From 44e2c79344e0090d4e829e0dde4f533d8d0273ec Mon Sep 17 00:00:00 2001 From: JoyboyBrian Date: Thu, 22 Oct 2026 12:02:18 -0700 Subject: [PATCH] Certify the first nonterminal QQ16 C8 tree and parking boundary --- research/qq16-nonterminal-c8-tree/README.md | 198 + research/qq16-nonterminal-c8-tree/RESULT.json | 4059 +++++++++++++++++ .../qq16-nonterminal-c8-tree/SOURCES.json | 102 + research/qq16-nonterminal-c8-tree/TASK.json | 100 + research/qq16-nonterminal-c8-tree/VERIFY.json | 45 + research/qq16-nonterminal-c8-tree/verify.py | 278 ++ 6 files changed, 4782 insertions(+) create mode 100644 research/qq16-nonterminal-c8-tree/README.md create mode 100644 research/qq16-nonterminal-c8-tree/RESULT.json create mode 100644 research/qq16-nonterminal-c8-tree/SOURCES.json create mode 100644 research/qq16-nonterminal-c8-tree/TASK.json create mode 100644 research/qq16-nonterminal-c8-tree/VERIFY.json create mode 100644 research/qq16-nonterminal-c8-tree/verify.py diff --git a/research/qq16-nonterminal-c8-tree/README.md b/research/qq16-nonterminal-c8-tree/README.md new file mode 100644 index 0000000000..55bd5ce668 --- /dev/null +++ b/research/qq16-nonterminal-c8-tree/README.md @@ -0,0 +1,198 @@ +# QQ16's first genuine nonterminal C8 band + +**Scoped source-tree result, not a complete cost sign or new κ.** At the +historical #4177 root family `p=2^8500`, the first nonterminal removed C8 +occurs at **λ=45**, not merely when its width exceeds 73. Precisely +**45≤λ≤72** gives one generation of selected-C children below each removed +C8, while every added C1 and every such grandchild is terminal. + +That generation has **510,662 Γ selected child calls** per C8. Removing the +sixteen C8 calls per outer cover therefore removes **8,170,592 Γ² internal +parking pairs**. These are inside the removed complete C8 bodies, not the +already credited generic outer-call parking optimisation. A literal subtrace +alone contributes at least + +``` +(reads, writes, unit moves) + >= (16,341,184, 40,852,960, 40,852,960) Γ² v, +``` + +where `v` is one complete C8 input bank's bit length. This is a lower bound on +one removed expense, **not a lower bound on the whole improvement**. Remaining +candidate costs and original nonchild/native costs prevent a sign conclusion. + +## Exact boundary and proof + +The predecessor's genuine descriptor family has + +``` +p = 2^8500, d = floor(sqrt(2^16949)), K = floor(d^(1/500)) = 126519, +G = 34006, H = dG, F = 14336 Γ, +Γ = 2^1296 product(j=1..36, 2^(2j)-1). +``` + +The actual source tests `w<73 OR w^1000 48 floor(w/73)`. Exact arithmetic checks `selected≤d`, strict fast entry, +`d≤(73λ)^1000`, guard residues, and the complete root address rectangle. +These are descriptor/admission arithmetic, not production payload execution. +The source/numerical/native/hosting/long-record premises of #4166/#4177 remain +inherited; the selected result is unchanged. + +Root rows are padded to a positive multiple of `F^D`. The outer selected node +consumes one F; a nonterminal C8 consumes one further F. D≥2 supplies both +positive divisions. Terminal grandchildren do not divide the stock again. +This explains exact divisions on the reached tree; it installs no smaller +root stock and does not replace the conservative all-root coarse envelope. +The giant `2^(q0K)` row count is kept symbolic, never allocated. + +Let R be C8's incoming rows and let +`v=P R 2H_b c 2^b` be its whole physical input volume. The C8 remainder leaf +preserves b by moving δ active axes into `before`. A rank-r grandchild moves +`(73-r)q` active axes into `after`; it also preserves b. However its rows are +**R/F**, so each selected grandchild's volume is **v/F**, not v. Consequently + +``` +sum of all grandchild payload volumes = (510662 / 14336) v. +``` + +The owner factor Γ cancels here because F contains it. It does **not** cancel +from the count of parent parking operations. Spectator axes, prefixes, +coefficient width and coefficient count are retained throughout. + +## What is priced, and what still needs a price + +The B* boundary is pinned to the literal #4167 adapter retained inside +#4177's PR4172 archive. `RootLayer` first constructs the original `Machine`. +`install` saves that object as `original`, passes it as `native_child` to the +new external parent, and replaces only `root_layer.machine`. The parent's +`enter_child` calls `self.native_child.run`; the adapter does not patch that +original object's `run` or `enter_child`. The adoption flag controls the +parent's returned packet. Thus the C8 body and its descendants still use the +original embedded `Machine.enter_child`, even for B*. The verifier authenticates +both nested archives/member bytes and checks these literal bindings without +executing predecessor code. This is a callgraph argument, not an assumption +that an outer optimisation recursively applies. + +The original `Machine.enter_child` parks all controller roles, including the +entire current bank; `BankPackets.gather` borrows that bank and preserves it. +Each successful selected child performs one park and one matching restore. +For every dense symbol of a parked role, the literal `Parking.park` loop alone +performs two reads, five writes and five unit moves. Rewinds, delimiters, +other roles and the entire restore contribute additional nonnegative work. +Since the current bank contains v bits, each pair has this conservative +componentwise lower bound `(2,5,5)v`. Multiplying by all `16·510662·Γ²` reached +pairs gives the bound at the top. This deliberately does not rederive or claim +#4167's stronger exact `56S+22r+11` full parking formula. + +A complete source partition for **one** external C8 call is + +``` +E8 = entry/setup + remainder-leaf + nonchild-work + final-return/cleanup + + sum(j over 510662 Γ selected children) + [prepare_j + park_j + complete-leaf_j + restore/return_j]. +``` + +The nonchild term includes all selected scalar, copy, monomial, native/Ordinary, +bank acquisition/publication and control work. Child bodies are terminal on +this band, but their argument geometry is v/F. Native internals remain inside +the appropriate nonchild term. The parent-call startup/return is outside the +sum; the remainder leaf precedes it. This partitions successful execution and +omits no source interval; most terms are **unpriced**. + +Substitute this E8, once, in the inherited fair comparison + +``` +T_D - T_B = ΔN + Δshell + 14298088 Γ + 368 Γ E1 - 16 Γ E8. +``` + +For B* retain its additional, already proved return-adoption credit against D. +The internal parking term is already inside `16ΓE8`: adding it again would +double count. The known positive cost of this removed subtrace cannot be +compared with a lower bound on candidate work to infer a winning sign. +This is a useful new bill boundary; it is not a supplier or κ claim. + +## Reproduction and scope + +``` +python3.12 -B scripts/research_package.py --package research/qq16-nonterminal-c8-tree +``` + +The standard-library verifier authenticates all inputs before data loading, +checks source control order, rederives all 482 event rows, proves the exact +integer descriptor band, and exercises ten rejecting controls. It runs in +normal and optimized modes without artifact writes. Only explicit `--write` +regenerates RESULT.json. No predecessor executable is imported. + +This is an exact host certificate and written source argument. It does not +execute the enormous root, a complete physical C8, embedded parking at that +geometry, native internals or a full RootLayer. The positive action bound is +proved from the source loop, not timed. It does not claim full numerical or +independent human/formal-kernel acceptance. + +Canonical investigation: [Discussion #4744](https://github.com/CrocSwap/integer-mult-bounds/discussions/4744). +Base main `b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`, priority revision 7. +Entry overlap: 506 open PRs, 3650 Discussion records and 5860 base local notes; +exact nonterminal queries found the predecessor's open question and audit +limits. Closed histories/code and unpublished work were not exhaustively searched. + +## Open next questions + +- Bound the candidate's **complete** unmatched nonchild/shell work above and + the removed C8 work below at the same full geometry. The explicit internal + parking floor is a starting term, not an affordability decision. +- Build a source-action evaluator for the reached one-generation C8, retaining + monomial/native calls and before/after spectators. Small payloads require a + separately labelled reduced binding; they cannot certify production cost. +- Beyond λ=72, derive the next selected-C generation with unchanged global d + and fresh-row divisions. First recheck live work and a full favorable budget; + deeper enumeration by itself is not a reason for another construction round. + +Credit Chris R / Clear1nsight's #4166/#4167/#4172/#4177; Jose Manuel's original +physical C, Ordinary and Compact machinery; ywz65, Sagar Thakrar, Tekalign, +Ali Romman, Arham Tahir and the retained source/native lineage. Prior census, +root family, generic parking optimisation and terminal exclusion retain their +attribution. New source-tree audit and proof: JoyboyBrian, with substantial +OpenAI Codex assistance. 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"root_stock_depth": 13999, + "selected_le_d": true, + "source_width_after_remainder": 511, + "spacing": 126519, + "stock_divisions_from_root": 2, + "tensor_columns": 7 + }, + { + "C1_terminal": true, + "C8_selected_child_tree_depth": 1, + "C8_width": 576, + "all_descendants_terminal": true, + "guard": 34006, + "lambda": 72, + "largest_grandchild_width": 336, + "leading_remainder_leaf_width": 65, + "root_stock_depth": 13999, + "selected_le_d": true, + "source_width_after_remainder": 511, + "spacing": 126519, + "stock_divisions_from_root": 2, + "tensor_columns": 7 + } + ], + "children_per_C8_per_Gamma": 510662, + "controls": [ + "width-alone nonleaf classification", + "equality called terminal", + "prune after removing remainder", + "lambda44 admitted to new band", + "lambda73 still one generation", + "missing later source events", + "grandchild keeps parent row volume", + "Gamma divided twice", + "one stock division is enough", + "terminal C8 bound reused" + ], + 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paid work?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/qq16-caller-install/README.md" + ], + "methods": [ + "Derive the matched whole-caller physical bill for installed and baseline protocols.", + "Change the actual demanded observations and prove a cheaper legal producer/consumer contract." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4166 COST.md and ADMISSION.json. An actual caller connection is now proposed. Its native-component profile loses; parent park/restore versus external-call costs remain unresolved. Retain the producer and recovery lineage rather than rebuild it.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "At the actual installed cut, compare matched complete parent park/restore and external input/return protocols at the same bank/packet geometry, including every later root call and service cost. Alternatively pin both bridge observations and derive a genuinely smaller source-compatible demand. Stop if the complete necessary inequality fails or an essential cost is unknown; no larger decoder scan from a local tape-action saving.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair.", + "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations.", + "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.", + "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate.", + "Recreating completed-output recovery or caller wiring already supplied by #4166 without new independent coverage.", + "Dropping retained later root calls or claiming native-profile dominance from the isolated publication saving." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969", + "2540", + "early record", + "output-bank retention", + "complete native decoder", + "2965", + "producer defect", + "dirty-helper range", + "F17 consumer", + "4166", + "qq16-caller-install" + ], + "existing_checks": [ + { + "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.", + "evidence": "research/qq16-caller-install/README.md", + "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.", + "status": "author-checked", + "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "refined", + "actual_scope": "Actual p=2^8500 RootPlan first nonterminal C8 band, complete one-generation selected-C tree, stock/volume and internal parking lower term", + "scope_change_reason": "The original card has been advanced through the terminal-band complete exclusion #4177; take its explicitly remaining nonterminal-body boundary.", + "bottleneck_link": "The terminal exclusion omits no descendants only in its stated band. Nonterminal C8 bodies introduce a large embedded parking term that must enter the fair comparison exactly once.", + "budget_minutes": 60, + "stop_rule": "Stop at the sharp first-generation band and complete symbolic bill. Do not infer the full sign with unpriced native/nonchild work or expand into a deeper search.", + "outcome": "partial", + "evidence": "Exact source-data census, integer RootPlan/cutoff certificate, written source-loop lower bound and ten rejecting controls; no production payload execution.", + "author": "JoyboyBrian, with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance for source analysis, proof, implementation and checking.", + "open_questions": [ + { + "question": "What is the complete signed D versus B* cost in the first nonterminal C8 band?", + "why_it_matters": "A removed internal parking term appears, but the full nonchild and native comparison remains unpriced.", + "first_step": "Price candidate nonchild/shell terms above and original complete C8 terms below at identical descriptors, charging descendants exactly once.", + "blocked_by": "Unpriced monomial/native internals and full candidate action upper bounds." + } + ], + "canonical_discussion": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4744", + "checkpoint": { + "base": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51", + "priority_revision": 7, + "open_prs": 506, + "discussion_records": 3650, + "base_local_notes": 5860, + "overlap_utc": "2026-10-22T18:50:37.698158+00:00", + "predecessor": "4177@4cdda81c2ad99ffe5add0ac5d894094c3cca101a" + } +} diff --git a/research/qq16-nonterminal-c8-tree/VERIFY.json b/research/qq16-nonterminal-c8-tree/VERIFY.json new file mode 100644 index 0000000000..d235c056ac --- /dev/null +++ b/research/qq16-nonterminal-c8-tree/VERIFY.json @@ -0,0 +1,45 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/community-frontier1094-audit/selected-replay.tar.gz", + "research/physical-complex-controller/bank_packets.py", + "research/physical-complex-controller/machine.py", + "research/physical-complex-controller/native_program.py", + "research/physical-complex-controller/parking.py", + "research/physical-complex-controller/root_layer.py", + "research/physical-complex-controller/root_plan.py", + "research/physical-complex-controller/selected_binding.py", + "research/physical-complex-controller/selected_source.py", + "research/qq16-caller-install/COST.md", + "research/qq16-complete-cost/PROOF.md", + "research/qq16-complete-cost/README.md", + "research/qq16-complete-cost/checker.py", + "research/qq16-complete-cost/inputs/PR4172.tar" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 30, + "checks": "source-tree-cutoff-stock-volume-controls" + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 30, + "checks": "source-tree-cutoff-stock-volume-controls-optimized" + } + ] +} diff --git a/research/qq16-nonterminal-c8-tree/verify.py b/research/qq16-nonterminal-c8-tree/verify.py new file mode 100644 index 0000000000..2ed6c07dd8 --- /dev/null +++ b/research/qq16-nonterminal-c8-tree/verify.py @@ -0,0 +1,278 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Independent data-only census and exact first-nonterminal domain certificate. + +JoyboyBrian, with substantial OpenAI Codex assistance. Source construction: +Chris R / Clear1nsight, Jose Manuel and the retained QQ16 source authors. +""" +import argparse +import ast +from collections import Counter +from fractions import Fraction +import gzip +import io +from hashlib import sha256 +import json +from math import isqrt, prod +from pathlib import Path +import tarfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +ARCHIVE = 'research/community-frontier1094-audit/selected-replay.tar.gz' +PREFIX = 'candidate/strict/global/' +MEMBERS = { + 'programs': ('base/providers/gauge44/LOCAL-PROGRAMS.json.gz', '241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a'), + 'template': ('hosted/GLOBAL-TEMPLATE.json.gz', '2acf02b418078e37090495c601fe550448751d4f35912757b13a1f778efc7760'), + 'phases': ('base/work/complex-nine-native/DATA-PHASES.json', 'c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa'), + 'native': ('base/providers/gauge44/CLIFFORD-RECIPES.json', 'd0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731'), +} +EXPECTED = {1: 349604, 2: 60192, 3: 62585, 4: 20448, 5: 11808, 7: 7, 8: 1152, 48: 4866} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(',', ':')).encode() + + +def authenticate(): + manifest = json.loads((HERE / 'SOURCES.json').read_text()) + for record in manifest['files']: + if record['usage'] == 'input': + need(sha256((ROOT / record['path']).read_bytes()).hexdigest() == record['sha256'], + 'source digest: ' + record['path']) + + +def load(): + result = {} + with tarfile.open(ROOT / ARCHIVE, 'r:gz') as archive: + members = archive.getmembers() + for name, (suffix, digest) in MEMBERS.items(): + matches = [m for m in members if m.name == PREFIX + suffix] + need(len(matches) == 1 and matches[0].isfile(), 'unique regular source member') + raw = archive.extractfile(matches[0]).read() + need(sha256(raw).hexdigest() == digest, 'member digest: ' + name) + result[name] = json.loads(gzip.decompress(raw) if suffix.endswith('.gz') else raw) + return result + + +def census(data): + template = data['template'] + need(template['m'] == 73 and template['live'] == 14336, 'source geometry') + events, calls = template['execution_schedule'], template['calls'] + need(len(events) == 482 and len(calls) == 144, 'complete source schedule') + by_time = {c['time']: c for c in calls} + need(len(by_time) == len(calls), 'unique local times') + edges = {(e['old'], e['new']): e['rank'] for e in data['native']['children']} + local = {} + for orientation, word in data['programs'].items(): + need(orientation in ('forward', 'backward') and len(word) == 24767, 'complete local word') + counts = Counter() + for op in word: + if op[0] in ('climb', 'center'): + old, new, rank = op[-3:] + need(type(rank) is int and edges[old, new] == rank and 0 < rank < 73, + 'literal directed native child') + counts[rank] += 1 + local[orientation] = counts + idle = {(r['replica'], r['child'], r['port']): r for r in template['idle_children']} + need(len(idle) == len(template['idle_children']), 'unique idle remainders') + rows, total, visited = [], Counter(), set() + nonchildren = {'bridge', 'terminal', 'terminal_Y_translations', + 'bank_padding_cover_sweep', 'translate_every_live_family'} + for index, event in enumerate(events): + counts = Counter() + if event['kind'] == 'local_cover_sweep': + call = by_time[event['time']] + counts.update(local[call['orientation']]) + elif event['kind'] == 'idle_cover_sweep': + for side in range(2): + for port in range(112): + key = event['replica'], event['child_indices'][side], port + if key not in idle: + continue + item = idle[key] + family = 896 * event['replica'] + (2 * event['pair'] + side) * 112 + port + axes = data['phases']['recipes'][port]['idle_children'][key[1]]['orthogonal_axes'] + need(item['family'] == family and + len(axes[item['pending_offset']:]) == item['rank'], 'actual idle suffix') + need(key not in visited, 'idle occurrence counted once') + visited.add(key) + counts[item['rank']] += 1 + else: + need(event['kind'] in nonchildren, 'complete child-emitting alphabet') + total.update(counts) + rows.append({'event': index, 'kind': event['kind'], 'ranks': dict(sorted(counts.items()))}) + need(visited == set(idle), 'all idle source records consumed') + need(dict(total) == EXPECTED, 'independent histogram agrees with prior full source census') + return total, rows + + +def root_only_adapter(): + def member(archive, name): + found = [m for m in archive.getmembers() if m.name == name] + need(len(found) == 1 and found[0].isfile(), 'unique regular retained adapter input') + return archive.extractfile(found[0]).read() + with tarfile.open(ROOT / 'research/qq16-complete-cost/inputs/PR4172.tar') as archive: + nested = member(archive, 'research/qq16-native-history/inputs/PR4167.tar') + need(sha256(nested).hexdigest() == '68ff3b4b541434cb9df15884d027838cbc80300e9d78015eb82c395c5168d166', + 'retained original protocol archive') + with tarfile.open(fileobj=io.BytesIO(nested)) as archive: + adapter = member(archive, 'research/qq16-protocol-comparison/adapter.py') + digest = sha256(adapter).hexdigest() + need(digest == '77c01376ac43339a7c99ab377c7947cb89b44e96ff4a826becb545cccd045fef', 'retained adapter bytes') + text = ast.unparse(ast.parse(adapter)) + root = ast.unparse(ast.parse((ROOT / 'research/physical-complex-controller/root_layer.py').read_text())) + need('self.machine = Machine(binding, native, catalogue, observe)' in root, + 'RootLayer constructs original Machine') + need('original = root_layer.machine' in text and + 'original.scalar.recipes, original, adopt=adopt, shared=shared)' in text and + 'self.native_child = native_child' in text and + "result = self.native_child.run(self.capsule['current'], descriptors)" in text and + 'root_layer.machine = parent' in text, 'original backend retained behind outer adapter') + assignments = [ast.unparse(n) for n in ast.walk(ast.parse(adapter)) + if isinstance(n, (ast.Assign, ast.AnnAssign, ast.AugAssign))] + need(not any('.enter_child =' in a or '.run =' in a for a in assignments), + 'adapter does not patch original recursive methods') + return {'adapter_sha256':digest, 'outer_root_replaced_only':True, + 'native_child_type':'original Machine', 'descendant_enter_child':'original embedded parking'} + + +def floor_root(value, exponent): + lo, hi = 0, 1 << ((value.bit_length() + exponent - 1) // exponent) + while lo + 1 < hi: + mid = (lo + hi) // 2 + if mid ** exponent <= value: + lo = mid + else: + hi = mid + return lo + + +def terminal(width, d): + need(type(width) is int and width >= 0 and type(d) is int and d > 0, 'cutoff domain') + return width < 73 or width ** 1000 < d + + +def source_order(): + text = (ROOT / 'research/physical-complex-controller/machine.py').read_text() + tree = ast.parse(text) + cls = next(n for n in tree.body if isinstance(n, ast.ClassDef) and n.name == 'Machine') + methods = {n.name: n for n in cls.body if isinstance(n, ast.FunctionDef)} + node = ast.unparse(methods['node']) + cut = "test = fixed_power(self.c('width'), 1000, self.c('root_width'))" + divide = 'delta = columns.divide_small(self.binding.dimension)' + need(node.index(cut) < node.index(divide) and node.count('fixed_power(') == 1, + 'cutoff precedes remainder and is not repeated') + enter = ast.unparse(methods['enter_child']) + ret = ast.unparse(methods['return_node']) + need(enter.count('self.parking.park()') == 1 and ret.count('self.parking.restore()') == 1, + 'one embedded parking pair per successful selected child') + init = ast.unparse(methods['__init__']) + need("'current'" in init and 'self.roles.values()' in init and 'Parking(self.parked)' in init, + 'whole current bank belongs to parked roles') + return sha256(ast.dump(methods['node']).encode()).hexdigest() + + +def domain(columns, d, gamma): + need(type(columns) is int and 45 <= columns <= 72, 'first one-generation band') + width = 8 * columns + q, delta = divmod(width, 73) + need(not terminal(width, d), 'C8 actually enters nonterminal branch') + need(terminal(columns, d) and terminal(48 * q, d), 'C1 and every C8 child terminal') + K = floor_root(d, 500) + guard, H = 34006, d * 34006 + F = 14336 * gamma + current, depth = d, 0 + while current >= 73: + current = 48 * (current // 73) + depth += 1 + q0 = depth * (F - 1).bit_length() + qF, qB = (2 * H + K - 1) // K, (H + K - 1) // K + selected = q0 + qF + qB + 73 * columns + need(selected <= d and selected > q0 + qF + qB, 'actual fast-root admission') + need(d <= (73 * columns) ** 1000, 'root nonterminal after reservation') + need(depth >= 2 and depth * F.bit_length() <= q0 * K, 'original stock supports two divisions') + front, back = qF * K - 2 * H, qB * K - H + need(0 <= front < K and 0 <= back < K, 'exact root guard residues') + address = 3 * H + front + 73 * columns * K + back + need(address == (selected - q0) * K, 'whole packet address rectangle') + after = 65 * columns * K + need(front + width * K + after == front + delta * K + (73 * q) * K + after, + 'remainder leaf preserves complete volume') + for rank in EXPECTED: + next_after = after + (73 - rank) * q * K + need(front + delta*K + rank*q*K + next_after == front + 73*columns*K, + 'every descendant keeps all spectator axes') + return {'lambda': columns, 'C8_width': width, 'tensor_columns': q, + 'leading_remainder_leaf_width': delta, 'source_width_after_remainder': 73*q, + 'largest_grandchild_width': 48*q, 'root_stock_depth': depth, + 'spacing': K, 'guard': guard, 'selected_le_d': True, + 'stock_divisions_from_root': 2, 'C1_terminal': True, + 'C8_selected_child_tree_depth': 1, 'all_descendants_terminal': True} + + +def run(): + authenticate() + node_hash = source_order() + adapter = root_only_adapter() + data = load() + counts, events = census(data) + d = isqrt(1 << 16949) + need(d*d <= 1 << 16949 < (d+1)*(d+1), 'exact RootPlan floor power') + cutoff = floor_root(d-1, 1000) + 1 + need(cutoff == 356 and terminal(355, d) and not terminal(356, d), 'strict global-height boundary') + gamma = (1 << 1296) * prod((1 << (2*j)) - 1 for j in range(1, 37)) + rows = [domain(c, d, gamma) for c in range(45, 73)] + need(terminal(8*44, d) and not terminal(48*((8*73)//73), d), 'both adjacent band endpoints') + n = sum(counts.values()) + need(n == 510662, 'complete per-cover child multiplicity') + # A descendant consumes exactly one fresh family/cover divisor of rows. + volume = Fraction(n, 14336) + need(volume == Fraction(n*gamma, 14336*gamma), 'cover cancels only in sum of child payload volumes') + rejected = [] + def rejects(label, test): + try: + test() + except (ValueError, AssertionError): + rejected.append(label) + else: + raise ValueError('control did not reject: ' + label) + rejects('width-alone nonleaf classification', lambda: need(not terminal(144,d), 'global cutoff')) + rejects('equality called terminal', lambda: need(terminal(356,356**1000), 'strict inequality')) + rejects('prune after removing remainder', lambda: need(not terminal(292,d), 'do not repeat cutoff')) + rejects('lambda44 admitted to new band', lambda: domain(44,d,gamma)) + rejects('lambda73 still one generation', lambda: domain(73,d,gamma)) + rejects('missing later source events', lambda: need(sum(sum(x['ranks'].values()) for x in events[:7])==n, 'suffix included')) + rejects('grandchild keeps parent row volume', lambda: need(Fraction(n*gamma)==volume, 'fresh stock divisor')) + rejects('Gamma divided twice', lambda: need(Fraction(n,14336*gamma)==volume, 'one owner-cover factor')) + rejects('one stock division is enough', lambda: need(1>=rows[0]['stock_divisions_from_root'], 'outer and C8 nodes')) + rejects('terminal C8 bound reused', lambda: need(terminal(8*45,d), 'no descendants is false')) + return {'status':'PASS_QQ16_FIRST_NONTERMINAL_TREE', 'precision':'2^8500', + 'global_d':'floor(sqrt(2^16949))', 'first_nonterminal_width':cutoff, + 'sharp_one_generation_lambda_interval':[45,72], 'source_node_ast_sha256':node_hash, 'fair_baseline_binding':adapter, + 'cases':rows, 'source_event_census':events, 'rank_histogram':dict(sorted(counts.items())), + 'children_per_C8_per_Gamma':n, 'removed_C8_calls_per_Gamma':16, + 'embedded_parking_pairs_per_Gamma_squared':16*n, + 'grandchild_payload_sum_over_C8_payload':str(volume), + 'park_only_RWM_lower_coefficients_per_Gamma_squared_v':[16*n*x for x in (2,5,5)], + 'controls':rejected, 'full_cost_sign':'not established', + 'production_payload_executed':False, 'native_monomial_internals_priced':False, + 'new_kappa':False} + + +def main(): + parser=argparse.ArgumentParser();parser.add_argument('--write',action='store_true');args=parser.parse_args() + result=run() + if args.write: + (HERE/'RESULT.json').write_text(json.dumps(result,sort_keys=True,indent=2)+'\n') + else: + need(canonical(json.loads((HERE/'RESULT.json').read_text())) == canonical(json.loads(json.dumps(result))), 'whole typed deterministic receipt') + print(result['status'], 'lambda=45..72', 'parking_pairs=8170592*Gamma^2', 'full_sign=unknown') + +if __name__=='__main__': + main()