 302, + 303 + ], + "pivots": [ + 264, + 265, + 312, + 313, + 314, + 315, + 350, + 351 + ] + }, + { + "E": [ + 102 + ], + "donors": [ + 252, + 253, + 254, + 255, + 278, + 279, + 290, + 291 + ], + "pivots": [ + 276, + 277, + 324, + 325, + 326, + 327, + 338, + 339 + ] + }, + { + "E": [ + 120 + ], + "donors": [ + 238, + 239, + 244, + 245, + 268, + 269, + 292, + 293 + ], + "pivots": [ + 262, + 263, + 322, + 323, + 328, + 329, + 352, + 353 + ] + }, + { + "E": [ + 126 + ], + "donors": [ + 240, + 241, + 242, + 243, + 280, + 281, + 304, + 305 + ], + "pivots": [ + 274, + 275, + 310, + 311, + 316, + 317, + 340, + 341 + ] + }, + { + "E": [ + 480 + ], + "donors": [ + 286, + 287, + 288, + 289, + 298, + 300, + 334, + 335, + 336, + 337, + 346, + 348, + 358, + 360 + ], + "pivots": [ + 299, + 301, + 347, + 349, + 359, + 361, + 370, + 371, + 372, + 373 + ] + }, + { + "E": [ + 486 + ], + "donors": [ + 362, + 363, + 364, + 365, + 374, + 376 + ], + "pivots": [ + 375, + 377 + ] + } + ] + }, + "raw_semantic": "e00e571c80795516eff434392fe48f64ff430a866afd42608808e2f302064275", + "base_semantic": "39a1b5a6b237f52f59ebf55f39b22dc06292bc43403c04aa1f086a0277128b33", + "output_semantic": "f6183f32b354e0feec39170ee29bfad577af23e4697e9f25a0ad9dc2d5c2d9d4", + "profile": { + "1": 2204, + "4": 280, + "8": 8, + "3": 184, + "2": 728, + "6": 56, + "5": 56 + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/SOURCE-MANIFEST.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..468918ea58 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/SOURCE-MANIFEST.json @@ -0,0 +1,16 @@ +{ + "audit_scalar.py": "d22159087c1d0df0edf452aae3a1a7a45bf2cde4ce6e177850e415f9620151e1", + "build.py": "31d68795916985e2abb3207b07c1d3e39ed3560f1b46f18ade0a509278c710dc", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "META-SOURCES.json": "b30c82ad1d707b68e84af85e90b1bab0e41e49ccacda3069b952c790092be920", + "NOTICE-upstream.md": "1547136e6d269fdcef2b68c10a97a786a79a4732a12738363f679bfb282430cd", + "PROOF.md": "d1dafe41a1698d6df575ec86f796bcba08c54fe14b6d69e78f5f6cff8b55de4a", + "README.md": "c4b3ce02012fe97598e76a77877541a8f3387ba4305cee600ee557a48b3493e8", + "RECIPE.json": "973f1975213398f2b711e8ce4eddece181d4cbea83be5b6b650115b9bc43f2eb", + "replay.py": "5b12ea184b3afde41b1028d1926a0d158f2f05585dae6d9024e31424c290bccf", + "gk/gk_common.py": "e68d190fd436b2f3955decb590adb53344d5d4ea0a19d62d86df1e4b55ecd198", + "gk/gk_word.py": "f027a9273bcf4e0971258c160b7d3b3c196366b32a529cff6e6a0e666b03826b", + "inputs/BASE535.json.gz": "edfffb8e8735e0d1f07c81d818022b705ef0889c2bccc193a2f7a661b9f7d390", + "inputs/OLD-RECIPE.json": "7e5c179246261edd9e1019e81e6e979537f02559da773b993a318f771cb7d763", + "inputs/RAW504.json.gz": "1c6144791dbedf6427e3ee7b4c24fb05b5bf407f6346592f50f8dd8d9638108d" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/audit_scalar.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/audit_scalar.py new file mode 100644 index 0000000000..834e8b5103 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/audit_scalar.py @@ -0,0 +1,55 @@ +"""Independent exact scalar witness for a selected complex kernel word. +Uses immutable correct-word compensation for omission controls; no repaired +compensation is silently supplied to a mutant. No physical-hosting claim. +""" +import sys,json,gzip,hashlib,copy +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +p=Path(__file__).resolve().parent +path=Path(sys.argv[1]);selection=Path(sys.argv[2]);out=Path(sys.argv[3]);w=json.loads(gzip.decompress(path.read_bytes()));sel=json.loads(selection.read_text());v=len(w['ports']);n=2*v+w['report']['R'] +def ident():return[{r:Q(1)}for r in range(n)] +def apply(e,rows): + if e[0]=='scale': + _,t,a,b,*_=e;q=Q(a,b);rows[t]={j:q*x for j,x in rows[t].items()};return + _,t,s,a,b,*_=e;q=Q(a,b) + for j,x in list(rows[s].items()): + z=rows[t].get(j,Q(0))+q*x + if z:rows[t][j]=z + else:rows[t].pop(j,None) +def inv(e,dual=False): + e=copy.deepcopy(e) + if e[0]=='add': + e[3]*=-1 + if dual:e[1],e[2]=e[2],e[1] + else:e[2],e[3]=e[3],e[2] + return e +def replay(es): + rows=ident() + for e in es:apply(e,rows) + return rows +main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(n)] +for r in range(v,2*v):dirty[r]={j:x for j,x in mx[r].items()if j>=2*v} +for e in w['precondition']:apply(e,dirty) +comp=[] +for r in range(v,2*v): + for j,x in sorted(dirty[r].items()): + assert not w.get('start_extra',{}).get(str(j)),('nonzero-frame compensation',j) + comp.append(['add',r,j,-x.numerator,x.denominator,[]]) +cleanup=[inv(e)for e in reversed(w['A']+w['B'])if not v<=e[1]<2*v] +assert[e[:-1]for e in cleanup]==[e[:-1]for e in w['cleanup']] +program=w['precondition']+comp+main+cleanup;expected=ident() +for t in range(v):expected[v+t][t]=Q(1) +assert replay(program)==expected +back=ident() +for t in range(v):back[t][v+t]=Q(-1) +assert replay([inv(e,True)for e in program])==back +controls={} +for cl in sel['kernel']: + for h in cl['pivots']: + aa=[e for e in w['A']if not(e[0]=='add'and e[2]==2*v+h and e[1]>=2*v and e[-1]==cl['E'])] + assert len(aa)> p & 1: x ^= b[p] + if x: + p = x.bit_length() - 1 + for q in b: + if b[q] >> p & 1: b[q] ^= x + b[p] = x + return tuple(b[p] for p in sorted(b, reverse=True)) + + +def widths_of(word): + """residual width of every helper: 9 - dim(entrance frame); 9 when the word has no extension""" + R = word['report']['R'] if 'R' not in word else word['R'] + w = [L] * R + for r, E in word.get('start_extra', {}).items(): + assert 2 * V <= int(r) < 2 * V + R + w[int(r) - 2 * V] = L - len(basis(E)) + return w + + +def split_pad(p): + """a pad of rank p is paid as nested commuting children of rank <= 51 (so that 73^2 > 2*child^2); rank 1 stays 1""" + if p == 0: return [] + n = -(-p // 51); return [p // n + (1 if i < p % n else 0) for i in range(n)] + + +def tile(items): + """Bank tiling of unhosted residuals. items: list of (rep, helper, width); a bank has M = 73 cells. + * width-9 residuals (no wrapper acts on them): first fit in the given order, packed from offset 0, eight per bank, pad rank 1 + (PR #433/#442's tiling and routes [2, slot]); + * ENTERING residuals (width w < 9, paid wrappers, e = 9 - w spectators): banks of their own in which every entering helper is the ONLY + owner of its bank family in its invocation (the one-helper rule of PR #458 extended to banks): bank j holds the j-th entering + helper of each replica, residuals packed from offset 0 in replica order (at most one helper per replica, hence per invocation). + The spectators of an entering helper are the first e cells of the bank beyond every residual cell of the bank (the pad, which no call + uses for a residual, is paid as before: rank 73 - sum of widths; the spectators are borrowed inside it and not deducted). + Returns (assign, banks, pads): assign[(rep, helper)] = (bank, offset, width, pure, spectators) with pure = the bank holds only width-9 + residuals and spectators = () for width 9; pads = Counter of pad ranks (split into children of rank <= 51).""" + assign = {}; pads = Counter(); fill = [] + for z, (rep, h, w) in enumerate(items): # width 9: first fit, as PR #433 (all widths 9 reproduces it exactly) + if w != L: continue + for b, f in enumerate(fill): + if f + w <= M: break + else: + b = len(fill); fill.append(0) + assign[(rep, h)] = (b, fill[b], w, True, ()); fill[b] += w + nwide = len(fill); byrep = {} + for rep, h, w in items: + if w < L: byrep.setdefault(rep, []).append((h, w)) + cells = [0] * max((len(v) for v in byrep.values()), default=0); emax = [0] * len(cells); place = {} + for rep in sorted(byrep): # the j-th entering helper of every replica goes to entering bank j + for j, (h, w) in enumerate(byrep[rep]): + place[(rep, h)] = (nwide + j, cells[j], w); cells[j] += w; emax[j] = max(emax[j], L - w) + for j in range(len(cells)): assert cells[j] + emax[j] <= M, ('entering bank without room for its spectators', j) + for (rep, h), (b, off, w) in place.items(): + assign[(rep, h)] = (b, off, w, False, tuple(range(cells[b - nwide], cells[b - nwide] + L - w))) + fill += cells + for f in fill: + for part in split_pad(M - f): pads[part] += 1 + return assign, len(fill), pads + + +def route(off, w, pure, sp=()): + """owner route of a banked helper residual: PR #433's [2, slot] for width 9 (pure width-9 bank); an entering helper (w < 9) is + [2, offset, width, [spectator cells]] with e = 9 - w spectators""" + if w == L: assert pure and not sp; return [2, off // L] + assert not pure and len(sp) == L - w; return [2, off, w, list(sp)] + + +def unhosted_stock(widths): + """live stock and padding histogram of the unhosted (parent) template, per stage x nine""" + R = len(widths) + _, nb, pads = tile([(rep, h, widths[h]) for rep in range(T) for h in range(R)]) + return DATA + L * nb, Counter({r: z * L for r, z in pads.items()}) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/gk/gk_word.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/gk/gk_word.py new file mode 100644 index 0000000000..15782ba625 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/gk/gk_word.py @@ -0,0 +1,194 @@ +"""Apply a frozen selection (shared-donor kernel + entrance gauges) to PR #433's complex word. Apache-2.0. +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +usage: gk_word.py BASE_FULL-WORD.json.gz SELECTION.json OUT_FULL-WORD.json.gz +An empty selection ({}) copies the input byte for byte (regression anchor). + +selection = {"kernel": [{"E": [x], "donors": [h..], "pivots": [h..]}..], "gauge": {"h": [x..]}} (h = helper index 0..R-1) +Kernel (PR #417/#435/#434/#440): a pivot starts at E; every donor receives donor += -q * pivot at frame E before the main +word, where col(pivot) = sum q_d col(d) are the exact dirty-response columns; the pivot's frame-zero compensation vanishes. +Gauge (#401/#408-#416): the compensation target += -C[t,h] * helper of helper h is executed at frame E_h as the first gates +of the main word; h starts at E_h and its targets climb to the level L_t = largest E over their entering helpers. +The exact verification is the arbitrary-dirt replay of audit_gk.py; this module also checks the structural conditions.""" +import copy, gzip, hashlib, json, sys +from collections import Counter, defaultdict +from fractions import Fraction as Q +from pathlib import Path +sys.path.insert(0, str(Path(__file__).resolve().parent)) +from gk_common import * + + +def apply_op(e, rows): + if e[0] == 'scale': + _, t, a, b, *_ = e; q = Q(a, b); rows[t] = {j: q * x for j, x in rows[t].items()} + else: + _, t, s, a, b, *_ = e; q = Q(a, b) + for j, x in list(rows[s].items()): + z = rows[t].get(j, Q(0)) + q * x + if z: rows[t][j] = z + else: rows[t].pop(j, None) + + +def inverse(e, F): + e = copy.deepcopy(e) + if e[0] == 'add': e[3] *= -1 + else: e[2], e[3] = e[3], e[2] + e[-1] = list(F); return e + + +def responses(word): + """dirty-response columns col[h] = {target: coefficient} of the unmodified word (after the frame-zero preconditioner)""" + R = word['report']['R']; n = 2 * V + R + rows = [{r: Q(1)} for r in range(n)] + for e in word['A'] + word['cut'] + word['B']: apply_op(e, rows) + dirty = [{} for _ in range(n)] + for r in range(V, 2 * V): dirty[r] = {j: x for j, x in rows[r].items() if j >= 2 * V} + for e in word['precondition']: apply_op(e, dirty) + col = [{} for _ in range(R)] + for r in range(V, 2 * V): + for j, x in dirty[r].items(): col[j - 2 * V][r - V] = x + return col + + +def first_frames(word): + first = {} + for seq in (word['A'], word['B']): + for e in seq: + F = basis(e[-1]) + for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): + if r >= 2 * V: first.setdefault(r - 2 * V, F) + return first + + +def solve_relation(col, donors, p): + """exact rational c with col[p] = sum_d c_d col[d]; None if p is not in the span""" + ts = sorted({t for d in donors for t in col[d]} | set(col[p])) + idx = {t: i for i, t in enumerate(ts)} + Mx = [[Q(0)] * (len(donors) + 1) for _ in ts] + for ci, d in enumerate(donors): + for t, x in col[d].items(): Mx[idx[t]][ci] = x + for t, x in col[p].items(): Mx[idx[t]][-1] = x + piv = []; r = 0 + for c in range(len(donors)): + pr = next((i for i in range(r, len(Mx)) if Mx[i][c]), None) + if pr is None: continue + Mx[r], Mx[pr] = Mx[pr], Mx[r]; q = Mx[r][c]; Mx[r] = [x / q for x in Mx[r]] + for i in range(len(Mx)): + if i != r and Mx[i][c]: + f = Mx[i][c]; Mx[i] = [a - f * b for a, b in zip(Mx[i], Mx[r])] + piv.append(c); r += 1 + if any(Mx[i][-1] for i in range(r, len(Mx))): return None + assert r == len(donors), 'donors must have independent response columns' + return {donors[c]: Mx[i][-1] for i, c in enumerate(piv) if Mx[i][-1]} + + +def span(U): + s = {0} + for b in U: s |= {x ^ b for x in s} + return s + + +def perp(x): return basis([z for z in range(1, 512) if not (x & z).bit_count() % 2]) + + +def profile(word): + """local paid profile of a gk word by direct simulation of the frame chains (second implementation: audit_gk.py)""" + R = word['report']['R']; n = 2 * V + R; P = word['ports'] + cur = {} + for r in range(n): + cur[r] = (P[r],) if r < V else ((basis(word['start_extra'][str(r)]) if str(r) in word.get('start_extra', {}) else ()) if r >= 2 * V else ()) + paid = Counter() + def climb(r, F): + F = basis(F); o = cur[r] + assert basis(list(o) + list(F)) == F, ('frame violation', r, o, F) + if o != F: paid[len(F) - len(o)] += 1; cur[r] = F + lev = {int(t): basis(E) for t, E in word.get('target_levels', {}).items()} + for seq, part in ((word['A'], 'A'), (word['B'], 'B')): + if part == 'B': + for r, f in zip(word['centers'], word['center_frames']): + assert cur[r] == basis(f), 'centre frame' + served = sorted({lev.get(e[1] - V, ()) for e in word['cut'] if e[2] == r}, key=lambda E: -len(E)) + o = basis(f) + for Lv in served: + assert span(Lv) <= span(o), 'served levels must descend inside the centre frame' + if Lv != o: paid[len(o) - len(Lv)] += 1; o = Lv + for t in range(V): assert cur[V + t] == lev.get(t, ()), 'target level at the centre scatter' + for e in seq: + for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): climb(r, e[-1]) + for r in range(n): climb(r, FULL if (r < V or r >= 2 * V) else perp(P[r - V])) + return paid + + +def global_profile(local, widths): + """unhosted nine-stage profile: local x (stages*replicas) + the 240*8 idle children per rank + bank pads""" + live, pads = unhosted_stock(widths) + g = Counter({r: z * L * T for r, z in local.items()}) + for r in (16, 8, 32, 8, 48, 8, 48, 32, 16): g[r] += 240 * T + g.update(pads) + return live, g + + +def build(word, sel, check=True): # check=False only for the mutation controls that must be caught by the certifying scripts + if not sel: return word + w = copy.deepcopy(word); R = w['report']['R'] + col = responses(word); first = first_frames(word) + gauge = {int(h): basis(E) for h, E in sel.get('gauge', {}).items()} + classes = sel.get('kernel', []) + pivots = {p for c in classes for p in c['pivots']}; donors = {d for c in classes for d in c['donors']} + assert not (pivots & donors) and not (pivots | donors) & set(gauge) and len(pivots) == sum(len(c['pivots']) for c in classes) + # --- structural conditions ------------------------------------------------------------------------------------- + for h, E in gauge.items(): + assert not check or span(E) <= span(first[h]), ('gauge entrance outside the first frame', h) + levels = defaultdict(list) + for h, E in gauge.items(): + for t in col[h]: levels[t].append(E) + for t, Es in levels.items(): # pairwise nested comps per target + for a in Es: + for b in Es: assert not check or span(a) <= span(b) or span(b) <= span(a), ('non-nested gauges at target', t) + lev = {t: max(Es, key=len) for t, Es in levels.items()} + for k, r in enumerate(w['centers']): # chain per centre, inside the centre frame + served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == r} + for a in served: + for b in served: assert not check or span(a) <= span(b) or span(b) <= span(a), ('centre chain', k) + top = max(served, key=len) + assert not check or span(top) <= span(basis(w['center_frames'][k])), ('level outside centre frame', k) + # --- gates ---------------------------------------------------------------------------------------------------------- + gates = [] + for h, E in sorted(gauge.items(), key=lambda kv: (len(kv[1]), kv[0])): + for t, x in sorted(col[h].items()): + c = -x; gates.append(['add', V + t, 2 * V + h, c.numerator, c.denominator, list(E)]) + pre = [] + start = {2 * V + h: list(E) for h, E in gauge.items()} + for cl in sorted(classes, key=lambda c: (len(c['E']), c['E'])): + E = basis(cl['E']) + for x in [*cl['donors'], *cl['pivots']]: assert span(E) <= span(first[x]), ('kernel entrance outside the first frame', x) + for p in cl['pivots']: + rel = solve_relation(col, cl['donors'], p) + assert rel is not None, ('pivot response not in the donor span', p) + start[2 * V + p] = list(E) + for d, c in rel.items(): + q = -c; pre.append(['add', 2 * V + d, 2 * V + p, q.numerator, q.denominator, list(E)]) + w['A'] = gates + pre + w['A'] + w['cleanup'] = [inverse(e, FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V] + w['start_extra'] = {str(r): list(E) for r, E in sorted(start.items())} + w['target_levels'] = {str(t): list(E) for t, E in sorted(lev.items()) if E} + if not check: return w + prof = profile(w); widths = widths_of(w) + live, g = global_profile(prof, widths) + w['report']['local_profile'] = {str(k): z for k, z in sorted(prof.items())} + w['report']['global_profile'] = {str(k): z for k, z in sorted(g.items())} + w['report']['live'] = live + w['report']['entrance_rank'] = sum(L - x for x in widths); w['report']['entering_helpers'] = sum(1 for x in widths if x < L) + w['report']['selection_sha256'] = hashlib.sha256(json.dumps(sel, sort_keys=True).encode()).hexdigest() + return w + + +def dump(w): return gzip.compress(json.dumps(w, sort_keys=True, separators=(',', ':')).encode(), mtime=0) + + +if __name__ == '__main__': + src, selp, out = map(Path, sys.argv[1:4]) + sel = json.loads(selp.read_text()) + if not sel: out.write_bytes(src.read_bytes()); print('empty selection: copied 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a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/replay.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/replay.py new file mode 100644 index 0000000000..ef5642ccfd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/static44/replay.py @@ -0,0 +1,9 @@ +"""Standalone exact local-only static44 reconstruction and scalar audit.""" +from pathlib import Path +import argparse,subprocess,sys +if not __debug__:raise SystemExit('Assertions must remain enabled.') +p=Path(__file__).resolve().parent +ap=argparse.ArgumentParser();ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert not a.out.exists() +subprocess.run([sys.executable,'-B',str(p/'build.py'),'--raw',str(p/'inputs/RAW504.json.gz'),'--base',str(p/'inputs/BASE535.json.gz'),'--old-recipe',str(p/'inputs/OLD-RECIPE.json'),'--recipe',str(p/'RECIPE.json'),'--gk-dir',str(p/'gk'),'--out',str(a.out)],check=True) +subprocess.run([sys.executable,'-B',str(p/'audit_scalar.py'),str(a.out/'FULL-WORD.json.gz'),str(a.out/'SELECTION.json'),str(a.out/'SCALAR-AUDIT.json')],check=True) +print('PASS standalone local-only appendix') diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/DAG-STRUCTURES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/DAG-STRUCTURES.json new file mode 100644 index 0000000000..699b69e691 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/DAG-STRUCTURES.json @@ -0,0 +1,208 @@ +{ + "\"Submodule\" \"inf\" \"le\"": [ + [ + "Mathproof.CrossCombine100.finrank_inf_le_of_invariantsAdditive", + "project::Mathproof.CrossCombine100", + "theorem finrank_inf_le_of_invariantsAdditive [FiniteDimensional K V]\n {U U' inv : Submodule K V} (h : InvariantsAdditive U U' inv) :\n Module.finrank K \u21a5((U \u2294 U') \u2293 inv)\n \u2264 Module.finrank K \u21a5(U \u2293 inv) + Module.finrank K \u21a5(U' \u2293 inv)" + ], + [ + "Mathproof.CrossCombine100.finrank_inf_le_trivial", + "project::Mathproof.CrossCombine100", + "theorem finrank_inf_le_trivial [FiniteDimensional K V] (U inv : Submodule K V) :\n Module.finrank K \u21a5(U \u2293 inv) \u2264 Module.finrank K \u21a5U" + ], + [ + "map_inf_le", + "package:mathlib::Mathlib.Algebra.Lie.Submodule", + "theorem map_inf_le : (N \u2293 N\u2082).map f \u2264 N.map f \u2293 N\u2082.map f" + ], + [ + "invtSubmodule_inf_invtSubmodule_le_invtSubmodule_add", + "package:mathlib::Mathlib.Algebra.Module.Submodule.Invariant", + "lemma invtSubmodule_inf_invtSubmodule_le_invtSubmodule_add :\r\n f.invtSubmodule \u2293 g.invtSubmodule \u2264 (f + g).invtSubmodule" + ], + [ + "map_inf_le", + "package:mathlib::Mathlib.Algebra.Module.Submodule.Map", + "theorem map_inf_le (f : M \u2192\u209b\u2097[\u03c3\u2081\u2082] M\u2082) {p q : Submodule R M} :\r\n (p \u2293 q).map f \u2264 p.map f \u2293 q.map f" + ], + [ + "inf_comap_le_comap_add", + "package:mathlib::Mathlib.Algebra.Module.Submodule.Map", + "theorem inf_comap_le_comap_add (f\u2081 f\u2082 : M \u2192\u209b\u2097[\u03c4\u2081\u2082] M\u2082) :\r\n comap f\u2081 q \u2293 comap f\u2082 q \u2264 comap (f\u2081 + f\u2082) q" + ] + ], + "\"GaloisConnection\" \"map\" \"comap\"": [ + [ + "gc_map_comap", + "package:mathlib::Mathlib.Algebra.Algebra.NonUnitalSubalgebra", + "theorem gc_map_comap (f : F) :\r\n GaloisConnection (map f : NonUnitalSubalgebra R A \u2192 NonUnitalSubalgebra R B) (comap f)" + ], + [ + "gc_map_comap", + "package:mathlib::Mathlib.Algebra.Algebra.Subalgebra.Basic", + "theorem gc_map_comap (f : A \u2192\u2090[R] B) : GaloisConnection (map f) (comap f)" + ], + [ + "gc_map_comap", + "package:mathlib::Mathlib.Algebra.Field.Subfield.Basic", + "theorem gc_map_comap (f : K \u2192+* L) : GaloisConnection (map f) (comap f)" + ], + [ + "gc_map_comap", + "package:mathlib::Mathlib.Algebra.Group.Subgroup.Map", + "theorem gc_map_comap (f : G \u2192* N) : GaloisConnection (map f) (comap f)" + ], + [ + "gc_map_comap", + "package:mathlib::Mathlib.Algebra.Group.Submonoid.Operations", + "theorem gc_map_comap (f : F) : GaloisConnection (map f) (comap f)" + ], + [ + "gc_map_comap", + "package:mathlib::Mathlib.Algebra.Group.Subsemigroup.Operations", + "theorem gc_map_comap (f : M \u2192\u2099* N) : GaloisConnection (map f) (comap f)" + ] + ], + "\"Filtration\" \"monotone\"": [ + [ + "filtration_monotone", + "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex", + "lemma filtration_monotone : Monotone f.filtration" + ], + [ + "w", + "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex", + "lemma w (j : \u03b9) :\r\n f.t j \u226b homOfLE (f.filtration_monotone (Order.le_succ j)) = f.m j \u226b f.b j" + ], + [ + "isPullback", + "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex", + "lemma isPullback (j : \u03b9) :\r\n IsPullback (f.t j) (f.m j) (homOfLE (f.filtration_monotone (Order.le_succ j))) (f.b j) where\r\n w" + ], + [ + "range_homOfLE_app_union_range_b_app", + "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex", + "lemma range_homOfLE_app_union_range_b_app (j : \u03b9) (d : SimplexCategory\u1d52\u1d56) :\r\n Set.range ((homOfLE (f.filtration_monotone (Order.le_succ j))).app d) \u2294\r\n Set.range ((f.b j).app d) = Set.univ" + ], + [ + "isPushout", + "package:mathlib::Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex", + "lemma isPushout (j : \u03b9) :\r\n IsPushout (f.t j) (f.m j) (homOfLE (f.filtration_monotone (Order.le_succ j))) (f.b j) where\r\n w" + ], + [ + "succEquiv_coherence", + "package:mathlib::Mathlib.FieldTheory.CardinalEmb", + "theorem succEquiv_coherence (i : \u03b9) (f) : (succEquiv i f).1 =\r\n f.comp (Subalgebra.inclusion <| strictMono_filtration.monotone <| le_succ i)" + ] + ], + "\"finrank\" \"ker\"": [ + [ + "MathproofImported", + "project::MathproofImported", + "/-\n# MathproofImported \u2014 root for the audited ChatGPT-archive formalizations (2026-08-30)\n\nThe 23 modules under Mathproof/Imported/ were produced by five auditing agents from\nVPVNP_CHAT_RESULTS_ALL_SO_FAR_2026-08-30.zip, each verified twice (agent + independent sweep)\nat 0 errors / 0 sorry / 0 axiom. They import Mathproof, so this SEPARATE root avoids a cycle;\nnot in defaultTargets. Every theorem gets #print axioms; acceptable dependencies are exactly\nthe classical trio. Findings: D:/Proof/grind/notes/ARCHIVE_G*_FINDINGS_2026-08-30.md.\n-/\nimport Mathproof.Imported.G1Coherence\nimport Mathproof.Imported.G1Fca\nimport Mathproof.Imported.G1FirstLoss\nimport Mathproof.Imported.G2BalancedSplit\nimport Mathproof.Imported.G2ContextIdentity\nimport Mathproof.Imported.G2Homogenization\nimport Mathproof.Imported.G2ParseCount\nimport Mathproof.Imported.G2Recurrences\nimport Mathproof.Imported.G3CompletionFibers\nimport Mathproof.Imported.G3GeneratorAllocation\nimport Mathproof.Imported.G3InnovationRank\nimport Mathproof.Imported.G3RefinementTelescope\nimport Mathproof.Imported.G3RowDescent\nimport Mathproof.Imported.G4CrossThreshold\nimport Mathproof.Imported.G4OneShotSaving\nimport Mathproof.Imported.G4SavingParameter\nimport Mathproof.Imported.G4VerifierAudit\nimport Mathproof.Imported.G5BottomFanin\nimport Mathproof.Imported.G5BottomSupport\nimport Mathproof.Imported.G5Multilinearity\nimport Mathproof.Imported.G5RestrictionAudit\nimport Mathproof.Imported.G5TopFanin\nimport Mathproof.Imported.G5UniqueParse\n\n#print axioms Mathproof.Imported.G1.exists_independent_subset\n#print axioms Mathproof.Imported.G1.rows_linearIndependent_of_diagonal_on\n#print axioms Mathproof.Imported.G1.coherence_capacity\n#print axioms Mathproof.Imported.G1.coherence_dichotomy\n#print axioms Mathproof.Imported.G1.anchorId_diag\n#print axioms Mathproof.Imported.G1.anchorId_rowFan\n#print axioms Mathproof.Imported.G1.anchorId_colFan\n#print axioms Mathproof.Imported.G1.anchorId_rank\n#print axioms Mathproof.Imported.G1.anchorId_bound\n#print axioms Mathproof.Imported.G1.anchorId_tight\n#print axioms Mathproof.Imported.G1.anchorOnes_diag\n#print axioms Mathproof.Imported.G1.anchorOnes_rowFan\n#print axioms Mathproof.Imported.G1.anchorOnes_colFan\n#print axioms Mathproof.Imported.G1.anchorOnes_rank\n#print axioms Mathproof.Imported.G1.anchorOnes_bound\n#print axioms Mathproof.Imported.G1.anchorOnes_slack\n#print axioms Mathproof.Imported.G1.finrank_ker_comp_of_comp\n#print axioms Mathproof.Imported.G1.finrank_prod_submodule\n#print axioms Mathproof.Imported.G1.finrank_ker_prodMap\n#print axioms Mathproof.Imported.G1.fca_one_step\n#print axioms Mathproof.Imported.G1.mem_ker_addGate\n#print axioms Mathproof.Imported.G1.crossResp_ne_zero\n#print axioms Mathproof.Imported.G1.crossResp_injective\n#print axioms Mathproof.Imported.G1.crossResp_cancels\n#print axioms Mathproof.Imported.G1.crossResp_not_linearIndependent\n#print axioms Mathproof.Imported.G1.not_distinctContextsIndependent\n#print axioms Mathproof.Imported.G1.FTree\n#print axioms Mathproof.Imported.G1.FTree\n#print axioms Mathproof.Imported.G1.FTree\n#print axioms Mathproof.Imported.G1.FTree\n#print axioms Mathproof.Imported.G1.finrank_ker_addGate_rat\n#print axioms Mathproof.Imported.G1.anchorTree_leafKerSum\n#print axioms Mathproof.Imported.G1.anchorTree_size\n#print axioms Mathproof.Imported.G1.anchorTree_collisionSum\n#print axioms Mathproof.Imported.G1.anchorTree_fca\n#print axioms Mathproof.Imported.G1.firstLossMap_apply\n#print axioms Mathproof.Imported.G1.firstLossMap_surjective\n#print axioms Mathproof.Imported.G1.firstLossMap_ker\n#print axioms Mathproof.Imported.G1.finrank_ker_comp\n#print axioms Mathproof.Imported.G1.cumul_succ\n#print axioms Mathproof.Imported.G1.ker_cumul_finrank\n#print axioms Mathproof.Imported.G1.ssfl\n#print axioms Mathproof.Imported.G1.ssfl_total_kill\n#print axioms Mathproof.Imported.G1.ssfl_detector\n#print axioms Mathproof.Imported.G1.exists_stage_first_loss\n#print axioms Mathproof.Imported.G1.collision_stack_ssfl\n#print axioms Math" + ], + [ + "probe_qv", + "project::probe_qv", + "import Mathproof.Meta.BipartiteCancellation20260902\nimport Mathlib\n\nopen Mathproof.Meta.BipartiteCancellation20260902 in\n#check @BRep\n#check @Mathproof.Meta.BipartiteCancellation20260902.BRep.SimEquiv\n#check @Mathproof.Meta.BipartiteCancellation20260902.BRep.dsum\n#check @Mathproof.Meta.BipartiteCancellation20260902.bipartite_cancel\n#check @Mathproof.Meta.KrullSchmidtCancellation20260902.Indecomposable\n#check @Mathproof.Meta.KrullSchmidtCancellation20260902.isUnit_or_isNilpotent\n#check @Mathproof.Meta.KrullSchmidtCancellation20260902.cancel_of_finiteDimensional\n\n#check @Submodule.prodEquivOfIsCompl\n#check @Submodule.coe_prodEquivOfIsCompl\n#check @Submodule.exists_isCompl\n#check @LinearEquiv.ofBijective\n#check @LinearMap.rangeRestrict\n#check @LinearMap.finrank_range_add_finrank_ker\n#check @LinearEquiv.ofFinrankEq\n#check @Module.finrank_prod\n#check @Fintype.sum_bool\n#check @Finset.sum_const\n#check @Submodule.mem_sup\n#check @LinearEquiv.prodCongr\n#check @LinearEquiv.ofEq\n#check @Submodule.disjoint_def\n#check @LinearMap.ker_eq_bot\n#check @Quiver\n#check @Quiver.Path\n" + ], + [ + "codim_iInf_ker_le_fintypeCard", + "project::APAP.Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", + "lemma codim_iInf_ker_le_fintypeCard [Fintype \u03b9] :\r\n Module.finrank (ZMod q) G - (\u2a05 i, (\u03b3 i).toAddMonoidHom.ker.toZModSubmodule q).finrank\r\n \u2264 Fintype.card \u03b9" + ], + [ + "codim_iInf_ker_le_finsetCard", + "project::APAP.Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality", + "lemma codim_iInf_ker_le_finsetCard :\r\n Module.finrank (ZMod q) G - ((\u2a05 i \u2208 s, (\u03b3 i).toAddMonoidHom.ker).toZModSubmodule q).finrank\r\n \u2264 #s" + ], + [ + "codim_iInf_ker_le_fintypeCard", + "project::APAP.Mathlib.LinearAlgebra.FiniteDimensional.Lemmas", + "lemma codim_iInf_ker_le_fintypeCard [Fintype \u03b9] :\r\n finrank K V - (\u2a05 i, (f i).ker).finrank \u2264 Fintype.card \u03b9" + ], + [ + "codim_biInf_ker_le_finsetCard", + "project::APAP.Mathlib.LinearAlgebra.FiniteDimensional.Lemmas", + "lemma codim_biInf_ker_le_finsetCard : finrank K V - (\u2a05 i \u2208 s, (f i).ker).finrank \u2264 #s" + ] + ], + "typed:\"Submodule\" \"inf_le_left\"": [ + [ + "AlgebraicGeometry.SmallExtension.naturality_pair_comp_eq_and_quotient_comp_eq_of_local_lifts_hom", + "theorem AlgebraicGeometry.SmallExtension.naturality_pair_comp_eq_and_quotient_comp_eq_of_local_lifts_hom\n (T' T : Type u) [CommRing T'] [IsLocalRing T'] [IsArtinianRing T']\n [CommRing T] (\u03c0 : T' \u2192+* T) (h\u03c0 : Function.Surjective \u03c0) (hker : IsNilpotent (RingHom.ker \u03c0))\n (hsmall : RingHom.ker \u03c0 * maximalIdeal T' = \u22a5)\n\n (hI : RingHom.ker \u03c0 \u2264 maximalIdeal T')\n (\u03c1 : T \u2192+* ResidueField T') (h\u03c1 : \u03c1.comp \u03c0 = residue T')\n (V : Type u) [AddCommGroup V] [Module (ResidueField T') V] [Module.Finite (ResidueField T') V]\n [Module T' V] [IsScalarTower T' (ResidueField T') V]\n [Module (ResidueField T')\u1d50\u1d52\u1d56 V] [IsCentralScalar (ResidueField T') V]\n (\u03b9 : V \u2192\u2097[T'] T') (h\u03b9 : Function.Injective \u03b9)\n (h\u03b9I : LinearMap.range \u03b9 = Submodule.restrictScalars T' (RingHom.ker \u03c0))\n\n {A\u2080 : Scheme.{u}} (f\u2080 : A\u2080 \u27f6 Spec (CommRingCat.of T)) [IsSeparated f\u2080] [Smooth f\u2080]\n\n (\ud835\udcb0 : A\u2080.OrderedAffineCover)\n (Y : \ud835\udcb0.\u03b9 \u2192 Scheme.{u}) (q : \u2200 a, Y a \u27f6 Spec (CommRingCat.of T')) (hq : \u2200 a, Smooth (q a))\n (g : \u2200 a, (\u2191(\ud835\udcb0.U a) : Scheme.{u}) \u27f6 Y a)\n (hg : \u2200 a, IsPullback (g a) ((\ud835\udcb0.U a).\u03b9 \u226b f\u2080) (q a) (Spec.map (CommRingCat.ofHom \u03c0)))\n\n {Ak : Scheme.{u}} (fk : Ak \u27f6 Spec (CommRingCat.of (ResidueField T'))) [IsSeparated fk]\n (Lk : RelativeGroupLaw (ResidueField T') fk)\n (i\u2080 : Ak \u27f6 A\u2080) [IsAffineHom i\u2080] (hi\u2080 : IsPullback i\u2080 fk f\u2080 (Spec.map (CommRingCat.ofHom \u03c1)))\n (Ue : Ak.Opens) (hUe : IsAffineOpen Ue)\n (e\u2081 : Spec (CommRingCat.of (ResidueField T')) \u27f6 (Ue : Scheme.{u})) (he\u2081 : e\u2081 \u226b Ue.\u03b9 = (Lk.one (\ud835\udfd9 _)).1)\n\n (O : \u2200 a, A\u2080.Opens \u2192 (Y a).Opens)\n (hO : \u2200 (a : \ud835\udcb0.\u03b9) (W : A\u2080.Opens), g a \u207b\u00b9\u1d41 O a W = (\ud835\udcb0.U a).\u03b9 \u207b\u00b9\u1d41 W)\n (hOm : \u2200 a, Monotone (O a))\n (hOtop : \u2200 a, O a (\ud835\udcb0.U a) = \u22a4)\n (hOinf : \u2200 (a : \ud835\udcb0.\u03b9) (W W' : A\u2080.Opens), O a W \u2293 O a W' \u2264 O a (W \u2293 W'))\n (hOaff : \u2200 (a : \ud835\udcb0.\u03b9) (W : A\u2080.Opens), IsAffineOpen W \u2192 W \u2264 \ud835\udcb0.U a \u2192 IsAffineOpen (O a W))\n\n (\u03c3 : \u2200 {n : \u2115} (s : \ud835\udcb0.Idx n),\n letI := algebraOfHom (q (s.1 0)) (O (s.1 0) (\ud835\udcb0.inter s))\n ((ResidueField T') \u2297[T'] \u0393(Y (s.1 0), O (s.1 0) (\ud835\udcb0.inter s))) \u2243+* \u0393(Ak, (\ud835\udcb0.comap i\u2080).inter s))\n (h\u03c3\u2081 : \u2200 {n : \u2115} (s : \ud835\udcb0.Idx n),\n letI := algebraOfHom (q (s.1 0)) (O (s.1 0) (\ud835\udcb0.inter s))\n (Scheme.OrderedAffineCover.isAffineOpen_inter fk (\ud835\udcb0.comap i\u2080) s).isoSpec.hom \u226b\n Spec.map (CommRingCat.ofHom (\u03c3 s).toRingHom) \u226b\n Spec.map (CommRingCat.ofHom\n (Algebra.TensorProduct.includeRight : \u0393(Y (s.1 0), O (s.1 0) (\ud835\udcb0.inter s)) \u2192\u2090[T']\n (ResidueField T') \u2297[T'] \u0393(Y (s.1 0), O (s.1 0) (\ud835\udcb0.inter s))).toRingHom) \u226b\n (hOaff (s.1 0) (\ud835\udcb0.inter s) (Scheme.OrderedAffineCover.isAffineOpen_inter f\u2080 \ud835\udcb0 s) (\ud835\udcb0.inter_le s 0)).fromSpec =\n Ak.homOfLE (\ud835\udcb0.comap_inter_le i\u2080 s) \u226b (i\u2080 \u2223_ \ud835\udcb0.inter s) \u226b A\u2080.homOfLE (\ud835\udcb0.inter_le s 0) \u226b g (s.1 0))\n (h\u03c3\u2082 : \u2200 {n : \u2115} (s : \ud835\udcb0.Idx n) (x : ResidueField T'),\n letI := algebraOfHom (q (s.1 0)) (O (s.1 0) (\ud835\udcb0.inter s))\n letI := algebraOfHom fk ((\ud835\udcb0.comap i\u2080).inter s)\n \u03c3 s (x \u2297\u209c[T'] (1 : \u0393(Y (s.1 0), O (s.1 0) (\ud835\udcb0.inter s)))) = algebraMap (ResidueField T') \u0393(Ak, (\ud835\udcb0.comap i\u2080).inter s) x)\n\n (\u03c6 : \u2200 (a b : \ud835\udcb0.\u03b9), a < b \u2192 ((\u2191(O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)) : Scheme.{u}) \u2245 \u2191(O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b))))\n (h\u03c6q : \u2200 (a b : \ud835\udcb0.\u03b9) (h : a < b),\n (\u03c6 a b h).hom \u226b (O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 \u226b q b = (O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 \u226b q a)\n (h\u03c6g : \u2200 (a b : \ud835\udcb0.\u03b9) (h : a < b),\n \u2203 (\u03b3 : (\u2191(\ud835\udcb0.U a \u2293 \ud835\udcb0.U b) : Scheme.{u}) \u27f6 \u2191(O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)))\n (\u03b3' : (\u2191(\ud835\udcb0.U a \u2293 \ud835\udcb0.U b) : Scheme.{u}) \u27f6 \u2191(O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b))),\n \u03b3 \u226b (O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 = A\u2080.homOfLE inf_le_left \u226b g a \u2227\n \u03b3' \u226b (O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 = A\u2080.homOfLE inf_le_right \u226b g b \u2227\n \u03b3 \u226b (\u03c6 a b h).hom = \u03b3')\n (h\u03c6O : \u2200 (a b : \ud835\udcb0.\u03b9) (h : a < b) (W : A\u2080.Opens),\n (\u03c6 a b h).hom \u207b\u00b9\u1d41 ((O b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 \u207b\u00b9\u1d41 O b W) = (O a (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b)).\u03b9 \u207b\u00b9\u1d41 O a W)\n\n (\u03c1ab : \u2200 r : \ud835\udcb0.Idx 2, ((\u2191(O (r.1 0) (\ud835\udcb0.inter r)) : Scheme.{u}) \u2245 \u2191(O (r.1 1) (\ud835\udcb0.inter r))))\n (\u03c1bc : \u2200 r : \ud835\udcb0.Idx 2, ((\u2191(O (r.1 1) (\ud835\udcb0.inter r)) : Scheme.{u}) \u2245 \u2191(O (r.1 2) (\ud835\udcb0.inter r))))\n (\u03c1ac : \u2200 r : \ud835\udcb0.Idx 2, ((\u2191(O (r.1 0) (\ud835\udcb0.inter r)) : Scheme.{u}) \u2245 \u2191(O (r.1 2) (\ud835\udcb0.inter r))))\n (h\u03c1ab : \u2200 r : \ud835\udcb0.Idx 2,\n (\u03c1ab r).hom \u226b (Y (r.1 1)).homOfLE (hOm (r.1 1) (le_inf (\ud835\udcb0.inter_le r 0) (\ud835\udcb0.inter_le r 1))) =\n (Y (r.1 0)).homOfLE (hOm (r.1 0) (le_inf (\ud835\udcb0.inter_le r 0) (\ud835\udcb0.inter_le r 1))) \u226b\n (\u03c6 (r.1 0) (r.1 1) (r.2 (by decide))).hom)\n (h\u03c1bc : \u2200 r : \ud835\udcb0.Idx 2,\n (\u03c1bc r).hom \u226b (Y (r.1 2)).homOfLE (hOm (r.1 2) (le_inf (\ud835\udcb0.inter_le r 1) (\ud835\udcb0.inter_le r 2))) =\n (Y (r.1 1)).homOfLE (hOm (r.1 1) (le_inf (\ud835\udcb0.inter_le r 1) (\ud835\udcb0.inter_le r 2))) \u226b\n (\u03c6 (r.1 1) (r.1 2) (r.2 (by decide))).hom)\n (h\u03c1ac : \u2200 r : \ud835\udcb0.Idx 2,\n (\u03c1ac r).hom \u226b (Y (r.1 2)).homOfLE (hOm (r.1 2) (le_inf (\ud835\udcb0.inter_le r 0) (\ud835\udcb0.inter_le r 2))) =\n (Y (r.1 0)).homOfLE (hOm (r.1 0) (le_inf (\ud835\udcb0.inter_le r 0) (\ud835\udcb0.inter_le r 2))) \u226b\n (\u03c6 (r.1 0) (r.1 2) (r.2 (by decide))).hom)\n\n (\u03c9 : letI := algebraOfHom fk Ue\n \u21a5(Algebra.PointDerivations (ResidueField T') \u0393(Ak, Ue)\n ((Ue.topIso.inv \u226b e\u2081.appTop \u226b (Scheme.\u0393SpecIso (CommRingCat.of (ResidueField T'))).hom).hom)\n (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T'] (OModulePresheaf.unit fk).cochain (\ud835\udcb0.comap i\u2080) 2)))\n (h\u03c9 : \u2200 r : \ud835\udcb0.Idx 2,\n letI := algebraOfHom (q (r.1 0)) (O (r.1 0) (\ud835\udcb0.inter r))\n letI := algebraOfHom fk Ue\n \u2203 cs : \u0393(Ak, Ue) \u2192 (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T']\n ((ResidueField T') \u2297[T'] \u0393(Y (r.1 0), O (r.1 0) (\ud835\udcb0.inter r)))),\n IsTangentCoordsOfPairAtVia (RingHom.ker \u03c0) V \u03b9 \u0393(Y (r.1 0), O (r.1 0) (\ud835\udcb0.inter r))\n ((hOaff (r.1 0) (\ud835\udcb0.inter r) (Scheme.OrderedAffineCover.isAffineOpen_inter f\u2080 \ud835\udcb0 r) (\ud835\udcb0.inter_le r 0)).isoSpec.inv \u226b\n (\u03c1ac r).hom \u226b (O (r.1 2) (\ud835\udcb0.inter r)).\u03b9)\n ((hOaff (r.1 0) (\ud835\udcb0.inter r) (Scheme.OrderedAffineCover.isAffineOpen_inter f\u2080 \ud835\udcb0 r) (\ud835\udcb0.inter_le r 0)).isoSpec.inv \u226b\n (\u03c1ab r).hom \u226b (\u03c1bc r).hom \u226b (O (r.1 2) (\ud835\udcb0.inter r)).\u03b9)\n fk Lk (i\u2080 \u207b\u00b9\u1d41 \ud835\udcb0.U (r.1 2)) ((i\u2080 \u2223_ \ud835\udcb0.U (r.1 2)) \u226b g (r.1 2)) Ue cs \u2227\n \u2200 (a : \u0393(Ak, Ue)) (\u03be : Module.Dual (ResidueField T') V), \u03c3 r (cs a \u03be) = \u03c9.1 a \u03be r)\n (h\u03c9Z : letI := algebraOfHom fk Ue\n \u2200 (a : \u0393(Ak, Ue)) (\u03be : Module.Dual (ResidueField T') V),\n (OModulePresheaf.unit fk).d (\ud835\udcb0.comap i\u2080) 2 (\u03c9.1 a \u03be) = 0)\n {X\u2080 : Scheme.{u}} (fX\u2080 : X\u2080 \u27f6 Spec (CommRingCat.of T)) [IsSeparated fX\u2080] [Smooth fX\u2080]\n\n (\ud835\udcb1 : X\u2080.OrderedAffineCover)\n (Z : \ud835\udcb1.\u03b9 \u2192 Scheme.{u}) (qZ : \u2200 a, Z a \u27f6 Spec (CommRingCat.of T')) (hqZ : \u2200 a, Smooth (qZ a))\n (gZ : \u2200 a, (\u2191(\ud835\udcb1.U a) : Scheme.{u}) \u27f6 Z a)\n (hgZ : \u2200 a, IsPullback (gZ a) ((\ud835\udcb1.U a).\u03b9 \u226b fX\u2080) (qZ a) (Spec.map (CommRingCat.ofHom \u03c0)))\n\n {Xk : Scheme.{u}} (fXk : Xk \u27f6 Spec (CommRingCat.of (ResidueField T'))) [IsSeparated fXk]\n (LX : RelativeGroupLaw (ResidueField T') fXk)\n (j\u2080 : Xk \u27f6 X\u2080) [IsAffineHom j\u2080] (hj\u2080 : IsPullback j\u2080 fXk fX\u2080 (Spec.map (CommRingCat.ofHom \u03c1)))\n (UXe : Xk.Opens) (hUXe : IsAffineOpen UXe)\n (eX\u2081 : Spec (CommRingCat.of (ResidueField T')) \u27f6 (UXe : Scheme.{u})) (heX\u2081 : eX\u2081 \u226b UXe.\u03b9 = (LX.one (\ud835\udfd9 _)).1)\n\n (OX : \u2200 a, X\u2080.Opens \u2192 (Z a).Opens)\n (hOX : \u2200 (a : \ud835\udcb1.\u03b9) (W : X\u2080.Opens), gZ a \u207b\u00b9\u1d41 OX a W = (\ud835\udcb1.U a).\u03b9 \u207b\u00b9\u1d41 W)\n (hOXm : \u2200 a, Monotone (OX a))\n (hOXtop : \u2200 a, OX a (\ud835\udcb1.U a) = \u22a4)\n (hOXinf : \u2200 (a : \ud835\udcb1.\u03b9) (W W' : X\u2080.Opens), OX a W \u2293 OX a W' \u2264 OX a (W \u2293 W'))\n (hOXaff : \u2200 (a : \ud835\udcb1.\u03b9) (W : X\u2080.Opens), IsAffineOpen W \u2192 W \u2264 \ud835\udcb1.U a \u2192 IsAffineOpen (OX a W))\n\n (\u03c3X : \u2200 {n : \u2115} (s : \ud835\udcb1.Idx n),\n letI := algebraOfHom (qZ (s.1 0)) (OX (s.1 0) (\ud835\udcb1.inter s))\n ((ResidueField T') \u2297[T'] \u0393(Z (s.1 0), OX (s.1 0) (\ud835\udcb1.inter s))) \u2243+* \u0393(Xk, (\ud835\udcb1.comap j\u2080).inter s))\n (h\u03c3X\u2081 : \u2200 {n : \u2115} (s : \ud835\udcb1.Idx n),\n letI := algebraOfHom (qZ (s.1 0)) (OX (s.1 0) (\ud835\udcb1.inter s))\n (Scheme.OrderedAffineCover.isAffineOpen_inter fXk (\ud835\udcb1.comap j\u2080) s).isoSpec.hom \u226b\n Spec.map (CommRingCat.ofHom (\u03c3X s).toRingHom) \u226b\n Spec.map (CommRingCat.ofHom\n (Algebra.TensorProduct.includeRight : \u0393(Z (s.1 0), OX (s.1 0) (\ud835\udcb1.inter s)) \u2192\u2090[T']\n (ResidueField T') \u2297[T'] \u0393(Z (s.1 0), OX (s.1 0) (\ud835\udcb1.inter s))).toRingHom) \u226b\n (hOXaff (s.1 0) (\ud835\udcb1.inter s) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 s) (\ud835\udcb1.inter_le s 0)).fromSpec =\n Xk.homOfLE (\ud835\udcb1.comap_inter_le j\u2080 s) \u226b (j\u2080 \u2223_ \ud835\udcb1.inter s) \u226b X\u2080.homOfLE (\ud835\udcb1.inter_le s 0) \u226b gZ (s.1 0))\n (h\u03c3X\u2082 : \u2200 {n : \u2115} (s : \ud835\udcb1.Idx n) (x : ResidueField T'),\n letI := algebraOfHom (qZ (s.1 0)) (OX (s.1 0) (\ud835\udcb1.inter s))\n letI := algebraOfHom fXk ((\ud835\udcb1.comap j\u2080).inter s)\n \u03c3X s (x \u2297\u209c[T'] (1 : \u0393(Z (s.1 0), OX (s.1 0) (\ud835\udcb1.inter s)))) = algebraMap (ResidueField T') \u0393(Xk, (\ud835\udcb1.comap j\u2080).inter s) x)\n\n (\u03c6X : \u2200 (a b : \ud835\udcb1.\u03b9), a < b \u2192 ((\u2191(OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)) : Scheme.{u}) \u2245 \u2191(OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b))))\n (h\u03c6Xq : \u2200 (a b : \ud835\udcb1.\u03b9) (h : a < b),\n (\u03c6X a b h).hom \u226b (OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 \u226b qZ b = (OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 \u226b qZ a)\n (h\u03c6Xg : \u2200 (a b : \ud835\udcb1.\u03b9) (h : a < b),\n \u2203 (\u03b3 : (\u2191(\ud835\udcb1.U a \u2293 \ud835\udcb1.U b) : Scheme.{u}) \u27f6 \u2191(OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)))\n (\u03b3' : (\u2191(\ud835\udcb1.U a \u2293 \ud835\udcb1.U b) : Scheme.{u}) \u27f6 \u2191(OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b))),\n \u03b3 \u226b (OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 = X\u2080.homOfLE inf_le_left \u226b gZ a \u2227\n \u03b3' \u226b (OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 = X\u2080.homOfLE inf_le_right \u226b gZ b \u2227\n \u03b3 \u226b (\u03c6X a b h).hom = \u03b3')\n (h\u03c6XO : \u2200 (a b : \ud835\udcb1.\u03b9) (h : a < b) (W : X\u2080.Opens),\n (\u03c6X a b h).hom \u207b\u00b9\u1d41 ((OX b (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 \u207b\u00b9\u1d41 OX b W) = (OX a (\ud835\udcb1.U a \u2293 \ud835\udcb1.U b)).\u03b9 \u207b\u00b9\u1d41 OX a W)\n\n (\u03c1Xab : \u2200 r : \ud835\udcb1.Idx 2, ((\u2191(OX (r.1 0) (\ud835\udcb1.inter r)) : Scheme.{u}) \u2245 \u2191(OX (r.1 1) (\ud835\udcb1.inter r))))\n (\u03c1Xbc : \u2200 r : \ud835\udcb1.Idx 2, ((\u2191(OX (r.1 1) (\ud835\udcb1.inter r)) : Scheme.{u}) \u2245 \u2191(OX (r.1 2) (\ud835\udcb1.inter r))))\n (\u03c1Xac : \u2200 r : \ud835\udcb1.Idx 2, ((\u2191(OX (r.1 0) (\ud835\udcb1.inter r)) : Scheme.{u}) \u2245 \u2191(OX (r.1 2) (\ud835\udcb1.inter r))))\n (h\u03c1Xab : \u2200 r : \ud835\udcb1.Idx 2,\n (\u03c1Xab r).hom \u226b (Z (r.1 1)).homOfLE (hOXm (r.1 1) (le_inf (\ud835\udcb1.inter_le r 0) (\ud835\udcb1.inter_le r 1))) =\n (Z (r.1 0)).homOfLE (hOXm (r.1 0) (le_inf (\ud835\udcb1.inter_le r 0) (\ud835\udcb1.inter_le r 1))) \u226b\n (\u03c6X (r.1 0) (r.1 1) (r.2 (by decide))).hom)\n (h\u03c1Xbc : \u2200 r : \ud835\udcb1.Idx 2,\n (\u03c1Xbc r).hom \u226b (Z (r.1 2)).homOfLE (hOXm (r.1 2) (le_inf (\ud835\udcb1.inter_le r 1) (\ud835\udcb1.inter_le r 2))) =\n (Z (r.1 1)).homOfLE (hOXm (r.1 1) (le_inf (\ud835\udcb1.inter_le r 1) (\ud835\udcb1.inter_le r 2))) \u226b\n (\u03c6X (r.1 1) (r.1 2) (r.2 (by decide))).hom)\n (h\u03c1Xac : \u2200 r : \ud835\udcb1.Idx 2,\n (\u03c1Xac r).hom \u226b (Z (r.1 2)).homOfLE (hOXm (r.1 2) (le_inf (\ud835\udcb1.inter_le r 0) (\ud835\udcb1.inter_le r 2))) =\n (Z (r.1 0)).homOfLE (hOXm (r.1 0) (le_inf (\ud835\udcb1.inter_le r 0) (\ud835\udcb1.inter_le r 2))) \u226b\n (\u03c6X (r.1 0) (r.1 2) (r.2 (by decide))).hom)\n\n (\u03c9X : letI := algebraOfHom fXk UXe\n \u21a5(Algebra.PointDerivations (ResidueField T') \u0393(Xk, UXe)\n ((UXe.topIso.inv \u226b eX\u2081.appTop \u226b (Scheme.\u0393SpecIso (CommRingCat.of (ResidueField T'))).hom).hom)\n (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T'] (OModulePresheaf.unit fXk).cochain (\ud835\udcb1.comap j\u2080) 2)))\n (h\u03c9X : \u2200 r : \ud835\udcb1.Idx 2,\n letI := algebraOfHom (qZ (r.1 0)) (OX (r.1 0) (\ud835\udcb1.inter r))\n letI := algebraOfHom fXk UXe\n \u2203 cs : \u0393(Xk, UXe) \u2192 (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T']\n ((ResidueField T') \u2297[T'] \u0393(Z (r.1 0), OX (r.1 0) (\ud835\udcb1.inter r)))),\n IsTangentCoordsOfPairAtVia (RingHom.ker \u03c0) V \u03b9 \u0393(Z (r.1 0), OX (r.1 0) (\ud835\udcb1.inter r))\n ((hOXaff (r.1 0) (\ud835\udcb1.inter r) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 r) (\ud835\udcb1.inter_le r 0)).isoSpec.inv \u226b\n (\u03c1Xac r).hom \u226b (OX (r.1 2) (\ud835\udcb1.inter r)).\u03b9)\n ((hOXaff (r.1 0) (\ud835\udcb1.inter r) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 r) (\ud835\udcb1.inter_le r 0)).isoSpec.inv \u226b\n (\u03c1Xab r).hom \u226b (\u03c1Xbc r).hom \u226b (OX (r.1 2) (\ud835\udcb1.inter r)).\u03b9)\n fXk LX (j\u2080 \u207b\u00b9\u1d41 \ud835\udcb1.U (r.1 2)) ((j\u2080 \u2223_ \ud835\udcb1.U (r.1 2)) \u226b gZ (r.1 2)) UXe cs \u2227\n \u2200 (a : \u0393(Xk, UXe)) (\u03be : Module.Dual (ResidueField T') V), \u03c3X r (cs a \u03be) = \u03c9X.1 a \u03be r)\n (h\u03c9XZ : letI := algebraOfHom fXk UXe\n \u2200 (a : \u0393(Xk, UXe)) (\u03be : Module.Dual (ResidueField T') V),\n (OModulePresheaf.unit fXk).d (\ud835\udcb1.comap j\u2080) 2 (\u03c9X.1 a \u03be) = 0)\n\n (h\u2080 : X\u2080 \u27f6 A\u2080) (hh\u2080 : h\u2080 \u226b f\u2080 = fX\u2080)\n (lam : \ud835\udcb1.\u03b9 \u2192 \ud835\udcb0.\u03b9) (hlam\u2080 : \u2200 w, \ud835\udcb1.U w \u2264 h\u2080 \u207b\u00b9\u1d41 \ud835\udcb0.U (lam w))\n (hk : Xk \u27f6 Ak) (hhk : hk \u226b i\u2080 = j\u2080 \u226b h\u2080) (hhkf : hk \u226b fk = fXk)\n (hhom : \u2200 {S : Scheme.{u}} (t : S \u27f6 Spec (CommRingCat.of (ResidueField T'))) (P Q : SchemeHomOver t fXk),\n (LX.mul t P Q).1 \u226b hk =\n (Lk.mul t \u27e8P.1 \u226b hk, by rw [Category.assoc, hhkf, P.2]\u27e9 \u27e8Q.1 \u226b hk, by rw [Category.assoc, hhkf, Q.2]\u27e9).1)\n (hUX : UXe \u2264 hk \u207b\u00b9\u1d41 Ue)\n (hlamk : \u2200 w, (\ud835\udcb1.comap j\u2080).U w \u2264 hk \u207b\u00b9\u1d41 (\ud835\udcb0.comap i\u2080).U (lam w))\n (hZ : \u2200 w, Z w \u27f6 Y (lam w)) (hhZq : \u2200 w, hZ w \u226b q (lam w) = qZ w)\n (hhZg : \u2200 w, gZ w \u226b hZ w = X\u2080.homOfLE (hlam\u2080 w) \u226b (h\u2080 \u2223_ \ud835\udcb0.U (lam w)) \u226b g (lam w))\n\n (\u03a6 : \u2200 (a b : \ud835\udcb0.\u03b9) (W : A\u2080.Opens), W \u2264 \ud835\udcb0.U a \u2192 W \u2264 \ud835\udcb0.U b \u2192 ((\u2191(O a W) : Scheme.{u}) \u2245 \u2191(O b W)))\n (h\u03a6q : \u2200 (a b : \ud835\udcb0.\u03b9) (W : A\u2080.Opens) (ha : W \u2264 \ud835\udcb0.U a) (hb : W \u2264 \ud835\udcb0.U b),\n (\u03a6 a b W ha hb).hom \u226b (O b W).\u03b9 \u226b q b = (O a W).\u03b9 \u226b q a)\n (h\u03a6g : \u2200 (a b : \ud835\udcb0.\u03b9) (W : A\u2080.Opens) (ha : W \u2264 \ud835\udcb0.U a) (hb : W \u2264 \ud835\udcb0.U b)\n (\u03b3 : (\u2191W : Scheme.{u}) \u27f6 \u2191(O a W)) (\u03b3' : (\u2191W : Scheme.{u}) \u27f6 \u2191(O b W)),\n \u03b3 \u226b (O a W).\u03b9 = A\u2080.homOfLE ha \u226b g a \u2192 \u03b3' \u226b (O b W).\u03b9 = A\u2080.homOfLE hb \u226b g b \u2192 \u03b3 \u226b (\u03a6 a b W ha hb).hom = \u03b3')\n (h\u03a6res : \u2200 (a b : \ud835\udcb0.\u03b9) (W W' : A\u2080.Opens) (ha : W \u2264 \ud835\udcb0.U a) (hb : W \u2264 \ud835\udcb0.U b) (ha' : W' \u2264 \ud835\udcb0.U a) (hb' : W' \u2264 \ud835\udcb0.U b)\n (hWW : W' \u2264 W),\n (\u03a6 a b W' ha' hb').hom \u226b (Y b).homOfLE (hOm b hWW) = (Y a).homOfLE (hOm a hWW) \u226b (\u03a6 a b W ha hb).hom)\n (h\u03a6refl : \u2200 (a : \ud835\udcb0.\u03b9) (W : A\u2080.Opens) (ha ha' : W \u2264 \ud835\udcb0.U a), (\u03a6 a a W ha ha').hom = \ud835\udfd9 _)\n (h\u03a6symm : \u2200 (a b : \ud835\udcb0.\u03b9) (W : A\u2080.Opens) (ha : W \u2264 \ud835\udcb0.U a) (hb : W \u2264 \ud835\udcb0.U b),\n (\u03a6 a b W ha hb).hom \u226b (\u03a6 b a W hb ha).hom = \ud835\udfd9 _)\n (h\u03a6\u03c6 : \u2200 (a b : \ud835\udcb0.\u03b9) (h : a < b), (\u03a6 a b (\ud835\udcb0.U a \u2293 \ud835\udcb0.U b) inf_le_left inf_le_right).hom = (\u03c6 a b h).hom)\n\n (\u03a6X : \u2200 (x y : \ud835\udcb1.\u03b9), x < y \u2192 \u2200 (W : X\u2080.Opens), W \u2264 \ud835\udcb1.U x \u2293 \ud835\udcb1.U y \u2192 ((\u2191(OX x W) : Scheme.{u}) \u2245 \u2191(OX y W)))\n (h\u03a6X : \u2200 (x y : \ud835\udcb1.\u03b9) (h : x < y) (W : X\u2080.Opens) (hW : W \u2264 \ud835\udcb1.U x \u2293 \ud835\udcb1.U y),\n (\u03a6X x y h W hW).hom \u226b (Z y).homOfLE (hOXm y hW) = (Z x).homOfLE (hOXm x hW) \u226b (\u03c6X x y h).hom)\n\n (\u2113 : \u2200 (x : \ud835\udcb1.\u03b9) (WX : X\u2080.Opens) (WA : A\u2080.Opens), WX \u2264 h\u2080 \u207b\u00b9\u1d41 WA \u2192 ((\u2191(OX x WX) : Scheme.{u}) \u27f6 \u2191(O (lam x) WA)))\n (h\u2113 : \u2200 (x : \ud835\udcb1.\u03b9) (WX : X\u2080.Opens) (WA : A\u2080.Opens) (h : WX \u2264 h\u2080 \u207b\u00b9\u1d41 WA),\n \u2113 x WX WA h \u226b (O (lam x) WA).\u03b9 = (OX x WX).\u03b9 \u226b hZ x)\n :\n (\u2200 t : \ud835\udcb1.Idx 1,\n letI := algebraOfHom (qZ (t.1 0)) (OX (t.1 0) (\ud835\udcb1.inter t))\n (((hOXaff (t.1 0) (\ud835\udcb1.inter t) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 t) (\ud835\udcb1.inter_le t 0)).isoSpec.inv \u226b\n (\u03a6X (t.1 0) (t.1 1) (t.2 (by decide)) (\ud835\udcb1.inter t) (le_inf (\ud835\udcb1.inter_le t 0) (\ud835\udcb1.inter_le t 1))).hom \u226b\n \u2113 (t.1 1) (\ud835\udcb1.inter t) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) (by rw [Scheme.Hom.preimage_inf]; exact le_inf ((\ud835\udcb1.inter_le t 0).trans (hlam\u2080 (t.1 0))) ((\ud835\udcb1.inter_le t 1).trans (hlam\u2080 (t.1 1)))) \u226b (O (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1)))).\u03b9)) \u226b q (lam (t.1 1)) = Spec.map (CommRingCat.ofHom (algebraMap T' \u0393(Z (t.1 0), OX (t.1 0) (\ud835\udcb1.inter t)))) \u2227\n (((hOXaff (t.1 0) (\ud835\udcb1.inter t) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 t) (\ud835\udcb1.inter_le t 0)).isoSpec.inv \u226b\n \u2113 (t.1 0) (\ud835\udcb1.inter t) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) (by rw [Scheme.Hom.preimage_inf]; exact le_inf ((\ud835\udcb1.inter_le t 0).trans (hlam\u2080 (t.1 0))) ((\ud835\udcb1.inter_le t 1).trans (hlam\u2080 (t.1 1)))) \u226b\n (\u03a6 (lam (t.1 0)) (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) inf_le_left inf_le_right).hom \u226b (O (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1)))).\u03b9)) \u226b q (lam (t.1 1)) = Spec.map (CommRingCat.ofHom (algebraMap T' \u0393(Z (t.1 0), OX (t.1 0) (\ud835\udcb1.inter t))))) \u2227\n (\u2200 t : \ud835\udcb1.Idx 1,\n letI := algebraOfHom (qZ (t.1 0)) (OX (t.1 0) (\ud835\udcb1.inter t))\n Spec.map (CommRingCat.ofHom (Ideal.Quotient.mk ((RingHom.ker \u03c0).map (algebraMap T' \u0393(Z (t.1 0), OX (t.1 0) (\ud835\udcb1.inter t)))))) \u226b\n (((hOXaff (t.1 0) (\ud835\udcb1.inter t) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 t) (\ud835\udcb1.inter_le t 0)).isoSpec.inv \u226b\n (\u03a6X (t.1 0) (t.1 1) (t.2 (by decide)) (\ud835\udcb1.inter t) (le_inf (\ud835\udcb1.inter_le t 0) (\ud835\udcb1.inter_le t 1))).hom \u226b\n \u2113 (t.1 1) (\ud835\udcb1.inter t) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) (by rw [Scheme.Hom.preimage_inf]; exact le_inf ((\ud835\udcb1.inter_le t 0).trans (hlam\u2080 (t.1 0))) ((\ud835\udcb1.inter_le t 1).trans (hlam\u2080 (t.1 1)))) \u226b (O (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1)))).\u03b9)) =\n Spec.map (CommRingCat.ofHom (Ideal.Quotient.mk ((RingHom.ker \u03c0).map (algebraMap T' \u0393(Z (t.1 0), OX (t.1 0) (\ud835\udcb1.inter t)))))) \u226b\n (((hOXaff (t.1 0) (\ud835\udcb1.inter t) (Scheme.OrderedAffineCover.isAffineOpen_inter fX\u2080 \ud835\udcb1 t) (\ud835\udcb1.inter_le t 0)).isoSpec.inv \u226b\n \u2113 (t.1 0) (\ud835\udcb1.inter t) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) (by rw [Scheme.Hom.preimage_inf]; exact le_inf ((\ud835\udcb1.inter_le t 0).trans (hlam\u2080 (t.1 0))) ((\ud835\udcb1.inter_le t 1).trans (hlam\u2080 (t.1 1)))) \u226b\n (\u03a6 (lam (t.1 0)) (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1))) inf_le_left inf_le_right).hom \u226b (O (lam (t.1 1)) (\ud835\udcb0.U (lam (t.1 0)) \u2293 \ud835\udcb0.U (lam (t.1 1)))).\u03b9)))" + ], + [ + "AlgebraicGeometry.OModulePresheaf.unitPullback_prodCover_cup_sub_cup_unitPullback_mem", + "theorem AlgebraicGeometry.OModulePresheaf.unitPullback_prodCover_cup_sub_cup_unitPullback_mem\n {k : Type u} [Field k] {X Y : Scheme.{u}}\n (\u03c0X : X \u27f6 Spec (CommRingCat.of k)) (\u03c0Y : Y \u27f6 Spec (CommRingCat.of k)) [IsSeparated \u03c0X] [IsSeparated \u03c0Y]\n (\ud835\udd18 : X.OrderedAffineCover) (\ud835\udd19 : Y.OrderedAffineCover)\n (haff : \u2200 i j, IsAffineOpen ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).U i \u2293 (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)).U j))\n (hcov : \u2a06 ij : \ud835\udd18.\u03b9 \u00d7 \ud835\udd19.\u03b9,\n (\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).U ij.1 \u2293 (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)).U ij.2 = \u22a4)\n\n (\ud835\udcb2 : (pullback \u03c0X \u03c0Y).OrderedAffineCover) (lam\u2081 : \ud835\udcb2.\u03b9 \u2192 \ud835\udd18.\u03b9) (lam\u2082 : \ud835\udcb2.\u03b9 \u2192 \ud835\udd19.\u03b9)\n (h\u2081 : \u2200 w, \ud835\udcb2.U w \u2264 pullback.fst \u03c0X \u03c0Y \u207b\u00b9\u1d41 \ud835\udd18.U (lam\u2081 w))\n (h\u2082 : \u2200 w, \ud835\udcb2.U w \u2264 pullback.snd \u03c0X \u03c0Y \u207b\u00b9\u1d41 \ud835\udd19.U (lam\u2082 w))\n (h\u03bc : \u2200 w, \ud835\udcb2.U w \u2264 (\ud835\udfd9 (pullback \u03c0X \u03c0Y)) \u207b\u00b9\u1d41\n ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov).U\n (toLex (lam\u2081 w, lam\u2082 w)))\n (p q n : \u2115) (hn : p + q = n)\n (\u03b1 : \u21a5(LinearMap.ker ((OModulePresheaf.unit \u03c0X).d \ud835\udd18 p))) (\u03b2 : \u21a5(LinearMap.ker ((OModulePresheaf.unit \u03c0Y).d \ud835\udd19 q))) :\n (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (\ud835\udfd9 (pullback \u03c0X \u03c0Y)) \ud835\udcb2\n ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov)\n (fun w => toLex (lam\u2081 w, lam\u2082 w)) h\u03bc n\n ((OModulePresheaf.unit (pullback.fst \u03c0X \u03c0Y \u226b \u03c0X)).cup\n ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov) p q n hn\n (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (pullback.fst \u03c0X \u03c0Y)\n ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov) \ud835\udd18\n (fun ij => (ofLex ij).1) (fun ij => inf_le_left) p \u03b1.1)\n (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (pullback.snd \u03c0X \u03c0Y)\n ((\ud835\udd18.preimageFamily (pullback.fst \u03c0X \u03c0Y)).prodCover (\ud835\udd19.preimageFamily (pullback.snd \u03c0X \u03c0Y)) haff hcov) \ud835\udd19\n (fun ij => (ofLex ij).2) (fun ij => inf_le_right) q \u03b2.1)) -\n (OModulePresheaf.unit (pullback.fst \u03c0X \u03c0Y \u226b \u03c0X)).cup \ud835\udcb2 p q n hn\n (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (pullback.fst \u03c0X \u03c0Y) \ud835\udcb2 \ud835\udd18 lam\u2081 h\u2081 p \u03b1.1)\n (OModulePresheaf.unitPullback (\u03c0X := pullback.fst \u03c0X \u03c0Y \u226b \u03c0X) (pullback.snd \u03c0X \u03c0Y) \ud835\udcb2 \ud835\udd19 lam\u2082 h\u2082 q \u03b2.1))\n \u2208 (show Submodule k ((OModulePresheaf.unit (pullback.fst \u03c0X \u03c0Y \u226b \u03c0X)).cochain \ud835\udcb2 n) from\n match n with\n | 0 => \u22a5\n | m + 1 => LinearMap.range ((OModulePresheaf.unit (pullback.fst \u03c0X \u03c0Y \u226b \u03c0X)).d \ud835\udcb2 m))" + ], + [ + "AlgebraicGeometry.RelPicard.IsDeformationClassMap.exists_crossSections", + "theorem IsDeformationClassMap.exists_crossSections\n {R : Type u} [CommRing R] {C : Scheme.{u}}\n (c : C \u27f6 Spec (.of R)) (\u03b5 : SchemeHomOver (\ud835\udfd9 (Spec (.of R))) c)\n (A : Type u) [CommRing A] [Algebra R A]\n [IsSeparated (pullback.snd c (Scheme.TwoAffineOpenCover.specMap R A))]\n (\ud835\udcb2 \ud835\udcb2' : C.TwoAffineOpenCover)\n {\u03b4 : RigKerDualNumber c \u03b5 A \u2192 H1StructureSheaf c A \ud835\udcb2}\n {\u03b4' : RigKerDualNumber c \u03b5 A \u2192 H1StructureSheaf c A \ud835\udcb2'}\n (h\u03b4 : IsDeformationClassMap c \u03b5 A \ud835\udcb2 \u03b4) (h\u03b4' : IsDeformationClassMap c \u03b5 A \ud835\udcb2' \u03b4')\n (x : RigKerDualNumber c \u03b5 A)\n (s : ((\ud835\udcb2.pullback c A).cover (pullback.snd c (Scheme.TwoAffineOpenCover.specMap R A))).A01)\n (s' : ((\ud835\udcb2'.pullback c A).cover (pullback.snd c (Scheme.TwoAffineOpenCover.specMap R A))).A01)\n (hs : \u03b4 x = Submodule.Quotient.mk s) (hs' : \u03b4' x = Submodule.Quotient.mk s') :\n let X' := Limits.pullback c (Scheme.TwoAffineOpenCover.specMap R A)\n let W0 := (\ud835\udcb2.pullback c A).U0; let W1 := (\ud835\udcb2.pullback c A).U1\n let V0 := (\ud835\udcb2'.pullback c A).U0; let V1 := (\ud835\udcb2'.pullback c A).U1\n \u2203 (g00 : \u0393(X', W0 \u2293 V0)) (g01 : \u0393(X', W0 \u2293 V1)) (g10 : \u0393(X', W1 \u2293 V0)) (g11 : \u0393(X', W1 \u2293 V1)),\n (X'.presheaf.map (homOfLE (inf_le_inf_right V0 inf_le_left : (W0 \u2293 W1) \u2293 V0 \u2264 W0 \u2293 V0)).op).hom g00\n = (X'.presheaf.map (homOfLE (inf_le_inf_right V0 inf_le_right : (W0 \u2293 W1) \u2293 V0 \u2264 W1 \u2293 V0)).op).hom g10\n + (X'.presheaf.map (homOfLE (inf_le_left : (W0 \u2293 W1) \u2293 V0 \u2264 W0 \u2293 W1)).op).hom s \u2227\n (X'.presheaf.map (homOfLE (inf_le_inf_right V1 inf_le_left : (W0 \u2293 W1) \u2293 V1 \u2264 W0 \u2293 V1)).op).hom g01\n = (X'.presheaf.map (homOfLE (inf_le_inf_right V1 inf_le_right : (W0 \u2293 W1) \u2293 V1 \u2264 W1 \u2293 V1)).op).hom g11\n + (X'.presheaf.map (homOfLE (inf_le_left : (W0 \u2293 W1) \u2293 V1 \u2264 W0 \u2293 W1)).op).hom s \u2227\n (X'.presheaf.map (homOfLE (inf_le_inf_left W0 inf_le_right : W0 \u2293 (V0 \u2293 V1) \u2264 W0 \u2293 V1)).op).hom g01\n = (X'.presheaf.map (homOfLE (inf_le_inf_left W0 inf_le_left : W0 \u2293 (V0 \u2293 V1) \u2264 W0 \u2293 V0)).op).hom g00\n + (X'.presheaf.map (homOfLE (inf_le_right : W0 \u2293 (V0 \u2293 V1) \u2264 V0 \u2293 V1)).op).hom s' \u2227\n (X'.presheaf.map (homOfLE (inf_le_inf_left W1 inf_le_right : W1 \u2293 (V0 \u2293 V1) \u2264 W1 \u2293 V1)).op).hom g11\n = (X'.presheaf.map (homOfLE (inf_le_inf_left W1 inf_le_left : W1 \u2293 (V0 \u2293 V1) \u2264 W1 \u2293 V0)).op).hom g10\n + (X'.presheaf.map (homOfLE (inf_le_right : W1 \u2293 (V0 \u2293 V1) \u2264 V0 \u2293 V1)).op).hom s'" + ], + [ + "AlgebraicGeometry.SmallExtension.exists_overlap_iso_isTangentCoordsOfPairAtVia_of_pointDerivations", + "theorem AlgebraicGeometry.SmallExtension.exists_overlap_iso_isTangentCoordsOfPairAtVia_of_pointDerivations\n (T' T : Type u) [CommRing T'] [IsLocalRing T'] [IsArtinianRing T']\n [CommRing T] (\u03c0 : T' \u2192+* T) (h\u03c0 : Function.Surjective \u03c0) (hker : IsNilpotent (RingHom.ker \u03c0))\n (hsmall : RingHom.ker \u03c0 * maximalIdeal T' = \u22a5)\n (hI : RingHom.ker \u03c0 \u2264 maximalIdeal T')\n (V : Type u) [AddCommGroup V] [Module (ResidueField T') V] [Module.Finite (ResidueField T') V]\n [Module T' V] [IsScalarTower T' (ResidueField T') V]\n [Module (ResidueField T')\u1d50\u1d52\u1d56 V] [IsCentralScalar (ResidueField T') V]\n (\u03b9 : V \u2192\u2097[T'] T') (h\u03b9 : Function.Injective \u03b9)\n (h\u03b9I : LinearMap.range \u03b9 = Submodule.restrictScalars T' (RingHom.ker \u03c0))\n {A\u2080 : Scheme.{u}} (f\u2080 : A\u2080 \u27f6 Spec (CommRingCat.of T))\n (Ua Ub : A\u2080.Opens)\n {Ya Yb : Scheme.{u}} (qa : Ya \u27f6 Spec (CommRingCat.of T')) (qb : Yb \u27f6 Spec (CommRingCat.of T')) (hqa : Smooth qa)\n (ga : (\u2191Ua : Scheme.{u}) \u27f6 Ya) (gb : (\u2191Ub : Scheme.{u}) \u27f6 Yb)\n (hgb : IsPullback gb (Ub.\u03b9 \u226b f\u2080) qb (Spec.map (CommRingCat.ofHom \u03c0)))\n (Oa : A\u2080.Opens \u2192 Ya.Opens) (Ob : A\u2080.Opens \u2192 Yb.Opens)\n (hOb : \u2200 W : A\u2080.Opens, gb \u207b\u00b9\u1d41 Ob W = Ub.\u03b9 \u207b\u00b9\u1d41 W)\n (hOaffa : IsAffineOpen (Oa (Ua \u2293 Ub))) (hOaffb : IsAffineOpen (Ob (Ua \u2293 Ub)))\n\n {Ak : Scheme.{u}} (fk : Ak \u27f6 Spec (CommRingCat.of (ResidueField T'))) (Lk : RelativeGroupLaw (ResidueField T') fk)\n (W : Ak.Opens) (aW : (W : Scheme.{u}) \u27f6 Yb)\n (haW : IsPullback aW (W.\u03b9 \u226b fk) qb (Spec.map (CommRingCat.ofHom (residue T'))))\n (Ue : Ak.Opens) (hUe : IsAffineOpen Ue)\n (e\u2081 : Spec (CommRingCat.of (ResidueField T')) \u27f6 (Ue : Scheme.{u})) (he\u2081 : e\u2081 \u226b Ue.\u03b9 = (Lk.one (\ud835\udfd9 _)).1)\n\n (\u03c6 : (\u2191(Oa (Ua \u2293 Ub)) : Scheme.{u}) \u2245 \u2191(Ob (Ua \u2293 Ub)))\n (h\u03c6q : \u03c6.hom \u226b (Ob (Ua \u2293 Ub)).\u03b9 \u226b qb = (Oa (Ua \u2293 Ub)).\u03b9 \u226b qa)\n (h\u03c6g : \u2203 (\u03b3 : (\u2191(Ua \u2293 Ub) : Scheme.{u}) \u27f6 \u2191(Oa (Ua \u2293 Ub))) (\u03b3' : (\u2191(Ua \u2293 Ub) : Scheme.{u}) \u27f6 \u2191(Ob (Ua \u2293 Ub))),\n \u03b3 \u226b (Oa (Ua \u2293 Ub)).\u03b9 = A\u2080.homOfLE inf_le_left \u226b ga \u2227\n \u03b3' \u226b (Ob (Ua \u2293 Ub)).\u03b9 = A\u2080.homOfLE inf_le_right \u226b gb \u2227\n \u03b3 \u226b \u03c6.hom = \u03b3')\n (h\u03c6O : \u2200 W' : A\u2080.Opens, \u03c6.hom \u207b\u00b9\u1d41 ((Ob (Ua \u2293 Ub)).\u03b9 \u207b\u00b9\u1d41 Ob W') = (Oa (Ua \u2293 Ub)).\u03b9 \u207b\u00b9\u1d41 Oa W')\n\n (\u03b4 : letI := algebraOfHom qa (Oa (Ua \u2293 Ub)); letI := algebraOfHom fk Ue\n \u21a5(Algebra.PointDerivations (ResidueField T') \u0393(Ak, Ue)\n ((Ue.topIso.inv \u226b e\u2081.appTop \u226b (Scheme.\u0393SpecIso (CommRingCat.of (ResidueField T'))).hom).hom)\n (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T'] (ResidueField T' \u2297[T'] \u0393(Ya, Oa (Ua \u2293 Ub)))))) :\n letI := algebraOfHom qa (Oa (Ua \u2293 Ub)); letI := algebraOfHom fk Ue\n \u2203 \u03c6' : (\u2191(Oa (Ua \u2293 Ub)) : Scheme.{u}) \u2245 \u2191(Ob (Ua \u2293 Ub)),\n \u03c6'.hom \u226b (Ob (Ua \u2293 Ub)).\u03b9 \u226b qb = (Oa (Ua \u2293 Ub)).\u03b9 \u226b qa \u2227\n (\u2203 (\u03b3 : (\u2191(Ua \u2293 Ub) : Scheme.{u}) \u27f6 \u2191(Oa (Ua \u2293 Ub))) (\u03b3' : (\u2191(Ua \u2293 Ub) : Scheme.{u}) \u27f6 \u2191(Ob (Ua \u2293 Ub))),\n \u03b3 \u226b (Oa (Ua \u2293 Ub)).\u03b9 = A\u2080.homOfLE inf_le_left \u226b ga \u2227\n \u03b3' \u226b (Ob (Ua \u2293 Ub)).\u03b9 = A\u2080.homOfLE inf_le_right \u226b gb \u2227\n \u03b3 \u226b \u03c6'.hom = \u03b3') \u2227\n (\u2200 W' : A\u2080.Opens, \u03c6'.hom \u207b\u00b9\u1d41 ((Ob (Ua \u2293 Ub)).\u03b9 \u207b\u00b9\u1d41 Ob W') = (Oa (Ua \u2293 Ub)).\u03b9 \u207b\u00b9\u1d41 Oa W') \u2227\n IsTangentCoordsOfPairAtVia (RingHom.ker \u03c0) V \u03b9 \u0393(Ya, Oa (Ua \u2293 Ub))\n (hOaffa.isoSpec.inv \u226b \u03c6.hom \u226b (Ob (Ua \u2293 Ub)).\u03b9)\n (hOaffa.isoSpec.inv \u226b \u03c6'.hom \u226b (Ob (Ua \u2293 Ub)).\u03b9)\n fk Lk W aW Ue\n (fun x => (\u03b4 : \u0393(Ak, Ue) \u2192\u2097[ResidueField T']\n (Module.Dual (ResidueField T') V \u2192\u2097[ResidueField T'] (ResidueField T' \u2297[T'] \u0393(Ya, Oa (Ua \u2293 Ub))))) x)" + ], + [ + "M4aHerbrand.exists_unit_forall_exists_localFundamentalClass_eq_smul_res_and_pow_dvd_of_forall_map_inclusion_eq", + "theorem M4aHerbrand.exists_unit_forall_exists_localFundamentalClass_eq_smul_res_and_pow_dvd_of_forall_map_inclusion_eq\n (p : \u2115) [Fact p.Prime] (hp2 : p \u2260 2)\n (E F : Type) [Field E] [NumberField E] [Field F] [NumberField F] [Algebra E F] [IsGalois E F]\n (D : IdeleGaloisDescent (\ud835\udcde F) E F)\n [MulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)]\n (hact : \u2200 (g : F \u2243\u2090[E] F) (c : IdeleClassGroup (\ud835\udcde F) F), g \u2022 c = D.classAct g c)\n (\u03b9 : \u2200 w : HeightOneSpectrum (\ud835\udcde F), (w.adicCompletion F)\u02e3 \u2192* (AdeleRing (\ud835\udcde F) F)\u02e3)\n (h\u03b9 : \u2200 (w : HeightOneSpectrum (\ud835\udcde F)) (x : (w.adicCompletion F)\u02e3),\n finPart w (\u03b9 w x) = x \u2227 (\u2200 w' : HeightOneSpectrum (\ud835\udcde F), w' \u2260 w \u2192 finPart w' (\u03b9 w x) = 1) \u2227 infPart (\u03b9 w x) = 1)\n (lam : \u2200 w : HeightOneSpectrum (\ud835\udcde F),\n Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (w.adicCompletion F)\u02e3 \u27f6\n Rep.res (NumberField.PlaceDecomp.decomp E F w).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)))\n (hlam : \u2200 (w : HeightOneSpectrum (\ud835\udcde F)) (x : (w.adicCompletion F)\u02e3),\n (lam w).hom (Additive.ofMul x) = Additive.ofMul (QuotientGroup.mk (\u03b9 w x) : IdeleClassGroup (\ud835\udcde F) F))\n (u\u2080 : groupCohomology (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)) 2)\n (h2 : \u2200 (S : Subgroup (F \u2243\u2090[E] F)) [Fintype S], Nat.card\n (groupCohomology (Rep.res S.subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))) 2) = Fintype.card S)\n (h3 : \u2200 S : Subgroup (F \u2243\u2090[E] F), Submodule.span \u2124\n {(groupCohomology.map S.subtype (\ud835\udfd9 (Rep.res S.subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)))) 2).hom u\u2080} = \u22a4)\n (P : Subgroup (F \u2243\u2090[E] F)) (hP : IsPGroup p P) (hPidx : \u00ac p \u2223 P.index)\n (uP : groupCohomology (Rep.res P.subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))) 2) (hspan : Submodule.span \u2124 {uP} = \u22a4)\n (hloc :\n \u2200 (w : HeightOneSpectrum (\ud835\udcde F))\n (q : \u2115) [Fact q.Prime] (L' : IntermediateField \u211a_[q] (PadicAlgCl q)) [FiniteDimensional \u211a_[q] L']\n [MulSemiringAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) L'] [MulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3]\n (\u03a6 : w.adicCompletion F \u2243+* L')\n (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (x : \u211a_[q]), g \u2022 algebraMap \u211a_[q] L' x = algebraMap \u211a_[q] L' x)\n (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (v : (\u21a5L')\u02e3), ((g \u2022 v : (\u21a5L')\u02e3) : L') = g \u2022 (v : L'))\n (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (x : w.adicCompletion F), \u03a6 (g \u2022 x) = g \u2022 \u03a6 x)\n (K\u2080 : IntermediateField \u211a_[q] (PadicAlgCl q)) [FiniteDimensional \u211a_[q] K\u2080]\n (_ : ExtCitation.LocalLevel.IsBase q L' (\u21a5(NumberField.PlaceDecomp.decomp E F w)) K\u2080)\n (\u03b8 : Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3 \u27f6\n Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (w.adicCompletion F)\u02e3)\n (_ : \u2200 v : (\u21a5L')\u02e3, ((Additive.toMul (\u03b8.hom (Additive.ofMul v)) : (w.adicCompletion F)\u02e3) : w.adicCompletion F) = \u03a6.symm (v : L'))\n (u' : groupCohomology.H2 (Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3))\n (_ : ExtCitation.LocalLevel.IsLocalFundamentalClass q L' (\u21a5(NumberField.PlaceDecomp.decomp E F w)) K\u2080 u'),\n ((groupCohomology.map (Subgroup.inclusion (inf_le_left : (NumberField.PlaceDecomp.decomp E F w) \u2293 P \u2264 (NumberField.PlaceDecomp.decomp E F w)))\n (\ud835\udfd9 (Rep.res (Subgroup.inclusion (inf_le_left : (NumberField.PlaceDecomp.decomp E F w) \u2293 P \u2264 (NumberField.PlaceDecomp.decomp E F w))) (Rep.res (NumberField.PlaceDecomp.decomp E F w).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))))) 2).hom\n ((groupCohomology.map (MonoidHom.id \u21a5(NumberField.PlaceDecomp.decomp E F w)) (lam w) 2).hom ((groupCohomology.map (MonoidHom.id \u21a5(NumberField.PlaceDecomp.decomp E F w)) \u03b8 2).hom u')) : groupCohomology (Rep.res ((NumberField.PlaceDecomp.decomp E F w) \u2293 P).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))) 2) =\n ((groupCohomology.map (Subgroup.inclusion (inf_le_right : (NumberField.PlaceDecomp.decomp E F w) \u2293 P \u2264 P))\n (\ud835\udfd9 (Rep.res (Subgroup.inclusion (inf_le_right : (NumberField.PlaceDecomp.decomp E F w) \u2293 P \u2264 P)) (Rep.res P.subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))))) 2).hom\n uP : groupCohomology (Rep.res ((NumberField.PlaceDecomp.decomp E F w) \u2293 P).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F))) 2)) :\n \u2203 a : \u2124, \u00ac (p : \u2124) \u2223 a \u2227\n \u2200 (w : HeightOneSpectrum (\ud835\udcde F))\n (q : \u2115) [Fact q.Prime] (L' : IntermediateField \u211a_[q] (PadicAlgCl q)) [FiniteDimensional \u211a_[q] L']\n [MulSemiringAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) L'] [MulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3]\n (\u03a6 : w.adicCompletion F \u2243+* L')\n (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (x : \u211a_[q]), g \u2022 algebraMap \u211a_[q] L' x = algebraMap \u211a_[q] L' x)\n (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (v : (\u21a5L')\u02e3), ((g \u2022 v : (\u21a5L')\u02e3) : L') = g \u2022 (v : L'))\n (_ : \u2200 (g : \u21a5(NumberField.PlaceDecomp.decomp E F w)) (x : w.adicCompletion F), \u03a6 (g \u2022 x) = g \u2022 \u03a6 x)\n (K\u2080 : IntermediateField \u211a_[q] (PadicAlgCl q)) [FiniteDimensional \u211a_[q] K\u2080]\n (_ : ExtCitation.LocalLevel.IsBase q L' (\u21a5(NumberField.PlaceDecomp.decomp E F w)) K\u2080)\n (\u03b8 : Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3 \u27f6\n Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (w.adicCompletion F)\u02e3)\n (_ : \u2200 v : (\u21a5L')\u02e3, ((Additive.toMul (\u03b8.hom (Additive.ofMul v)) : (w.adicCompletion F)\u02e3) : w.adicCompletion F) = \u03a6.symm (v : L'))\n (u' : groupCohomology.H2 (Rep.ofMulDistribMulAction (\u21a5(NumberField.PlaceDecomp.decomp E F w)) (\u21a5L')\u02e3))\n (_ : ExtCitation.LocalLevel.IsLocalFundamentalClass q L' (\u21a5(NumberField.PlaceDecomp.decomp E F w)) K\u2080 u'),\n \u2203 c : \u2124, ((groupCohomology.map (MonoidHom.id \u21a5(NumberField.PlaceDecomp.decomp E F w)) (lam w) 2).hom ((groupCohomology.map (MonoidHom.id \u21a5(NumberField.PlaceDecomp.decomp E F w)) \u03b8 2).hom u')) = c \u2022 ((groupCohomology.map (NumberField.PlaceDecomp.decomp E F w).subtype (\ud835\udfd9 (Rep.res (NumberField.PlaceDecomp.decomp E F w).subtype (Rep.ofMulDistribMulAction (F \u2243\u2090[E] F) (IdeleClassGroup (\ud835\udcde F) F)))) 2).hom u\u2080) \u2227\n \u2200 n : \u2115, p ^ n \u2223 Nat.card \u21a5(NumberField.PlaceDecomp.decomp E F w) \u2192 (p : \u2124) ^ n \u2223 c * a - 1" + ], + [ + "AlgebraicGeometry.OModulePresheaf.exists_forall_eq_thread_and_eq_zero_of_forall_eq_zero_of_isAdicComplete_of_isProper", + "theorem AlgebraicGeometry.OModulePresheaf.exists_forall_eq_thread_and_eq_zero_of_forall_eq_zero_of_isAdicComplete_of_isProper\n {A : Type u} [CommRing A] [IsNoetherianRing A] (I : Ideal A)\n {P : Scheme.{u}} (q : P \u27f6 Spec (CommRingCat.of A)) [IsProper q]\n {Z : Scheme.{u}} (i : Z \u27f6 P) [IsClosedImmersion i]\n {V' : Scheme.{u}} (g : V' \u27f6 Z) [IsProper g] (K' : V'.OrderedAffineCover)\n (U : Z.Opens) (hU : IsIso (CategoryTheory.Limits.pullback.snd g U.\u03b9))\n (T' : Closeds P) (hT' : \u2200 z : Z, z \u2209 U \u2192 i.base z \u2208 T')\n\n (F : \u2115 \u2192 OModulePresheaf q) (hFc : \u2200 k, (F k).IsCoherent) (hFq : \u2200 k, (F k).IsQuasicoherent)\n (\u03c6 : \u2200 k, OModulePresheaf.AffHom (F (k + 1)) (F k))\n (h\u03c6s : \u2200 (k : \u2115) (U : P.affineOpens), Function.Surjective ((\u03c6 k).app U))\n (h\u03c6k : \u2200 (k : \u2115) (U : P.affineOpens),\n LinearMap.ker ((\u03c6 k).app U) = I ^ (k + 1) \u2022 (\u22a4 : Submodule A ((F (k + 1)).obj U.1)))\n (hFZ : \u2200 k, OModulePresheaf.IdealAnnihilates q i.ker (F k))\n\n (F' : \u2115 \u2192 OModulePresheaf ((g \u226b i) \u226b q)) (\u03c6' : \u2200 k, OModulePresheaf.AffHom (F' (k + 1)) (F' k))\n (\u03b7 : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V : V'.affineOpens), V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1 \u2192\n ((F k).obj U\u2080.1 \u2192\u2097[A] (F' k).obj V.1))\n (h\u03b7s : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1) (a : \u0393(P, U\u2080.1))\n (x : (F k).obj U\u2080.1), \u03b7 k U\u2080 V h (a \u2022 x) = ((g \u226b i).appLE U\u2080.1 V.1 h).hom a \u2022 \u03b7 k U\u2080 V h x)\n (h\u03b7V : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V\u2081 V\u2082 : V'.affineOpens) (h\u2081 : V\u2081.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1)\n (h\u2082 : V\u2082.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1) (hV : V\u2081.1 \u2264 V\u2082.1) (x : (F k).obj U\u2080.1),\n (F' k).res hV (\u03b7 k U\u2080 V\u2082 h\u2082 x) = \u03b7 k U\u2080 V\u2081 h\u2081 x)\n (h\u03b7U : \u2200 (k : \u2115) (U\u2081 U\u2082 : P.affineOpens) (V : V'.affineOpens) (h\u2081 : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2081.1)\n (h\u2082 : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2082.1) (hU\u2081\u2082 : U\u2081.1 \u2264 U\u2082.1) (x : (F k).obj U\u2082.1),\n \u03b7 k U\u2082 V h\u2082 x = \u03b7 k U\u2081 V h\u2081 ((F k).res hU\u2081\u2082 x))\n (h\u03b7\u03c6 : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1)\n (x : (F (k + 1)).obj U\u2080.1), (\u03c6' k).app V (\u03b7 (k + 1) U\u2080 V h x) = \u03b7 k U\u2080 V h ((\u03c6 k).app U\u2080 x))\n (h\u03b2 : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 U\u2080.1),\n letI := ((g \u226b i).appLE U\u2080.1 V.1 h).hom.toAlgebra\n \u2203 \u03b2 : \u0393(V', V.1) \u2297[\u0393(P, U\u2080.1)] (F k).obj U\u2080.1 \u2243\u2097[\u0393(V', V.1)] (F' k).obj V.1,\n \u2200 x : (F k).obj U\u2080.1, \u03b2 (1 \u2297\u209c x) = \u03b7 k U\u2080 V h x)\n\n (v : \u2200 k, OModulePresheaf.AffHom (F k) (OModulePresheaf.cechPushforward (g \u226b i) q K' (F' k)))\n (hv\u03b7 : \u2200 (k : \u2115) (U\u2080 : P.affineOpens) (x : (F k).obj U\u2080.1) (j : K'.\u03b9),\n ((v k).app U\u2080 x).1 j\n = \u03b7 k U\u2080 (OModulePresheaf.AffHom.affineChart (g \u226b i) q K' U\u2080 j)\n (OModulePresheaf.cechPushforward.chart_le_preimage (g \u226b i) K' U\u2080.1 j) x)\n\n (W : P.affineOpens)\n (R : Type u) [CommRing R] [Algebra \u0393(P, W.1) R]\n (L : Type u) [AddCommGroup L] [Module \u0393(P, W.1) L] [Module R L] [IsScalarTower \u0393(P, W.1) R L]\n [Module.Finite R L]\n (pr : \u2200 n : \u2115, L \u2192\u2097[\u0393(P, W.1)] (F n).obj W.1)\n (hprc : \u2200 (n : \u2115) (x : L), (\u03c6 n).app W (pr (n + 1) x) = pr n x)\n (hpri : \u2200 x : L, (\u2200 n : \u2115, pr n x = 0) \u2192 x = 0)\n (hprs : \u2200 n : \u2115, Function.Surjective (pr n))\n (hprk : \u2200 n : \u2115, LinearMap.ker (pr n) = (I.map ((Scheme.\u0393SpecIso (CommRingCat.of A)).inv \u226b q.appLE \u22a4 W.1 le_top).hom) ^ (n + 1) \u2022 (\u22a4 : Submodule \u0393(P, W.1) L))\n [IsNoetherianRing R] (hRc : IsAdicComplete (I.map ((algebraMap \u0393(P, W.1) R).comp ((Scheme.\u0393SpecIso (CommRingCat.of A)).inv \u226b q.appLE \u22a4 W.1 le_top).hom)) R)\n\n {Y : Scheme.{u}} (sY : Y \u27f6 Spec (CommRingCat.of R)) [IsProper sY] (t : Y \u27f6 V')\n (hY : IsPullback t sY (g \u226b i) (Spec.map (CommRingCat.ofHom (algebraMap \u0393(P, W.1) R)) \u226b W.2.fromSpec))\n (hta : \u2200 V : V'.affineOpens, V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1 \u2192 IsAffineOpen (t \u207b\u00b9\u1d41 V.1))\n\n (G : OModulePresheaf sY) (hGc : G.IsCoherent) (hGq : G.IsQuasicoherent)\n (\u03b5 : \u2200 U : Y.Opens, L \u2192\u2097[R] G.obj U)\n (h\u03b5r : \u2200 (U U' : Y.Opens) (h : U \u2264 U') (x : L), G.res h (\u03b5 U' x) = \u03b5 U x)\n (h\u03b5\u03b2 : \u2200 U : Y.affineOpens,\n letI := Scheme.TwoAffineOpenCover.algebraOfHom sY U.1\n \u2203 \u03b2 : \u0393(Y, U.1) \u2297[R] L \u2243\u2097[\u0393(Y, U.1)] G.obj U.1, \u2200 x : L, \u03b2 (1 \u2297\u209c x) = \u03b5 U.1 x)\n\n (\u03b8 : \u2200 (n : \u2115) (V : V'.affineOpens), V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1 \u2192 (G.obj (t \u207b\u00b9\u1d41 V.1) \u2192+ (F' n).obj V.1))\n (h\u03b8s : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (c : \u0393(V', V.1))\n (y : G.obj (t \u207b\u00b9\u1d41 V.1)), \u03b8 n V h ((t.app V.1).hom c \u2022 y) = c \u2022 \u03b8 n V h y)\n (h\u03b8r : \u2200 (n : \u2115) (V\u2081 V\u2082 : V'.affineOpens) (h\u2081 : V\u2081.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (h\u2082 : V\u2082.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1)\n (hV : V\u2081.1 \u2264 V\u2082.1) (y : G.obj (t \u207b\u00b9\u1d41 V\u2082.1)),\n (F' n).res hV (\u03b8 n V\u2082 h\u2082 y) = \u03b8 n V\u2081 h\u2081 (G.res ((Opens.map t.base).monotone hV) y))\n (h\u03b8\u03c6 : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (y : G.obj (t \u207b\u00b9\u1d41 V.1)),\n (\u03c6' n).app V (\u03b8 (n + 1) V h y) = \u03b8 n V h y)\n (h\u03b8\u03b5 : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (x : L),\n \u03b8 n V h (\u03b5 (t \u207b\u00b9\u1d41 V.1) x) = \u03b7 n W V h (pr n x))\n (h\u03b8o : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1), Function.Surjective (\u03b8 n V h))\n (h\u03b8k : \u2200 (n : \u2115) (V : V'.affineOpens) (h : V.1 \u2264 (g \u226b i) \u207b\u00b9\u1d41 W.1) (y : G.obj (t \u207b\u00b9\u1d41 V.1)),\n \u03b8 n V h y = 0 \u2194 y \u2208 (I.map ((algebraMap \u0393(P, W.1) R).comp ((Scheme.\u0393SpecIso (CommRingCat.of A)).inv \u226b q.appLE \u22a4 W.1 le_top).hom)) ^ (n + 1) \u2022 (\u22a4 : Submodule R (G.obj (t \u207b\u00b9\u1d41 V.1)))) :\n (\u2200 (\u2113 : \u2200 n, (OModulePresheaf.cechPushforward (g \u226b i) q K' (F' n)).obj W.1),\n (\u2200 n, ((\u03c6' n).cechPushforward (g \u226b i) q K').app W (\u2113 (n + 1)) = \u2113 n) \u2192\n \u2203 c : \u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j)),\n (\u2200 j j' : K'.\u03b9,\n G.res ((Opens.map t.base).monotone (inf_le_left : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j)\n = G.res ((Opens.map t.base).monotone (inf_le_right : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j')) \u2227\n \u2200 (n : \u2115) (j : K'.\u03b9),\n \u03b8 n (OModulePresheaf.AffHom.affineChart (g \u226b i) q K' W j)\n (OModulePresheaf.cechPushforward.chart_le_preimage (g \u226b i) K' W.1 j) (c j) = (\u2113 n).1 j) \u2227\n (\u2200 c : \u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j)),\n (\u2200 j j' : K'.\u03b9,\n G.res ((Opens.map t.base).monotone (inf_le_left : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j)\n = G.res ((Opens.map t.base).monotone (inf_le_right : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j')) \u2192\n (\u2200 (n : \u2115) (j : K'.\u03b9),\n \u03b8 n (OModulePresheaf.AffHom.affineChart (g \u226b i) q K' W j)\n (OModulePresheaf.cechPushforward.chart_le_preimage (g \u226b i) K' W.1 j) (c j) = 0) \u2192\n c = 0) \u2227\n (\u2203 s : Finset (\u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j))),\n (\u2200 c \u2208 s, (\u2200 j j' : K'.\u03b9,\n G.res ((Opens.map t.base).monotone (inf_le_left : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j)\n = G.res ((Opens.map t.base).monotone (inf_le_right : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j'))) \u2227\n \u2200 c : \u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j)),\n (\u2200 j j' : K'.\u03b9,\n G.res ((Opens.map t.base).monotone (inf_le_left : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j)\n = G.res ((Opens.map t.base).monotone (inf_le_right : (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j) \u2293 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j') \u2264 _)) (c j')) \u2192 c \u2208 Submodule.span R (s : Set (\u2200 j : K'.\u03b9, G.obj (t \u207b\u00b9\u1d41 (OModulePresheaf.cechPushforward.chart (g \u226b i) K' W.1 j)))))" + ] + ], + "typed:\"GaloisConnection\"": [ + [ + "segment_galois_connection", + "theorem segment_galois_connection (hm : StrictMono f) (h0 : f 0 = 0) :\r\n GaloisConnection f (segment f)" + ], + [ + "gc_map_comap", + "theorem gc_map_comap (f : F) :\r\n GaloisConnection (map f : NonUnitalSubalgebra R A \u2192 NonUnitalSubalgebra R B) (comap f)" + ], + [ + "gc", + "protected theorem gc : GaloisConnection (adjoin R : Set A \u2192 NonUnitalSubalgebra R A) (\u2191)" + ], + [ + "gc_map_comap", + "theorem gc_map_comap (f : A \u2192\u2090[R] B) : GaloisConnection (map f) (comap f)" + ], + [ + "gc", + "protected theorem gc : GaloisConnection (adjoin R : Set A \u2192 Subalgebra R A) (\u2191)" + ], + [ + "gc_map_comap", + "theorem gc_map_comap (f : K \u2192+* L) : GaloisConnection (map f) (comap f)" + ] + ], + "typed:\"finrank\" \"ker\"": [ + [ + "parentHamiltonianGroundSpaceES_finrank_eq_ker", + "theorem parentHamiltonianGroundSpaceES_finrank_eq_ker\r\n (A : MPSTensor d D) (L N : \u2115) :\r\n Module.finrank \u2102 (parentHamiltonianGroundSpaceES A L N) =\r\n Module.finrank \u2102 (LinearMap.ker (parentHamiltonian A L N))" + ], + [ + "HasBNTSectorData.eventually_parentHamiltonian_groundSpace_finrank_eq", + "theorem HasBNTSectorData.eventually_parentHamiltonian_groundSpace_finrank_eq\r\n {d : \u2115} {P : SectorDecomposition d}\r\n (hBNT : HasBNTSectorData P)\r\n (hNNCPH : HasNNCPHGroundSpaces P.toTensor P.basis) :\r\n \u2203 N\u2080 : \u2115, \u2200 N : \u2115, N\u2080 < N \u2192\r\n Module.finrank \u2102 (LinearMap.ker (parentHamiltonian P.toTensor 2 N)) =\r\n P.basisCount" + ], + [ + "codim_iInf_ker_le_fintypeCard", + "lemma codim_iInf_ker_le_fintypeCard [Fintype \u03b9] :\r\n Module.finrank (ZMod q) G - (\u2a05 i, (\u03b3 i).toAddMonoidHom.ker.toZModSubmodule q).finrank\r\n \u2264 Fintype.card \u03b9" + ], + [ + "codim_iInf_ker_le_finsetCard", + "lemma codim_iInf_ker_le_finsetCard :\r\n Module.finrank (ZMod q) G - ((\u2a05 i \u2208 s, (\u03b3 i).toAddMonoidHom.ker).toZModSubmodule q).finrank\r\n \u2264 #s" + ], + [ + "codim_iInf_ker_le_fintypeCard", + "lemma codim_iInf_ker_le_fintypeCard [Fintype \u03b9] :\r\n finrank K V - (\u2a05 i, (f i).ker).finrank \u2264 Fintype.card \u03b9" + ], + [ + "codim_biInf_ker_le_finsetCard", + "lemma codim_biInf_ker_le_finsetCard : finrank K V - (\u2a05 i \u2208 s, (f i).ker).finrank \u2264 #s" + ] + ] +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-AVALANCHE-INDEPENDENT-REVIEW.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-AVALANCHE-INDEPENDENT-REVIEW.json new file mode 100644 index 0000000000..37deca7fcb --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-AVALANCHE-INDEPENDENT-REVIEW.json @@ -0,0 +1,112 @@ +{ + "status": "PASS_INDEPENDENT_EIGHT_HYPERPLANE_WAVE_REVIEW", + "source_sha256": "29b11448963546b959bda379d82711c25f768d5579dcd6bc004887de808e8ae6", + "word_sha256": "931fa9d365eabacacbed055f00ce589ce29647ea904270dfe8943dd5d4ea609d", + "nodes": 5471, + "register_edges": 8372, + "waves": [ + { + "functional": 33, + "node_count": 9, + "delta": { + "1": 2, + "2": -2, + "3": -2, + "4": 2 + } + }, + { + "functional": 33, + "node_count": 10, + "delta": { + "1": 2, + "2": -2, + "3": -2, + "4": 2 + } + }, + { + "functional": 39, + "node_count": 8, + "delta": { + "1": 2, + "2": -2, + "3": -2, + "4": 2 + } + }, + { + "functional": 39, + "node_count": 10, + "delta": { + "1": 2, + "2": -2, + "3": -2, + "4": 2 + } + }, + { + "functional": 192, + "node_count": 10, + "delta": { + "1": 2, + "2": -2, + "3": -2, + "4": 2 + } + }, + { + "functional": 192, + "node_count": 10, + "delta": { + "1": 2, + "2": -2, + "3": -2, + "4": 2 + } + }, + { + "functional": 198, + "node_count": 10, + "delta": { + "1": 2, + "2": -2, + "3": -2, + "4": 2 + } + }, + { + "functional": 198, + "node_count": 10, + "delta": { + "1": 2, + "2": -2, + "3": -2, + "4": 2 + } + } + ], + "exact_paid_delta": { + "1": 16, + "2": -16, + "3": -16, + "4": 16 + }, + "all_edges_nested": true, + "fixed_boundary_nodes_unchanged": true, + "scalar_coefficients_destinations_sources_unchanged": true, + "retained_cut_cleanup_and_dirt_interfaces_unchanged": true, + "strict_moment_proof": "For 0(z,h,y+Jz) after literal inverse cleanup of its background updates. Initial h is arbitrary dirt and its target contribution is cancelled by the explicit input preconditioner. + +The following algorithm is a sufficient elimination procedure, provided every emitted nonzero coefficient and inverse is allowed and every emitted frame passes the ordinary incidence checks. Simulate the old program with initial h=0. Maintain an exact expression h=sum_j g_j z_j in the CURRENT surviving registers, rather than in stale inputs. + +* At h+=a*z_s set g_s+=a. At h*=a multiply all g by a. Emit neither old update. +* At a surviving z_t+=a*z_s not reading h, emit the update and change g_s to g_s-a*g_t. At z_t*=a, divide g_t by a. +* At a read z_t+=a*h, put lambda=1+a*g_t. Require lambda!=0. Emit z_t*=lambda followed by z_t+=a*g_s*z_s for every s!=t with nonzero g_s. Then divide every g coefficient by lambda. These formulas are precisely one-coordinate Schur elimination and its reconstruction map. When t is a target, g_t=0 by the no-feedback assumption, hence lambda=1. + +Proof of the invariant: after an ordinary surviving addition, substitute old z_t=new z_t-a*z_s into the maintained expression. For a read of h, new z_t=lambda*old z_t+a*sum_(s!=t)g_s*z_s. Solving this equation and substituting into h divides every coefficient by lambda. The required nonzero pivot is explicitly checked; it is not an assumed oracle. Induction now proves equality with the old h=0 execution on every surviving input column. Restrict the old initial dirt preconditioner by removing its h term, or recompute the exact response preconditioner. Regenerate inverse cleanup from the actually emitted background sequence. Every emitted update is invertible by its checked lambda or elementary transvection, so surviving background dirt is restored. The target map is the same J on all surviving inputs. The deleted register has no physical initial value to restore. + +For the framed compiler, each added read/write must climb monotonically to its actual gate frame. Every fill-in addition, scale, inverse scale, cleanup gate, copy and normalization wrapper is charged. Deleting a helper does not itself establish a kappa gain: it changes local rank mass and the required residual inventory together; the new complete global assignment and invoice are compulsory. For dyadic circuits, exact denominator/pivot checks are additional sufficient hypotheses, tested on a constructed witness rather than replaced by arbitrary-field division. + +A one-variable example is h=a*x+b*z, y+=c*h with h initially zero. Eliminating h emits y+=ca*x and y+=cb*z. For arbitrary initial h, the old preconditioner contributes -c*h_initial; the new program has no such coordinate. This example demonstrates correctness, not an uncharged saving: the two products and both cleanup implications must be billed. + +## B. Whole-region path transfer and triangular factorization + +Time-expand every linear assignment: each register version becomes a vertex, carry edges have weight1, and an addition creates an edge with its actual scalar coefficient. The resulting graph is acyclic in time. The coefficient from a boundary input to a boundary output equals the sum of products of weights over directed paths. Proof is induction on the destination time: updating a coordinate adds exactly the paths whose final edge is that update. Thus two finite regions with equal exact boundary path matrices can replace each other on arbitrary input/dirt columns. + +A useful special case is a unitriangular region. Its strict-upper matrix N is nilpotent, so (I-N)^-1=I+N+...+N^(d-1). Every entry of N^k is the sum of k-edge path weights. Schur elimination removes an internal vertex by adding each incoming-weight times outgoing-weight to the corresponding boundary edge. Repeated elimination therefore computes the same finite path sum, including all length-three and longer cross terms. The construction terminates after the finite vertex set is eliminated; it never assumes an unknown circuit synthesis oracle. + +For three ordered vertices, the exact source theorem gives + + U = T12(U12) T13(U13-U12*U23) T23(U23). + +The correction U13-U12*U23 subtracts the length-two path already created by the outer factors. In larger regions one may eliminate coordinates in a fixed order, reading the residual coefficients after each step. Equality follows inductively from elementary row identities, not from matching an approximate objective. This is a region-level procedure, rather than the last round's fixed seven three-gate cells. + +A replacement becomes a sufficient compiler optimization only after: exact boundary matrix equality; legal actual frame labels for every new gate; unchanged or explicitly reconstructed retained-copy interfaces; regenerated background inverse; full paid profile and coefficient-prefix recount; and any changed whole-owner inventory allocation. No equality of unframed transfer matrices alone makes an illegal physical frame move admissible. + +## Bounded application record + +Current target was the tn24 complex syndrome word, the binding supplier after public PR543/545 improved the bit side. Native C++ gates tested284 cold helper eliminations with explicit current-expression substitution: all were rejected by the prescribed fixed-frame incidence gate. Another screen multiplied1,669 maximal equal-frame regions and found no coordinate whose boundary row AND column both became identity, so that narrow coordinate-removal resynthesis had no nominee. Exact signed critical-pair comparisons found235 legal candidates with no paid improvement. The same bounded screens were rerun on root's avalanche8 frame rewrite, with the same counts and outcomes. + +The helper-elimination nominator uses a prime-field support image only; no successful exact characteristic-zero witness or impossibility statement is claimed from it. Likewise, the equal-frame gate is merely a cheap nomination filter for one restricted reduction. These are not barriers to other Schur decompositions, alternate frames, new source words or larger path regions. The universal sufficient transformations above remain applicable when their explicit checks pass. + +A preliminary old-bit screen also found seven further rank1+rank1->rank2 merges unlocked by the preceding Steinberg word. That smaller bit route became nonbinding when PR543/545 arrived and was not represented as a new numerical contribution. No native or final kappa claim is attached to these two routes in this round. Root's independently constructed frame avalanche, if fully admitted, is the numerical candidate. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-SCREEN-REVIEW.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-SCREEN-REVIEW.json new file mode 100644 index 0000000000..720db44ac3 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-SCREEN-REVIEW.json @@ -0,0 +1,15 @@ +{ + "status": "BOUNDED_CONSTRUCTIVE_ROUTE_SCREENS_COMPLETE", + "complex_source_sha256": "a8adc158c7253c2e89783df0b874418b1eeecde3bbfc86da0cad5fbfe4d3a54c", + "base": { + "cold_elimination_candidates": 284, + "cold_frame_passes": 0, + "signed_critical_candidates": 235, + "paid_critical_wins": 0, + "equal_frame_regions": 1669, + "inactive_coordinates": 0 + }, + "avalanche8_same_counts": true, + "claimed_new_numerical_gain": false, + "scope": "Sufficient transformations proved in companion note; restricted screens are nominations only, not global impossibility results." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-SOURCES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-SOURCES.json new file mode 100644 index 0000000000..33f50caa28 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/ELIMINATION-SOURCES.json @@ -0,0 +1,34 @@ +[ + { + "connection": "schur", + "path": "D:/proof/lean/mathproof/.lake/packages/mathlib/Mathlib/LinearAlgebra/Matrix/SchurComplement.lean", + "sha256": "1db6e549ad08177da0ed454199b62ddbb162fd821be159b76a81526ccd5ff219", + "declarations": [ + "Matrix.fromBlocks_eq_of_invertible\u2081\u2081", + "Matrix.fromBlocks_eq_of_invertible\u2082\u2082", + "Matrix.invOf_fromBlocks_zero\u2082\u2081_eq" + ], + "source_only": true + }, + { + "connection": "quiver", + "path": "D:/proof/external/openai-math/lean/OAI/Topology/CoarseAssembly/CongruenceElementary.lean", + "sha256": "9b1839abca1a2b02440e1221dc7d2ef365eb6e2285b2ad9e460c69051b3e5552", + "declarations": [ + "elementary_row_same", + "elementary_row_other", + "upperUnitriangular_mem_elementaryReduction" + ], + "source_only": true + }, + { + "connection": "filtered_pattern", + "path": "D:/proof/external/openai-math/lean/OAI/GroupTheory/Congruence/Patterns.lean", + "sha256": "65dbc74c8e955c8aa314fb4f56059fd463d0048dbaa049ff287c9c8c5de35d65", + "declarations": [ + "reindexSL_E", + "upper_prime_power" + ], + "source_only": true + } +] diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/FRAME-SOURCES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/FRAME-SOURCES.json new file mode 100644 index 0000000000..c6cbc8f794 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/FRAME-SOURCES.json @@ -0,0 +1,12 @@ +[ + { + "path": "Algebra/Module/Submodule/Map.lean", + "sha256": "ac82f62923e5f25850b6e6977c6f88924be3401869d331c9c98ebbc84ed6ea22", + "source_only": true + }, + { + "path": "LinearAlgebra/FiniteDimensional/Lemmas.lean", + "sha256": "c5374ea73d4011cb0cddafac24ed494f4f43c563b2ab5676601de7b7ec442157", + "source_only": true + } +] diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/FRAME-TRANSFERS.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/FRAME-TRANSFERS.md new file mode 100644 index 0000000000..f078183102 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/docs/FRAME-TRANSFERS.md @@ -0,0 +1,66 @@ +# Two exact cross-field transfers behind the frame improvement + +The useful connection is structural, not a claim that disparate fields were historically unrelated. A frame history is literally a finite diagram of vector spaces with injective maps. Its admissible edits are order-preserving edits of that diagram. We use that identification to discover a construction that isolated gate edits miss. + +## 1. Persistence diagrams of inclusions become frame histories + +Let an acyclic event graph have a vertex for each scalar gate and immutable vertices for every register entrance, exit, retained-copy observation and target cut. Every register supplies directed edges between its successive occurrences. A vertex e carries a subspace F_e of a finite-dimensional vector space. The legal frame condition is exactly F_e <= F_f on every edge e -> f. A two-register gate is a shared vertex; its two histories must agree there. + +Restricted to a register chain, this is a persistence module with injective structure maps. A basis adapted to its flag decomposes it into coordinates with birth times. A jump of rank r means r births at that point. The compiler's paid histogram counts these jumps. Its recurrence moment charges a concave function of the number born together. Delaying births so they occur in a larger group can therefore improve cost, provided all shared-event constraints are respected. + +This is an identification of the finite linear objects, not an application of persistent-homology stability estimates. We do not assume that the entire branching diagram has an interval decomposition or that one common coordinate basis works for all frames. The explicit subspace updates below avoid both assumptions. + +Fix a nonzero linear functional lambda and H=ker(lambda). On a chain, F -> F intersect H is a sub-persistence module, and the exact sequence + + 0 -> F intersect H -> F -> lambda(F) -> 0 + +shows that each affected space loses exactly one dimension. The quotient is either zero or the one-dimensional field. Thus intersecting a chosen time region with H modifies a concrete birth history by a rank-one change. The algorithm uses the actual spaces, not just their dimensions or a guessed barcode. + +## 2. Galois adjunction becomes a legality-closure algorithm + +For the inclusion j:H -> V, image and preimage of subspaces form an adjunction: + + j(S) <= F iff S <= j^-1(F). + +The counit in the ambient space is F intersect H. This is the same meet operation that appears in the modular subspace lattice underlying type-A flag geometry. It is monotone and deflationary. Its dual operation is adding a fixed line, a monotone inflationary operation. These order properties give a concrete compiler transformation. + +Sufficient contraction theorem. Start from any legal frame diagram with its immutable vertices. Choose a set S of mutable vertices satisfying, for every edge e -> f with f in S and e outside S, F_e <= H. Replace F_e by F_e intersect H for e in S and leave all other vertices unchanged. The resulting diagram is legal and has identical immutable boundaries. + +Proof, edge by edge. If both vertices are changed, intersection is monotone. If neither changes, use the original inclusion. If only the source changes, it only shrinks, so inclusion survives. If only the destination changes, the stated boundary condition gives F_e <= F_f intersect H. These are all cases. No unknown extension, common apartment or unproved gadget appears. + +Construct S from a seed by following predecessor edges. Whenever a predecessor's frame is not contained in H, include it as well. Stop with failure if this would change an immutable vertex. Otherwise the resulting finite closure satisfies the theorem. It is the smallest predecessor closure for this prescribed uniform-intersection action after vertices already inside H are ignored. Minimal closure does not imply optimal cost. A cost bound is computed from every affected register edge, including internal edges when codimension exceeds one. + +The dual sufficient theorem adds a fixed line L on a successor closure, stopping when a successor already contains L. The same four-edge-case proof applies. This gives a second family of checked moves, even though the selected witness uses only contractions. + +## Operator correctness is a separate obligation + +Only frames change; the full scalar instructions, order, cuts, preconditioner, compensation and literal inverse cleanup are held fixed. The scalar endpoint therefore stays the same on arbitrary inputs. Changing frames changes the physical lifted word and its phases, however. The old phase receipt cannot be reused wholesale. The actual construction rebuilds changed Clifford phases, wrappers and local programs, audits all728 columns in both orientations, then rebuilds every global owner chart and the complete finite invoice. This is the necessary bridge from the order-theoretic theorem to the retained compiler interface. + +## Concrete witness and universal moment improvement + +The frozen input is the prior static44/PR534/syndrome word. Single-event frame changes over999 present frames, followed by whole equal-frame-plateau changes, found no improvement. The closure search instead selected eight hyperplane waves, using functionals33,33,39,39,192,192,198,198 on F2^9. Each wave changes8 to10 scalar-event frames together; no scalar instruction is deleted or reordered. + +Every wave changes the complete local paid histogram by + + 2 e1 - 2 e2 - 2 e3 + 2 e4. + +All eight give16 copies of the same replacement. Rank mass, helper widths and complete-call signatures remain unchanged. The pair (2,3) is a doubly stochastic averaging of (1,4): use the matrix with diagonal2/3 and off-diagonal1/3. Strict concavity therefore proves + + 1^a + 4^a < 2^a + 3^a for every 0 2: + x /= 2 + k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + # Outward rational rounding keeps later certificates compact. + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + + +def exp_bounds(x): + require(0 <= x < 1, "exponential range") + term = total = Q(1) + for j in range(1, 13): + term *= x/j + total += term + tail = term*x/13/(1-x/14) + return total, total+tail + + +def moment(m, W, entries, saving): + lo = hi = Q(0) + for t, count in entries: + t, count = int(t), int(count) + require(0 < t < m and count > 0, "improper child") + l, u = log_bounds(Q(m, t)) + lower = exp_bounds(saving*l)[0] + upper = exp_bounds(saving*u)[1] + lo += Q(t*count, m*W)*lower + hi += Q(t*count, m*W)*upper + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/engines/moment.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/engines/moment.py new file mode 100644 index 0000000000..7d697cb452 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/engines/moment.py @@ -0,0 +1,113 @@ +"""Independent prospective ordinary five-stage cost, never supplier admission. + +Consumes a raw one-invocation ledger made from the actual source/internal/target +paths. No packed profile is used as an input. Missing physical/finite/compiler +obligations must remain explicit in the accompanying report. +""" +from collections import Counter +from decimal import Decimal, localcontext, ROUND_FLOOR +from fractions import Fraction as F +from functools import lru_cache +from math import factorial +import hashlib, json, sys +from pathlib import Path + +DYAD = 1 << 224 + +def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) +def ceil(x): return -floor(-x) + +@lru_cache(None) +def logarithm(x): + """Mercator bounds after binary reduction; ln(2) via two Mercator sums. + + For 1 <= y < 2, log(y) is an alternating series in z=y-1. + We instead reduce to 1 <= y < 3/2, and bound log(3/2) and + log(2) by the same alternating series at z=1/2 and z=1/3, + using log(2)=log(3/2)+log(4/3). All sums are exact rationals. + """ + assert x >= 1 + k = 0 + while x >= 2: x /= 2; k += 1 + j = int(x >= F(3, 2)) + if j: x /= F(3, 2) + def mercator(y): + z=y-1 + assert 0 <= z <= F(1,2) + # An even partial sum is below log; the next term bounds its tail. + t=z; s=F(0) + for n in range(1, 225): + s += (t if n & 1 else -t)/n + t *= z + return s, s+t/225 + a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3)) + return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f) + +def exponential(l,u): + assert 0 <= l <= u < F(1,10) + def poly(x): + s=t=F(1) + for j in range(1,25): t=t*x/j; s+=t + return s,t + lo,_=poly(l);hi,last=poly(u) + return floor(lo),ceil(hi+last*u/25/(1-u/26)) + +def moment(H,m,W,a,bad=False): + lo=hi=F(0) + for r,n in H.items(): + assert 0 < r < m and n > 0 + l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u) + p=F(r*n,m*W);lo+=p*e;hi+=p*f + if bad: + # Existing envelope shape, only conditionally portable to the new cover. + l,u=logarithm(F(m));e,f=exponential(a*l,a*u) + p=F(32*m*sum(H.values()),10**16*W) + lo+=p*e;hi+=p*f + return floor(lo),ceil(hi) + +def decimal(x): + with localcontext() as c: + c.prec=70 + return str(Decimal(x.numerator)/Decimal(x.denominator)) + +def certify(H,m,W,bad=False): + with localcontext() as c: + c.prec=70 + terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()] + fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0) + lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003') + for _ in range(210): + a=(lo+hi)/2 + if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a + else:hi=a + q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR)) + lo=F(q,10**24);hi=lo+F(1,10**24) + lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad) + assert lv[1]<10 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2 + assert 1-eps*(1+c)==eta-eps*eta/4 + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/COMPLEX-INVOICE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/COMPLEX-INVOICE.json new file mode 100644 index 0000000000..2cd1365bdd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/COMPLEX-INVOICE.json @@ -0,0 +1,106 @@ +{ + "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE", + "template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "parent_template_sha256": "7eddf21720ce26ff72069a0e94fa7f0e692cfe3bea2defb1a3769bea352cf471", + "owner_audit_sha256": "6572e69d9df9a72a600d7ee88404f96c525fea760b76cb6607273d85681579d1", + "controller_audit_sha256": "01d37b06d35ffb1995533cc618b0baaa093f55d288786153406fc46c94ab9926", + "independent_local_replay_sha256": "e871d8d56014146c19963430e4822714aadbf57367f783dc1dd42fa3f5b0a0ce", + "canonical_word_sha256": "995e46ed6dc8377f02bf05a3370171796364cedefdfeaeae47c2a207b5a8b173", + "local_programs_sha256": "7b191ec016ab99a0e1415206b898a8a6c5485fe9e8d91e59539e7c3710725563", + "local_checks_sha256": "2c51cdb9b282aadb99ea00d05b6c4bee140577111bdfd5c675b038373e309a17", + "global_prefix_bits": 225, + "charged_prefix_bits": 512, + "complete_invocation_sweeps": 72, + "bridge_sweeps": 72, + "row_prefix_extra": 1024, + "local": { + "backward": { + "events": 21483, + "macros": 16290, + "real_component_primitives": 161356, + "prefix_l1": "1044730572396", + "prefix_bits": 40, + "coefficient_work_primitive_count": 79906, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 212, + "post_wrappers": 212, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + }, + "forward": { + "events": 21483, + "macros": 16290, + "real_component_primitives": 161308, + "prefix_l1": "88876257700", + "prefix_bits": 37, + "coefficient_work_primitive_count": 79874, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 212, + "post_wrappers": 212, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + } + }, + "helpers": 504, + "centres": 8, + "live": 7168, + "physical": 7682, + "physical_stock_identity": { + "data_and_owner_families": 7168, + "local_helpers": 504, + "private_centres": 8, + "coefficient_work": 2 + }, + "entering_helpers": 212, + "entrance_rank": 380, + "width_inventory": { + "5": 56, + "8": 156, + "9": 292 + }, + "local_adapters": 333344, + "local_primitive_bound": 8645055460940, + "wrapper_elementary_factors_charged": 4396032, + "factors_per_wrapper": 144, + "compiler": 25934336, + "unhosted_pervertex": 1574554051175192, + "hosted_rebased_pervertex": 1574554050875816, + "conservative_pervertex_used": 4452501040899760, + "retained_prior_overcharge": { + "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478", + "previous_pervertex_allowance": 2877946989724568, + "added_complete_new_pervertex": 1574554051175192, + "policy": "Retain old allowance and add the entire fresh recount." + }, + "finite": { + "physical_stock_bits": 2641, + "router_bits": 7985, + "literal_bits": 35282, + "physical_row_coefficient": 16467, + "retained_row_coefficient": 20161, + "required_C0_bits": 200012, + "halving_integer_inequality": [ + 5329, + 4608 + ], + "G_exponent": 30000, + "E_exponent": 100000, + "C0_exponent": 210000 + }, + "strict_checks": { + "local_primitive_bound": true, + "logical": true, + "router": true, + "literal": true, + "mass": true, + "precision": true, + "tape": true, + "row": true, + "halving": true + }, + "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/EXACT-ASSEMBLY.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/EXACT-ASSEMBLY.json new file mode 100644 index 0000000000..104ff571e6 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/EXACT-ASSEMBLY.json @@ -0,0 +1,169 @@ +{ + "status": "PASS_FRESH_WAVE_COMPLEX_AND_CITED_R420_COMPOSITION", + "kappa": "795984451416673/500000000000000000", + "kappa_decimal": "0.001591968902833346", + "complex_lower": "1594507308884431019637/1000000000000000000000000", + "complex_decimal": "0.001594507308884431019637", + "bit_lower": "413456747036699736067/250000000000000000000000", + "bit_decimal": "0.001653826988146798944268", + "binding": "complex", + "gain_over547_percent": 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The unchanged bit operator is cited, not rebuilt in this package. Inherited all-size compiler, common-label/mutable-source, hosting, precision/tape and analytic interfaces remain conditional. R420 interleaved phase-B source writes rely on its stated H1-H5 interface argument." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/FINAL-RESOURCE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/FINAL-RESOURCE.json new file mode 100644 index 0000000000..694d910171 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/FINAL-RESOURCE.json @@ -0,0 +1,44 @@ +{ + "status": "PASS_FINAL_WEIGHTED_COSET_WAVE_RESOURCE_AND_INVOICE", + "complex_lower": "1594507308884431019637/1000000000000000000000000", + "template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "roles": 36288, + "charts": 2972, + "profile": { + "1": 165600, + "2": 32128, + "3": 35907, + "4": 13248, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "prefix_required": 225, + "prefix_charged": 512, + "row": 16467, + "local": { + "backward": { + "events": 21483, + "prefix_bits": 40, + "all_exact_columns": 728 + }, + "forward": { + "events": 21483, + "prefix_bits": 37, + "all_exact_columns": 728 + } + }, + "negative_controls": [ + "alias two whole owners", + "helper on active data family", + "owner in private namespace", + "wrong residual width", + "wrong spectator coordinate", + "omit idle remainder", + "understate physical reserve" + ], + "frozen_manifest_sha256": "af4e9eecb006a98f78a024ee6558f27641b3be8c8b0771e6fa22d0c7cddf38cf" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/WAVE-REVIEW.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/WAVE-REVIEW.json new file mode 100644 index 0000000000..434c9c1de3 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/evidence/WAVE-REVIEW.json @@ -0,0 +1,228 @@ +{ + "status": "PASS_COLLECTIVE_HYPERPLANE_FRAME_CONTRACTION", + "source_content_sha256": "7f7bf2315c83eb5dc0bb3502ceae575bfcffa00ad37fd32839114744ac18182c", + "word_content_sha256": "c09f3e70225419542f3e8ed8099ac349064b3a6bca4e75aaf3ebdca9532ff79e", + "before": { + "1": 2284, + "4": 168, + "8": 8, + "3": 488, + "2": 456, + "6": 56, + "5": 56 + }, + "after": { + "1": 2300, + "4": 184, + "8": 8, + "3": 472, + "2": 440, + "6": 56, + "5": 56 + }, + "delta": { + "1": 16, + "2": -16, + "3": -16, + "4": 16 + }, + "changes": [ + { + "wave": 0, + "events": 9, + "covectors": [ + 33 + ], + "profile": { + "1": 2286, + "4": 170, + "8": 8, + "3": 486, + "2": 454, + "6": 56, + "5": 56 + } + }, + { + "wave": 1, + "events": 10, + "covectors": [ + 33 + ], + "profile": { + "1": 2288, + "4": 172, + "8": 8, + "3": 484, + "2": 452, + "6": 56, + "5": 56 + } + }, + { + "wave": 2, + "events": 8, + "covectors": [ + 39 + ], + "profile": { + "1": 2290, + "4": 174, + "8": 8, + "3": 482, + "2": 450, + "6": 56, + "5": 56 + } + }, + { + "wave": 3, + "events": 10, + "covectors": [ + 39 + ], + "profile": { + "1": 2292, + "4": 176, + "8": 8, + "3": 480, + "2": 448, + "6": 56, + "5": 56 + } + }, + { + "wave": 4, + "events": 10, + "covectors": [ + 192 + ], + "profile": { + "1": 2294, + "4": 178, + "8": 8, + "3": 478, + "2": 446, + "6": 56, + "5": 56 + } + }, + { + "wave": 5, + "events": 10, + "covectors": [ + 192 + ], + "profile": { + "1": 2296, + "4": 180, + "8": 8, + "3": 476, + "2": 444, + "6": 56, + "5": 56 + } + }, + { + "wave": 6, + "events": 10, + "covectors": [ + 198 + ], + "profile": { + "1": 2298, + "4": 182, + "8": 8, + "3": 474, + "2": 442, + "6": 56, + "5": 56 + } + }, + { + "wave": 7, + "events": 10, + "covectors": [ + 198 + ], + "profile": { + "1": 2300, + "4": 184, + "8": 8, + "3": 472, + "2": 440, + "6": 56, + "5": 56 + } + } + ], + "controls": [ + { + "wave": 0, + "omitted_event": [ + "B", + 1460 + ], + "rejected": true + }, + { + "wave": 1, + "omitted_event": [ + "B", + 1468 + ], + "rejected": true + }, + { + "wave": 2, + "omitted_event": [ + "B", + 1456 + ], + "rejected": true + }, + { + "wave": 3, + "omitted_event": [ + "B", + 1464 + ], + "rejected": true + }, + { + "wave": 4, + "omitted_event": [ + "B", + 1876 + ], + "rejected": true + }, + { + "wave": 5, + "omitted_event": [ + "B", + 1884 + ], + "rejected": true + }, + { + "wave": 6, + "omitted_event": [ + "B", + 1872 + ], + "rejected": true + }, + { + "wave": 7, + "omitted_event": [ + "B", + 1880 + ], + "rejected": true + } + ], + "scalar_program_unchanged": true, + "boundaries_unchanged": true, + "scope": "Exact finite subspace chains and unchanged scalar word. 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+ [ + "B", + 884 + ], + [ + "B", + 868 + ], + [ + "B", + 894 + ], + [ + "B", + 878 + ] + ] + } + ] +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-PATH-APPLICATION.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-PATH-APPLICATION.md new file mode 100644 index 0000000000..d01ea9c4d0 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-PATH-APPLICATION.md @@ -0,0 +1,35 @@ +# Independent path-transfer review of the twelve weighted-coset substitutions + +This review supplies an independent exact scalar audit of the selected provider. It does not claim an additional numerical gain, a new physical-frame theorem, or a replay of the unchanged bit supplier. The source hashes are in COSET-SOURCE-BINDING.json; the numerical receipt is COSET-PATH-REVIEW.json. + +## Sufficient transfer statement + +Let a finite linear straight-line circuit have initial coordinates split into protected inputs P and cold helper dirt C. Expand each assignment into a new register version, retaining unchanged versions by unit-weight edges. The coefficient of an initial coordinate in any output is the sum of all directed path weights from that input to the output. Induction on assignment order proves this statement: a scale multiplies the old paths, and an addition joins the old destination paths with the scaled source paths. Thus exact propagation of coefficient rows computes the boundary transfer matrix over the dyadic rationals, including all long paths and cancellation. + +Suppose a source rewrite at an addition preserves the destination and gate coefficient/frame, and its current prefix error has zero restriction to P. Subsequent linear maps cannot introduce a protected component into that error. Therefore the final difference is supported on C. If the retained compiler subtracts the actual cold response and then performs the inverse of the actual background program, the two compensated endpoints agree on every initial column and restore all background dirt. This conclusion requires checking the actual changed program, not merely the clean-input action or a source equality before earlier rewrites. When target decoding occurs after the background circuit it is included in the boundary map before deriving the cold response. + +In this witness P includes all 112 source coordinates, all 112 initial target coordinates, and 212 warm helper coordinates. The actual raw section named `precondition` is a final target decoder; it is included after A, cut, B. It is not mistaken for the compiler's initial cold-dirt compensation. The latter must be regenerated and charged by the physical pipeline. + +## Independent finite application + +A fresh C++ implementation, using Boost cpp_int dyadic arithmetic and no imported nomination, gk, or suffix-derivative routines, computes both complete 728-column boundary matrices. All 48,832 entries on 112 target rows and 436 protected columns agree exactly. The cold target-response nonzero count falls from 9,756 to 9,132, a saving of 624 entries. This is a compensation-count result, not an independent kappa increment. + +It separately reconstructs the current prefix at each of the twelve selected rewrites, incorporating every earlier rewrite, and checks all 728 coefficients of the stated source error. All 8,736 comparisons pass, and each error vanishes on P. The selected A indices are 205, 340, 1555, 1690, 207, 342, 475, 477, 610, 612, 745, and 747. + +The portable exporter proves that these exact twelve operations reconstruct the entire candidate A, that all fields other than A and cleanup remain equal, and that the 2,847 cleanup operations are precisely the reverse inverses of the actual nontarget A+B operations, at the full frame. The source audit is bound to candidate raw SHA-256 fd8ea67a1f4e8d754ffe29cc18a12aaa15c1704e58b688895e7ba51eb832b719. + +The path-algebra connection is actually used here as an independent exact boundary-transfer and version-error audit. Triangular elimination gives an alternative mathematical derivation of the same boundary matrix: eliminate internal time-expanded vertices, adding incoming times outgoing path weights. This is the relevant Schur/path relationship. The implementation does not separately run a second Schur-complement algorithm, and the earlier attempted register-elimination optimization had no admitted winner. There is one independent implementation, not two independent successful optimization techniques. + +Actual physical frame incidence, normalized operator endpoints, coefficient bounds, whole-owner maps and the assembly are checked separately by the changed-provider pipeline. This scalar audit does not replace those checks. Likewise, the source analogy is not a new Lean kernel certificate or a claim of global mathematical originality. + +## Optional reproduction + +The main verifier need not build this independent optional checker. With Python, a C++17 compiler, and genuine Boost headers installed: + +``` +python export_coset_paths.py --baseline BASELINE.json.gz --candidate CANDIDATE.json.gz --selection SELECTION.json --out audit-out +c++ -O2 -std=c++17 -I BOOST_INCLUDE audit_coset_paths.cpp -o audit_coset_paths +./audit_coset_paths audit-out/coset-path-input.txt audit-out/COSET-PATH-REVIEW.json +``` + +Do not compile with NDEBUG: the exact comparisons use C++ assertions. The included coset-path-input.txt is also a complete fixed independent arithmetic input; its SHA-256 is recorded by the source-binding receipt. The exporter accepts paths as arguments and contains no machine-specific locations. No executable binary is required in the submission. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-PATH-REVIEW.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-PATH-REVIEW.json new file mode 100644 index 0000000000..db16f78ef3 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-PATH-REVIEW.json @@ -0,0 +1 @@ +{"status":"PASS_INDEPENDENT_DYADIC_BOUNDARY_PATH_AND_VERSION_ERRORS","initial_columns":728,"target_rows":112,"protected_columns_including_targets":436,"protected_entries_checked":48832,"old_cold_response_nnz":9756,"new_cold_response_nnz":9132,"cold_response_nnz_saved":624,"changed_cold_entries":816,"version_witnesses":12,"exact_error_coefficients_checked":8736,"arithmetic":"independent cpp_int dyadics, no imported gk implementation"} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-SOURCE-BINDING.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-SOURCE-BINDING.json new file mode 100644 index 0000000000..59a6b488a2 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/COSET-SOURCE-BINDING.json @@ -0,0 +1,23 @@ +{ + "status": "PASS_EXACT_SOURCE_BINDING_AND_LITERAL_CLEANUP", + "baseline_sha256": "931fa9d365eabacacbed055f00ce589ce29647ea904270dfe8943dd5d4ea609d", + "candidate_sha256": "fd8ea67a1f4e8d754ffe29cc18a12aaa15c1704e58b688895e7ba51eb832b719", + "selection_sha256": "d4f7ccff66f361adc06f63cdd4bafd44c0ea2dbaaf755fe619423a93a5bb1519", + "native_input_sha256": "779b497d52b6896a04f41d6c55424e65030a939945ca80858c369a3a3320a341", + "moves": 12, + "preserved_keys": [ + "B", + "center_frames", + "centers", + "cut", + "ports", + "precondition", + "report", + "root_lines", + "scatter", + "start_extra", + "target_levels" + ], + "cleanup_count": 2847, + "all_cleanup_full_frame": true +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/audit_coset_paths.cpp b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/audit_coset_paths.cpp new file mode 100644 index 0000000000..12bfd181ee --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/audit_coset_paths.cpp @@ -0,0 +1,15 @@ +#include +#include +using namespace std;using boost::multiprecision::cpp_int; +struct D{cpp_int n=0;int e=0;D(){}D(long long x):n(x){}void norm(){if(n==0){e=0;return;}cpp_int a=n<0?-n:n;int k=min(e,(int)boost::multiprecision::lsb(a));n>>=k;e-=k;}D mul(long long a,long long b)const{assert(b>0&&(b&(b-1))==0);D x=*this;x.n*=a;x.e+=__builtin_ctzll((unsigned long long)b);x.norm();return x;}D operator+(const D&b)const{D c;c.e=max(e,b.e);c.n=(n<<(c.e-e))+(b.n<<(c.e-b.e));c.norm();return c;}D operator-(const D&b)const{return *this+b.mul(-1,1);}bool operator==(const D&b)const{return n==b.n&&e==b.e;}}; +struct Op{int kind,t,s;long long a,b;};int N,V;using Mat=vector>; +Op readop(istream&in){Op e;in>>e.kind>>e.t>>e.s>>e.a>>e.b;return e;} +Mat ident(){Mat x(N,vector(N));for(int i=0;i>N>>V>>K>>PN;setP;for(int i=0,r;i>r;P.insert(r);}vector results;for(int v=0;v<2;v++){int m;in>>m;Mat x=ident();for(int j=0;j>ac;vector A(ac);for(auto&e:A)e=readop(in);long long exacterrors=0; +for(int k=0;k>index;Op change=readop(in);in>>m;vectorexpected(N);for(int j=0,c;j>c>>a>>b;expected[c]=D(1).mul(a,b);}Mat x=ident();for(int j=0;j=224 and j not in protected for j in err) + assert err=={int(j):Q(x)for j,x in move['cold_difference'].items()} + n0=sum(map(len,g.responses(w)));w['A'][i]=copy.deepcopy(new);assert g.profile(w)==profile + n1=sum(map(len,g.responses(w)));assert n0-n1==move['compensation_saved']>0 + receipts.append(dict(index=i,compensation_before=n0,compensation_after=n1,cold_error_checked=True,protected_columns_preserved=True,frame_profile_unchanged=True)) +w['cleanup']=[g.inverse(e,g.FULL)for e in reversed(w['A']+w['B'])if not V<=e[1]<2*V] +w['report']['local_profile']=dict(profile) +assert semantic(w)==r['output_semantic_sha256'] +after=sum(map(len,g.responses(w)));assert after==r['after_compensation']and before-after==r['total_saved']==624 +assert dict(profile)=={int(k):v for k,v in r['profile'].items()} +a.out.mkdir(parents=True,exist_ok=False);(a.out/'FULL-WORD.json.gz').write_bytes(g.dump(w)) +receipt=dict(status='PASS_FROZEN_WEIGHTED_COSET_FAMILY',input_semantic_sha256=r['input_semantic_sha256'],output_semantic_sha256=semantic(w),moves=receipts,compensation_before=before,compensation_after=after,total_saved=before-after,profile=dict(profile),scope='Exact rational prefix errors, all protected columns, frame chains and complete compensation table. Native phases, emitted programs and global assembly checked separately.') +(a.out/'WEIGHTED-COSET-REPLAY.json').write_text(json.dumps(receipt,indent=2)+'\n');print('PASS frozen weighted coset family',len(receipts),before-after) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/verify.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/verify.py new file mode 100644 index 0000000000..a1205552fd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/vendor/pr552/verify.py @@ -0,0 +1,39 @@ +"""Offline changed-word replay. No network and no optimizer are required.""" +import argparse,gzip,hashlib,json,os,shutil,subprocess,sys,time +from pathlib import Path +TEXT={'.py','.json','.md','.txt','.sh','.lean','.cpp','.h','.hpp','.sha256','.yml','.yaml','.toml'} +def textfile(p):return p.suffix.lower()in TEXT or p.name in {'LICENSE','NOTICE','SOURCE'} +def read(p):return json.loads(p.read_text(encoding='utf-8')) +def dump(p,z):p.write_text(json.dumps(z,indent=2)+'\n',encoding='utf-8',newline='\n') +def main(): + if not __debug__:raise SystemExit('Assertions must be enabled; do not use Python -O.') + ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--work',type=Path,required=True);a=ap.parse_args() + root=Path(__file__).resolve().parent;work=a.work.resolve();assert not work.exists()and root not in work.parents + import numpy # Required by the unchanged Clifford phase compiler. + man=read(root/'MANIFEST.json');assert man['format']=='sha256-lf-text-v1';expect=read(root/'EXPECTED.json') + present={x.relative_to(root).as_posix()for x in root.rglob('*')if x.is_file()and '__pycache__'not in x.parts} + assert present==set(man['files'])|{'MANIFEST.json'},('unlisted/missing',present^(set(man['files'])|{'MANIFEST.json'})) + for rel,z in man['files'].items(): + f=(root/rel).resolve();assert root in f.parents;b=f.read_bytes() + if z['mode']=='lf-text':b=b.replace(b'\r\n',b'\n') + assert hashlib.sha256(b).hexdigest()==z['sha256'],('input hash changed',rel) + t=time.monotonic();work.mkdir(parents=True);src=work/'source';shutil.copytree(root,src,ignore=shutil.ignore_patterns('__pycache__')) + for f in src.rglob('*'): + if f.is_file()and textfile(f):f.write_bytes(f.read_bytes().replace(b'\r\n',b'\n')) + stages=[];env=dict(os.environ,PYTHONUTF8='1',PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0') + def run(name,script,*args): + began=time.monotonic() + with(work/(name+'.log')).open('w',encoding='utf-8')as log:r=subprocess.run([sys.executable,'-B',str(script),*map(str,args)],stdout=log,stderr=subprocess.STDOUT,env=env) + stages.append(dict(name=name,exit=r.returncode,seconds=time.monotonic()-began));dump(work/'STAGES.json',stages) + if r.returncode:print((work/(name+'.log')).read_text(encoding='utf-8'),file=sys.stderr);raise SystemExit(name+' failed') + print('PASS',name,round(stages[-1]['seconds'],2),flush=True) + local=work/'complex-local';cg=work/'complex-global' + run('complex-reconstruction-and-local-checks',src/'complex-local/run_local.py','--out',local,'--vendor',src/'complex-global/vendor531') + run('complete-owner-physical-and-invoice',src/'complex-global/replay.py','--local',local/'local','--out',cg) + run('exact-two-supplier-assembly',src/'code/assemble.py',src,cg,work/'ASSEMBLY.json') + ans=read(work/'ASSEMBLY.json');ci=read(cg/'audit/PREFIX-AND-INVOICE.json');co=read(cg/'audit/OWNERS-AND-PROFILE.json');wave=read(local/'wave/WAVE-REVIEW.json');coset=read(local/'weighted/WEIGHTED-COSET-REPLAY.json') + result=dict(status='PASS_FILTRATION_WAVEFRONT',kappa=ans['kappa'],kappa_decimal=ans['kappa_decimal'],bit_lower=ans['bit_lower'],complex_lower=ans['complex_lower'],complex_template_sha256=ci['template_sha256'],complex_canonical_word_sha256=ci['canonical_word_sha256'],complex_global_profile=co['paid_profile'],complex_prefix_bits=ci['global_prefix_bits'],forward_events=ci['local']['forward']['events'],backward_events=ci['local']['backward']['events'],waves=len(wave['changes']),wave_omission_controls=len(wave['controls']),coset_rewrites=len(coset['moves']),compensation_additions_saved=coset['total_saved'],outer_constraints=len(ans['outer']),bit_operator='Pinned PR543 cited dependency, not physically replayed here',stages=stages,elapsed_seconds=time.monotonic()-t,scope=ans['scope']) + for k,x in expect.items():assert result[k]==x,('frozen result mismatch',k,result[k],x) + assert result['outer_constraints']==47 and result['waves']==8 and result['compensation_additions_saved']==624 + dump(work/'RESULT.json',result);print(json.dumps({k:result[k]for k in ['status','kappa_decimal','elapsed_seconds']}),flush=True) +if __name__=='__main__':main() diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/verify.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/verify.py new file mode 100644 index 0000000000..f958a077fa --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr558/verify.py @@ -0,0 +1,47 @@ +"""Fresh deterministic complex replay. Default requires literalnewownerplan. +Prepared with OpenAI Codex assistance. Apache-2.0. +The --local-only diagnostic does not certify global hosting or a kappa record. +""" +import argparse,gzip,hashlib,json,os,subprocess,sys,time +from pathlib import Path +if not __debug__:raise SystemExit('Assertions must remain enabled') +P=Path(__file__).resolve().parent +ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--work',type=Path,required=True);ap.add_argument('--local-only',action='store_true');a=ap.parse_args();O=a.work.resolve();assert not O.exists()and not O.is_relative_to(P) +def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +def dump(p,v):p.write_text(json.dumps(v,indent=2)+'\n') +# Final package manifest is supplied after the literalownerplan and assembly +# have been integrated; source pins are mandatory even for localdiagnostics. +if(P/'MANIFEST.json').exists(): + actual={q.relative_to(P).as_posix():sha(q)for q in P.rglob('*')if q.is_file()and q!=P/'MANIFEST.json'and'__pycache__'not in q.parts};assert actual==read(P/'MANIFEST.json'),'package manifest' +else:assert a.local_only,'full replay requires final manifest' +for rel,pin in read(P/'SOURCE-PINS.json')['files'].items():assert sha(P/rel)==pin['sha256'],rel +if not a.local_only:assert(P/'data/OWNERS.json.gz').is_file()and(P/'data/PLAN.json').is_file(),'literal new owners and plan required' +O.mkdir(parents=True);steps=[];start=time.monotonic();env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0',PYTHONUTF8='1');env.pop('PYTHONOPTIMIZE',None) +def run(name,script,*args): + t=time.monotonic();log=O/(name+'.log');print('RUN',name,flush=True) + with log.open('w')as f:r=subprocess.run([sys.executable,'-B',str(P/'code/run_portable.py'),str(script),*map(str,args)],stdout=f,stderr=subprocess.STDOUT,env=env) + steps.append(dict(name=name,exit_code=r.returncode,seconds=time.monotonic()-t,log_sha256=sha(log)));dump(O/'STAGES.json',steps) + if r.returncode:raise RuntimeError(name+' failed\n'+log.read_text()[-6000:]) + print('PASS',name,flush=True) +v=P/'vendor/pr552';V=v/'complex-global/vendor531';local=O/'complex-local' +run('reconstruct552-and-promote8',P/'code/reconstruct.py','--out',O/'reconstruction') +run('all-columns-native-frames',V/'code/audit_and_transport.py','--raw',O/'reconstruction/promoted/FULL-WORD.json.gz','--routing',v/'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz','--out',local) +run('emit-both-reflected-ledgers',V/'code/emit_local.py',local) +run('independent-local-and-controls',V/'code/audit_local.py',local) +run('normalized-wrappers',V/'code/adapters_local.py',local/'CANONICAL-WORD.json.gz',local/'RESIDUAL-ADAPTERS.json',local/'WRAPPER-CHECKS.json') +if a.local_only: + dump(O/'RESULT.json',dict(status='PASS_LOCAL_DIAGNOSTIC_ONLY',word_sha256=sha(O/'reconstruction/promoted/FULL-WORD.json.gz'),local=read(local/'INDEPENDENT-LOCAL-REPLAY.json'),scope='No phase/global/invoice/assembly admission claimed.'));sys.exit(0) +run('all-phase-recipes',P/'code/phases_full.py',local,V/'vendor/clifford') +run('literal-owners-full-invoice',v/'complex-global/run_complex44.py',V,v/'complex-global/vendor535',local,P/'data/OWNERS.json.gz',P/'data/PLAN.json',P/'code/run_portable.py',O/'complex-global') +run('two-engine-exact-assembly',P/'code/assemble.py',P,O/'complex-global',O/'ASSEMBLY.json') +run('assembly-admission-controls',P/'code/assembly_controls.py','--owner',O/'complex-global/audit/OWNERS-AND-PROFILE.json','--invoice',O/'complex-global/audit/PREFIX-AND-INVOICE.json','--out',O/'ASSEMBLY-CONTROLS.json') +assembly=read(O/'ASSEMBLY.json');phase=read(local/'CLIFFORD-REVIEW.json');native=read(local/'INDEPENDENT-LOCAL-REPLAY.json');owners=read(O/'complex-global/audit/OWNERS-AND-PROFILE.json');invoice=read(O/'complex-global/audit/PREFIX-AND-INVOICE.json') +assert phase['all_child_equalities_include_global_phase']and phase['endpoint_adapters']==224 and phase['directed_edges']==2929 +assert len(read(O/'complex-global/audit/ASYNC-AUDIT.json')['mutations_rejected'])==7 +assert native['paid_profiles']['forward']==native['paid_profiles']['backward']and len(native['negative_controls_rejected'])==11 +assert all(invoice['strict_checks'].values())and owners['template_sha256']==invoice['template_sha256'] +result=dict(status='PASS_COMPLEX_EIGHT_RANK5_PIVOTS_AND_CITED_BIT',kappa=assembly['kappa'],kappa_decimal=assembly['kappa_decimal'],complex_lower=assembly['complex_lower'],bit_lower=assembly['bit_lower'],word_sha256=sha(O/'reconstruction/promoted/FULL-WORD.json.gz'),local_profile=native['paid_profiles']['forward'],global_profile=owners['paid_profile'],seconds=time.monotonic()-start,scope=assembly['scope']);assert result['kappa_decimal']=='0.001592517889315014' +dump(O/'RESULT.json',result) +dump(O/'RECEIPT.json',dict(status=result['status'],steps=steps,artifacts={name:sha(O/name)for name in ['RESULT.json','ASSEMBLY.json','ASSEMBLY-CONTROLS.json','reconstruction/promoted/PROMOTION.json','complex-local/INDEPENDENT-LOCAL-REPLAY.json','complex-local/CLIFFORD-REVIEW.json','complex-global/audit/ASYNC-AUDIT.json','complex-global/audit/OWNERS-AND-PROFILE.json','complex-global/audit/PREFIX-AND-INVOICE.json']},manifest_sha256=sha(P/'MANIFEST.json'))) +print(json.dumps(result,indent=2)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/EXPECTED.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/EXPECTED.json new file mode 100644 index 0000000000..9fc6616a33 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/EXPECTED.json @@ -0,0 +1,8 @@ +{ + "kappa": "1591968905569359/1000000000000000000", + "kappa_decimal": "0.001591968905569359", + "complex_lower": "398626827907293921411/250000000000000000000000", + "complex_decimal": "0.001594507311629175685644", + "old_kappa": "795984451416673/500000000000000000", + "absolute_gain": "2736013/1000000000000000000" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/EXPECTED558.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/EXPECTED558.json new file mode 100644 index 0000000000..0d4ec1740e --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/EXPECTED558.json @@ -0,0 +1,8 @@ +{ + "kappa": "796258946026667/500000000000000000", + "kappa_decimal": "0.001592517892053334", + "complex_lower": "797529025268839550469/500000000000000000000000", + "complex_decimal": "0.001595058050537679100938", + "old_kappa": "796258944657507/500000000000000000", + "absolute_gain": "34229/12500000000000000" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/LICENSE b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/LICENSE new file mode 100644 index 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index 0000000000..643510d841 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/MANIFEST.json @@ -0,0 +1,40 @@ +{ + "EXPECTED.json": "a79dc7eec1301a69560a2e7fd6ed69634463272696ee96f09e15db1aad8ab0b0", + "EXPECTED558.json": "1e922eef350748956f4cd785d7fc5f73297b0ed6f53b130aca2da29d26777c34", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE.md": "02e74770785e31234d863b36ad2291e04267eaf32a4ba82f67cb1c804da1de44", + "PROOF-REVIEW-STATUS.json": "f54fcf048c5e24f5d3ccf308259b4b1b291b736e014fee81b4518980d358786c", + "PROOF.md": "d5d498edc56fdef8c5798af7f5ec66948bd2f66c553b9efe366cdaab01bd3453", + "README.md": "74f5cd377861bdff57a2825b19ac6c2b0bb6aa62f3b0354c7ceec0a76866c61c", + "REVIEW.json": "518fd773b1287c9be19563316f55acfa443667946d1f5bc7cc7b884bb9005094", + "SOURCES.json": "32e1466dd29be472e63e11e8ad76b228c0a1e3ec33596ce4319a64b89bd6d912", + "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098", + "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482", + "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "evidence/PR552-INDEPENDENT-REPLAY.json": "6db0dfeedce73cf9a6eb31bea0a499f06dc4961da40a60d91059bb9ab48fd73c", + "evidence/PR552-PUBLISHED-INVOICE.json": "a21fd7e02d3001b1e8065e9eb6084d80e1f64c44035733ed1115a38675a01fd0", + "evidence/PR552-packaged311.json": "8a06db71ab002a9e080f0d60d22ee32a3a6a848a0cc633f37fc8fde22d21694b", + "evidence/PR552-packaged314.json": "53142566b590fdde9258e36e6fe62991c2f39331fc2822bf0105f812e52d6aa6", + "evidence/PR552-regression-final.json": "0c8bb51c2234a3190fab3e0e33187dee1bd4f2aab32483a69452366abb3b2567", + "evidence/PR558-COMPILER-LINEAGE.json": "db1e3390ade85f2299fc1ff0652e12fe1384c35bdcaf5c49e5403e4eb6b255b9", + "evidence/PR558-INDEPENDENT-RECEIPT.json": "c121cb83baeeb950a42eac4bec73676119dd836386b822e03bf7820fa1bf5262", + "evidence/PR558-INDEPENDENT-REPLAY.json": "b32113b56745cd5c142c982426ce31f0fe8d4f1a4ba219541e8c8befc69f017c", + "evidence/PR558-packaged311.json": "fed5ee89ea9f6b3c3ffb150898fc95f9a057a0c598b18de6df59e66908342b2e", + "evidence/PR558-packaged314.json": "71251eee88024f14982a4e7328377f50eb9d04314f692b891b53b5911498e3c2", + "inputs/PR543-EXPECTED.json": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d", + "inputs/PR552-EXACT-ASSEMBLY.json": "c7495a6787f48a9c5184a00daa841f4a972e37c580c6ff3dacc07bd947914f99", + "inputs/PR552-EXPECTED.json": "00c462828be76f6d65c1311ad9ef102f18f088029e039cffa599eaeb41668fb6", + "inputs/PR552-INVOICE.json": "4ac060dbf2ea2624dd1f4bda23bdb81c0a3013dfe49b77c092b631885529947f", + "inputs/PR552-OWNERS.json": "ecac65c65418641abf598db74d588ba8f53b3f358505bd31e215f09562922e3f", + "inputs/PR558-BASELINE-ASSEMBLY.json": "9f5e050486c3c337793d09e4ce96769336a3653de0a3a84a77c39431cf062f16", + "inputs/PR558-EXPECTED.json": "6c16d41d9c10bc04c65b548ff34422ee2d90d63c37e9bdea4adbdf06fa959f44", + "inputs/PR558-INVOICE.json": "4b6977a049663ab958bd9a48c2864f7a7bddb26aef03e14f3068aede020ef76f", + "inputs/PR558-OWNERS.json": "0bcaa62bf4723672113f2acdc3ae30c6faa18e5aefa3992e0ec7dc46b9cdd552", + "inputs/PR558-RESULT.json": "81618cefc1df42f827d0a7da838b13b9167d3500ca5cd598963c3e09e62ceb4e", + "inputs/UPSTREAM-LINEAGE.md": "2ec1c9b1f25e2f3d2556bee7369069ec2340cf126b54fa112e0bff9e269ef0e0", + "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54", + "notes/three-stage-cover-assembly.tex": "ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d", + "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511", + "notes/three-stage-cover-complex.tex": "1c5b638aa9b75365b8addec9c8eeee6bc5e499722901079b94c65fce033fde8a", + "verify.py": "6b444c686891b20b3a92385d025818fc86d9a6ddd2f77504d9223afaa47acd21" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/NOTICE.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/NOTICE.md new file mode 100644 index 0000000000..f173f442dc --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/NOTICE.md @@ -0,0 +1 @@ +Apache-2.0; original notices retained in source files. PR552: Dugongue. PR543: eumemic. Original Clifford/complex-cover notes and PR531/535: icekylinx with stated assistance. PR534 frame work: rohanarun/Claude. Inherited PR541/510/503/493/484/463/444/442/386 compiler and hosting lineage remains credited in inputs/UPSTREAM-LINEAGE.md. New audit and arithmetic composition by Rohan Arun with OpenAI Codex assistance. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/PROOF-REVIEW-STATUS.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/PROOF-REVIEW-STATUS.json new file mode 100644 index 0000000000..30032f58d8 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/PROOF-REVIEW-STATUS.json @@ -0,0 +1,7 @@ +{ + "status": "INDEPENDENT_SOURCE_SCOPE_REVIEW_ACCEPTED", + "packaged_verification": "PASS on Python 3.11 and 3.14 for PR558 composition, identical mathematical fields; PR552 regression PASS", + "initial_preflight_failure": "Published source invoice was accidentally paired with independently replayed owner receipt; hash guard rejected it. Fixed by pairing both receipts from the same completed independent replay. Original published invoice retained in evidence. No mathematical result accepted from mismatched receipts.", + "independent_provider_replay": "PR558 full physical/admission replay PASS at 060b137c8a6f9d73fd7864c7f8cf2736d6441774", + "draft_history": "Initial PR552 draft and subsequent PR558 update were published before their respective packaged checks, as requested. Receipts supersede pending status." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/PROOF.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/PROOF.md new file mode 100644 index 0000000000..9adf304048 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/PROOF.md @@ -0,0 +1,47 @@ +# Independent review: the PR552 complex bad-class surcharge + +**Assessment: removal is justified under the same inherited exact complex-cover/compiler assumptions.** This review supports omitting the additional bad-residue fallback from the complex recurrence only. It does not certify a numerical improvement, weaken the bit recurrence, or discharge any inherited all-size theorem. + +## Original recurrence distinction + +The pinned `notes/three-stage-cover-assembly.tex` at commit12a4934d15006e8c10f9b2264f13f8f341be802b gives the complex moment as the exact child-profile sum, divided by the complex live stock. It then separately introduces the entire32*m_b^2-child fallback on a10^-16 fraction of every ideal edge of the **bit** ledger. Its precision/router guard explicitly retains the full finite orthogonal group and Clifford routers. + +The adjacent pinned `notes/general-clifford-frames.tex` constructs exact Gaussian-dyadic representatives for every binary subspace, exact nested transitions, rank-zero adapters, and dirty-tail/reverse identities. It gives exact algebraic operators, not good-class operators accompanied by a failed residue-class fraction. Fixed binary GL matrices that choose these representatives are invertible address maps over F2; they are not the q-adic selectors responsible for bit-side fallback. + +Both original note hashes and Git-blob identities were independently checked against the parent acquisition pins; see REVIEW.json. + +## Actual PR552 compiler audit + +This conclusion follows from the emitted program and its exact controller, not merely from an absence of keywords: + +1. `emit_local.py` emits both orientations from the selected source. Every positive-rank frame climb and center descent is explicitly a recursive child; all scalar operations, coefficient work, phases, and residual adapters remain separate finite work. It checks all exact scalar columns and paid-profile equality. +2. `emit_supplier_hosted.py` assigns each entire helper invocation to an explicit physical family and orthogonal chart. Its profile is the sum over all72 complete local invocations plus every nonempty idle remainder. The emitted asynchronous schedule retains every source event on each replica and the final correction. +3. `audit_supplier_hosted.py` independently checks all owner windows, one-owner exclusivity, residual/spectator axes, phase bindings, and every explicit remainder. It reconstructs actual orthogonal73-column charts and the same global histogram. It rejects omitted idle children and invalid owner assignments. +4. `invoice_final.py` recounts all scalar/Horner work, wrappers, adapters, movement, and router costs. It charges the full finite orthogonal group and preserves the precision, tape, external-row and halving guards. Its prefix argument uses exact right-translation bijections on the cover group, so every cover vertex obeys the same operator construction. + +The prior independent physical replay receipts have been checked for PASS and matching template/owner hashes. This review does not rerun that full physical verifier. The actual2,972 owner-chart types are finitely checked; the enormous entire orthogonal group is not enumerated element-by-element. The translation-bijection argument supplies the uniform passage to the full cover. + +Consequently the complex controller has an exact exhaustive recursive-child profile. There is no further width-dependent good/bad q-adic selector in this construction requiring a fraction of additional recursive fallback children. The finite Clifford routers and adapters are already paid in the unchanged finite invoice. Removing them, or removing other precision/row guards, would not follow from this argument. + +## Where the extra term enters + +`vendor535/code/assemble_combined.py` uses one generic `two_moments` function for both suppliers. It calls the moment engine with `bad=True` and explicitly adds the fallback through the second engine for the complex profile as well as the bit profile. The original moment engine labels that option an inherited envelope and makes the default `bad=False`. Thus the correction is a recurrence-model choice at assembly, not a changed scalar word, owner schedule, or hidden physical optimization. + +For complex profile H, dimension m, and live stock W, retain exactly + + sum_r H[r] * (r/m)^(1-b) / W. + +Omit only the additional complex term proportional to32*m^2*sum(H)/10^16. Keep the entire bit bad-class surcharge and all its mutable-source/selector assumptions. + +## Scope and relation to PR557 + +This remains conditional on the retained all-size realization, common-label/compiler, completed-call hosting, semantic precision, fixed-tape/exact-recovery, and analytic-transfer interfaces. The review does not replace these assumptions with a new theorem. Under those same interfaces, a uniform exact complex cover uses its pure child moment, matching the original complex assembly argument. A port to a different complex implementation that actually has exceptional residue classes would require its own analysis. + +PR557 explicitly fixes its conservative bad-class charge and excludes alternative charges from its ceiling. Changing that unnecessary complex surcharge therefore lies outside that certificate's stated model; it does not contradict the verified fixed-charge ceiling. Separately, PR557 fixes the PR551 scalar word and does not directly cover final PR552. + +No numerical value is claimed by this review. Both rational engines, the next endpoint, all strict outer inequalities, and a publication package must be checked by the parent before announcing a new conditional bound. No PR or provider source was edited, and all artifacts remain on the mounted SSD. + + +## Transfer to PR558 + +PR558 changes eight kernel entrances and repacks complete owners, while retaining byte-identical local emission, scalar audit, phase/adapters, complete-owner emission/audit and invoice code from reviewed PR552. Its new exact finite witness uses the same native binary-Clifford/orthogonal-cover contract and introduces no q-adic selector. The same pure-complex recurrence therefore applies after its new finite admission. The published receipts are pinned; an independent full replay passed at head 060b137c8a6f9d73fd7864c7f8cf2736d6441774. Fresh admission and compiler-lineage receipts are preserved in evidence/. The bit supplier and its bad-class charge remain unchanged. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/README.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/README.md new file mode 100644 index 0000000000..3e5e80b917 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/README.md @@ -0,0 +1,20 @@ +# Native complex moment: PR558 plus the exact recurrence correction + +Conditional **kappa = 0.001592517892053334**, above PR558's0.001592517889315014 by **2.738320e-12** (+0.00000017194909%). This is a tiny accounting correction on eumemic's structural result; it is not another geometry or circuit improvement. + +The exact binary-Clifford complex cover has a complete recursive-child histogram. Generic pricing adds the bit supplier's GL local-ring bad-residue surcharge to both sides. This package returns the complex side to its native moment. The bit charge, selected scalar word, owner schedule and finite invoice remain unchanged. [Independent proof-scope review](PROOF.md) gives the uniform chart/right-translation argument. + +Complex b becomes0.001595058050537679100938. Cited PR543 c stays0.001653826988146798944268. Both rational discovery engines pass the new endpoint and reject the next10^-24 tick; seven bootstrap levels and47 strict outer inequalities give the displayed kappa. + +## Verification + +The full independent PR558 replay passed in 126.92 seconds, including fresh phase, owner, invoice and assembly checks. The updated packaged checks passed on Python 3.11 and 3.14 with identical mathematical outputs, and the PR552 regression passed. Receipts are in `evidence/`. CI status must be read separately from GitHub; local success is not a green CI claim. This arithmetic-only verifier cites unchanged physical operators rather than rebuilding them. + + python -B verify.py --work /absolute/new/output + python -B verify.py --provider 552 --work /absolute/new/regression-output + +Python3.11+, standard library, offline, assertions enabled. Inputs/owner/invoice and exact baseline are bound; the original bit contamination is checked in both engines. The new complex endpoint and next tick,47 outer inequalities, seven bootstrap cutoffs and parameter controls are checked. The552 regression retains six bootstrap levels and its original candidate0.001591968905569359. + +All inherited all-size compiler, common-label/mutable-source, complete-call hosting, precision/tape and analytic assumptions remain, including PR543 H1-H5. Explicit checks cover chart types; full-group validity uses right-translation bijections. No unconditional theorem, new Lean proof or practical speedup. PR557 fixes the old surcharge and different boundaries, so this is outside its scope. + +Credits: eumemic/Codex PR558; Dugongue PR552; eumemic/Claude PR543; icekylinx original Clifford/complex-cover notes and PR531/535; all inherited compiler/hosting authors. New source audit and arithmetic by Rohan Arun with OpenAI Codex assistance. Original notices remain preserved. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/REVIEW.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/REVIEW.json new file mode 100644 index 0000000000..381201476a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/REVIEW.json @@ -0,0 +1,99 @@ +{ + "status": "CONDITIONALLY_JUSTIFIED_ZERO_COMPLEX_BADCLASS_SURCHARGE", + "source_pr552_head": "33c33af0b7697155be1ea708e08cbd3f0707d94c", + "notes_pins": [ + { + "path": "notes/general-clifford-frames.tex", + "commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "blob": "0367eeb005298601f28a673861d6f71bf1d0ebbb", + "sha256": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54" + }, + { + "path": "notes/three-stage-cover-assembly.tex", + "commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "blob": "983ffb6ac8fb9117360cd0797c00c05dfa071c9d", + "sha256": "ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d" + } + ], + "read_source_bindings": [ + { + "path": "complex552-fallback-audit/general-clifford-frames.tex", + "sha256": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54" + }, + { + "path": "complex552-fallback-audit/three-stage-cover-assembly.tex", + "sha256": "ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d" + }, + { + "path": "source552-review/complex-global/vendor531/code/emit_local.py", + "sha256": "eefc76e0bee003015fe21ac685c2cce658033d5444add404d2d509c7d6f39bac" + }, + { + "path": "source552-review/complex-global/vendor531/code/emit_supplier_hosted.py", + "sha256": "53c0b653b3a5100756d6a9473c90101b8c3ab72723d7047983906ab997bdf920" + }, + { + "path": "source552-review/complex-global/vendor531/code/audit_supplier_hosted.py", + "sha256": "301e9b5c593b6d583065337eb7b3ef207cf039e265f099f89080a4bf25856b43" + }, + { + "path": "source552-review/complex-global/vendor531/code/invoice_final.py", + "sha256": "96b6bed96ca8b60dfc064cd1c7962c45a5cb53c4e52cd90aaea6ccf8d109db97" + }, + { + "path": "source552-review/complex-global/vendor535/code/assemble_combined.py", + "sha256": "41216e8da3b647fe6eead9079858f25b2592cab090154aca43f3cc73ff36dc9b" + }, + { + "path": "source552-review/engines/moment.py", + "sha256": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482" + }, + { + "path": "source552-review/README.md", + "sha256": "79cc63fc45ea52c04f32555676704a1664a3eafdd917b25689b1acd390a4636d" + }, + { + "path": "pr552-independent314/complex-local/local/INDEPENDENT-LOCAL-REPLAY.json", + "sha256": "e871d8d56014146c19963430e4822714aadbf57367f783dc1dd42fa3f5b0a0ce" + }, + { + "path": "pr552-independent314/complex-global/audit/OWNERS-AND-PROFILE.json", + "sha256": "ecac65c65418641abf598db74d588ba8f53b3f358505bd31e215f09562922e3f" + }, + { + "path": "pr552-independent314/complex-global/audit/ASYNC-AUDIT.json", + "sha256": "01d37b06d35ffb1995533cc618b0baaa093f55d288786153406fc46c94ab9926" + }, + { + "path": "pr552-independent314/complex-global/audit/PREFIX-AND-INVOICE.json", + "sha256": "4ac060dbf2ea2624dd1f4bda23bdb81c0a3013dfe49b77c092b631885529947f" + }, + { + "path": "pr552-independent314/complex-global/audit/GLOBAL-PREFIX.json", + "sha256": "789d003bce7c6b6fcc6dad6b2bfb2d1bd05e8bba68aa87139a05c6752b861529" + } + ], + "independent_owner_status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE", + "independent_invoice_status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE", + "independent_local_status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY", + "complex_live": 7168, + "physical": 7682, + "profile": { + "1": 165600, + "2": 32128, + "3": 35907, + "4": 13248, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "actual_73column_sigmas": 2972, + "template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "decision": "The actual complete finite complex controller meets the exact-cover alternative in the retained complex recurrence, under the same inherited all-size compiler and semantic interfaces. No exceptional bad-residue fraction is introduced by its fixed exact Clifford maps or orthogonal cover translations. The bit bad-class fallback must remain.", + "new_numerical_claim": false, + "new_allsize_proof": false, + "unconditional_multiplication_claim": false +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/SOURCES.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/SOURCES.json new file mode 100644 index 0000000000..12ace451da --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/SOURCES.json @@ -0,0 +1,47 @@ +{ + "pr552": { + "head": "33c33af0b7697155be1ea708e08cbd3f0707d94c", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/552" + }, + "pr543": { + "head": "2065fe4f72a914d907f1046603f5a36f17018535", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/543" + }, + "original_notes": [ + { + "path": "notes/general-clifford-frames.tex", + "commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "blob": "0367eeb005298601f28a673861d6f71bf1d0ebbb", + "sha256": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54" + }, + { + "path": "notes/three-stage-cover-assembly.tex", + "commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "blob": "983ffb6ac8fb9117360cd0797c00c05dfa071c9d", + "sha256": "ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d" + } + ], + "other_notes": { + "commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "files": [ + { + "path": "notes/three-stage-cover-complex.tex", + "sha": "c54cb3d5ff13281fe2aa44ac3baeaac7fce75469" + }, + { + "path": "notes/three-stage-cover-bit.tex", + "sha": "f05225d21f92cf8cef21b6e12601d5b4d61991f0" + }, + { + "path": "notes/three-stage-cover-note.tex", + "sha": "f5ad09a450cc5dd31a5c6aa07ff08523064d7281" + } + ] + }, + "input_receipts": "PR552 owner and invoice are from the same completed independent replay. Published original invoice is preserved separately; profile/template match pinned EXPECTED.", + "pr558": { + "head": "060b137c8a6f9d73fd7864c7f8cf2736d6441774", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/558", + "inputs": "Exact published python314 validation receipts; normalized EXPECTED copies result plus profile alias and invoice template, checked at runtime." + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/engines/base_two_moment.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/engines/base_two_moment.py new file mode 100644 index 0000000000..14a90fa0e7 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/engines/base_two_moment.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Maintainer arithmetic cross-check of the pinned PR39 certificate. + +Uses no producer/checker imports. Counts are inputs, not proved by this script. +80-term rational logarithms and 12-term exponentials independently enclose +the two moments. The accompanying written review addresses their realization. +""" +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[1] +GRID = 10**30 + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def log_unit(x): + require(1 <= x <= 2, "logarithm range") + z = (x-1)/(x+1) + lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0)) + return lo, lo+2*z**161/(161*(1-z*z)) + + +def log_bounds(x): + k = 0 + while x > 2: + x /= 2 + k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + # Outward rational rounding keeps later certificates compact. + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + + +def exp_bounds(x): + require(0 <= x < 1, "exponential range") + term = total = Q(1) + for j in range(1, 13): + term *= x/j + total += term + tail = term*x/13/(1-x/14) + return total, total+tail + + +def moment(m, W, entries, saving): + lo = hi = Q(0) + for t, count in entries: + t, count = int(t), int(count) + require(0 < t < m and count > 0, "improper child") + l, u = log_bounds(Q(m, t)) + lower = exp_bounds(saving*l)[0] + upper = exp_bounds(saving*u)[1] + lo += Q(t*count, m*W)*lower + hi += Q(t*count, m*W)*upper + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/engines/moment.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/engines/moment.py new file mode 100644 index 0000000000..7d697cb452 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/engines/moment.py @@ -0,0 +1,113 @@ +"""Independent prospective ordinary five-stage cost, never supplier admission. + +Consumes a raw one-invocation ledger made from the actual source/internal/target +paths. No packed profile is used as an input. Missing physical/finite/compiler +obligations must remain explicit in the accompanying report. +""" +from collections import Counter +from decimal import Decimal, localcontext, ROUND_FLOOR +from fractions import Fraction as F +from functools import lru_cache +from math import factorial +import hashlib, json, sys +from pathlib import Path + +DYAD = 1 << 224 + +def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD) +def ceil(x): return -floor(-x) + +@lru_cache(None) +def logarithm(x): + """Mercator bounds after binary reduction; ln(2) via two Mercator sums. + + For 1 <= y < 2, log(y) is an alternating series in z=y-1. + We instead reduce to 1 <= y < 3/2, and bound log(3/2) and + log(2) by the same alternating series at z=1/2 and z=1/3, + using log(2)=log(3/2)+log(4/3). All sums are exact rationals. + """ + assert x >= 1 + k = 0 + while x >= 2: x /= 2; k += 1 + j = int(x >= F(3, 2)) + if j: x /= F(3, 2) + def mercator(y): + z=y-1 + assert 0 <= z <= F(1,2) + # An even partial sum is below log; the next term bounds its tail. + t=z; s=F(0) + for n in range(1, 225): + s += (t if n & 1 else -t)/n + t *= z + return s, s+t/225 + a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3)) + return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f) + +def exponential(l,u): + assert 0 <= l <= u < F(1,10) + def poly(x): + s=t=F(1) + for j in range(1,25): t=t*x/j; s+=t + return s,t + lo,_=poly(l);hi,last=poly(u) + return floor(lo),ceil(hi+last*u/25/(1-u/26)) + +def moment(H,m,W,a,bad=False): + lo=hi=F(0) + for r,n in H.items(): + assert 0 < r < m and n > 0 + l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u) + p=F(r*n,m*W);lo+=p*e;hi+=p*f + if bad: + # Existing envelope shape, only conditionally portable to the new cover. + l,u=logarithm(F(m));e,f=exponential(a*l,a*u) + p=F(32*m*sum(H.values()),10**16*W) + lo+=p*e;hi+=p*f + return floor(lo),ceil(hi) + +def decimal(x): + with localcontext() as c: + c.prec=70 + return str(Decimal(x.numerator)/Decimal(x.denominator)) + +def certify(H,m,W,bad=False): + with localcontext() as c: + c.prec=70 + terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()] + fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0) + lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003') + for _ in range(210): + a=(lo+hi)/2 + if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a + else:hi=a + q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR)) + lo=F(q,10**24);hi=lo+F(1,10**24) + lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad) + assert lv[1]<10 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2 + assert 1-eps*(1+c)==eta-eps*eta/4 + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-INDEPENDENT-REPLAY.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-INDEPENDENT-REPLAY.json new file mode 100644 index 0000000000..8117926d22 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-INDEPENDENT-REPLAY.json @@ -0,0 +1,49 @@ +{ + "status": "PASS_FILTRATION_WAVEFRONT", + "kappa": "795984451416673/500000000000000000", + "kappa_decimal": "0.001591968902833346", + "bit_lower": "413456747036699736067/250000000000000000000000", + "complex_lower": "1594507308884431019637/1000000000000000000000000", + "complex_template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "complex_canonical_word_sha256": "995e46ed6dc8377f02bf05a3370171796364cedefdfeaeae47c2a207b5a8b173", + "complex_global_profile": { + "1": 165600, + "2": 32128, + "3": 35907, + "4": 13248, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "complex_prefix_bits": 225, + "forward_events": 21483, + "backward_events": 21483, + "waves": 8, + "wave_omission_controls": 8, + "coset_rewrites": 12, + "compensation_additions_saved": 624, + "outer_constraints": 47, + "bit_operator": "Pinned PR543 cited dependency, not physically replayed here", + "stages": [ + { + "name": "complex-reconstruction-and-local-checks", + "exit": 0, + "seconds": 13.987790917046368 + }, + { + "name": "complete-owner-physical-and-invoice", + "exit": 0, + "seconds": 7.874530042055994 + }, + { + "name": "exact-two-supplier-assembly", + "exit": 0, + "seconds": 0.24127279093954712 + } + ], + "elapsed_seconds": 22.136513874982484, + "scope": "Exact composition of the freshly rebuilt and physically audited wave complex supplier with the pinned PR543 published bit receipt. The unchanged bit operator is cited, not rebuilt in this package. Inherited all-size compiler, common-label/mutable-source, hosting, precision/tape and analytic interfaces remain conditional. R420 interleaved phase-B source writes rely on its stated H1-H5 interface argument." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-PUBLISHED-INVOICE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-PUBLISHED-INVOICE.json new file mode 100644 index 0000000000..2cd1365bdd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-PUBLISHED-INVOICE.json @@ -0,0 +1,106 @@ +{ + "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE", + "template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "parent_template_sha256": "7eddf21720ce26ff72069a0e94fa7f0e692cfe3bea2defb1a3769bea352cf471", + "owner_audit_sha256": "6572e69d9df9a72a600d7ee88404f96c525fea760b76cb6607273d85681579d1", + "controller_audit_sha256": "01d37b06d35ffb1995533cc618b0baaa093f55d288786153406fc46c94ab9926", + "independent_local_replay_sha256": "e871d8d56014146c19963430e4822714aadbf57367f783dc1dd42fa3f5b0a0ce", + "canonical_word_sha256": "995e46ed6dc8377f02bf05a3370171796364cedefdfeaeae47c2a207b5a8b173", + "local_programs_sha256": "7b191ec016ab99a0e1415206b898a8a6c5485fe9e8d91e59539e7c3710725563", + "local_checks_sha256": "2c51cdb9b282aadb99ea00d05b6c4bee140577111bdfd5c675b038373e309a17", + "global_prefix_bits": 225, + "charged_prefix_bits": 512, + "complete_invocation_sweeps": 72, + "bridge_sweeps": 72, + "row_prefix_extra": 1024, + "local": { + "backward": { + "events": 21483, + "macros": 16290, + "real_component_primitives": 161356, + "prefix_l1": "1044730572396", + "prefix_bits": 40, + "coefficient_work_primitive_count": 79906, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 212, + "post_wrappers": 212, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + }, + "forward": { + "events": 21483, + "macros": 16290, + "real_component_primitives": 161308, + "prefix_l1": "88876257700", + "prefix_bits": 37, + "coefficient_work_primitive_count": 79874, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 212, + "post_wrappers": 212, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + } + }, + "helpers": 504, + "centres": 8, + "live": 7168, + "physical": 7682, + "physical_stock_identity": { + "data_and_owner_families": 7168, + "local_helpers": 504, + "private_centres": 8, + "coefficient_work": 2 + }, + "entering_helpers": 212, + "entrance_rank": 380, + "width_inventory": { + "5": 56, + "8": 156, + "9": 292 + }, + "local_adapters": 333344, + "local_primitive_bound": 8645055460940, + "wrapper_elementary_factors_charged": 4396032, + "factors_per_wrapper": 144, + "compiler": 25934336, + "unhosted_pervertex": 1574554051175192, + "hosted_rebased_pervertex": 1574554050875816, + "conservative_pervertex_used": 4452501040899760, + "retained_prior_overcharge": { + "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478", + "previous_pervertex_allowance": 2877946989724568, + "added_complete_new_pervertex": 1574554051175192, + "policy": "Retain old allowance and add the entire fresh recount." + }, + "finite": { + "physical_stock_bits": 2641, + "router_bits": 7985, + "literal_bits": 35282, + "physical_row_coefficient": 16467, + "retained_row_coefficient": 20161, + "required_C0_bits": 200012, + "halving_integer_inequality": [ + 5329, + 4608 + ], + "G_exponent": 30000, + "E_exponent": 100000, + "C0_exponent": 210000 + }, + "strict_checks": { + "local_primitive_bound": true, + "logical": true, + "router": true, + "literal": true, + "mass": true, + "precision": true, + "tape": true, + "row": true, + "halving": true + }, + "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-packaged311.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-packaged311.json new file mode 100644 index 0000000000..b964eea61a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR552-packaged311.json @@ -0,0 +1,146 @@ +{ + "status": "PASS_NATIVE_COMPLEX_MOMENT_AND_CONDITIONAL_COMPOSITION", + "baseline_kappa": "795984451416673/500000000000000000", + "baseline_kappa_decimal": "0.001591968902833346", + "candidate_kappa": "1591968905569359/1000000000000000000", + "candidate_kappa_decimal": "0.001591968905569359", + "old_complex_lower": "1594507308884431019637/1000000000000000000000000", + "complex_lower": "398626827907293921411/250000000000000000000000", + "complex_decimal": "0.001594507311629175685644", + 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the unchanged pinned selected exact binary-Clifford complex supplier, with cited PR543 bit supplier and unchanged bit bad-class charge. Original source distinguishes exact complex recursion from GL local-ring bit selectors. All inherited all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic assumptions remain conditional. This verifier does not rerun unchanged physical operators." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-COMPILER-LINEAGE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-COMPILER-LINEAGE.json new file mode 100644 index 0000000000..1a58a75b96 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-COMPILER-LINEAGE.json @@ -0,0 +1,41 @@ +{ + "status": "IDENTICAL_EXACT_COMPLEX_COMPILER_LINEAGE", + "files": [ + { + "path": "complex-global/vendor531/code/emit_local.py", + "sha256": "eefc76e0bee003015fe21ac685c2cce658033d5444add404d2d509c7d6f39bac", + "byte_identical_to_reviewed552": true + }, + { + "path": "complex-global/vendor531/code/audit_local.py", + "sha256": "69b12c45d0a961175a824c1967353c7f3b94818a7dd6ac7bbcf56a6d1a5ed8e8", + "byte_identical_to_reviewed552": true + }, + { + "path": "complex-global/vendor531/code/adapters_local.py", + "sha256": "4e89a5c517cd87ff6a5aa9b7334c0d74821179ae5777d31284da25b9d8abf113", + "byte_identical_to_reviewed552": true + }, + { + "path": "complex-global/vendor531/code/emit_supplier_hosted.py", + "sha256": "53c0b653b3a5100756d6a9473c90101b8c3ab72723d7047983906ab997bdf920", + "byte_identical_to_reviewed552": true + }, + { + "path": "complex-global/vendor531/code/audit_supplier_hosted.py", + "sha256": "301e9b5c593b6d583065337eb7b3ef207cf039e265f099f89080a4bf25856b43", + "byte_identical_to_reviewed552": true + }, + { + "path": "complex-global/vendor531/code/invoice_final.py", + "sha256": "96b6bed96ca8b60dfc064cd1c7962c45a5cb53c4e52cd90aaea6ccf8d109db97", + "byte_identical_to_reviewed552": true + }, + { + "path": "complex-global/vendor531/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "byte_identical_to_reviewed552": true + } + ], + "assessment": "The existing zero-complex-badclass scope argument carries to the promoted supplier conditional on fresh phase/owner/invoice admission. Changing starts, widths and owners does not introduce a probabilistic/q-adic selector; it changes the exact profile and requires the fresh admission now running." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-INDEPENDENT-RECEIPT.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-INDEPENDENT-RECEIPT.json new file mode 100644 index 0000000000..2064abce71 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-INDEPENDENT-RECEIPT.json @@ -0,0 +1,71 @@ +{ + "status": "PASS_COMPLEX_EIGHT_RANK5_PIVOTS_AND_CITED_BIT", + "steps": [ + { + "name": "reconstruct552-and-promote8", + "exit_code": 0, + "seconds": 14.96228679199703, + "log_sha256": "b7b035547780f64e33ea2432fd2cc79ed5795bf88c9791cbb913d9ec2a7c6a2b" + }, + { + "name": "all-columns-native-frames", + "exit_code": 0, + "seconds": 0.4768510829890147, + "log_sha256": "b3b7b19f1d9c7baa563cfa169302daa4486727169334c8102bc9b6b606a3c3e5" + }, + { + "name": "emit-both-reflected-ledgers", + "exit_code": 0, + "seconds": 0.44516691705211997, + "log_sha256": "f382385a67f705b446978a73fc6492ce127cb2ae76011e87e36fdbe9977f4347" + }, + { + "name": "independent-local-and-controls", + "exit_code": 0, + "seconds": 1.4429402919486165, + "log_sha256": "b694b4b22abb9d1de9a70bbbdf9e9b0e030ec00a7eddc264e4c18376dd859cee" + }, + { + "name": "normalized-wrappers", + "exit_code": 0, + "seconds": 0.8871639160206541, + "log_sha256": "284cce3149354d057b4e2f04163535c0d8b0a924898e5b771ba8af2740314154" + }, + { + "name": "all-phase-recipes", + "exit_code": 0, + "seconds": 100.04125804197975, + "log_sha256": "33aa90a041ba29ebb44f21206dc7990a45b29297ef134780940f608844a4722c" + }, + { + "name": "literal-owners-full-invoice", + "exit_code": 0, + "seconds": 8.275277458014898, + "log_sha256": "2fee1e317b9601b87b6e96b23d8f6077abf7ea38b7154aa215c46c1a9bde9a53" + }, + { + "name": "two-engine-exact-assembly", + "exit_code": 0, + "seconds": 0.1878548749955371, + "log_sha256": "b50e71a1c084e221ca32b43001f5383c8cffb09d72e66b1436f22aa240795a9c" + }, + { + "name": "assembly-admission-controls", + "exit_code": 0, + "seconds": 0.19738204102031887, + "log_sha256": "9cc0577eb648247a02f4352eaf5187000a8378657f388e8ffa8cbeb55a43b9ec" + } + ], + "artifacts": { + "RESULT.json": "b32113b56745cd5c142c982426ce31f0fe8d4f1a4ba219541e8c8befc69f017c", + "ASSEMBLY.json": "de60471def08f776e5de1b79bb80d871a4f528ecda8fb8eaf99f3757173c520e", + "ASSEMBLY-CONTROLS.json": "a97f22aeb8ca732f9bfce074c30be73564da8892118395136456ec7533654331", + "reconstruction/promoted/PROMOTION.json": "9ad34faa8611a6ea7f161d2e1fe331ab1ba5ccec8fca3978e31c3e7bf789bc31", + "complex-local/INDEPENDENT-LOCAL-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26", + "complex-local/CLIFFORD-REVIEW.json": "a1d49f9272a5427d3d34086f7cc3c3e6c6fd24655b600277c1e816970e8cfb66", + "complex-global/audit/ASYNC-AUDIT.json": "177cfc604cd7085019b615945f33c04197eee181e8c30ec13831cf253c138e23", + "complex-global/audit/OWNERS-AND-PROFILE.json": "33bf86f3968796cb2f98214674846c9d51e4f6bb55c6d4dd7159b0a8cdf6a21b", + "complex-global/audit/PREFIX-AND-INVOICE.json": "0518f59792aaf017af7669fa3d617aaadb391a4d4ffd8498916dcd7a3d2bfbbf" + }, + "manifest_sha256": "f28c04eecbea7599fa9e0867dd8d0311a463af12cab79f90a43733b162527164" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-INDEPENDENT-REPLAY.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-INDEPENDENT-REPLAY.json new file mode 100644 index 0000000000..2521c93be8 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-INDEPENDENT-REPLAY.json @@ -0,0 +1,31 @@ +{ + "status": "PASS_COMPLEX_EIGHT_RANK5_PIVOTS_AND_CITED_BIT", + "kappa": "796258944657507/500000000000000000", + "kappa_decimal": "0.001592517889315014", + "complex_lower": "199382255973827096291/125000000000000000000000", + "bit_lower": "413456747036699736067/250000000000000000000000", + "word_sha256": "375bd23001cd805707968005a9342827d5464e3f8e3a754197b31c46fc3f63c2", + "local_profile": { + "1": 2316, + "4": 192, + "8": 8, + "3": 464, + "2": 424, + "6": 56, + "5": 56 + }, + "global_profile": { + "1": 166880, + "2": 30528, + "3": 35779, + "4": 13824, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "seconds": 126.92180670797825, + "scope": "Conditional finite complex witness composed with cited unchanged PR543 bit supplier. 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No unconditional theorem or full Lean certification." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-packaged311.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-packaged311.json new file mode 100644 index 0000000000..463a2b1174 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/evidence/PR558-packaged311.json @@ -0,0 +1,152 @@ +{ + "status": "PASS_NATIVE_COMPLEX_MOMENT_AND_CONDITIONAL_COMPOSITION", + "provider": "558", + "baseline_kappa": "796258944657507/500000000000000000", + "baseline_kappa_decimal": "0.001592517889315014", + "candidate_kappa": "796258946026667/500000000000000000", + "candidate_kappa_decimal": "0.001592517892053334", + "old_complex_lower": "199382255973827096291/125000000000000000000000", + "complex_lower": "797529025268839550469/500000000000000000000000", + "complex_decimal": "0.001595058050537679100938", + 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Original source distinguishes exact complex recursion from GL local-ring bit selectors. All inherited all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic assumptions remain conditional. This verifier does not rerun unchanged physical operators." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR543-EXPECTED.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR543-EXPECTED.json new file mode 100644 index 0000000000..b61d859826 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR543-EXPECTED.json @@ -0,0 +1,239 @@ +{ + "word": { + "file": "data/bitE8mut-r420.json.gz", + "file_sha256": "9721a3819efd68307f66f00d84a952eb28eb7c3ad2ce79653ce295c98a764784", + "content_sha256": "e597e3885c0a8daa262afa5985ee2930443329126aece76d33159d81882bdcc2", + "plan_sha256": "d5c2494b4baae801143049e172db303b3c8e25a002e9d9715a1d79dcb2d74c58", + "R": 420, + "retained_totals": 9, + "gates": { + "D": 120, + "A": 2064, + "B": 837, + "C": 2661 + }, + "local_histogram": { + "1": 1320, + "2": 1440, + "4": 60, + "5": 120, + "8": 9 + }, + "legality": { + "records": 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"15615077643704555604994425885436776413026753051081759442584659149990102084077935377970027573490939593604820736101011172907705849/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "cutoff_log2": "147643456746455004602217631773182069" + }, + { + "gap": "24788109816909242260870500225499627723644532489569312798749735575207324411482233239583707631312250354296798781303533719966836301725924238770077838843/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "cutoff_log2": "58588944991775862180494665844538845859209" + } + ], + "complex_template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "owner_audit_sha256": "ecac65c65418641abf598db74d588ba8f53b3f358505bd31e215f09562922e3f", + "invoice_sha256": "4ac060dbf2ea2624dd1f4bda23bdb81c0a3013dfe49b77c092b631885529947f", + "bit_scope": "Pinned PR510 published profile and operator are cited dependencies. Both exact moments are freshly repriced here; the unchanged physical bit operator is not cold-reconstructed. See PR510-MUTABLE-SOURCE-CARRYOVER.md.", + "scope": "Conditional finite witness under the retained all-size compiler, common-label/mutable-basis, whole-call hosting, restored-work, precision/tape and analytic-transfer contracts. Fresh complex admission and finite invoice are separately hash-bound; no unconditional theorem is claimed." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-EXPECTED.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-EXPECTED.json new file mode 100644 index 0000000000..7ee2fb720a --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-EXPECTED.json @@ -0,0 +1,30 @@ +{ + "status": "PASS_FILTRATION_WAVEFRONT", + "kappa": "795984451416673/500000000000000000", + "kappa_decimal": "0.001591968902833346", + "bit_lower": "413456747036699736067/250000000000000000000000", + "complex_lower": "1594507308884431019637/1000000000000000000000000", + "complex_template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "complex_canonical_word_sha256": "995e46ed6dc8377f02bf05a3370171796364cedefdfeaeae47c2a207b5a8b173", + "complex_global_profile": { + "1": 165600, + "2": 32128, + "3": 35907, + "4": 13248, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "complex_prefix_bits": 225, + "forward_events": 21483, + "backward_events": 21483, + "waves": 8, + "wave_omission_controls": 8, + "coset_rewrites": 12, + "compensation_additions_saved": 624, + "outer_constraints": 47, + "bit_operator": "Pinned PR543 cited dependency, not physically replayed here" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-INVOICE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-INVOICE.json new file mode 100644 index 0000000000..fc99981f77 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-INVOICE.json @@ -0,0 +1,106 @@ +{ + "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE", + "template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "parent_template_sha256": "7eddf21720ce26ff72069a0e94fa7f0e692cfe3bea2defb1a3769bea352cf471", + "owner_audit_sha256": "ecac65c65418641abf598db74d588ba8f53b3f358505bd31e215f09562922e3f", + "controller_audit_sha256": "01d37b06d35ffb1995533cc618b0baaa093f55d288786153406fc46c94ab9926", + "independent_local_replay_sha256": "e871d8d56014146c19963430e4822714aadbf57367f783dc1dd42fa3f5b0a0ce", + "canonical_word_sha256": "995e46ed6dc8377f02bf05a3370171796364cedefdfeaeae47c2a207b5a8b173", + "local_programs_sha256": "7b191ec016ab99a0e1415206b898a8a6c5485fe9e8d91e59539e7c3710725563", + "local_checks_sha256": "2c51cdb9b282aadb99ea00d05b6c4bee140577111bdfd5c675b038373e309a17", + "global_prefix_bits": 225, + "charged_prefix_bits": 512, + "complete_invocation_sweeps": 72, + "bridge_sweeps": 72, + "row_prefix_extra": 1024, + "local": { + "backward": { + "events": 21483, + "macros": 16290, + "real_component_primitives": 161356, + "prefix_l1": "1044730572396", + "prefix_bits": 40, + "coefficient_work_primitive_count": 79906, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 212, + "post_wrappers": 212, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + }, + "forward": { + "events": 21483, + "macros": 16290, + "real_component_primitives": 161308, + "prefix_l1": "88876257700", + "prefix_bits": 37, + "coefficient_work_primitive_count": 79874, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 212, + "post_wrappers": 212, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + } + }, + "helpers": 504, + "centres": 8, + "live": 7168, + "physical": 7682, + "physical_stock_identity": { + "data_and_owner_families": 7168, + "local_helpers": 504, + "private_centres": 8, + "coefficient_work": 2 + }, + "entering_helpers": 212, + "entrance_rank": 380, + "width_inventory": { + "5": 56, + "8": 156, + "9": 292 + }, + "local_adapters": 333344, + "local_primitive_bound": 8645055460940, + "wrapper_elementary_factors_charged": 4396032, + "factors_per_wrapper": 144, + "compiler": 25934336, + "unhosted_pervertex": 1574554051175192, + "hosted_rebased_pervertex": 1574554050875816, + "conservative_pervertex_used": 4452501040899760, + "retained_prior_overcharge": { + "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478", + "previous_pervertex_allowance": 2877946989724568, + "added_complete_new_pervertex": 1574554051175192, + "policy": "Retain old allowance and add the entire fresh recount." + }, + "finite": { + "physical_stock_bits": 2641, + "router_bits": 7985, + "literal_bits": 35282, + "physical_row_coefficient": 16467, + "retained_row_coefficient": 20161, + "required_C0_bits": 200012, + "halving_integer_inequality": [ + 5329, + 4608 + ], + "G_exponent": 30000, + "E_exponent": 100000, + "C0_exponent": 210000 + }, + "strict_checks": { + "local_primitive_bound": true, + "logical": true, + "router": true, + "literal": true, + "mass": true, + "precision": true, + "tape": true, + "row": true, + "halving": true + }, + "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-OWNERS.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-OWNERS.json new file mode 100644 index 0000000000..fbb8ae601b --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR552-OWNERS.json @@ -0,0 +1,40 @@ +{ + "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE", + "template_sha256": "1ddb317665797be007dfcc06e295f46bf9115ddeb308a21a60f98b9c28c6aff0", + "paid_profile": { + "1": 165600, + "2": 32128, + "3": 35907, + "4": 13248, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "live": 7168, + "physical": 7682, + "rank_mass": 520704, + "deficit": 2560, + "hosted_residuals": 36288, + "banked_residuals": 0, + "all_live_owners_per_call_distinct": true, + "owners_per_call": 728, + 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"work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + "controller_audit_sha256": "01d37b06d35ffb1995533cc618b0baaa093f55d288786153406fc46c94ab9926" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-BASELINE-ASSEMBLY.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-BASELINE-ASSEMBLY.json new file mode 100644 index 0000000000..3f005b6df6 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-BASELINE-ASSEMBLY.json @@ -0,0 +1,187 @@ +{ + "status": "PASS_FRESH_EIGHT_PIVOT_EXACT_ASSEMBLY", + "kappa": "796258944657507/500000000000000000", + "kappa_decimal": "0.001592517889315014", + "complex_lower": "199382255973827096291/125000000000000000000000", + "complex_decimal": "0.001595058047790616770328", + "bit_lower": "413456747036699736067/250000000000000000000000", + "bit_decimal": 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"14877392976763984315995128567051112906056099979615949599188147496749943753967882560235230110226014800083946653429542815585165131533369678193550526981588733270300705639966102157823603252081839658687574656766489097267912922909305167679635206308314925562695207171003562765976700875295852492726074600039810099486156273700021019573020758689892934067138142165582653197951139619385161185136222703519817319402164004168467998653/14924929410931328188930259715020111434228714651950937358972945684038556203876789242624229565253675378829308255683053557195630995743180191024171819344616648259371164400854208673712462282437496511529345657119960577884026412473959734631101365191629989815653932277208363717744466238750020086080051018374136029778448669404147709285520700115788096516373238041119425591943969604863997369307208587901607924560500000000000000000" + }, + "controls": [ + "next_grid", + "zero_eta", + "zero_beta", + "unit_beta" + ], + "scope": "Conditional finite complex witness composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-EXPECTED.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-EXPECTED.json new file mode 100644 index 0000000000..1f6a020cb1 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-EXPECTED.json @@ -0,0 +1,44 @@ +{ + "status": "PASS_COMPLEX_EIGHT_RANK5_PIVOTS_AND_CITED_BIT", + "kappa": "796258944657507/500000000000000000", + "kappa_decimal": "0.001592517889315014", + "complex_lower": "199382255973827096291/125000000000000000000000", + "bit_lower": "413456747036699736067/250000000000000000000000", + "word_sha256": "375bd23001cd805707968005a9342827d5464e3f8e3a754197b31c46fc3f63c2", + "local_profile": { + "1": 2316, + "4": 192, + "8": 8, + "3": 464, + "2": 424, + "6": 56, + "5": 56 + }, + "global_profile": { + "1": 166880, + "2": 30528, + "3": 35779, + "4": 13824, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "seconds": 125.83695875003468, + "scope": "Conditional finite complex witness composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.", + "complex_global_profile": { + "1": 166880, + "2": 30528, + "3": 35779, + "4": 13824, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "complex_template_sha256": "cdc651b7fd865a9b0b468c519078610ea2b6f14558168a257ac0ee3d593729ae" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-INVOICE.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-INVOICE.json new file mode 100644 index 0000000000..0a0318e6bd --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-INVOICE.json @@ -0,0 +1,107 @@ +{ + "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE", + "template_sha256": "cdc651b7fd865a9b0b468c519078610ea2b6f14558168a257ac0ee3d593729ae", + "parent_template_sha256": "7db047a427a7979d69e163c78a1e32bd445628fb86723e131a3138361355a9c3", + "owner_audit_sha256": "0bcaa62bf4723672113f2acdc3ae30c6faa18e5aefa3992e0ec7dc46b9cdd552", + "controller_audit_sha256": "177cfc604cd7085019b615945f33c04197eee181e8c30ec13831cf253c138e23", + "independent_local_replay_sha256": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26", + "canonical_word_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844", + "local_programs_sha256": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde", + "local_checks_sha256": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea", + "global_prefix_bits": 225, + "charged_prefix_bits": 512, + "complete_invocation_sweeps": 72, + "bridge_sweeps": 72, + "row_prefix_extra": 1024, + "local": { + "backward": { + "events": 21483, + "macros": 16290, + "real_component_primitives": 161356, + "prefix_l1": "1044730572396", + "prefix_bits": 40, + "coefficient_work_primitive_count": 79906, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 212, + "post_wrappers": 212, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + }, + "forward": { + "events": 21483, + "macros": 16290, + "real_component_primitives": 161308, + "prefix_l1": "88876257700", + "prefix_bits": 37, + "coefficient_work_primitive_count": 79874, + "all_exact_columns": 728, + "dirty_helper_columns": 504, + "all_dirty_helper_columns_restored": true, + "private_centres_and_coefficient_work_cleared": true, + "pre_wrappers": 212, + "post_wrappers": 212, + "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json" + } + }, + "helpers": 504, + "centres": 8, + "live": 7168, + "physical": 7682, + "physical_stock_identity": { + "data_and_owner_families": 7168, + "local_helpers": 504, + "private_centres": 8, + "coefficient_work": 2 + }, + "entering_helpers": 212, + "entrance_rank": 388, + "width_inventory": { + "4": 8, + "5": 48, + "8": 156, + "9": 292 + }, + "local_adapters": 333344, + "local_primitive_bound": 8645055460940, + "wrapper_elementary_factors_charged": 4396032, + "factors_per_wrapper": 144, + "compiler": 25934336, + "unhosted_pervertex": 1574554051175192, + "hosted_rebased_pervertex": 1574554050875816, + "conservative_pervertex_used": 4452501040899760, + "retained_prior_overcharge": { + "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478", + "previous_pervertex_allowance": 2877946989724568, + "added_complete_new_pervertex": 1574554051175192, + "policy": "Retain old allowance and add the entire fresh recount." + }, + "finite": { + "physical_stock_bits": 2641, + "router_bits": 7985, + "literal_bits": 35282, + "physical_row_coefficient": 16467, + "retained_row_coefficient": 20161, + "required_C0_bits": 200012, + "halving_integer_inequality": [ + 5329, + 4608 + ], + "G_exponent": 30000, + "E_exponent": 100000, + "C0_exponent": 210000 + }, + "strict_checks": { + "local_primitive_bound": true, + "logical": true, + "router": true, + "literal": true, + "mass": true, + "precision": true, + "tape": true, + "row": true, + "halving": true + }, + "scope": "Fresh emitted primitive/Horner, prefix, wrapper and finite recount, using the hash-bound independent local all-column/frame replay and actual whole-owner audit. No old INTEGRATION receipt is used to certify the changed word. The inherited all-size compiler, precision/tape and analytic-transfer contracts remain conditional. Retained payload 512 and physical row allowance 20161 are unchanged." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-OWNERS.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-OWNERS.json new file mode 100644 index 0000000000..668ef2ad07 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-OWNERS.json @@ -0,0 +1,40 @@ +{ + "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE", + "template_sha256": "cdc651b7fd865a9b0b468c519078610ea2b6f14558168a257ac0ee3d593729ae", + "paid_profile": { + "1": 166880, + "2": 30528, + "3": 35779, + "4": 13824, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "live": 7168, + "physical": 7682, + "rank_mass": 520704, + "deficit": 2560, + "hosted_residuals": 36288, + "banked_residuals": 0, + "all_live_owners_per_call_distinct": true, + "owners_per_call": 728, + "actual_helper_owner_charts": 36288, + "actual_73column_sigmas": 3178, + "cross_replica_helper_roles": 28380, + "explicit_idle_remainder_children": 4368, + "source_idle_children_charged": 16128, + "source_artifacts": { + "split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844", + "split-centres/LOCAL-PROGRAMS.json.gz": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde", + "split-centres/LOCAL-CHECKS.json": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea", + "split-centres/RESIDUAL-ADAPTERS.json": "baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275", + "split-centres/CLIFFORD-RECIPES.json": "534ace870cabe515987e00f50f71550030965006ea18978e0924590ac6944345", + "split-centres/CLIFFORD-REVIEW.json": "a0b7b6cc3b8c50d90752637640be54ccdc0604af0e8f2432a1aed8d53f3d36dc", + "split-centres/INDEPENDENT-LOCAL-REPLAY.json": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26", + "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + "controller_audit_sha256": "177cfc604cd7085019b615945f33c04197eee181e8c30ec13831cf253c138e23" +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-RESULT.json b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-RESULT.json new file mode 100644 index 0000000000..2ab78d484b --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/PR558-RESULT.json @@ -0,0 +1,31 @@ +{ + "status": "PASS_COMPLEX_EIGHT_RANK5_PIVOTS_AND_CITED_BIT", + "kappa": "796258944657507/500000000000000000", + "kappa_decimal": "0.001592517889315014", + "complex_lower": "199382255973827096291/125000000000000000000000", + "bit_lower": "413456747036699736067/250000000000000000000000", + "word_sha256": "375bd23001cd805707968005a9342827d5464e3f8e3a754197b31c46fc3f63c2", + "local_profile": { + "1": 2316, + "4": 192, + "8": 8, + "3": 464, + "2": 424, + "6": 56, + "5": 56 + }, + "global_profile": { + "1": 166880, + "2": 30528, + "3": 35779, + "4": 13824, + "5": 4032, + "6": 4032, + "7": 208, + "8": 576, + "39": 1, + "48": 1660 + }, + "seconds": 125.83695875003468, + "scope": "Conditional finite complex witness composed with cited unchanged PR543 bit supplier. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification." +} diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/UPSTREAM-LINEAGE.md b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/UPSTREAM-LINEAGE.md new file mode 100644 index 0000000000..48a59836b2 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/inputs/UPSTREAM-LINEAGE.md @@ -0,0 +1,17 @@ +# Pinned upstream lineage + +Snapshot through PR547. Exact changed heads and read scope are in PUBLIC-PINS.json. The refreshed conversations cover89 recently created/updated PRs with zero fetch errors; every changed source package in that snapshot was acquired, with no cold revalidation of unchanged external operators. + +Direct numerical and source dependencies: + +- [PR543](https://github.com/CrocSwap/integer-mult-bounds/pull/543), head2065fe4f72a914d907f1046603f5a36f17018535: R420 bit supplier, its actual paid profile, finite invoice and H1-H5 interleaved source-write argument. The original word's content hash and source file hash are retained in inputs/PR543-EXPECTED.json. Physical operator admission is cited, not rerun here. +- [PR547](https://github.com/CrocSwap/integer-mult-bounds/pull/547), head4e25588aac914732bde23ab0bd6628d25a3df0db: exact two-supplier assembly pattern and comparison kappa. This package replaces its complex operand with a freshly reconstructed improved supplier. +- [PR534](https://github.com/CrocSwap/integer-mult-bounds/pull/534): source of the477 previously accepted frame lifts, preserved in the construction chain. +- [PR535](https://github.com/CrocSwap/integer-mult-bounds/pull/535) and [PR531](https://github.com/CrocSwap/integer-mult-bounds/pull/531): source complex word,parent controller,phase/local verification,complete-owner admission and invoice implementations. +- [PR541](https://github.com/CrocSwap/integer-mult-bounds/pull/541): predecessor preload/curvature and static44 work. The prior delivered wave input includes its subsequent frame/syndrome/owner composition; we do not attribute those new collective contractions to PR541. +- [PR510](https://github.com/CrocSwap/integer-mult-bounds/pull/510), [PR503](https://github.com/CrocSwap/integer-mult-bounds/pull/503), [PR493](https://github.com/CrocSwap/integer-mult-bounds/pull/493): retained nine-stage bit and mutable-carrier ancestry. +- [PR484](https://github.com/CrocSwap/integer-mult-bounds/pull/484), [PR463](https://github.com/CrocSwap/integer-mult-bounds/pull/463), [PR444](https://github.com/CrocSwap/integer-mult-bounds/pull/444), [PR442](https://github.com/CrocSwap/integer-mult-bounds/pull/442), [PR386](https://github.com/CrocSwap/integer-mult-bounds/pull/386): retained exact realization,Clifford/local and whole-owner interfaces. + +Read but not added as independent gains: PR542 sliced bit frames;PR544 selective/static44 composition;PR546 prior composition;PR545 punctured111 draft bit supplier;updated PR540 literal-invocation Lean scope. The stronger PR545 bit saving cannot move the minimum while this complex supplier binds, so the existing R420 conditional route is sufficient. PR539's sharper bad-class charge is not needed or used for this bound. + +OpenAI/math,Mathlib and the registered project DAG supplied structural research references. Each lane records the actual declarations/files or primary literature it used. Source-only inspection is labelled as such; no Lean-import or kernel-check claim is inferred from a matching theorem name. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/notes/general-clifford-frames.tex b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/notes/general-clifford-frames.tex new file mode 100644 index 0000000000..0367eeb005 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/notes/general-clifford-frames.tex @@ -0,0 +1,102 @@ +\subsection{Preimage frames for arbitrary binary subspaces} +This frame construction is due to icekylinx with OpenAI GPT-6 Astra assistance; +the present exposition and integration use Codex. +Let $H=\mathbb F_2^h$ with the standard dot product. In the binary +symplectic space $H\oplus H$ put +\[ + L_0=\{(0,z)\},\qquad + F=\begin{pmatrix}I&I\\0&I\end{pmatrix},\qquad + L_F=FL_0=\{(z,z)\}. +\] +We also write $F$ for the exact Gaussian-dyadic operator $C^{\otimes h}$. +Its exact square is a Pauli translation; only its binary symplectic square +is the identity. For an exact Clifford operator $T$ the frame label is +$L(T)=T^{-1}L_0$. The physical transition from $T$ to $S$ is $ST^{-1}$, +and its Fourier rank is +$d(L(S),L(T))$, where $d(L,L')=h-\dim(L\cap L')$. +This follows by transporting the intersection by $S$: the intersection +with $L_0$ computes the kernel dimension of the $B$ block of $ST^{-1}$. + +\begin{lemma} +For every subspace $U\subseteq H$, including degenerate subspaces, +\[ + L_U=\{(u,u+v):u\in U,\ v\in U^\perp\} +\] +is Lagrangian, and +\[ + d(L_U,L_V)=\dim U+\dim V-2\dim(U\cap V),\qquad + FL_U=L_{U^\perp}. +\] +\end{lemma} +\begin{proof} +The displayed parametrization is injective and has dimension $h$. +Its symplectic pairing is $u\cdot v'+v\cdot u'=0$. +In an intersection, $u$ belongs to $U\cap V$ and $v$ to +$(U+V)^\perp$, giving the asserted dimension and distance. +Finally $F(u,u+v)=(v,u+v)$ proves the complement identity. +\end{proof} + +\subsection{Exact representatives and nested children} +Choose a deterministic invertible binary matrix $G$ carrying the first +$r=\dim U$ coordinate space $E_r$ to $U$, and set +\[ + K_G=\begin{pmatrix}G&0\\G+G^{-T}&G^{-T}\end{pmatrix},\qquad + T_U=K_G T_{E_r}K_G^{-1}. +\] +Here $T_{E_r}$ is the exact coordinate $C$ operator, and the $K_G$ are +exact Gaussian-dyadic Clifford lifts. The matrix $K_G$ is symplectic +because $G^TG+I$ is symmetric. It fixes both $L_0,L_F$ and maps $L_V$ +to $L_{GV}$. Thus both $K_G$ and $FK_GF^{-1}$ have Fourier rank zero; +their lifts are fixed binary address permutations with unit quadratic +phases. In particular, +\[ + L(T_U)=L_U,\quad \operatorname{rank}B(T_U)=r,\quad + \operatorname{rank}B(FT_UF^{-1})=r,\quad T_U^2\text{ is Pauli}. +\] +Set $V_U=GE_r^\perp$, a direct complement of $U$. The binary action gives +$T_U^{-1}L_F=L_{V_U}$ and hence +$\operatorname{rank}B(FT_U^{-1})=h-r$. +No assertion $V_U=U^\perp$ is needed. +For the norm-one source lines and their orthogonal target hyperplanes, +retain the inherited exact representatives; set $T_0=I,T_H=F$. +At every common scalar gate use one identical exact representative on all +incident registers. If separately transported representatives have the +same preimage, their physical ratio has rank zero and is implemented as +an actual left adapter before the gate. + +For $U\subseteq V$, the exact transition $T_VT_U^{-1}$ has rank +$\dim V-\dim U$. Clifford elimination expresses it as two rank-zero +adapters surrounding that many coordinate Fourier factors. These factors +are a single $C^{\otimes r}$ child: the scaled Hadamard satisfies +\[ + \frac{1+i}{2}\begin{pmatrix}1&1\\1&-1\end{pmatrix} + =SCS,\qquad S=\operatorname{diag}(1,i). +\] +Thus no new irrational field is introduced. All adapters are charged +finite movement and scalar operations. Exact transitions telescope; +commutativity between distinct $T_U$ is unnecessary. + +\subsection{Dirty tails and reverse/complement words} +A dirty role entering with gauge $T_\sigma$ and whose last active frame +is $T_U$, with $\sigma\subseteq U$, is assigned terminal gauge +$FT_\sigma$. Its logical value is restored by the complete transparent +scalar word, so its physical action is exactly $F$. The tail is +$FT_\sigma T_U^{-1}$. Its rank is +\[ + d(L_U,L_{V_\sigma})=h-\dim U+\dim\sigma. +\] +Indeed $H=\sigma\oplus V_\sigma$ and $U\supseteq\sigma$ imply +$\dim(U\cap V_\sigma)=\dim U-\dim\sigma$. +An inactive exterior adds $m-h$, giving $m-\dim U+\dim\sigma$. + +For the complete time-reversed word use +\[ + D_U=T_UF^{-1},\qquad L(D_U)=L_{U^\perp},\qquad + D_UD_V^{-1}=T_UT_V^{-1}. +\] +The last equality is exact, so reversal preserves every inverse transition +rank. Reverse the scalar signs and the whole transparent word, including +old-value corrections and final cleanup. The endpoints $D_0=F^{-1}$ +and $F$ differ by a Pauli, and the inherited norm-one endpoints are +reconciled by actual rank-zero adapters. Neither equality of binary +matrices nor equality of frame cosets substitutes for these operators. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/notes/three-stage-cover-assembly.tex b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/notes/three-stage-cover-assembly.tex new file mode 100644 index 0000000000..983ffb6ac8 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/notes/three-stage-cover-assembly.tex @@ -0,0 +1,117 @@ +\subsection{Local inventory and strict supplier moments} +The selected complex local word has +\[ + h=24,\quad v=2024,\quad c=91770,\quad q_{\rm roots}=8120, + \quad |\mathcal M|=71185,\quad R=28705,\quad\ell=552. +\] +Its complete scalar word, full backward subspace intersections and 4,599 +partial source gauges are regenerated from the pinned compressed DAG by +\path{scripts/three_stage_cover_producer.py}. The source and target chains, +remaining first transitions, inverse cleanup and copied centers remain in +\path{certificates/three-stage-cover-complex-input.json}. +At each cover vertex its child inventory is exactly the three-stage table +proved above. Thus $m_c=70$, $w_c=90163$, $s_c=6309018$ and +$w_cm_c-s_c=2392$; the largest child is 68. + +For $a_c=786999/2500000000$, the rational enclosure proves +\[ + \frac1{w_c}\sum_r n_r(r/70)^{1-a_c} + <1-2.3047018455\times10^{-10}. +\] +The bit local ledger has $h=23,v=1771,R=28866,\ell=506$. +Three copies of its physical local increments and exteriors give +$m_b=67,w_b=90140,s_b=6037356$, with deficit 2024. +The contaminated moment includes the entire $32\cdot67^2$-child fallback +on a fraction $10^{-16}$ of every ideal edge. At $a_0=747/2000000$ its +strict gap exceeds $6.3397366396\times10^{-7}$, and its rank moment also +contracts. The stopped ordinary saving is +\[ + a_b=(1-10^{-3})a_0+10^{-3}\frac{384599}{10^{10}} + =\frac{3731649599}{10^{13}}. +\] +These are exact rational certificates; the lower tolerances displayed +here do not substitute for their saved fractions. + +\subsection{Full finite router and completed-child guard} +Let $V_0=|O(70,2)|$, $N=V_0v$, $W=V_0(2v+3R)$ and $s=V_0s_c$. +All these finite counts appear in the certificate. Define +\[ + L=4(c+v)+10v+4hv+4h^2+8h+8+2h + +8Rv(M+16), +\] +where $M$ is the number of actual local mixer operations. +The source-witness bound for the positive DAG gives dirty-readout +coefficients of magnitude at most $h+4$, with denominators dividing +$2(h-3)$. The last term conservatively pays their binary-addition +implementation. Include the finite group and fixed Clifford routers by +\[ + G=N+3V_0L+64(m_c+1)^3W^2. +\] +A fixed role permutation has at most $W^2$ elementary exchanges; the +polynomial factor also covers the binary matrix and quadratic-phase +adapters. These finite costs retain their ordinary movement charge. +Set +\[ + E=64(W+m_c+G+1)^3,\quad B=s+E,\quad C_0=32m_cB^2. +\] +The exact calculation checks +\[ + 2GW^2+8s+4W+4+32m_c0. +\] +Thus the fixed external reserve $p^{160000}$ meets the inherited product +stock contract. The width-dependent q-adic selectors are supplied by +the separate internal borrowing proof, rather than multiplied into this +external polynomial stock. One preceding prefix and one final padding +suffice, and sequential completed calls reuse restored rows. + +Put $b=a_c$, $\eta=10^{-8}$, $\beta=10^{-6}$ and +\[ + a=(1-\beta)b-10^{-10}2^{80}$ avoiding all fixed rational denominators and rank witnesses. +At atom width $w$ use the finite cover $\operatorname{GL}_m(R_w)$ and its +right-multiplication edges $g\mapsto gR_s$. Every vertex has the unique chart +\[ + g=g_0+qG_1,\quad g_0\in\operatorname{GL}_m(\mathbb F_q), + \quad G_1\in(\mathbb Z/q^{w-1}\mathbb Z)^{m^2}, +\] +using fixed representatives for $g_0$. Right multiplication permutes $g_0$ +and acts affinely on $G_1$, with a carry determined by $g_0$. Its fixed +dimensional rational linear part factors into fixed scalings, ordered +shifts and a constant number of old width-$O(w)$ interchanges. Thus each +fixed port routing costs $O(Vw^{1-a_{\rm old}})$. + +Let $W_0=|\operatorname{GL}_m(\mathbb F_q)|(2v+3R_{\rm loc})$. +The full role count is $W(w)=W_0q^{m^2(w-1)}$. Split preceding rows into +low role type, high matrix and unused stock. Batch \emph{all} high matrices +for each low type in one stream. A frame edge is one child on this whole +batch, of volume $V/W_0$, and routing is executed once per fixed operation +type. Consequently neither the number of tapes nor the number of child +programs grows with $w$. High cardinality cancels in the normalized moment, +but its $m^2(w-1)$ digits are charged in the row reserve. + +For each fixed projector require the leading minors of sizes $1$ through +$r$ to be units. Each cleared minor polynomial in $g_0$ is nonzero: +similarity to $\operatorname{diag}(I_r,0)$ supplies a witness after the +fixed rank is preserved modulo $q$. Their total degree is at most $m^3$. +The polynomial zero bound and conditioning on invertibility (a factor at +most two) give bad fraction at most $2m^3/q<10^{-16}$ for each edge type. +No simultaneous union bound over edge types is needed, since their moments +are averaged separately. Good classes use the whole-rank child; bad +classes use the full $32m^2$-child fallback just proved. + +Let $H_r$ be the three-stage histogram described above and +$W=2v+3R_{\rm loc}=90140$. The retained ledger gives +\[ + \sum_r rH_r=6037356,\qquad Wm-\sum_r rH_r=2024=2v-3\ell, + \qquad \max\{r:H_r>0\}=66. +\] +For $a=747/2000000$, $\tau=1-a$, and $b=10^{-16}$ the conservative moment is +\[ + \mu_\tau\le + \sum_r\frac{H_r}{W}(r/m)^\tau+ + b\frac{32m^2\sum_rH_r}{W}(1/m)^\tau<1. +\] +The entire fallback is added; no displaced good contribution is subtracted. +The exact script \path{scripts/three_stage_cover_network.py} and certificate +\path{certificates/three-stage-cover-network.json}, from the retained axis +\path{certificates/three-stage-cover-bit-input.json}, give +$1-\mu_\tau>6.3397366396\cdot10^{-7}$. +The certificate uses the 32-term positive atanh logarithm series with its +geometric tail, $\exp(u)\le1+u+u^2/(2(1-u/3))$, and upward rounding to +the grid $2^{-120}$. All inputs have $0\le u<3$; these are rational upper +bounds, not floating-point root estimates. Since every child ratio is at +most one and $\tau<1$, this same strict bound implies $\mu_1<1$. + +With $T(n,w)$ denoting time divided by logical volume, the fixed low-type +profile $\{c_r\}$, including fallback classes, satisfies +\[ + T(n,w)\le\sum_rc_rT(r\lfloor n/m\rfloor,w)+Cn+Cw^{1-a_{\rm old}} + \quad(n\ge m),\qquad + T(n,w)\le Cw^{1-a_{\rm old}}\quad(n2\,68^d$ is 24, so the complex row coefficient is +$24\cdot2431=58344$. These full finite role counts are retained in the +scalar guard and row stock. Group elements and involutions are specified +by their binary matrices; the definition needs no numerical enumeration. +All fixed address adapters, endpoint Paulis and invocation permutations +are implemented inside the finite scalar/router guard of the assembly. diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/verify.py b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/verify.py new file mode 100644 index 0000000000..ee9399d676 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/vendor/pr559/verify.py @@ -0,0 +1,48 @@ +"""Exact arithmetic screen; zero complex contamination term requires source-scope review.""" +from pathlib import Path +from fractions import Fraction as Q +from decimal import Decimal,localcontext +import importlib.util,json,hashlib,time,argparse,sys +R=Path(__file__).resolve().parent;start=time.monotonic() +ap=argparse.ArgumentParser();ap.add_argument('--work',type=Path,required=True);ap.add_argument('--provider',choices=['552','558'],default='558');args=ap.parse_args();O=args.work.resolve();provider=args.provider;tag='PR'+provider +assert __debug__ and not O.exists() and not O.is_relative_to(R) +sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +manifest=json.loads((R/'MANIFEST.json').read_text());assert {p.relative_to(R).as_posix():sha(p)for p in R.rglob('*')if p.is_file()and p!=R/'MANIFEST.json'and '__pycache__'not in p.parts}==manifest +O.mkdir(parents=True) +def load(n): + p=R/'engines'/(n+'.py');s=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m +M,B,A=[load(n)for n in ['moment','base_two_moment','outer']] +parent=json.loads((R/'inputs'/(tag+'-EXPECTED.json')).read_text());P={int(r):n for r,n in parent['complex_global_profile'].items()};m=73;W=7168;c=Q(parent['bit_lower']);oldb=Q(parent['complex_lower']);oldk=Q(parent['kappa']);assert m*W-sum(r*n for r,n in P.items())==2560 +if provider=='558': + raw=json.loads((R/'inputs/PR558-RESULT.json').read_text()) + assert parent['complex_global_profile']==raw['global_profile'] and all(parent[k]==raw[k]for k in raw) +owner=json.loads((R/'inputs'/(tag+'-OWNERS.json')).read_text());invoice=json.loads((R/'inputs'/(tag+'-INVOICE.json')).read_text());bit=json.loads((R/'inputs/PR543-EXPECTED.json').read_text())['nine'] +assert owner['template_sha256']==invoice['template_sha256']==parent['complex_template_sha256'] +assert {int(k):v for k,v in owner['paid_profile'].items()}==P and owner['live']==W +assert invoice['owner_audit_sha256']==sha(R/'inputs'/(tag+'-OWNERS.json')) and all(invoice['strict_checks'].values()) +assert invoice['global_prefix_bits']1 and a>1) +baseline=M.certify(P,m,W,True);assert Q(baseline['lower'])==oldb +cert=M.certify(P,m,W,False);b=Q(cert['lower']);assert b>oldb +checks=[] +for endpoint,ok in [(b,True),(b+Q(1,10**24),False)]: + l,h=M.moment(P,m,W,endpoint,False);u,v=B.moment(m,W,list(P.items()),endpoint);assert(h<1 and v<1)if ok else(l>1 and u>1);checks.append(dict(endpoint=str(endpoint),accept=ok,mercator=[str(l-1),str(h-1)],base_two=[str(u-1),str(v-1)])) +assert M.moment(P,m,W,b,True)[0]>1 +eta=beta=Q(1,10**18);grid=Q(1,10**18);bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}} +def assemble(bb): + s=min(c,(1-beta)*bb)-Q(1,10**24);assert 00;ceil=lambda x:-(-x.numerator//x.denominator);cut=max(ceil(36/gap**2),ceil(2*(4+512)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+512);cuts.append(dict(exponent=str(a),gap=str(gap),cutoff_log2=str(cut)));chain.append(a) + q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;k=grid*((ticks.numerator-1)//ticks.denominator);a=A.assembly(chain[-1],bb,bridge,k,eta=eta,beta=beta);assert len(a['strict_constraints'])==47 and all(v>0 for v in a['strict_constraints'].values());return k,chain,cuts,a +assert assemble(oldb)[0]==oldk +k,chain,cuts,a=assemble(b);expected=json.loads((R/('EXPECTED558.json' if provider=='558' else 'EXPECTED.json')).read_text());assert k==Q(expected['kappa']) and b==Q(expected['complex_lower']);controls=['new_endpoint_rejected_by_old_charge'] +for name,kk,ee,bbeta in [('next_grid',k+grid,eta,beta),('zero_eta',k,Q(0),beta),('zero_beta',k,eta,Q(0)),('unit_beta',k,eta,Q(1))]: + try:A.assembly(chain[-1],b,bridge,kk,eta=ee,beta=bbeta) + except AssertionError:controls.append(name) + else:raise AssertionError(name) +def dec(v): + with localcontext()as ctx:ctx.prec=70;return str(Decimal(v.numerator)/Decimal(v.denominator)) +r=dict(status='PASS_NATIVE_COMPLEX_MOMENT_AND_CONDITIONAL_COMPOSITION',provider=provider,baseline_kappa=str(oldk),baseline_kappa_decimal=dec(oldk),candidate_kappa=str(k),candidate_kappa_decimal=dec(k),old_complex_lower=str(oldb),complex_lower=str(b),complex_decimal=dec(b),absolute_gain=str(k-oldk),relative_gain_percent=dec(100*(k/oldk-1)),profile=P,live=W,m=m,rank_deficit=2560,bit_lower=str(c),moments=checks,outer={n:str(v)for n,v in a['strict_constraints'].items()},bootstrap=cuts,controls=controls,seconds=time.monotonic()-start,python=sys.version,manifest_sha256=sha(R/'MANIFEST.json'),scope='Arithmetic repricing of the unchanged pinned selected exact binary-Clifford complex supplier, with cited PR543 bit supplier and unchanged bit bad-class charge. Original source distinguishes exact complex recursion from GL local-ring bit selectors. All inherited all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic assumptions remain conditional. This verifier does not rerun unchanged physical operators.') +(O/'RESULT.json').write_text(json.dumps(r,indent=2)+'\n');print({key:r[key]for key in ['status','candidate_kappa_decimal','complex_decimal','relative_gain_percent','seconds']}) diff --git a/research/pr643-improvement-20261013/witness/vendor/multicold/verify.py b/research/pr643-improvement-20261013/witness/vendor/multicold/verify.py new file mode 100644 index 0000000000..d98acd791d --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/multicold/verify.py @@ -0,0 +1,71 @@ +"""Reconstruct all three eight-cold complex providers and admit the complete mixed witness. +Prepared with OpenAI Codex assistance. Apache-2.0; see NOTICE.md. +""" +import argparse,gzip,hashlib,json,os,subprocess,sys,time,shutil +from pathlib import Path +from fractions import Fraction as Q +assert __debug__, 'Assertions required' +P=Path(__file__).resolve().parent +ap=argparse.ArgumentParser();ap.add_argument('--work',type=Path,required=True);a=ap.parse_args();O=a.work.resolve();assert not O.exists()and not O.is_relative_to(P) +def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +def dump(p,x):p.write_text(json.dumps(x,indent=2)+'\n') +actual={f.relative_to(P).as_posix():sha(f)for f in P.rglob('*')if f.is_file()and f!=P/'MANIFEST.json'and'__pycache__'not in f.parts};assert actual==read(P/'MANIFEST.json') +O.mkdir(parents=True);steps=[];start=time.monotonic();env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONUTF8='1',PYTHONINTMAXSTRDIGITS='0');env.pop('PYTHONOPTIMIZE',None) +def begin(name,script,*args): + log=O/(name+'.log');f=log.open('w');t=time.monotonic();print('RUN',name,flush=True) + proc=subprocess.Popen([sys.executable,'-B',str(P/'code/run_portable.py'),str(script),*map(str,args)],stdout=f,stderr=subprocess.STDOUT,env=env) + return name,log,f,t,proc +def finish(job): + name,log,f,t,proc=job;code=proc.wait();f.close();steps.append(dict(name=name,exit_code=code,seconds=time.monotonic()-t,log_sha256=sha(log)));dump(O/'STAGES.json',steps) + if code:raise RuntimeError(name+' failed\n'+log.read_text()[-6000:]) + print('PASS',name,flush=True) +def run(name,script,*args):finish(begin(name,script,*args)) +B=P/'vendor/pr558';F=B/'vendor/pr552';V=F/'complex-global/vendor531';baseline=O/'baseline558';zero=O/'zero-local';four=O/'four-local';G=O/'mixed-global' +run('frozen558-full-replay',B/'verify.py','--work',baseline) +run('construct-four-pivots',P/'code/build_four_portable.py','--input',baseline/'reconstruction/weighted/FULL-WORD.json.gz','--recipe',P/'data/FROZEN-FOUR-PROMOTION.json','--gk-dir',F/'complex-local/static44/gk','--out',O/'four-word') +run('four-promoted-scalar-omissions',B/'code/audit_promoted_scalar.py',O/'four-word/FULL-WORD.json.gz',baseline/'reconstruction/static44/SELECTION.json',O/'FOUR-SCALAR-CONTROLS.json') +providers={} +for name,raw in [('zero',baseline/'reconstruction/weighted/FULL-WORD.json.gz'),('four',O/'four-word/FULL-WORD.json.gz'),('eight',baseline/'reconstruction/promoted/FULL-WORD.json.gz')]: + local=O/(name+'-cold-local');cold=O/(name+'-cold-word');word=O/(name+'-multicold-word');recipe=P/'data'/(name.upper()+'-COLD.json');multi=P/'data'/(name.upper()+'-MULTICOLD.json');providers[name]=local + run(name+'-cold-construction',P/'code/build_cold_kernel.py','--input',raw,'--recipe',recipe,'--gk-dir',F/'complex-local/static44/gk','--out',cold) + run(name+'-cold-kernel-omissions',P/'code/audit_kernel_controls.py','--word',cold/'FULL-WORD.json.gz','--recipe',recipe,'--out',cold/'KERNEL-OMISSION-CONTROLS.json') + run(name+'-multicold-construction',P/'code/build_multicut_kernels.py','--input',cold/'FULL-WORD.json.gz','--recipe',multi,'--gk-dir',F/'complex-local/static44/gk','--out',word) + run(name+'-multicold-kernel-omissions',P/'code/audit_multicold_controls.py','--word',word/'FULL-WORD.json.gz','--recipe',multi,'--out',word/'MULTICOLD-OMISSION-CONTROLS.json') + run(name+'-inherited-44-omissions',F/'complex-local/static44/audit_scalar.py',word/'FULL-WORD.json.gz',baseline/'reconstruction/static44/SELECTION.json',word/'STATIC44-SCALAR-AUDIT.json') + if name!='zero': + shutil.copyfile(raw.parent/'PROMOTION.json',word/'PROMOTION.json') + run(name+'-promoted-omissions',B/'code/audit_promoted_scalar.py',word/'FULL-WORD.json.gz',baseline/'reconstruction/static44/SELECTION.json',word/'PROMOTED-SCALAR-AUDIT.json') + run(name+'-all-columns-native-frames',V/'code/audit_and_transport.py','--raw',word/'FULL-WORD.json.gz','--routing',F/'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz','--out',local) + run(name+'-both-reflected-ledgers',V/'code/emit_local.py',local) + run(name+'-independent-local-controls',V/'code/audit_local.py',local) + run(name+'-normalized-wrappers',V/'code/adapters_local.py',local/'CANONICAL-WORD.json.gz',local/'RESIDUAL-ADAPTERS.json',local/'WRAPPER-CHECKS.json') +phase_jobs=[begin(name+'-all-phase-edges',B/'code/phases_full.py',local,V/'vendor/clifford')for name,local in providers.items()] +for job in phase_jobs:finish(job) +zero,four,eight=[providers[k]for k in ('zero','four','eight')] +run('bind-three-providers',P/'code/bind_providers_portable.py','--baseline',baseline,'--zero',zero,'--four',four,'--eight',eight,'--plan',P/'data/PLAN.json','--out',G) +run('emit-three-provider-controller',P/'code/emit_allcold.py','--base',G/'base','--owners',P/'data/OWNERS.json.gz','--plan',G/'PLAN.json','--out',G/'hosted') +(G/'audit').mkdir() +run('independent-controller-and-controls',P/'code/audit_allcold.py',G/'base',G/'hosted',G/'audit/ASYNC-AUDIT.json','--mutation-controls') +run('fresh-three-provider-invoice',P/'code/invoice_allcold.py','--base',G/'base','--hosted',G/'hosted','--audit',G/'audit','--out',G/'audit','--retained-invoice',V/'evidence/audit/PREFIX-AND-INVOICE.json') +run('conservative-and-native-exact-assembly',P/'code/assemble.py',P,G,O/'ASSEMBLY.json') +run('fifty-four-admission-controls',P/'code/assembly_controls.py','--owner',G/'audit/OWNERS-AND-PROFILE.json','--invoice',G/'audit/PREFIX-AND-INVOICE.json','--out',O/'ASSEMBLY-CONTROLS.json') +run('phase-timing-portability-controls',P/'code/phase_timing_controls.py',G/'base',G/'audit',O/'PHASE-TIMING-CONTROLS.json') +for local in [zero,four,eight]: + r=read(local/'INDEPENDENT-LOCAL-REPLAY.json');ph=read(local/'CLIFFORD-REVIEW.json') + assert len(r['negative_controls_rejected'])==11 and r['paid_profiles']['forward']==r['paid_profiles']['backward'] + assert ph['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES' and ph['all_child_equalities_include_global_phase']is True and ph['directed_edges']==2929 and ph['endpoint_adapters']==224 +assert len(read(O/'FOUR-SCALAR-CONTROLS.json')['controls'])==4 +assert len(read(G/'audit/ASYNC-AUDIT.json')['mutations_rejected'])==16 +assert len(read(O/'ASSEMBLY-CONTROLS.json')['rejected_controls'])==54 +z=read(O/'ASSEMBLY.json');assert Q(z['kappa_decimal'])==Q('0.001596133352130093') and Q(z['conservative_kappa_decimal'])==Q('0.001596133349380077') +r=dict(status='PASS_THREE_PROVIDER_048_MULTICOLD_NATIVE_COMPLEX_AND_CITED_BIT',kappa=z['kappa'],kappa_decimal=z['kappa_decimal'],complex_lower=z['complex_lower'],bit_lower=z['bit_lower'],conservative_kappa_decimal=z['conservative_kappa_decimal'],conservative_complex_lower=z['conservative_complex_lower'],global_profile=z['complex_profile'],provider_counts=z['provider_counts'],surcharge_model=z['surcharge_model'],four_word_sha256=sha(O/'four-word/FULL-WORD.json.gz'),seconds=time.monotonic()-start,scope=z['scope']);dump(O/'RESULT.json',r) +paths=['PHASE-TIMING-CONTROLS.json','mixed-global/audit/IDLE-REMAINDER-FRAMES.json','RESULT.json','ASSEMBLY.json','ASSEMBLY-CONTROLS.json','FOUR-SCALAR-CONTROLS.json','four-word/CONSTRUCTION.json','mixed-global/BINDING.json','mixed-global/audit/ASYNC-AUDIT.json','mixed-global/audit/OWNERS-AND-PROFILE.json','mixed-global/audit/PREFIX-AND-INVOICE.json'] +for name in ('zero','four','eight'): + for fn in ('KERNEL-CONSTRUCTION.json','KERNEL-OMISSION-CONTROLS.json'):paths.append(name+'-cold-word/'+fn) + for fn in ('KERNEL-CONSTRUCTION.json','MULTICOLD-OMISSION-CONTROLS.json','STATIC44-SCALAR-AUDIT.json'):paths.append(name+'-multicold-word/'+fn) + for fn in ('INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json','WRAPPER-CHECKS.json'):paths.append(name+'-cold-local/'+fn) + assert len(read(O/(name+'-cold-word/KERNEL-OMISSION-CONTROLS.json'))['controls'])==6 + assert len(read(O/(name+'-multicold-word/MULTICOLD-OMISSION-CONTROLS.json'))['controls'])==32 +dump(O/'RECEIPT.json',dict(status=r['status'],steps=steps,artifacts={name:sha(O/name)for name in paths},manifest_sha256=sha(P/'MANIFEST.json'))) +print(json.dumps(r,indent=2)) diff --git a/research/pr643-improvement-20261013/witness/vendor/structural_gain/MANIFEST.json b/research/pr643-improvement-20261013/witness/vendor/structural_gain/MANIFEST.json new file mode 100644 index 0000000000..8ca0ebccbf --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/structural_gain/MANIFEST.json @@ -0,0 +1,438 @@ +{ + "schema": "structural-gain-research/1", + "publication_parent": "1424da81263a5305b35e4cf74ef686c275f03f3f", + "mathematical_parent": "f1db606a1416359229f944946667338305208064", + "external_pr564_source": "c18417b02b80594b2ca1c8c21185d28befafc935", + "files": { + "CHECKS.md": "f2c9524964401ad27efc67295004e6c453bb5618e90b60a44733c161d337ba70", + "NOTICE": "9e4e50378222cffff73a6a339621ff29b21821bc556354551d49755cb5b96784", + "README.md": "b9132c6bfa65a6a1187ace1f42b938dfeb1d1c7544bdb4c56b0a47409e2822d2", + "factory/CONTROLS.json": "af3da16ac5f38a8baa2f93e20e9bca19db2f81ce1dd1f32a4ee056d9902a8ee0", + "factory/PACKET-PLANE-BOUND.json": "cb96e4138db6c5467e4b86ae35e5ff7c03a5a52531fa3ca7197594cca9c5c3e8", + "factory/README.md": "a1b53429024c6b362c7b8f7b478429d98cb848f9cd47dde7e7ca788bd6fcc7f8", + "factory/packet_plane_bound.py": 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"d7a8b54f6c8a3989675857ff639c7cba5612cdd14fddd906359544c3a1c580f5", + "joint-basis/replay-evidence/prefix-screen/rank1-disjoint/CONSTRUCTION.json": "4d32b5db2fa8a45ca5eec9d61e190e109d665a83250f30e58aec3ebf958111e1", + "joint-basis/replay-evidence/prefix-screen/rank1-disjoint/FULL-WORD.json.gz": "5747e93c7cb600d5ff68a88428702e8864c81785364368d11e468c1661173c50", + "joint-basis/replay-evidence/prefix-screen/rank2-disjoint/CONSTRUCTION.json": "aac8588e3d39344776d5b86a3f47eca157a2b017dd60483dad7ab9910f4c5aa2", + "joint-basis/replay-evidence/prefix-screen/rank2-disjoint/FULL-WORD.json.gz": "a72ccc0a28ce8ad54ae03135a42f3bf1302346188428c01159820f4df14e5004", + "joint-basis/replay-evidence/prefix-screen/rank3-disjoint/CONSTRUCTION.json": "7947b787cd8457b84d98dbf2398b071e58ca60ca2f1ccb612b8ca11b561fa03b", + "joint-basis/replay-evidence/prefix-screen/rank3-disjoint/FULL-WORD.json.gz": "5fee4592b54aed857b573e3d1add49ee0fe58711288ecbb26a78bd9cfc600bbb", + "joint-basis/replay-evidence/prefix-screen/rank4-disjoint/CONSTRUCTION.json": "7947b787cd8457b84d98dbf2398b071e58ca60ca2f1ccb612b8ca11b561fa03b", + "joint-basis/replay-evidence/prefix-screen/rank4-disjoint/FULL-WORD.json.gz": "5fee4592b54aed857b573e3d1add49ee0fe58711288ecbb26a78bd9cfc600bbb", + "joint-basis/replay-evidence/shared-gauges/SEARCH.json": "8c0653ba46e39a62902ce8157e8ffbe63c31a684b106458235d116e8df5afad4", + "joint-basis/replay-evidence/suffix-unlocked/FULL-WORD.json.gz": "adf8b7194d22d7e28a54545ca902323f19a9881ff1804ad6ffe51f85587a01e0", + "joint-basis/replay-evidence/suffix-unlocked/UNLOCK.json": "e23be7a8b207e6d0788b6f23a0ab4dda947ee0d580d1beb9aab5cb8795f202ac", + "joint-basis/reproduce.py": "354223204830942c0d5366f47eed747c66d948575c0128ac9055ad90a1139e6e", + "joint-basis/search_joint_gauge_bases.py": "02dc0886d9c3ee179084c9997690de024045e67763e692521c6c31d515acc296", + "joint-basis/search_multicut.py": "4edebf39256bb6cdc6cde94c4b7a1c26905cb096a6d4ed29ce10ba64f06f9645", + "joint-basis/search_prefix_bases.py": "e312780e6ba9aa3e8cbcf6945a0626f30f37f08d76d3d257569e8d2262f47c4f", + "joint-basis/search_shared_gauges.py": "4d389c2991e88cae7023ef7702e40a32fca81761a6a1410d5e922b27a9a64d56", + "joint-basis/shared-gauges/SEARCH.json": "8c0653ba46e39a62902ce8157e8ffbe63c31a684b106458235d116e8df5afad4", + "joint-basis/suffix-unlocked/FULL-WORD.json.gz": "adf8b7194d22d7e28a54545ca902323f19a9881ff1804ad6ffe51f85587a01e0", + "joint-basis/suffix-unlocked/UNLOCK.json": "e23be7a8b207e6d0788b6f23a0ab4dda947ee0d580d1beb9aab5cb8795f202ac", + "joint-basis/unlock_suffix_kernels.py": "b2fc0e6c6ed65e20087599a95243fcc5a5fd91e28d152dffb7b6004cef7f54d9" + } +} diff --git a/research/pr643-improvement-20261013/witness/vendor/structural_gain/README.md b/research/pr643-improvement-20261013/witness/vendor/structural_gain/README.md new file mode 100644 index 0000000000..b48c635766 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/vendor/structural_gain/README.md @@ -0,0 +1,104 @@ +# Structural research after the width-seven construction + +This pass constructs and fully checks a smaller further improvement, +**conditional kappa = 0.001600682403612293**, while investigating the changes +needed for a materially larger gain. That is **0.03843% above PR569**, not a +new one-percent improvement. The larger-gain experiments below are separate +from this admitted finite construction. + +The work starts from PR569's numerical and attribution state at +`f1db606a1416359229f944946667338305208064`, followed by packaging-only commit +`1424da81263a5305b35e4cf74ef686c275f03f3f`, which adds seven already +manifest-bound replay logs previously excluded by Git's ignore rule. All +341 `research/larger-gain` artifacts retain their recorded hashes. PR564 +remains an external pinned dependency at +`c18417b02b80594b2ca1c8c21185d28befafc935`. Upstream main was fetched again +and remains `db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`. PR568 and PR567 were +fetched and examined for composition. The later PR570, fetched at +`9278e39baec4f23267336c7d212306d0c0003d08`, concerns explicit ceiling-log +tapes and supplies no new kappa theorem or constant-time indexing result. + +## A concrete new construction + +The new A-prefix selects different exact donor components, reducing its +69 gates to 57. PR568 contributes four further cold kernels beyond PR569's +overlapping relations. Their composition with the 32 width-seven promotions +has exactly PR569's residual-width inventory and changes its local paid +profile by `-12 H2 + 8 H3`. This permits reuse of its physical geometry after +an explicit helper permutation. + +Replacing the 63 width-seven calls, while retaining nine plain four-cold +calls, gives the global profile: + +```text +{1:169056, 2:40428, 3:26472, 4:13824, 5:4032, + 6:4032, 7:48, 8:576, 48:1808} +``` + +The native complex rate is `0.001603248695587935849402`. The separate +conservative assembly passes at kappa `0.001600682400830496`. Dimension 73, +live stock 7168, physical stock 7682 and deficit 2560 are unchanged. The +construction passes complete native and phase checks, literal hosting, +invoice and both exact arithmetic models. A fresh portable replay passed all +18 stages in 149.5 seconds and reproduced both kappa values. Its local omission controls reject +135 scalar mutations; the global checks include 16 owner mutations, +93 assembly mutations, two accepted timing changes and two rejected semantic +phase changes. See [the composition package](frontier-composition/README.md) +for the exact inputs, artifacts, dependencies and replay boundary. + +No new unconditional multiplier theorem, all-size compiler proof, complete +Lean proof or worst-case O(1) indexing theorem is claimed. All inherited +interfaces and assumptions remain. No code-review workflow was run in this +pass, as requested; the checks above verify the mathematical experiments. + +## What was actually tried for a larger gain + +| Direction | Experiment and result | +| --- | --- | +| Global frame choices and packing | Enumerated all allowed subspace states and transitions, existing entrance enlargements and capacity patterns together: 152,742 variables. An optimizer-independent rational certificate excludes kappa `0.00160062` for the three fixed four-cold words. This leaves less than 0.035% above PR569 in that family. | +| Joint donor bases | Unlocked all 44 static kernel pivots. Fixed and raised first-frame searches covered 1,357 and 1,997 compatible classes. The improved 57-gate prefix is positive; no rank-three or rank-four dependency appeared in those classes. | +| Shared multi-cut kernels | After unlocking eight B kernels, tested 16 rank-two circuits and all 256 paired mixtures. Of these, 192 had valid exact scalar/frame realizations; none improved the tested packing-price objective over keeping the rank-one circuits. This is a bounded search, not a universal exclusion. | +| Joint kernel and gauge choices | Tested projected response dependencies on forbidden output coordinates, permitting a compatible residual to be canceled by shared gauges. Of 2,789 entrance subspaces, 2,763 admitted no suitable output/center coordinate; the remaining 26 supplied no required dependency. | +| Cheaper packet factory | Verified a 224-helper lower bound for the current packet interface, and 392 including its required second copies. These bounds fix the packet planes, nested frames and scalar primitive model. | +| Borrowing foreign outputs | Found an injective geometric assignment for 28 actual helpers. Executed a literal partial inverse and 160 exact restoration-span checks. The current donor rows cannot clear the remaining source term within the output cap. A fresh replacement helper removes the apparent saving. | + +Details and replay commands are in [joint-basis](joint-basis/README.md), +[frame-optimization](frame-optimization/README.md), and +[factory](factory/README.md). The negative results have different scopes; +they must not be combined into an unrestricted impossibility claim. + +## The measured larger-gain target + +The 28 actual factory helpers identified by the borrowing experiment each +pay `3 H1 + H6` and occupy a width-nine residual. Their paths were checked in +all six original four-cold/width-seven words. Counterfactually removing those +paths and their corresponding demands, with **no replacement or output-path +cost**, produces the following exact fractional-packing moment prices: + +| Hypothetical paths removed per call | Complex-side kappa target | Relative to PR569 | +| ---: | ---: | ---: | +| 6 | 0.001611776947926596 | +0.73181% | +| 14 | 0.001626974089806911 | +1.68159% | +| 28 | 0.001654270333518889 | +3.38753% | + +These are design targets, not achieved constructions. The exact rational +packing and both moment engines verify only the stated hypothetical model. +They supply no cleanup circuit, physical owner assignment or bit-side +composition. The largest target also needs more bit-side headroom than the +currently cited PR543 supplier; PR555 is a possible separately replayable +source. See `frame-optimization/BORROW-SENSITIVITY.json` and +`borrow_sensitivity.py`. + +The next substantive change would retain part of the packet computation in +foreign output coordinates as part of their final desired values. It must +jointly change packet delivery, the output basis and the center injection, +instead of restoring outputs before their unchanged current loads. The +current experiments identify the exact residual source term and frame caps +that such a construction must overcome. Nonmonotone frame traversals cannot +be charged only as scalar gates: their added recursive rank mass directly +reduces the recurrence deficit. + +Prepared by Dominik Scholz with substantial OpenAI Codex (GPT-6 Astra) +assistance in research, implementation, exact verification and documentation. +See [NOTICE](NOTICE) for inherited contributors and source-specific credits. +Apache-2.0. diff --git a/research/pr643-improvement-20261013/witness/vendor/structural_gain/frontier-composition/combined-prefix-word/FULL-WORD.json.gz b/research/pr643-improvement-20261013/witness/vendor/structural_gain/frontier-composition/combined-prefix-word/FULL-WORD.json.gz new file mode 100644 index 0000000000..842a4392e0 Binary files /dev/null and b/research/pr643-improvement-20261013/witness/vendor/structural_gain/frontier-composition/combined-prefix-word/FULL-WORD.json.gz differ diff --git a/research/pr643-improvement-20261013/witness/verify.py b/research/pr643-improvement-20261013/witness/verify.py new file mode 100644 index 0000000000..1be6686ac9 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/verify.py @@ -0,0 +1,389 @@ +"""Spec-driven official replay: rebuild every provider word from pinned sources through typed construction steps, +localize each word with the unchanged vendor pipeline, then run the spec-driven global admission and assembly. +Prepared with Claude Code assistance. Apache-2.0; see NOTICE.md. Pinned external sources are unchanged packages. +Everything this script runs is named in data/SPEC.json "build" and must be one of the allowlisted step types below; +the spec contains no scripts or commands, only step types, pinned source files, recipes and expected hashes. +""" +import argparse,gzip,hashlib,json,os,subprocess,sys,time,shutil,threading +from concurrent.futures import ThreadPoolExecutor +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +assert __debug__, 'Assertions required' +P=Path(__file__).resolve().parent +ap=argparse.ArgumentParser();ap.add_argument('--work',type=Path,required=True) +ap.add_argument('--spec',type=Path,default=P/'data/SPEC.json',help=argparse.SUPPRESS) +ap.add_argument('--jobs',type=int,default=min(8,os.cpu_count() or 4),help='parallel provider chains') +ap.add_argument('--source',action='append',default=[],help='NAME=DIR pinned source package (default: sibling directory named in the spec)') +ap.add_argument('--check-pins',action='store_true',help='check package and source pins, then stop') +ap.add_argument('--until',choices=('locals','all'),default='all',help=argparse.SUPPRESS) +ap.add_argument('--reuse-baseline',type=Path,help=argparse.SUPPRESS) +ap.add_argument('--reuse-local',action='append',default=[],help=argparse.SUPPRESS) +a=ap.parse_args();O=a.work.resolve();SPECFILE=a.spec.resolve();SPEC=json.loads(SPECFILE.read_bytes());BUILD=SPEC['build'] +DISCOVER=os.environ.get('WITNESS_DISCOVER')=='1';discovered={} +given=dict(x.split('=',1)for x in a.source) +SRC={name:Path(given.get(name,P.parent/src['dir'])).resolve()for name,src in BUILD['sources'].items()};S=SRC['multicold'] +def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes()) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +def content(p):return hashlib.sha256(gzip.decompress(p.read_bytes())).hexdigest() +def dump(p,x):p.write_text(json.dumps(x,indent=2)+'\n',newline='\n') +def tree(root,skip):return{f.relative_to(root).as_posix():sha(f)for f in root.rglob('*')if f.is_file()and f!=root/skip and'__pycache__'not in f.parts} +def pinned(where,key,got,label): + """Compare against the spec value; a discovery build (propose.py) records values the spec does not yet hold.""" + if key in where:assert got==where[key],'BUILD PIN MISMATCH %s.%s: expected %s got %s'%(label,key,where[key],got) + else:assert DISCOVER,'BUILD PIN MISSING %s.%s'%(label,key);discovered[label+'.'+key]=got + return got +if SPECFILE==P/'data/SPEC.json':assert tree(P,'MANIFEST.json')==read(P/'MANIFEST.json'),'package MANIFEST' +for name,src in BUILD['sources'].items(): + root=SRC[name];manifest=read(root/'MANIFEST.json') + assert sha(root/'MANIFEST.json')==src['manifest_sha256'],name+' manifest pin' + if src.get('full_tree'):assert tree(root,'MANIFEST.json')==manifest,name+' tree' + files=manifest['sha256']if manifest.get('algorithm')=='sha256'else manifest.get('files',manifest) # PR531 manifests: {algorithm, sha256} + for rel,value in src['files'].items():assert sha(root/rel)==value==files[rel],(name,rel) +def ref(r,pin=True): + """'pkg:rel' (this package) or 'NAME:rel' (a pinned file of source NAME).""" + kind,rel=r.split(':',1) + if kind=='pkg':return P/rel + assert rel in BUILD['sources'][kind]['files'],'unpinned source file '+r + return SRC[kind]/rel +if a.check_pins:print('PINS OK',SPEC['name'],sha(SPECFILE));raise SystemExit(0) +assert not O.exists() and not any(O.is_relative_to(x)for x in (P,*SRC.values())) +O.mkdir(parents=True);steps=[];lock=threading.Lock();start=time.monotonic() +env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONUTF8='1',PYTHONINTMAXSTRDIGITS='0',MULTICOLD_SOURCE=str(S),GAIN_PR564_SOURCE=str(S),WITNESS_SPEC=str(SPECFILE));env.pop('PYTHONOPTIMIZE',None);env.pop('WITNESS_DISCOVER',None) +def run(name,script,*args): + log=O/(name+'.log');t=time.monotonic();print('RUN',name,flush=True) + with log.open('w')as f:code=subprocess.call([sys.executable,'-B',str(S/'code/run_portable.py'),str(script),*map(str,args)],stdout=f,stderr=subprocess.STDOUT,env=env) + with lock:steps.append(dict(name=name,exit_code=code,seconds=round(time.monotonic()-t,3),log_sha256=sha(log)));dump(O/'STAGES.json',steps) + if code:raise RuntimeError(name+' failed\n'+log.read_text()[-6000:]) + print('PASS',name,flush=True) +B=S/'vendor/pr558';F=B/'vendor/pr552';V=F/'complex-global/vendor531';GK=F/'complex-local/static44/gk' +if a.reuse_baseline:baseline=a.reuse_baseline.resolve() +else:baseline=O/'baseline558';run('frozen558-full-replay',B/'verify.py','--work',baseline) +SEL=baseline/'reconstruction/static44/SELECTION.json';RAW=baseline/'reconstruction/promoted/FULL-WORD.json.gz' +def omissions(path,s,label):pinned(s,'omission_controls',len(read(path)['controls']),label) +# Allowlisted step types: (constructor, paired omission audit), all scripts from the pinned multicold source. +def cold_kernel(word,s,out,tag): + recipe=ref(s['recipe']);pinned(s,'recipe_sha256',sha(recipe),tag) + run(tag+'-construction',S/'code/build_cold_kernel.py','--input',word,'--recipe',recipe,'--gk-dir',GK,'--out',out) + run(tag+'-omissions',S/'code/audit_kernel_controls.py','--word',out/'FULL-WORD.json.gz','--recipe',recipe,'--out',out/'KERNEL-OMISSION-CONTROLS.json') + omissions(out/'KERNEL-OMISSION-CONTROLS.json',s,tag) +def finalize(word,recipe,tag): + """Discovery only: a new recipe whose output hash is still open is pinned by a first build that must fail exactly at + the final output-hash assertion (every kernel check passed); the printed hash is written into a final recipe.""" + r=read(recipe);h=r.get('output_content_sha256','') + if len(h)==64 and all(c in '0123456789abcdef'for c in h):return recipe + assert DISCOVER,'recipe output hash not pinned: '+tag + r['output_content_sha256']='0'*64;probe=O/(tag+'-probe');probe.mkdir();dump(probe/'RECIPE.json',r) + p=subprocess.run([sys.executable,'-B',str(S/'code/run_portable.py'),str(S/'code/build_multicut_kernels.py'),'--input',str(word),'--recipe',str(probe/'RECIPE.json'),'--gk-dir',str(GK),'--out',str(probe/'out')],capture_output=True,text=True,env=env) + last=(p.stderr.strip().splitlines()or[''])[-1];assert p.returncode and last.startswith('AssertionError: ')and len(last)==16+64,'probe build failed before the output hash:\n'+p.stderr[-3000:] + r['output_content_sha256']=last[16:];final=O/(tag+'-RECIPE.json');final.write_text(json.dumps(r,indent=1)+'\n',newline='\n') + discovered[tag+'.final_recipe']=str(final);return final +def multicut(word,s,out,tag): + recipe=finalize(word,ref(s['recipe']),tag);pinned(s,'recipe_sha256',sha(recipe),tag) + run(tag+'-construction',S/'code/build_multicut_kernels.py','--input',word,'--recipe',recipe,'--gk-dir',GK,'--out',out) + run(tag+'-omissions',S/'code/audit_multicold_controls.py','--word',out/'FULL-WORD.json.gz','--recipe',recipe,'--out',out/'MULTICOLD-OMISSION-CONTROLS.json') + omissions(out/'MULTICOLD-OMISSION-CONTROLS.json',s,tag) +PROMOTER=('larger_gain','providers/build_entrance_promotions.py',('providers/coupled_frames_base.py','providers/search_suffix_kernels.py')) +def frame_only(source,word,recipes): + """Independent check that a promotion changed only entrance frames: identical scalar operations, start_extra changed + exactly at the recipe pivots (old -> new frame), frame fields only on scalar events, report changes limited.""" + assert source.keys()==word.keys() + for section in source: + if section in ('A','cut','B','cleanup','precondition'): + assert len(source[section])==len(word[section]) + assert all(x[:-1]==y[:-1]for x,y in zip(source[section],word[section])),'scalar operation changed' + elif section not in ('start_extra','report'):assert source[section]==word[section],'fixed field changed: '+section + entrances=dict(source['start_extra']) + for r in recipes: + k=str(r['pivot']);assert sorted(entrances[k])==sorted(r['old_frame']) and len(r['new_frame'])==len(r['old_frame'])+1,'wrong old entrance '+k + entrances[k]=word['start_extra'][k];assert sorted(entrances[k])==sorted(r['new_frame']),'wrong new entrance '+k + assert word['start_extra']==entrances,'entrance changed outside the recipe' + allowed={'local_profile','local_rank_mass','entrance_rank','entering_helpers','width_inventory'} + assert source['report'].keys()==word['report'].keys() and all(source['report'][k]==word['report'][k]for k in source['report']if k not in allowed) +def promote(word,s,out,tag): + src,builder,deps=PROMOTER;recipe=ref(s['recipe']);pinned(s,'recipe_sha256',sha(recipe),tag) + for f in deps:ref(src+':'+f) + run(tag+'-construction',ref(src+':'+builder),'--word',word,'--recipes',recipe,'--gk-dir',GK,'--out',out) + a,b,r=read(word),read(out/'FULL-WORD.json.gz'),read(recipe);frame_only(a,b,r) + import copy + rejected=[] + for name,mut in (('reverted_promotion',lambda w:w['start_extra'].__setitem__(str(r[0]['pivot']),list(r[0]['old_frame']))), + ('scalar_operation_changed',lambda w:w['B'][0].insert(0,'mutated')),('extra_entrance_changed',lambda w:w['start_extra'].__setitem__(next(k for k in w['start_extra']if k not in{str(x['pivot'])for x in r}),[])), + ('fixed_field_changed',lambda w:w.__setitem__('cut',w['cut'][:-1]))): + w=copy.deepcopy(b);mut(w) + try:frame_only(a,w,r) + except(AssertionError,KeyError,IndexError,TypeError):rejected.append(name) + else:raise AssertionError('frame-only control accepted: '+name) + dump(out/'FRAME-ONLY-CONTROLS.json',dict(status='PASS_FRAME_ONLY_PROMOTION_TRANSFER',promotions=len(r),controls=rejected)) + omissions(out/'FRAME-ONLY-CONTROLS.json',s,tag) +JOINT=('joint_prefix',('code/build_joint_prefix.py','code/audit_joint_prefix.py','code/audit_multicold_controls.py')) +def joint_prefix(word,s,out,tag): + """PR575's unchanged joint-prefix constructor with its paired audits: all-kernel omissions, rank-five omissions and + the independent literal-prefix/coverage audit (variant and kernel recipe named in the step).""" + src,(builder,audit,omit)=JOINT;recipe=ref(s['recipe']);kern=ref(s['kernel_recipes']);pinned(s,'recipe_sha256',sha(recipe),tag);pinned(s,'kernel_recipes_sha256',sha(kern),tag) + assert s['variant'] in ('eightcold','width7') + run(tag+'-construction',ref(src+':'+builder),'--input',word,'--recipe',recipe,'--variant',s['variant'],'--gk-dir',GK,'--out',out) + shutil.copyfile(RAW.parent/'PROMOTION.json',out/'PROMOTION.json') + run(tag+'-all-kernel-omissions',ref(src+':'+omit),'--word',out/'FULL-WORD.json.gz','--recipe',kern,'--out',out/'ALL-KERNEL-CONTROLS.json') + run(tag+'-rank5-omissions',B/'code/audit_promoted_scalar.py',out/'FULL-WORD.json.gz',SEL,out/'RANK5-CONTROLS.json') + run(tag+'-independent-joint-prefix-and-coverage',ref(src+':'+audit),'--source',word,'--word',out/'FULL-WORD.json.gz','--recipe',recipe,'--variant',s['variant'],'--kernel-recipes',kern,'--controls',out/'ALL-KERNEL-CONTROLS.json','--rank5-controls',out/'RANK5-CONTROLS.json','--promotion',out/'PROMOTION.json','--selection',SEL,'--out',out/'JOINT-PREFIX-AUDIT.json') + j=read(out/'JOINT-PREFIX-AUDIT.json');assert j['status']=='PASS_INDEPENDENT_LITERAL_PREFIX_AND_FINAL_KERNEL_COVERAGE' + c=read(out/'ALL-KERNEL-CONTROLS.json');assert all(x['forward_rejected'] and x['reflected_rejected'] for x in c['controls']) + omissions(out/'ALL-KERNEL-CONTROLS.json',s,tag);pinned(s,'rank5_controls',len(read(out/'RANK5-CONTROLS.json')['controls']),tag) + pinned(s,'joint_negative_controls',len(j['negative_controls_rejected']),tag) +COAL=('frame_coalescing','code/build_frames.py') +def frame_coalesce(word,s,out,tag): + """PR583's unchanged frame-coalescence constructor (it re-checks profiles, scalar operations, widths and helper + responses and rejects every omission/over-promotion control), plus an independent check that only the recipe's + gate frames changed (old -> new) and every other field of the word is identical.""" + src,builder=COAL;recipe=ref(s['recipe']);pinned(s,'recipe_sha256',sha(recipe),tag) + run(tag+'-construction',ref(src+':'+builder),'--input',word,'--recipe',recipe,'--gk-dir',GK,'--out',out) + r=read(recipe);c=read(out/'FRAME-CONSTRUCTION.json');assert c['status']=='PASS_SIX_EXACT_FRAME_COALESCENCES' + assert len(c['negative_controls_rejected'])==2*len(r['changes']);pinned(s,'negative_controls',len(c['negative_controls_rejected']),tag) + x,y=read(word),read(out/'FULL-WORD.json.gz');ch={(z['section'],z['index']):z for z in r['changes']};assert len(ch)==len(r['changes']) + assert x.keys()==y.keys() and all(x[k]==y[k]for k in x if k not in('A','B','report')) + for part in ('A','B'): + assert len(x[part])==len(y[part]) + for i,(u,v) in enumerate(zip(x[part],y[part])): + z=ch.pop((part,i),None) + if z is None:assert u==v,'frame changed outside the recipe %s %d'%(part,i) + else:assert u==z['before'] and v==z['after'] and u[:-1]==v[:-1],'wrong coalescence %s %d'%(part,i) + assert not ch,'recipe change outside A/B' + assert all(x['report'][k]==y['report'][k]for k in x['report']if k not in('local_profile','local_rank_mass','status')) +def gate_move_coalesce(word,s,out,tag): + """This package's code/build_gate_moves.py (PR583's constructor extended by commuting gate moves): every passed gate + must commute, helper responses and widths are unchanged, cleanup follows the inherited inverse rule, and every + omission/over-promotion/unmoved control is rejected; then the same independent comparison as frame_coalesce.""" + recipe=ref(s['recipe']);pinned(s,'recipe_sha256',sha(recipe),tag) + run(tag+'-construction',P/'code/build_gate_moves.py','--input',word,'--recipe',recipe,'--gk-dir',GK,'--out',out) + r=read(recipe);c=read(out/'FRAME-CONSTRUCTION.json');assert c['status']=='PASS_EXACT_GATE_MOVE_FRAME_COALESCENCES' + assert len(c['negative_controls_rejected'])==2*len(r['changes'])+len(r['moves']);pinned(s,'negative_controls',len(c['negative_controls_rejected']),tag) + x,y=read(word),read(out/'FULL-WORD.json.gz') + for m in r['moves']:L=x[m['section']];L.insert(m['to'],L.pop(m['from'])) + ch={(z['section'],z['index']):z for z in r['changes']};assert len(ch)==len(r['changes']) + assert x.keys()==y.keys() and all(x[k]==y[k]for k in x if k not in('A','B','cleanup','report')) + for part in ('A','B'): + assert len(x[part])==len(y[part]) + for i,(u,v) in enumerate(zip(x[part],y[part])): + z=ch.pop((part,i),None) + if z is None:assert u==v,'gate changed outside the recipe %s %d'%(part,i) + else:assert u==z['before'] and v==z['after'] and u[:-1]==v[:-1],'wrong coalescence %s %d'%(part,i) + assert not ch,'recipe change outside A/B' + meta=('width_inventory','entering_helpers','entrance_rank');assert all(x['report'][k]==y['report'][k]for k in x['report']if k not in('local_profile','local_rank_mass','status')+meta) + sys.path.insert(0,str(GK));import gk_common as GC;GC.V=112;ws=GC.widths_of(y) + assert y['report']['width_inventory']=={str(k):v for k,v in sorted(Counter(ws).items())} and y['report']['entering_helpers']==sum(v<9 for v in ws) and y['report']['entrance_rank']==sum(9-v for v in ws),'descriptive width metadata not normalized' +def hyperplane_end(word,s,out,tag): + """This package's code/build_hpe.py: cleanup gates that commute with the whole skipped cleanup prefix run right after B + at the join frame U of their registers, and the helper ends at U (residual T_U T_E^-1, width |U|-|E|; Lemma C, nested + children, Lemma A). Paired audit: code/hpe_controls_atc.py (exact replay of the reordered program plus HPE raw-word + mutations). Then an independent comparison: only early_cleanup, helper_final and the paid profile change.""" + recipe=ref(s['recipe']);pinned(s,'recipe_sha256',sha(recipe),tag) + run(tag+'-construction',P/'code/build_hpe.py','--input',word,'--recipe',recipe,'--out',out) + run(tag+'-controls',P/'code/hpe_controls_atc.py',out/'FULL-WORD.json.gz',F/'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz',out) + c=read(out/'HPE-ATC-CONTROLS.json');assert c['status']=='PASS_HPE_RAW_WORD_CONTROLS';pinned(s,'negative_controls',len(c['rejected']),tag) + r=read(recipe);x,y=read(word),read(out/'FULL-WORD.json.gz') + assert set(y)==set(x)|{'early_cleanup','helper_final'} and 'early_cleanup' not in x and all(x[k]==y[k]for k in x if k!='report') + assert y['early_cleanup']==[[z['cleanup_index'],z['frame']]for z in r['changes']] and y['helper_final']=={str(z['helper']):z['frame']for z in r['changes']} + assert x['report'].keys()==y['report'].keys() and all(x['report'][k]==y['report'][k]for k in x['report']if k not in('local_profile','local_rank_mass','width_inventory')) + inv=Counter({int(k):n for k,n in x['report']['width_inventory'].items()}) + for z in r['changes']:e=len(x['start_extra'][str(z['helper'])]);inv[9-e]-=1;inv[len(z['frame'])-e]+=1 + assert y['report']['width_inventory']=={str(k):n for k,n in sorted(inv.items())if n},'descriptive width metadata not |final|-|start|' +def cold_end(word,s,out,tag): + """This package's code/build_cold_end.py: cold helpers end at a low-dimensional frame U (width |U|) under a refactored + exact cleanup: a rank-0 premix at the head of A, multi-gate lower-frame cleanup gates in the early tail and an exact + dyadic FULL remainder that touches no helper ending below FULL. Paired audit: code/cold_end_controls.py (raw-word + mutations of premix placement, lower-frame gates, remainder, cold ends and marker, each rejected by the extended + transport audit). Then an independent comparison: only A's head, the cleanup, early_cleanup, helper_final, the + refactored_cleanup marker and the paid profile / width metadata change, and every inherited HPE end is kept.""" + recipe=ref(s['recipe']);pinned(s,'recipe_sha256',sha(recipe),tag) + run(tag+'-construction',P/'code/build_cold_end.py','--input',word,'--recipe',recipe,'--out',out) + run(tag+'-controls',P/'code/cold_end_controls.py',out/'FULL-WORD.json.gz',F/'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz',out) + c=read(out/'COLD-END-CONTROLS.json');assert c['status']=='PASS_COLD_END_RAW_WORD_CONTROLS';pinned(s,'negative_controls',len(c['rejected']),tag) + r=read(recipe);x,y=read(word),read(out/'FULL-WORD.json.gz') + assert set(y)==set(x)|{'refactored_cleanup'} and 'refactored_cleanup' not in x + assert all(x[k]==y[k]for k in x if k not in('A','cleanup','early_cleanup','helper_final','report')) + st=lambda h:sorted(x['start_extra'].get(str(h),[]));vv=x['report']['v'];nn=2*vv+x['report']['R'] + # premix: rank-0 helper gates at their start frames, or frame-[] target writes (target += q * cold helper; ColdBeyond) + tw=lambda e:e[0]=='add' and vv<=e[1]<2*vv + assert all(e[-1]==[] and 2*vv<=e[2]>k&1:z^=p[k] + if z: + k=z.bit_length()-1 + for j in p: + if p[j]>>k&1:p[j]^=z + p[k]=z + return tuple(p[k] for k in sorted(p,reverse=True)) + nA,nC=len(x['A']),len(x['cut']);inp=[('A',e) for e in x['A']]+[('C',e) for e in x['cut']]+[('B',e) for e in x['B']] + ins=r.get('forward_insertions',[]);ts=[t for t,_ in ins] + assert ts==sorted(ts) and all(0<=t R register map of the + removed packet copies. Controls, run once: PR531's unchanged constructor and this constructor with an empty schedule + each reproduce PR552's RAW504 (content), and the empty-schedule map is the identity.""" + sched=ref(base['schedule']);pinned(base,'schedule_sha256',sha(sched),tag) + with KT_LOCK: + if base['schedule'] in KT:pinned(base,'helper_map_sha256',sha(KT[base['schedule']][1]),tag);return KT[base['schedule']] + ham=[ref('direct_delivery:inputs/hamming/'+f)for f in('PROTOTYPE.json','PACKET-PROGRAMS.json.gz')][0].parent + raw504=F/'complex-local/static44/inputs/RAW504.json.gz' + if not KT: + K=O/'k-triangle-controls';K.mkdir();empty=K/'EMPTY-SCHEDULE.json';empty.write_text('{"full_pairs":[],"triangles":[]}\n',newline='\n') + run('k-triangle-control-pr531-construct504',ref('direct_delivery:code/construct_504.py'),ham,K/'pr531') + run('k-triangle-control-empty-schedule',P/'code/construct_k_triangle.py',ham,K/'empty',empty) + assert content(K/'pr531/FULL-WORD.json.gz')==content(K/'empty/FULL-WORD.json.gz')==content(raw504),'constructors do not reproduce RAW504' + assert all(int(k)==v for k,v in read(K/'empty/HELPER-MAP.json')['map'].items()) and len(read(K/'empty/HELPER-MAP.json')['map'])==728 + out=O/(tag+'-construction');run(tag+'-construction',P/'code/construct_k_triangle.py',ham,out,sched) + w=read(out/'FULL-WORD.json.gz');m=read(out/'HELPER-MAP.json');R=w['report']['R'] + assert R==504-3*len(read(sched)['triangles'])==len(m['map'])-224 and len(m['removed_504_helpers'])==504-R + pinned(base,'helper_map_sha256',sha(out/'HELPER-MAP.json'),tag) + KT[base['schedule']]=(out/'FULL-WORD.json.gz',out/'HELPER-MAP.json');return KT[base['schedule']] +def stage_word(r): + """'raw504' (PR552's RAW504), 'promoted558' (the frozen PR558 promoted word) or 'NAME:base' / 'NAME:i' (a word of + the shadow 504-helper chain NAME, built in this run).""" + if r=='raw504':return F/'complex-local/static44/inputs/RAW504.json.gz' + if r=='promoted558':return RAW + name,i=r.split(':');return STAGEWORDS[name][i] +def port_stage(word,s,out,tag): + """code/build_port_stage.py: one stage (I4 -> O4) of a 504-helper chain, rebuilt in this run from pinned sources, is + replayed onto the K-triangle word through the constructor's helper map. Gates are matched by scalar operation; the + stage's frame changes, introduced gates and entrance changes are applied; the K-triangle reads are kept; the cleanup is + the inherited inverse rule. The construction is a transfer only: every ported word is certified by the generalised + native audit (exact forward and inverse replay of all columns, native frame chains).""" + i4,o4=stage_word(s['shadow_input']),stage_word(s['shadow_output']) + pinned(s,'shadow_input_content_sha256',content(i4),tag);pinned(s,'shadow_output_content_sha256',content(o4),tag) + run(tag+'-construction',P/'code/build_port_stage.py','--shadow-input',i4,'--shadow-output',o4,'--input',word,'--map',KMAP[0],'--gk-dir',GK,'--out',out) + run(tag+'-native-audit',P/'code/hpe_audit_and_transport.py','--raw',out/'FULL-WORD.json.gz','--routing',F/'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz','--out',out/'native-audit') + assert read(out/'native-audit/SCALAR-FRAME-AUDIT.json')['status']=='PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES' + x,y=read(word),read(out/'FULL-WORD.json.gz');assert x['report']['R']==y['report']['R'] and all(x[k]==y[k]for k in x if k not in('A','B','cleanup','start_extra','target_levels','report')) + shutil.rmtree(out/'native-audit') +def frame_regroup(word,s,out,tag): + """code/build_frame_regroup.py (PR583's build_frames.py with recipe-pinned profile deltas): gate frames change, scalar + operations, widths and helper responses do not; omission and over-promotion controls are rejected. Then the same + independent comparison as frame_coalesce.""" + recipe=ref(s['recipe']);pinned(s,'recipe_sha256',sha(recipe),tag) + run(tag+'-construction',P/'code/build_frame_regroup.py','--input',word,'--recipe',recipe,'--gk-dir',GK,'--out',out) + r=read(recipe);c=read(out/'FRAME-CONSTRUCTION.json');assert c['status']=='PASS_EXACT_FRAME_REGROUPING' + assert len(c['negative_controls_rejected'])==2*len(r['changes']);pinned(s,'negative_controls',len(c['negative_controls_rejected']),tag) + x,y=read(word),read(out/'FULL-WORD.json.gz');ch={(z['section'],z['index']):z for z in r['changes']};assert len(ch)==len(r['changes']) + assert x.keys()==y.keys() and all(x[k]==y[k]for k in x if k not in('A','B','report')) + for part in ('A','B'): + assert len(x[part])==len(y[part]) + for i,(u,v) in enumerate(zip(x[part],y[part])): + z=ch.pop((part,i),None) + if z is None:assert u==v,'frame changed outside the recipe %s %d'%(part,i) + else:assert u==z['before'] and v==z['after'] and u[:-1]==v[:-1],'wrong regrouping %s %d'%(part,i) + assert not ch,'recipe change outside A/B' + assert all(x['report'][k]==y['report'][k]for k in x['report']if k not in('local_profile','local_rank_mass')) +KMAP=[None] +STEPS={'cold_end':cold_end,'hyperplane_end':hyperplane_end,'cold_kernel':cold_kernel,'multicut':multicut,'greedy_kernels':multicut,'promote':promote,'joint_prefix':joint_prefix,'frame_coalesce':frame_coalesce,'gate_move_coalesce':gate_move_coalesce,'port_stage':port_stage,'frame_regroup':frame_regroup} +def build_word(pid,d): + base=d['base'];assert base['kind']in('frozen558_promoted','source_file','k_triangle'),base['kind'] + if base['kind']=='k_triangle': + word,hmap=k_triangle(base,pid+'-base-k_triangle') + with KT_LOCK:assert KMAP[0] in(None,hmap);KMAP[0]=hmap + else:word=RAW if base['kind']=='frozen558_promoted' else ref(base['file']) + pinned(base,'content_sha256',content(word),pid+'.base');STAGEWORDS[pid]={'base':word} + for i,s in enumerate(d['steps']): + tag='%s-step%d-%s'%(pid,i,s['type']);out=O/tag + if s['type']=='frozen558_scalar_audits': + # inherited static44 and rank-five omission audits on a frozen558-descended word + out.mkdir();run(tag+'-static44',F/'complex-local/static44/audit_scalar.py',word,SEL,out/'STATIC44-SCALAR-AUDIT.json') + shutil.copyfile(RAW.parent/'PROMOTION.json',word.parent/'PROMOTION.json') + run(tag+'-rank5',B/'code/audit_promoted_scalar.py',word,SEL,out/'PROMOTED-SCALAR-AUDIT.json');STAGEWORDS[pid][str(i)]=word;continue + assert s['type'] in STEPS,'step type not allowlisted: '+s['type'] + pinned(s,'input_content_sha256',content(word),tag) + STEPS[s['type']](word,s,out,tag);word=out/'FULL-WORD.json.gz' + pinned(s,'output_content_sha256',content(word),tag);STAGEWORDS[pid][str(i)]=word + pinned(d,'word_content_sha256',content(word),pid) + return word +def localize(pid,word): + local=O/(pid+'-local') + # HPE words (helper_final present) use this package's generalised native chain; every other word the unchanged vendor531 one + hp='helper_final' in read(word);NC=(lambda f:P/'code'/('hpe_'+f))if hp else(lambda f:V/'code'/f) + run(pid+'-all-columns-native-frames',NC('audit_and_transport.py'),'--raw',word,'--routing',F/'complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz','--out',local) + run(pid+'-both-reflected-ledgers',NC('emit_local.py'),local) + run(pid+'-independent-local-controls',NC('audit_local.py'),local) + run(pid+'-normalized-wrappers',NC('adapters_local.py'),local/'CANONICAL-WORD.json.gz',local/'RESIDUAL-ADAPTERS.json',local/'WRAPPER-CHECKS.json') + run(pid+'-all-phase-edges',B/'code/phases_full.py',local,V/'vendor/clifford') + r=BUILD['providers'][pid].get('retained_local') + if r: # a pinned retained local must be reproduced byte for byte (phase review up to timing) + for name in ('CANONICAL-WORD.json.gz','LOCAL-PROGRAMS.json.gz','LOCAL-CHECKS.json','INDEPENDENT-LOCAL-REPLAY.json','RESIDUAL-ADAPTERS.json','WRAPPER-CHECKS.json','CLIFFORD-RECIPES.json'): + assert sha(local/name)==sha(ref(r+'/'+name)),(pid,name) + fresh,old=read(local/'CLIFFORD-REVIEW.json'),read(ref(r+'/CLIFFORD-REVIEW.json')) + assert {k:v for k,v in fresh.items()if k!='seconds'}=={k:v for k,v in old.items()if k!='seconds'} + return local +reuse=dict(x.split('=',1)for x in a.reuse_local) +words={} +def provider(pid): + word=words[pid]=build_word(pid,BUILD['providers'][pid]) + return Path(reuse[pid]).resolve()if pid in reuse else localize(pid,word) +SHADOWS=BUILD.get('shadows',{});assert not set(SHADOWS)&set(BUILD['providers']) +with ThreadPoolExecutor(max(1,min(a.jobs,len(SHADOWS)or 1)))as pool: # the 504-helper chains whose stages the providers port + for f in [pool.submit(build_word,name,SHADOWS[name])for name in sorted(SHADOWS)]:f.result() +with ThreadPoolExecutor(max(1,min(a.jobs,len(BUILD['providers']))))as pool: + futures={pid:pool.submit(provider,pid)for pid in sorted(BUILD['providers'])};locals_={pid:f.result()for pid,f in futures.items()} +SPOT504=[270,282,294,306] # PR558's width-8 spot helpers; a K-triangle package names their images under its helper map +if KMAP[0]:m=read(KMAP[0])['map'];assert SPEC['width_spot_helpers']==[m[str(224+h)]-224 for h in SPOT504],'width spot helpers are not the helper-map images' +else:assert SPEC.get('width_spot_helpers',SPOT504)==SPOT504 +dump(O/'LOCALS.json',dict(locals={pid:str(l)for pid,l in locals_.items()},words={pid:str(w)for pid,w in words.items()},baseline=str(baseline),discovered=discovered)) +if a.until=='locals':print('LOCALS READY');raise SystemExit(0) +assert not DISCOVER +G=O/'mixed-global' +run('bind-providers',P/'code/bind_providers_portable.py','--baseline',baseline,*[x for pid,l in sorted(locals_.items())for x in('--provider','%s=%s'%(pid,l))],'--plan',P/'data/PLAN.json','--out',G) +run('emit-controller',P/'code/emit_allcold.py','--base',G/'base','--owners',P/'data/OWNERS.json.gz','--plan',G/'PLAN.json','--out',G/'hosted') +(G/'audit').mkdir() +run('independent-controller-and-controls',P/'code/audit_allcold.py',G/'base',G/'hosted',G/'audit/ASYNC-AUDIT.json','--mutation-controls') +run('fresh-invoice',P/'code/invoice_allcold.py','--base',G/'base','--hosted',G/'hosted','--audit',G/'audit','--out',G/'audit','--retained-invoice',V/'evidence/audit/PREFIX-AND-INVOICE.json') +run('conservative-and-native-exact-assembly',P/'code/assemble.py',S,G,O/'ASSEMBLY.json') +run('admission-controls',P/'code/assembly_controls.py','--source-package',S,'--owner',G/'audit/OWNERS-AND-PROFILE.json','--invoice',G/'audit/PREFIX-AND-INVOICE.json','--out',O/'ASSEMBLY-CONTROLS.json') +run('phase-timing-portability-controls',P/'code/phase_timing_controls.py',S,G/'base',G/'audit',O/'PHASE-TIMING-CONTROLS.json') +run('actual-recompression-and-rebound-controls',P/'code/generated_identity_controls.py','--base',G/'base','--audit',G/'audit','--out',O/'GENERATED-IDENTITY-CONTROLS.json') +X=SPEC['expected'] +for pid,local in locals_.items(): + r=read(local/'INDEPENDENT-LOCAL-REPLAY.json');ph=read(local/'CLIFFORD-REVIEW.json') + assert len(r['negative_controls_rejected'])==SPEC['providers'][pid]['native_negative_controls'] and r['paid_profiles']['forward']==r['paid_profiles']['backward'] + assert ph['status']=='PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES' and ph['all_child_equalities_include_global_phase']is True and ph['directed_edges']==SPEC['providers'][pid]['phase_edges'] and ph['endpoint_adapters']==224 +assert len(read(G/'audit/ASYNC-AUDIT.json')['mutations_rejected'])==X['mutations_rejected'] +assert len(read(O/'ASSEMBLY-CONTROLS.json')['rejected_controls'])==X['assembly_controls_rejected'] +z=read(O/'ASSEMBLY.json');assert Q(z['kappa_decimal'])==Q(X['kappa_decimal']) and Q(z['conservative_kappa_decimal'])==Q(X['conservative_kappa_decimal']) +assert {str(k):v for k,v in z['complex_profile'].items()}==X['global_profile'] and z['provider_counts']==X['provider_counts'] +r=dict(status=SPEC['build']['status'],kappa=z['kappa'],kappa_decimal=z['kappa_decimal'],complex_lower=z['complex_lower'],bit_lower=z['bit_lower'],conservative_kappa_decimal=z['conservative_kappa_decimal'],conservative_complex_lower=z['conservative_complex_lower'],global_profile=z['complex_profile'],provider_counts=z['provider_counts'],surcharge_model=z['surcharge_model'],seconds=time.monotonic()-start,reused=dict(baseline=bool(a.reuse_baseline),locals=sorted(reuse)),scope=z['scope']);dump(O/'RESULT.json',r) +paths=['PHASE-TIMING-CONTROLS.json','GENERATED-IDENTITY-CONTROLS.json','mixed-global/audit/IDLE-REMAINDER-FRAMES.json','RESULT.json','ASSEMBLY.json','ASSEMBLY-CONTROLS.json','mixed-global/BINDING.json','mixed-global/audit/ASYNC-AUDIT.json','mixed-global/audit/OWNERS-AND-PROFILE.json','mixed-global/audit/PREFIX-AND-INVOICE.json'] +paths+=sorted(f.relative_to(O).as_posix()for f in O.glob('*-step*/*.json')) +for pid in sorted(set(locals_)-set(reuse)): + for fn in ('INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json','WRAPPER-CHECKS.json'):paths.append(pid+'-local/'+fn) +dump(O/'RECEIPT.json',dict(status=r['status'],steps=steps,artifacts={name:sha(O/name)for name in paths},manifest_sha256=sha(P/'MANIFEST.json'),spec_sha256=sha(SPECFILE),source_manifest_sha256={n:sha(SRC[n]/'MANIFEST.json')for n in SRC})) +print(json.dumps(r,indent=2)) diff --git a/research/pr643-improvement-20261013/witness/verify.sh b/research/pr643-improvement-20261013/witness/verify.sh new file mode 100644 index 0000000000..ddef97efc2 --- /dev/null +++ b/research/pr643-improvement-20261013/witness/verify.sh @@ -0,0 +1,31 @@ +#!/bin/sh +set -eu +HERE=$(CDPATH= cd -- "$(dirname -- "$0")" && pwd) +PYTHON=${PYTHON:-python3} +WORK=${1:?Choose a new replay output directory} +"$PYTHON" - <<'PY' +import sys +if sys.version_info < (3,10): + raise SystemExit('Python >=3.10 required') +if not __debug__: + raise SystemExit('Assertions required; unset PYTHONOPTIMIZE and do not use -O') +PY +"$PYTHON" -B "$HERE/verify.py" --jobs 2 --work "$WORK" \ + --source multicold="$HERE/vendor/multicold" \ + --source structural_gain="$HERE/vendor/structural_gain" \ + --source larger_gain="$HERE/vendor/larger_gain" \ + --source joint_prefix="$HERE/vendor/joint_prefix" \ + --source frame_coalescing="$HERE/vendor/frame_coalescing" \ + --source direct_delivery="$HERE/vendor/direct_delivery" +"$PYTHON" -I -O -B "$HERE/extras/check_native_owners.py" --package "$HERE" --replay "$WORK" --out "$WORK/INDEPENDENT-NATIVE-OWNERS.json" +"$PYTHON" -I -O -B "$HERE/extras/check_owner_controls.py" --package "$HERE" --replay "$WORK" --out "$WORK/INDEPENDENT-OWNER-CONTROLS.json" +"$PYTHON" -I -O -B "$HERE/extras/check_declarations.py" +"$PYTHON" -I -O -B "$HERE/owner-search/replay_owner_map.py" --base-data "$HERE/data/nominations/PR643" --out "$WORK/owner-map-rebuilt" --negative-controls +"$PYTHON" - "$WORK/owner-map-rebuilt/OWNERS.json.gz" "$HERE/data/OWNERS.json.gz" <<'PYCODE' +import gzip,sys +from pathlib import Path +if gzip.decompress(Path(sys.argv[1]).read_bytes()) != gzip.decompress(Path(sys.argv[2]).read_bytes()): + raise SystemExit('Owner nomination failed exact payload reproduction') +print('PASS exact owner nomination payload') +PYCODE +"$PYTHON" -I -O -B "$HERE/extras/check_u4_portable.py" --word "$WORK/jp8-step6-cold_end/FULL-WORD.json.gz" --provider jp8 --out "$WORK/INDEPENDENT-U4-CONTROLS.json" --negative-controls