From 98b6fc590a46b1067353fd04c89158f36580f2b7 Mon Sep 17 00:00:00 2001 From: rohanarun Date: Sun, 11 Oct 2026 23:03:16 -0400 Subject: [PATCH 1/3] Draft sliced R480 with causal minimum frames --- .../r480-sliced-minimal-frames/EXPECTED.json | 102 + research/r480-sliced-minimal-frames/LICENSE | 201 ++ .../r480-sliced-minimal-frames/MANIFEST.json | 24 + research/r480-sliced-minimal-frames/NOTICE.md | 108 + research/r480-sliced-minimal-frames/README.md | 29 + .../r480-sliced-minimal-frames/SOURCES.json | 17 + .../engines/base_two_moment.py | 63 + .../engines/moment.py | 113 + .../engines/outer.py | 58 + .../evidence/INDEPENDENT-SCALAR311.log | 7 + .../evidence/INTERFACE311.json | 13 + .../evidence/MINIMUM-FRAMES.json | 174 ++ .../evidence/SLICE.json | 1843 +++++++++++++++++ .../inputs/CANDIDATE.json.gz | Bin 0 -> 48223 bytes .../inputs/ORIGINAL.json.gz | Bin 0 -> 49414 bytes .../inputs/PR510-EXPECTED.json | 102 + .../inputs/PR535-EXPECTED.json | 62 + .../inputs/PR539-EXPECTED.json | 9 + .../inputs/three-stage-cover-bit.tex | 264 +++ .../scripts/minimum.py | 82 + .../scripts/price.py | 36 + .../scripts/slice.py | 107 + research/r480-sliced-minimal-frames/verify.py | 22 + 23 files changed, 3436 insertions(+) create mode 100644 research/r480-sliced-minimal-frames/EXPECTED.json create mode 100644 research/r480-sliced-minimal-frames/LICENSE create mode 100644 research/r480-sliced-minimal-frames/MANIFEST.json create mode 100644 research/r480-sliced-minimal-frames/NOTICE.md create mode 100644 research/r480-sliced-minimal-frames/README.md create mode 100644 research/r480-sliced-minimal-frames/SOURCES.json create mode 100644 research/r480-sliced-minimal-frames/engines/base_two_moment.py create mode 100644 research/r480-sliced-minimal-frames/engines/moment.py create mode 100644 research/r480-sliced-minimal-frames/engines/outer.py create mode 100644 research/r480-sliced-minimal-frames/evidence/INDEPENDENT-SCALAR311.log create mode 100644 research/r480-sliced-minimal-frames/evidence/INTERFACE311.json create mode 100644 research/r480-sliced-minimal-frames/evidence/MINIMUM-FRAMES.json create mode 100644 research/r480-sliced-minimal-frames/evidence/SLICE.json create mode 100644 research/r480-sliced-minimal-frames/inputs/CANDIDATE.json.gz create mode 100644 research/r480-sliced-minimal-frames/inputs/ORIGINAL.json.gz create mode 100644 research/r480-sliced-minimal-frames/inputs/PR510-EXPECTED.json create mode 100644 research/r480-sliced-minimal-frames/inputs/PR535-EXPECTED.json create mode 100644 research/r480-sliced-minimal-frames/inputs/PR539-EXPECTED.json create mode 100644 research/r480-sliced-minimal-frames/inputs/three-stage-cover-bit.tex create mode 100644 research/r480-sliced-minimal-frames/scripts/minimum.py create mode 100644 research/r480-sliced-minimal-frames/scripts/price.py create mode 100644 research/r480-sliced-minimal-frames/scripts/slice.py create mode 100644 research/r480-sliced-minimal-frames/verify.py 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Same480 width8 helpers and original owner schedule proposed. Physical template, chronological finite invoice and changed-frame geometric checks remain required; old outer finite constants used prospectively." +} diff --git a/research/r480-sliced-minimal-frames/LICENSE b/research/r480-sliced-minimal-frames/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/r480-sliced-minimal-frames/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/r480-sliced-minimal-frames/MANIFEST.json b/research/r480-sliced-minimal-frames/MANIFEST.json new file mode 100644 index 0000000000..077d8eb44a --- /dev/null +++ b/research/r480-sliced-minimal-frames/MANIFEST.json @@ -0,0 +1,24 @@ +{ + "EXPECTED.json": "ca226880c79eddffd43556aadd01c7534b6ec8c09f897ed2eff7d73a81a1569e", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE.md": "a16b8c2b6beea58c25a3cdda5f0345c6b7a1facdcf0272a23a7b4a3fb801b0db", + "README.md": "cab060bc25f40b5dd564e4be6232b0655b2c5696c04a78aba939c7c2d805e034", + "SOURCES.json": "61daf6ab993fc4df725352d96b48c534c3229f1e751b9d4f979248d8d0ca96ef", + "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098", + "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482", + "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "evidence/INDEPENDENT-SCALAR311.log": "42e960865be835a7b3e2598615c6077e9b6077bfc5801a5d67eca0e6c5a28854", + "evidence/INTERFACE311.json": "5c48a51887b1420083015eef35da59c371b9911bfcbc5032a1dbf0993f8fe886", + "evidence/MINIMUM-FRAMES.json": "c60b94107d56249887ed1d3adefb65745373f57791a0fb3c9e96e4625274de68", + "evidence/SLICE.json": "de878adca9979b59a707867425b9c1450250f3a54bffa57ccde355e109a8c517", + "inputs/CANDIDATE.json.gz": "37e84d9ace34138fc0a942d7cac37c46513a952b4d8ca5384545f830cc0948c9", + "inputs/ORIGINAL.json.gz": "92e399e9a486b55229b5624632ac54f800dd9e022f2aee97f1e5f264bbc0ef5c", + "inputs/PR510-EXPECTED.json": "883f7a1a84f31d9e4430e348bc8d9c1ec10210b206ff602dbe126349056af13d", + "inputs/PR535-EXPECTED.json": "cb734055c36681d38cf431a6926b7713351a94073cfba37d70a5384a9ef0d178", + "inputs/PR539-EXPECTED.json": "e2a71c1d49c68c35fb5c4f20f10377d708f55c3d25146fa811a99c7230d6ff0c", + "inputs/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511", + "scripts/minimum.py": "418f3143793ec981dbca953215f01a954c94e3097b8bc8a3833d5f726d9f5177", + "scripts/price.py": "f00306ed546f7d515763f3e9a192d3532759cb9d78863ee8a78036757209cfad", + "scripts/slice.py": "d72a4dadfc954aa51eb5b5976bbdeb661bb023201e7832fc9fe0340ef2845279", + "verify.py": "5e7e7780879e07393d86fa8f036bd9646ef0a2b98ea32e9a4c559d1e2f3ace80" +} diff --git a/research/r480-sliced-minimal-frames/NOTICE.md b/research/r480-sliced-minimal-frames/NOTICE.md new file mode 100644 index 0000000000..dfe09782a1 --- /dev/null +++ b/research/r480-sliced-minimal-frames/NOTICE.md @@ -0,0 +1,108 @@ +Prepared for rohanarun with OpenAI Codex assistance; Apache-2.0. New work: exact observable slicing and causal minimum-frame assignment on the R480 word, followed by prospective composition. No authorship of inherited circuitry or checkers is claimed. + +# Notice + +Apache-2.0 (`LICENSE`). Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. + +## New in this package + +- `code/assemble9.py`: the nine-stage bit invoice of PR #463's `assemble_k.py` (verbatim; its complex half is dropped) + followed by PR #493's per-supplier outer-assembly loop (verbatim). +- `code/adapt.py`: writes the adapted `audit_parent_k.py` (2 listed edits, each anchor checked to occur exactly once). +- `data/selection9-r480.json`: the nine-stage hosting selection, nominated by PR #442's programme through the vendored + `emit_k.py --discover` and rediscovered by `verify.py`. +- `code/findings/levels.py` (frame-level register visits). `code/findings/flowlp2.py` (the junk-dimension min-flow LP) and + `code/findings/piv0.py` (pivot classes) are byte-identical copies of DreamingOfClouds research scripts (Claude Sonnet 5.5 / + Claude Opus 5.5 via Claude Code), not from a PR; sha256 in `SOURCE.json`. +- `verify.py`, `EXPECTED.json`, `MANIFEST.json`, `SOURCE.json`, `README.md`. + +## Vendored, byte-identical (`vendor/`; git blob ids and sha256 in `SOURCE.json`, recomputed by `verify.py`) + +From PR #463 (DreamingOfClouds, branch e8-carrier-rekid-r715, head cdf0c1c6540df987467988fd771340670f4136f3): +- `research/e8-r715-eleven-stage-whole/code/{global_k,emit_k,audit_parent_k,audit_hosted_k,hosting_k,bank_routes_k}.py` + (DreamingOfClouds with Claude Opus 5.5, derived from PR #443 and PR #444 by chafreaky with OpenAI Codex, PR #442 by + DaysSky with Claude, and PR #386 by Zhihao Chen with OpenAI Codex; lineage per file in `SOURCE.json`); +- `research/e8-r740-replica32/code/{config,bank_routes,tile_m,e8core}.py` and `engines/{moment,base_two_moment,outer}.py` + (PR #443, chafreaky with OpenAI Codex; the engines are PR #315's, DreamingOfClouds); +- `research/idle-axis-hosting/hosting_core.py` (PR #442, DaysSky with Claude). + +## Used from the parents, unchanged + +- PR #503 (`research/e8-r480-dead-totals`): the R480 word and its verifier, run as the parent. +- PR #493 (`research/e8-bit-carrier-skeleton`, eumemic): the checkers (`columns_k.cpp` and its headers), the residual + isometry record, the nine-stage geometry builder (through the parent run) and the cited complex receipts + (`data/complex-b.json`). Provenance and licences are listed in PR #493's `NOTICE.md`. + + +# Notice + +Apache-2.0 (`LICENSE`). Prepared by eumemic with substantial Anthropic Claude assistance. + +## New in this package + +- `code/skeleton/`: the D4 quad-skeleton geometry (`geom.py`), the word builder with source registers as gate + destinations (`wordkit.py`), the generator (`gen.py`) and an E8 root-line helper (`e8.py`, #370's Hamming + coordinates and line order). +- `data/skeleton/plan-skB.json` (CP-SAT plan nominated by `discovery/plan.py`), `data/skeleton/d4part-pairs.json` + (the 5-pair D4 partition, found by `discovery/d4part.py`), `data/bit/bitE8mut-r489.json.gz` (the word), + `data/eleven/hosting.json` (frozen hosting selection nominated by `discovery/host_select.py` with #442's integer + programme), `data/eleven/residual-isometries.json` (the frame-zero record of #443's isometry format: every helper of + this word enters at frame zero). +- `code/bit/independent/relax.py` (generates the relaxed #370 checker), `interface.py` (#425 lemma hypotheses), + `mutate_mut.py` (word-level mutants and hypothesis controls), `code/bit/mutate_records_mut.py` (record-level + mutable-source mutants). +- `code/eleven/adapt.py` and the adapted files it checks, `code/eleven/{emit,audit,local_audit}.py` (PR #472's files + plus 19 listed edits: R = 489, package paths, a `--hosting` argument, one frame-zero entrance instead of eleven). +- `code/eleven/assemble.py`: PR #472's bit invoice and pricing arithmetic with R as a parameter, and its outer + assembly run once per cited complex supplier. +- `code/cited.py`, `data/complex-b.json`, `verify.sh`, `EXPECTED.json`, `requirements.txt`, `discovery/`, + `.github/workflows/e8-bit-carrier-skeleton.yml`. + +## Vendored, byte-identical (git blob ids in `SOURCE-pr*.json`, checked by `code/provenance.py`) + +- **PR #370 (Dylan Crow / utcorvusvolat-dotcom, with Anthropic Claude assistance), commit b7fe9cd:** the independent + checker `checkword.py` and its controls `mutate.py`; `export_records.py`, `mutate_records.py`, `stage_cohort.py`; + PR #266's official cohort checkers as generalised there (`legality_h.cpp`, `columns_h.cpp`, NCOPY); nlohmann/json + (`json.hpp`, MIT licence in its header); `gram_frames.py`; PR #315's engines (`code/pricing/`, DreamingOfClouds); + the R865 word `data/bit/bitE8-r865.json.gz` (read only for the E8 label table by the geometry scripts); `LICENSE`. +- **PR #381 (DaysSky, assisted with Claude), commit 00765b2:** `columns_k.cpp`. +- **PR #386 (Zhihao Chen / jacklightChen, with OpenAI Codex assistance), commit dd11cf8:** the nine-stage bit geometry + `code/nine/geometry.py` (parent geometry checked by the eleven-stage audit) and `portable-include/bits/stdc++.h`. +- **PR #436 (eumemic, with Anthropic Claude assistance), commit 8f6b829:** `code/provenance.py`. +- **PR #445 (chafreaky, with OpenAI Codex assistance), commit 40ab91d:** `code/hub/r740-hosted-eleven/code/geometry.py` + (eleven-stage geometry), `row_bound.py` (orthogonal-cover row bound), `emit.py` and `data/selection.json` (used + unchanged for the PR #445 control). +- **PR #451 (chafreaky, with OpenAI Codex assistance), commit f3a3815:** `code/hub/r740-hosted-rank149/`: its + eleven-stage bit emitter (byte-identical to PR #445's), frozen selection, R740 rank149 word and isometries + (PR #451 control). +- **PR #472 (chafreaky, with OpenAI Codex assistance), commit 259c684,** and files its branch carries unchanged: + - `code/hub/e8-r715-whole-hosted/`: PR #472's eight-replica pooled emitter, independent audit, local projector + audit and assembly (the originals of the adapted files), its R715 word, isometries and frozen hosting (used + unchanged for the PR #472 control); + - `code/hub/e8-r740-replica32/`: PR #443 (chafreaky): `bank_routes.py`, `tile_m.py`, `e8core.py`, the R740 rank138 + word and its isometries (PR #445 control); PR #315's engines (DreamingOfClouds) in `code/engines/`; + - `code/hub/idle-axis-hosting/hosting_core.py`: PR #442 (DaysSky, with Anthropic Claude assistance). +- **Receipts (`data/complex/`):** `EXPECTED.json` of PR #484 (DreamingOfClouds, 035845c), PR #471 (Dugongue, + 56b3da6), PR #458 (chafreaky, 44e9eae), PR #448 (higherbeing, 359022b), and of the bit-bound frontier PRs #483 + (Dugongue, 3738c3c), #473 (rohanarun, c7590f1) and #478 (Dugongue, bea1d52). + +The repository-level files `certificates/joint-dual-kappa.json`, `certificates/joint-dual-validation.json` and +`research/joint-dual/SOURCE.json` in this branch are byte-identical to rohanarun's PR #318 (a45747d). They repair +stale root-file pins so the repository's joint check passes; #417, #436 and #439 carry the same repair. + +## Cited, not rebuilt + +Complex coarse savings in `data/complex-b.json`, each bound to its PR's `EXPECTED.json` by `code/cited.py`: +PR #484 (primary; draft, conditional on its Lemmas A and G), PR #471 (the complex supplier of #473, #478 and #483), +PR #458 (the complex supplier of #472) and PR #448 (information only; disputed cross-copy split). No complex +construction is rebuilt here. + +## Ideas used + +PR #425 (Zhihao Chen, with OpenAI Codex assistance): the scalar-interface lemma that permits source registers as +gate destinations when the full-frame cleanup restores them. PR #463 (DreamingOfClouds, with Claude Opus 5.5): the +carrier bound (three registers leave a source's line). PR #433 (icekylinx): source rows written on the bit side. +PR #442 (DaysSky): idle-axis hosting of whole residuals. Jacob Sussman introduced the E8 unit. + + +Complex535 is cited at25f9b7c2310d40c9efdfbe368a40ba6e74d3b0a2: icekylinx with disclosed OpenAI assistance. Literal bad-class charge follows Srikrishnabalaji461 and464/465/539. The input source note and moment/outer engines retain predecessor attribution. diff --git a/research/r480-sliced-minimal-frames/README.md b/research/r480-sliced-minimal-frames/README.md new file mode 100644 index 0000000000..833ea3b11c --- /dev/null +++ b/research/r480-sliced-minimal-frames/README.md @@ -0,0 +1,29 @@ +# Sliced R480 with causal minimum frames + +**Draft candidate conditional kappa = 0.001586980532763499**, about **0.1293065%** above PR539. The scalar word, frame nesting and both exact moment engines pass; the new physical template and finite invoice remain pending. This is not yet a fully admitted supplier. + +## Change + +Starting from PR510's R480 word, an exact backward F2 target-response calculation identifies227 A gates with zero target response. Removing them and their227 inverse cleanup gates preserves the full scalar endpoint. This alone leaves the recursive histogram unchanged. + +Next process all remaining operations chronologically. At each A/B gate, replace its constructor frame by the exact rational span of the preceding operand frames. This produces the least feasible frame assignment in subspace inclusion for that fixed chronological word, with initial, center and final frames fixed. It is not a claim of global moment optimality.19 A-operation frames shrink, including three new rank-three root-closed frames. All frames remain nested, and phase B is unchanged. Source/helper inverse cleanup is literal at the full frame. + +The paid local histogram, including nine center copies, becomes + +`{1:1217,2:1421,4:169,5:1,6:130,8:9}` + +versus `{1:1200,2:1440,4:180,6:120,8:9}`. Rank mass,480 helpers and width-eight helper intervals remain unchanged. The prospective nine-stage profile reuses PR510's whole-owner selection and adds288 copies of the local histogram difference: + +`{1:350496,2:424608,4:64032,5:288,6:52800,7:23040,8:2592}`. + +Its bit endpoint is **0.001589503043149746028939**. PR535's unchanged cited complex endpoint is0.001589991533606044174031, so the bit side still binds. Literal bad-class charging follows PR539 and its461/464/465 ancestry. + +## Checks and pending work + +The inherited mutable-source independent checker passes all720 F2 columns, all120 source restorations,674 nondegenerate used frames with only prime2 in their Gram determinants, and the changed five-stage price on Python3.11.15. The PR425 interface-hypothesis audit passes. The prospective nine-stage profile passes both exact moment engines and47 strict outer inequalities; this currently assumes the preceding finite allowances remain valid. + +`python -B verify.py /absolute/new/output` reproduces the frozen input-to-candidate transformation and exact prospective price (Python3.11+, SymPy). Decimal arithmetic proposes an endpoint; rational intervals accept it and reject the next grid point. No optimizer or network is needed. Output must be outside this package. + +Full record-level geometry, chronological prefix bounds, explicit nine-stage whole-owner emission, mutation controls and finite invoice are being checked after draft submission. The old finite constants are not a substitute for that verification. No completed CI pass, full physical admission, all-size theorem, Lean completion or measured runtime gain is claimed. + +All inherited all-size bit/compiler, mutable-source/common-label realization, compressed geometry, whole-call hosting, restored-work, precision/tape and analytic-transfer assumptions remain conditional. See NOTICE.md for original attribution and SOURCES.json for pins. This is a new scalar/frame rewrite of the existing supplier; the complex supplier is cited rather than rebuilt. diff --git a/research/r480-sliced-minimal-frames/SOURCES.json b/research/r480-sliced-minimal-frames/SOURCES.json new file mode 100644 index 0000000000..bdb539de8c --- /dev/null +++ b/research/r480-sliced-minimal-frames/SOURCES.json @@ -0,0 +1,17 @@ +{ + "bit": { + "pr": 510, + "head": "64edee18af02aab0c1696b677a0287dd0146381b", + "word_sha256": "92e399e9a486b55229b5624632ac54f800dd9e022f2aee97f1e5f264bbc0ef5c" + }, + "complex": { + "pr": 535, + "head": "25f9b7c2310d40c9efdfbe368a40ba6e74d3b0a2", + "role": "cited complex endpoint, unchanged operator not rebuilt" + }, + "comparison": { + "pr": 539, + "head": "915ca69db7f98c70b97ce96e1fcc96818517584c" + }, + "scope": "Draft finite candidate. Physical emission and finite invoice pending." +} diff --git a/research/r480-sliced-minimal-frames/engines/base_two_moment.py b/research/r480-sliced-minimal-frames/engines/base_two_moment.py new file mode 100644 index 0000000000..14a90fa0e7 --- /dev/null +++ b/research/r480-sliced-minimal-frames/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/r480-sliced-minimal-frames/engines/moment.py b/research/r480-sliced-minimal-frames/engines/moment.py new file mode 100644 index 0000000000..7d697cb452 --- /dev/null +++ b/research/r480-sliced-minimal-frames/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/r480-sliced-minimal-frames/evidence/INDEPENDENT-SCALAR311.log b/research/r480-sliced-minimal-frames/evidence/INDEPENDENT-SCALAR311.log new file mode 100644 index 0000000000..11f2e08476 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/INDEPENDENT-SCALAR311.log @@ -0,0 +1,7 @@ +labels: 120 distinct lines of norm 2 (pairwise |ip| <= 1), spanning rank 8 +legality + exact F2 on all 720 columns: PASS (gates D/A/B/C = 120/2481/240/2481) +relaxed check: 712 gates have a source register as destination; all 120 sources restored exactly +nondegeneracy: 674 used frames, all Gram dets > 0 (positive-definite form); primes in dets: [2] +histogram {1: 6085, 2: 7105, 4: 1085, 5: 5, 6: 650, 7: 240, 8: 45, 14: 240, 18: 240} m 40 W 960 mass 38280 deficit 120 (4v-5L = 120 ) maxchild 18 +no envelope saving in [0.00128876435615175376, 0.00128876435615175376] +bad envelope saving in [0.00128876435528617710, 0.00128876435528617710] diff --git a/research/r480-sliced-minimal-frames/evidence/INTERFACE311.json b/research/r480-sliced-minimal-frames/evidence/INTERFACE311.json new file mode 100644 index 0000000000..b4227b9d9e --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/INTERFACE311.json @@ -0,0 +1,13 @@ +{ + "status": "PASS_PR425_INTERFACE_HYPOTHESES", + "source_destination_gates_A": 356, + "sources_rewritten": 69, + "source_write_frame_dims": { + "2": 12, + "3": 7, + "4": 337 + }, + "phase_B_reads_of_sources": 120, + "cleanup_gates": 2481, + "cleanup_source_gates": 356 +} \ No newline at end of file diff --git a/research/r480-sliced-minimal-frames/evidence/MINIMUM-FRAMES.json b/research/r480-sliced-minimal-frames/evidence/MINIMUM-FRAMES.json new file mode 100644 index 0000000000..c3f1918deb --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/MINIMUM-FRAMES.json @@ -0,0 +1,174 @@ +{ + "status": "COMPLETE_EXACT_CAUSAL_MINIMUM_FRAME_ASSIGNMENT", + "moves": [ + { + "section": "A", + "index": 2116, + "old": 482, + "new": 122, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2210, + "old": 484, + "new": 158, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2236, + "old": 485, + "new": 176, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2271, + "old": 486, + "new": 194, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2300, + "old": 487, + "new": 212, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2330, + "old": 488, + "new": 230, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2358, + "old": 489, + "new": 248, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2359, + "old": 489, + "new": 672, + "old_rank": 4, + "new_rank": 3 + }, + { + "section": "A", + "index": 2360, + "old": 489, + "new": 672, + "old_rank": 4, + "new_rank": 3 + }, + { + "section": "A", + "index": 2367, + "old": 489, + "new": 253, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2370, + "old": 489, + "new": 672, + "old_rank": 4, + "new_rank": 3 + }, + { + "section": "A", + "index": 2395, + "old": 490, + "new": 266, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2396, + "old": 490, + "new": 673, + "old_rank": 4, + "new_rank": 3 + }, + { + "section": "A", + "index": 2397, + "old": 490, + "new": 673, + "old_rank": 4, + "new_rank": 3 + }, + { + "section": "A", + "index": 2404, + "old": 490, + "new": 271, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2434, + "old": 491, + "new": 284, + "old_rank": 4, + "new_rank": 2 + }, + { + "section": "A", + "index": 2435, + "old": 491, + "new": 674, + "old_rank": 4, + "new_rank": 3 + }, + { + "section": "A", + "index": 2436, + "old": 491, + "new": 674, + "old_rank": 4, + "new_rank": 3 + }, + { + "section": "A", + "index": 2443, + "old": 491, + "new": 289, + "old_rank": 4, + "new_rank": 2 + } + ], + "new_frames": 3, + "baseline_chain_profile": { + "1": 1200, + "2": 1440, + "4": 180, + "6": 120 + }, + "new_chain_profile": { + "1": 1217, + "2": 1421, + "6": 130, + "4": 169, + "5": 1 + }, + "fee_delta": -0.04495826477563014, + "seconds": 2.2678134579909965, + "scope": "Least rational span of every preceding operand frame at each A/B gate, with source starts, center cut and cleanup/final frames fixed. All newly needed root closures generated exactly. This is the least feasible frame assignment in subspace inclusion for this fixed chronological word, not a moment optimum. 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"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 + } +} \ No newline at end of file diff --git a/research/r480-sliced-minimal-frames/inputs/PR535-EXPECTED.json b/research/r480-sliced-minimal-frames/inputs/PR535-EXPECTED.json new file mode 100644 index 0000000000..2c5a1a3262 --- /dev/null +++ b/research/r480-sliced-minimal-frames/inputs/PR535-EXPECTED.json @@ -0,0 +1,62 @@ +{ + "status": "PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY", + "kappa": "1584931111785787/1000000000000000000", + "kappa_decimal": "0.001584931111785787", + "complex_lower": "1589991533606044174031/1000000000000000000000000", + "complex_decimal": "0.001589991533606044174031", + "bit_lower": "396861776523137034277/250000000000000000000000", + "bit_decimal": "0.001587447106092548137108", + "binding_component": "bit", + "improvements": { + "PR531": { + "baseline": "1517760977820331/1000000000000000000", + "relative_gain": "67170133965456/1517760977820331", + "percent_display": "4.42560686" + }, + "rejected_POST208_checkpoint": { + "baseline": "771820390859371/500000000000000000", + "relative_gain": "41290330067045/1543640781718742", + "percent_display": "2.67486649" + }, + "PR533": { + "baseline": "381051987698311/250000000000000000", + "relative_gain": "60723160992543/1524207950793244", + "percent_display": "3.98391577" + } + }, + "global_template_content_sha256": "b9f4b60e56e5153c1fc89370e9ceb09f24b23e1c8ff56f2b47ef9d867aa04f2c", + "raw_word_content_sha256": "b9110e8ddb770a3874c2df2019e04a98c1a25684072f7f8e5772653f59f15db2", + "canonical_word_content_sha256": "7c84ac65c8b37173aa4293934f041915895e8ec30595844cc1534e2a19ae0d25", + "global_profile": { + "1": 158976, + "2": 52864, + "3": 15200, + "4": 20160, + "5": 4032, + "6": 4032, + "7": 352, + "8": 576, + "48": 1632 + }, + "local_profile": { + "1": 2208, + "2": 728, + "3": 184, + "4": 280, + "5": 56, + "6": 56, + "8": 8 + }, + "local_rank_mass": 6016, + "entrance_rank": 376, + "width_inventory": { + "5": 56, + "8": 152, + "9": 296 + }, + "global_prefix_bits": 225, + "live": 7168, + "physical": 7682, + "deficit": 2560, + "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/r480-sliced-minimal-frames/inputs/PR539-EXPECTED.json b/research/r480-sliced-minimal-frames/inputs/PR539-EXPECTED.json new file mode 100644 index 0000000000..6f09653ae5 --- /dev/null +++ b/research/r480-sliced-minimal-frames/inputs/PR539-EXPECTED.json @@ -0,0 +1,9 @@ +{ + "kappa": "49529097302971/31250000000000000", + "kappa_decimal": "0.001584931113695072", + "bit_lower": "793723554003949831983/500000000000000000000000", + "bit_decimal": "0.001587447108007899663966", + "old_kappa": "1584931111785787/1000000000000000000", + "fallback_per_edge": 98682, + "bad_fraction": "1/2305843009213693952" +} diff --git a/research/r480-sliced-minimal-frames/inputs/three-stage-cover-bit.tex b/research/r480-sliced-minimal-frames/inputs/three-stage-cover-bit.tex new file mode 100644 index 0000000000..f05225d21f --- /dev/null +++ b/research/r480-sliced-minimal-frames/inputs/three-stage-cover-bit.tex @@ -0,0 +1,264 @@ +\subsection{Atom contract and common endpoint} +Fix an odd prime $q$, chosen below, and put $R_w=\mathbb Z/q^w\mathbb Z$. +An atom is a complete consecutive $w$-digit address field. Write $C_n$ for +reversal of the $n$ atom positions, without reversing digits inside an atom. +The recursive contract is the involution +\[ + F_A(H,D)=(AC_nD,C_nA^{-1}H), +\] +where $A$ is a diagonal array of units on the head atoms. Its entries may +depend on exposed ancestor row fields and the atom index, but not on the +fresh role fields of this invocation or on the head/data values. Only the +polynomial-time descriptors generated by the construction are required; +no constant-cost oracle for arbitrary functions of a prefix is assumed. +Every call preserves all complete spectator fields and restores its row +coordinate. The original unweighted call has $A=I$. + +For a split idempotent $P$ on the head coordinates set +\[ + D_P=\begin{pmatrix}I-P&PC_n\\C_nP&I-C_nPC_n\end{pmatrix}, + \qquad F=D_I. +\] +These are involutions, and $D_P-I$ has split rank $\operatorname{rank}P$. +Nested commuting-projector identities are polynomial identities and require +no symmetry of $P$. For $n=mf$ and $G=g\otimes I_f$ define +\[ + Q_g=\operatorname{diag}(G,C_nGC_n). +\] +Then $Q_gF=FQ_g$ and $Q_gD_PQ_g^{-1}=D_{GPG^{-1}}$. +Consequently conjugating every base frame by any $g\in\operatorname{GL}_m(R_w)$ +leaves the same full physical endpoint $F$. + +Put $Q_A=\operatorname{diag}(A,I)$. Conjugate the entire completed scalar +word by $Q_A$. Scalar gates mix roles having the same address map, so they +commute with $Q_A$. A current role routing also commutes with $Q_A$, since +it changes only fresh fields. Thus only address residuals change, and the +completed endpoint is $Q_AFQ_A^{-1}=F_A$. More explicitly, when a port +changes charts from $g$ to $gR_s$, its local label changes from $M$ to +$R_s^{-1}MR_s$, and +\[ + (gR_s)(R_s^{-1}MR_s)(gR_s)^{-1}=gMg^{-1}. +\] +This routing is a change of row/chart, not an uncharged dense address map. +The adapted chart $Q_AQ_gQ_A^{-1}$ commutes with $F_A$. None of these +conjugations is executed as an extra normalization pass. + +\subsection{Explicit rational three-stage geometry} +Use the retained PR97 local producer with +\[ + h=23,\qquad v=1771,\qquad R_{\rm loc}=28866,\qquad \ell=506. +\] +Its physical projector ranks and scalar word are unchanged. On +$\mathcal A=\mathbb Q^{23}$ take the form $H_0=(I-J/9)/2$. +For a triple $S$ let $q_S=\chi_S$; then $q_S^tH_0q_S=1$. +Fix $q_0=\chi_{\{1,2,3\}}$ and $K=q_0^\perp$. A rational basis is +\[ + k_i=e_i-(e_i^tH_0q_0)q_0,\qquad 2\le i\le23. +\] +Projection along $q_0$ is injective on the span of $e_2,\ldots,e_{23}$, +since $q_0$ has nonzero first coordinate. Thus this is indeed a basis. +Let $\mathcal B,\mathcal C$ be orthogonal copies of $K$ and put +$\mathcal E=\mathcal A\perp\mathcal B\perp\mathcal C$, of dimension $m=67$. + +Choose a coordinate permutation $\pi_S$ taking $\{1,2,3\}$ to $S$. +It preserves $H_0$. The rational isometry $R_{12,S}$ fixes $q_S$ and +$\mathcal C$, and exchanges $\pi_Sk_i\in q_S^\perp\subset\mathcal A$ +with $k_i\in\mathcal B$. Define $R_{23,S}$ by exchanging the same vectors +with their copies in $\mathcal C$, fixing $q_S$ and $\mathcal B$. +Both maps are involutions. A hyperedge $(g,S)$ uses the invocations +$gR_{12,S},g,gR_{23,S}$, with active spaces +\[ + g(\mathcal B+\mathbb Qq_S),\qquad g\mathcal A, + \qquad g(\mathcal C+\mathbb Qq_S). +\] +Their projectors commute; their pairwise and common intersection is the +projector $P_{gq_S}$, and their sum is $I+2P_{gq_S}$. +This follows from the orthogonal decomposition +$\mathbb Qq_S\perp q_S^\perp\perp\mathcal B\perp\mathcal C$ before +conjugation. These are the cumulative-projector three-stage transfer +identities: the three scalar shears complete the interchange, with zero +interstage connectors and no rank-one endpoint correction. Each port +family visits the full cover bijectively, by right multiplication with +its displayed involution. The physical ledger is therefore three copies +of the local auxiliary, data and center histograms, and three copies of +the exterior histogram $m-\text{nullity}$. + +\subsection{One weighted child on a generic residue class} +Work first on one atom column. Let $g$ be its weighted residual involution, +of split rank $r$ relative to $I$. If the cross block has generic northeast +rank profile, unit lower row and column elimination, without normalizing +pivots, gives +\[ + Lg_{XY}R=ED_pF_0^t, + \quad E=(e_1,\ldots,e_r),\quad + F_0=(e_m,\ldots,e_{m-r+1}), +\] +with invertible diagonal $D_p$. Conjugate by $\operatorname{diag}(L,R^{-1})$. +Split rank and the unit pivot minor give a factorization +\[ + g-I=\binom EB(A_0,D_pF_0^t),\qquad + A_0E+D_pF_0^tB=-2I_r. +\] +For clarity, if $g-I=UV$, then $g^2=I$ gives +$U(VU+2I)V=0$. The unit minor supplies a left inverse of $U$ and a right +inverse of $V$, proving the identity over the local ring itself. +Set +\[ + K=-(B+F_0D_p^{-1})E^t+F_0D_p^{-1}A_0(I-EE^t), + \qquad S=\begin{pmatrix}I&0\\K&I\end{pmatrix}. +\] +The identities $KE=-B-F_0D_p^{-1}$ and +$D_pF_0^tK=A_0+E^t$ give +\[ + SgS^{-1}=\begin{pmatrix} + I-EE^t&ED_pF_0^t\\F_0D_p^{-1}E^t&I-F_0F_0^t + \end{pmatrix}. +\] +This is one weighted reversed interchange on the first $r$ head and last +$r$ tail coordinates. All other factors are unit lower intrabank maps or +lower cross-bank additive maps. Thus variable diagonal units remain in +the child's weight array rather than becoming unsupported routing passes. + +For $n=mf$, group atoms by coarse coordinate $i$ and column $j$. +If $L_P,R_P,D_P$ are unweighted normalizers for the current projector and +$A_j=\operatorname{diag}(A[if+j])$, then +$L_j=A_jL_PA_j^{-1}$ and $R_j=R_P$ are unit lower normalizers for +$A_jPC_m$. The child's exact contiguous index rule is +\[ + A_{\rm child}[kf+j]=A[i_kf+j]D_P[k]. +\] +The cross-bank atom pairing is reversed, and $C_r\otimes C_f=C_{rf}$. +Hence the middle operation is exactly one $rf$-atom call of the same +contract, with no interleaving or gathering. Its coefficients depend only +on parent prefix fields, which become ancestor spectators at the child; +the child's fresh roles come from disjoint unused row stock. + +All unit lower adapters require $O(n)$ atom passes. The retained ordered +affine lemma implements each later-target shear in $O(V)$, including +prefix-controlled offsets. The generated descriptors have polynomial cost +in $w$: good-class evaluation follows one ancestral index per level; +fallback evaluation branches by a constant per level. Since depth is +$O(\log e)$ and $w=\lceil e^{1/1000}\rceil$, this costs $e^{O(1)}=w^{O(1)}$. +Stored ancestor data use $O(w\log e)$ bits. The proof of the ordered affine +lemma still applies with these controls: polynomial preparation per prefix +is absorbed by the complete $q^w$ target fiber. Unrelated spectator counters +are incremented by ripple counting rather than read in their entirety. + +\subsection{Weighted leaves and a genuine local-ring fallback} +At one atom write $J_a=\left(\begin{smallmatrix}0&a\\a^{-1}&0\end{smallmatrix}\right)$, +$U(a)=\left(\begin{smallmatrix}1&a\\0&1\end{smallmatrix}\right)$ and +$L(b)=\left(\begin{smallmatrix}1&0\\b&1\end{smallmatrix}\right)$. +Then +\[ + J_a=\operatorname{diag}(1,-1)U(a)L(-a^{-1})U(a), + \qquad U(a)=J_1L(a)J_1. +\] +Thus a weighted leaf uses four old ordinary atom interchanges, three +prefix-controlled shifts and one fixed sign. With +$a_{\rm old}=384599/10^{10}$ it costs $O(Vw^{1-a_{\rm old}})$. +This constant occurs only at stopped leaves. + +A bad residue class cannot be treated by field Bruhat elimination: +an entry zero modulo $q$ need not vanish modulo $q^w$. Instead Gaussian +eliminate the full invertible residual of size $N_0=2m$ with unit pivots. +Each invertible Schur complement has a unit in its next pivot column; +row swaps and unnormalized additions clear that column. There are at most +$N_0(N_0-1)$ additions and $N_0$ swaps. Pivot choices are determined by +the unweighted low residue class: diagonal conjugation scales every +Schur-complement row and column by units and preserves its zero pattern. +The final diagonal has product a fixed sign, since the residual has +determinant $(-1)^r$ and row swaps change only the sign. + +A lower addition is a paid additive adapter. An upper addition is +conjugated into a lower addition by two ordinary coarse-field swaps. +For a field of $f$ atoms, let $R_{\rm tail}$ reverse the later field. +Then the ordinary weighted swap is +\[ + J_A=R_{\rm tail}F_AR_{\rm tail},\qquad + J_A(H,D)=(AD,A^{-1}H). +\] +Each $R_{\rm tail}$ is one unweighted reversed call on the first and last +$\lfloor f/2\rfloor$ atoms, fixing a possible middle atom. Thus $J_A$ +costs at most three children of widths $f,\lfloor f/2\rfloor, +\lfloor f/2\rfloor$. A paired diagonal scaling is $J_aJ_1$, at most six +children. The full diagonal is a product of $N_0-1$ such pairs and a fixed +sign. Across the two banks the reversed pairing already makes the swaps +and diagonal pairs directly reversed calls; the preceding ordinary bounds +remain conservative. Reindexing a tail weight by $j\mapsto f-1-j$ changes +only its descriptor. Charging every addition as upper therefore gives +\[ + 6N_0(N_0-1)+3N_0+6(N_0-1)<32m^2. +\] +Every child has width at most $f$, hence ratio at most $1/m$. Coefficients +are computed from constant-sized local-ring matrices and parent weight +descriptors; only units are inverted. This proves the fallback cost, +including its actual reversals, rather than assuming nonunit pivots away. + +\subsection{Finite covers, batching, and the strict moment} +Take $q>2^{80}$ 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(ndim[fa]:h[dim[fz]-dim[fa]]+=1 + return h +H0=profile();print('CATALOGUE',len(bs),'profile',dict(H0),'seconds',time.monotonic()-t0,flush=True) + +from functools import lru_cache +original_count=len(masks);idx={m:f for f,m in enumerate(masks)} +@lru_cache(None) +def join(mask): + basis=rref([lines[i]for i in range(len(lines))if mask>>i&1]);closed=sum(1<>i&1]for m in masks] +for k in mutable: + z=nodes[k];out[z['sec']][z['idx']][0]=z['F'] +(O/'WORD.json.gz').write_bytes(gzip.compress(json.dumps(out,sort_keys=True,separators=(',',':')).encode(),mtime=0)) +res=dict(status='COMPLETE_EXACT_CAUSAL_MINIMUM_FRAME_ASSIGNMENT',moves=moves,new_frames=len(masks)-original_count,baseline_chain_profile=dict(H0),new_chain_profile=dict(H),fee_delta=sum(fee(r)*n for r,n in H.items())-sum(fee(r)*n for r,n in H0.items()),seconds=time.monotonic()-t0,scope='Least rational span of every preceding operand frame at each A/B gate, with source starts, center cut and cleanup/final frames fixed. All newly needed root closures generated exactly. This is the least feasible frame assignment in subspace inclusion for this fixed chronological word, not a moment optimum. No new physical admission or kappa claimed.') +(O/'RESULT.json').write_text(json.dumps(res,indent=2)+'\n');print(res,flush=True) diff --git a/research/r480-sliced-minimal-frames/scripts/price.py b/research/r480-sliced-minimal-frames/scripts/price.py new file mode 100644 index 0000000000..fe91825ad6 --- /dev/null +++ b/research/r480-sliced-minimal-frames/scripts/price.py @@ -0,0 +1,36 @@ +"""Prospective exact price of sliced/minimum-frame R480 with unchanged PR510 hosting. +Not physical admission; finite invoice and owner-template replay remain pending. +""" +from pathlib import Path +from fractions import Fraction as Q +from decimal import Decimal,localcontext +from collections import Counter +import json,importlib.util +R=Path(__file__).resolve().parent;O=R/'bit510-sliced-minimal-price';O.mkdir(exist_ok=False);p=R/'r480-sharp535-publication/research/r480-sharp-charge535' +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,Outer=[load(x)for x in ['moment','base_two_moment','outer']] +x=json.loads((p/'inputs/PR510-EXPECTED.json').read_text())['nine'];loc=json.loads((R/'bit510-sliced-minimal-frames/RESULT.json').read_text());old={int(k):v for k,v in loc['baseline_chain_profile'].items()};new={int(k):v for k,v in loc['new_chain_profile'].items()};H=Counter({int(k):v for k,v in x['profile'].items()}) +for r,n in old.items():H[r]-=288*n +for r,n in new.items():H[r]+=288*n +H=+H;m=x['m'];W=x['bit']['live'];assert sum(r*n for r,n in H.items())==x['bit']['rank_mass'];factor=Q(1,2**61)*98682*sum(H.values()) +def bounds(c): + a,z=M.moment(H,m,W,c,False);g,h=M.moment({1:1},m,W,c,False);b,y=B.moment(m,W,list(H.items()),c);j,k=B.moment(m,W,[(1,1)],c);return a+factor*g,z+factor*h,b+factor*j,y+factor*k +with localcontext()as ctx: + ctx.prec=90;term=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln())for r,n in H.items()];fb=Decimal(factor.numerator)/Decimal(factor.denominator)/Decimal(m*W);lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003') + for _ in range(230): + c=(lo+hi)/2 + if sum(p*(c*l).exp()for p,l in term)+fb*(c*lm).exp()<1:lo=c + else:hi=c + c=Q(int(lo*10**24),10**24) +checks=[] +for a,accept in [(c,True),(c+Q(1,10**24),False)]: + l,h,ll,hh=bounds(a);assert (h<1 and hh<1)if accept else(l>1 and ll>1);checks.append(dict(endpoint=str(a),accept=accept,mercator=[str(l-1),str(h-1)],base_two=[str(ll-1),str(hh-1)])) +b=Q(json.loads((p/'inputs/PR535-EXPECTED.json').read_text())['complex_lower']);eta=beta=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24);chain=[Q(384599,10**10)] +for _ in range(6):chain.append((1-s)*s+s*chain[-1]) +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=Outer.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta);assert len(assembly['strict_constraints'])==47 and all(a>0 for a in assembly['strict_constraints'].values()) +def dec(a): + with localcontext()as ctx:ctx.prec=60;return str(Decimal(a.numerator)/Decimal(a.denominator)) +oldk=Q(json.loads((p/'EXPECTED.json').read_text())['kappa']);out=dict(status='PASS_PROSPECTIVE_EXACT_PRICE_PHYSICAL_ADMISSION_PENDING',profile=dict(sorted(H.items())),local_chain_profile=new,bit_lower=str(c),bit_decimal=dec(c),complex_lower=str(b),kappa=str(k),kappa_decimal=dec(k),relative_gain_percent=dec(100*(k-oldk)/oldk),binding='bit'if c<(1-beta)*b else'complex',moment_checks=checks,outer={n:str(z)for n,z in assembly['strict_constraints'].items()},scope='Derived global histogram adds288 copies of exact local profile delta to pinned PR510 profile. Same480 width8 helpers and original owner schedule proposed. Physical template, chronological finite invoice and changed-frame geometric checks remain required; old outer finite constants used prospectively.') +(O/'RESULT.json').write_text(json.dumps(out,indent=2)+'\n');print({k:v for k,v in out.items()if k not in ['moment_checks','outer']},flush=True) diff --git a/research/r480-sliced-minimal-frames/scripts/slice.py b/research/r480-sliced-minimal-frames/scripts/slice.py new file mode 100644 index 0000000000..3f37f14516 --- /dev/null +++ b/research/r480-sliced-minimal-frames/scripts/slice.py @@ -0,0 +1,107 @@ +"""Exact F2 suffix-response retarget screen on the R480 bit circuit. +Same-frame whole-gate retargeting and zero-response deletions; discovery only. +Prepared for rohanarun with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from collections import Counter,defaultdict +from fractions import Fraction as Q +import gzip,json,math,time,copy,hashlib +import sympy as S +R=Path(__file__).resolve().parent;O=R/'bit510-observable-slice';O.mkdir(exist_ok=False);t=time.monotonic();p=R/'bit510-review/research/e8-r480-dead-totals/data/bitE8mut-r480.json.gz';w=json.load(gzip.open(p));v=w['v'];n=2*v+w['R'];Zregs=list(range(v))+list(range(2*v,n));mask=[sum(1< Date: Sun, 11 Oct 2026 23:12:17 -0400 Subject: [PATCH 2/3] Compose PR541 trace refinement with frozen sliced R480 frame reductions --- .../r480-sliced-minimal-frames/EXPECTED.json | 116 +++++++++--------- .../r480-sliced-minimal-frames/MANIFEST.json | 28 ++++- research/r480-sliced-minimal-frames/NOTICE.md | 2 + research/r480-sliced-minimal-frames/README.md | 32 +++-- .../r480-sliced-minimal-frames/SOURCES.json | 8 +- .../evidence/BASE-BIT-INVOICE.json | 49 ++++++++ .../evidence/BASE-PACKAGED314.json | 10 ++ .../evidence/BASE-PHYSICAL-ADMISSION.json | 32 +++++ .../evidence/COMBINED-PROFILE.json | 11 ++ .../evidence/COMBINED-SCALAR311.log | 7 ++ .../evidence/FRAME-TRANSFER.json | 26 ++++ .../inputs/BASE-CANDIDATE.json.gz | Bin 0 -> 48223 bytes .../inputs/BASE-EXPECTED.json | 102 +++++++++++++++ .../inputs/CANDIDATE.json.gz | Bin 48223 -> 48424 bytes .../inputs/PR541-ACQUISITION.json | 66 ++++++++++ .../inputs/PR541-TRACE-PROOF.md | 92 ++++++++++++++ .../inputs/PR541-WORD.json.gz | Bin 0 -> 49627 bytes .../scripts/preload60.py | 48 ++++++++ .../scripts/profile.py | 19 +++ .../scripts/trace_price.py | 36 ++++++ .../scripts/trace_slice.py | 107 ++++++++++++++++ .../scripts/transfer.py | 24 ++++ research/r480-sliced-minimal-frames/verify.py | 14 ++- 23 files changed, 746 insertions(+), 83 deletions(-) create mode 100644 research/r480-sliced-minimal-frames/evidence/BASE-BIT-INVOICE.json create mode 100644 research/r480-sliced-minimal-frames/evidence/BASE-PACKAGED314.json create mode 100644 research/r480-sliced-minimal-frames/evidence/BASE-PHYSICAL-ADMISSION.json create mode 100644 research/r480-sliced-minimal-frames/evidence/COMBINED-PROFILE.json create mode 100644 research/r480-sliced-minimal-frames/evidence/COMBINED-SCALAR311.log create mode 100644 research/r480-sliced-minimal-frames/evidence/FRAME-TRANSFER.json create mode 100644 research/r480-sliced-minimal-frames/inputs/BASE-CANDIDATE.json.gz create mode 100644 research/r480-sliced-minimal-frames/inputs/BASE-EXPECTED.json create mode 100644 research/r480-sliced-minimal-frames/inputs/PR541-ACQUISITION.json create mode 100644 research/r480-sliced-minimal-frames/inputs/PR541-TRACE-PROOF.md create mode 100644 research/r480-sliced-minimal-frames/inputs/PR541-WORD.json.gz create mode 100644 research/r480-sliced-minimal-frames/scripts/preload60.py create mode 100644 research/r480-sliced-minimal-frames/scripts/profile.py create mode 100644 research/r480-sliced-minimal-frames/scripts/trace_price.py create mode 100644 research/r480-sliced-minimal-frames/scripts/trace_slice.py create mode 100644 research/r480-sliced-minimal-frames/scripts/transfer.py diff --git a/research/r480-sliced-minimal-frames/EXPECTED.json b/research/r480-sliced-minimal-frames/EXPECTED.json index 8b13335416..23a6a911d4 100644 --- a/research/r480-sliced-minimal-frames/EXPECTED.json +++ b/research/r480-sliced-minimal-frames/EXPECTED.json @@ -1,8 +1,9 @@ { "status": "PASS_PROSPECTIVE_EXACT_PRICE_PHYSICAL_ADMISSION_PENDING", "profile": { - "1": 350496, - "2": 424608, + "1": 370368, + "2": 395232, + "3": 12960, "4": 64032, "5": 288, "6": 52800, @@ -10,93 +11,94 @@ "8": 2592 }, "local_chain_profile": { - "1": 1217, - "2": 1421, - "6": 130, + "1": 1286, + "2": 1319, "4": 169, + "3": 45, + "6": 130, "5": 1 }, - "bit_lower": "1589503043149746028939/1000000000000000000000000", - "bit_decimal": "0.001589503043149746028939", + "bit_lower": "1590005077309865651707/1000000000000000000000000", + "bit_decimal": "0.001590005077309865651707", 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Same480 width8 helpers and original owner schedule proposed. Physical template, chronological finite invoice and changed-frame geometric checks remain required; old outer finite constants used prospectively." } diff --git a/research/r480-sliced-minimal-frames/MANIFEST.json b/research/r480-sliced-minimal-frames/MANIFEST.json index 077d8eb44a..861e20adb3 100644 --- a/research/r480-sliced-minimal-frames/MANIFEST.json +++ b/research/r480-sliced-minimal-frames/MANIFEST.json @@ -1,24 +1,40 @@ { - "EXPECTED.json": "ca226880c79eddffd43556aadd01c7534b6ec8c09f897ed2eff7d73a81a1569e", + "EXPECTED.json": "29e445acd36fd8bbe899e556e1ba9dfcb4d78ebbd65ee6c48611685196e5cac1", "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", - "NOTICE.md": "a16b8c2b6beea58c25a3cdda5f0345c6b7a1facdcf0272a23a7b4a3fb801b0db", - "README.md": "cab060bc25f40b5dd564e4be6232b0655b2c5696c04a78aba939c7c2d805e034", - "SOURCES.json": "61daf6ab993fc4df725352d96b48c534c3229f1e751b9d4f979248d8d0ca96ef", + "NOTICE.md": "c073cd776c23e35407efa41f97a5b95e88a242efdddad2b8376a397682de6def", + "README.md": "e0cc67c02a16a7f39bca8304aecbcbad6b80c438f892ecaafec89f7ea709ff48", + "SOURCES.json": "ff07b94d6d4d416571dd3f886e499e9e165f7bd11715cca42fb4418880b98475", "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098", "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482", "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "evidence/BASE-BIT-INVOICE.json": "1da82f7aa0d7f3602c76de1d43aa84a450337c23519069cbe36dd1340e376630", + "evidence/BASE-PACKAGED314.json": "99ad3fb030ba73ef54ef070ef2ea3bca16901420c96ab6a32412791ea531fbbe", + "evidence/BASE-PHYSICAL-ADMISSION.json": "f49bb90ed00ca0aad67ac754707de033b3840add6b0b40be1b77d9625d3083ae", + "evidence/COMBINED-PROFILE.json": "6ad46b246e5a555986f0566a2c8c2538eecebf7638eac8a765a1a5c44033cbb3", + "evidence/COMBINED-SCALAR311.log": "d7cf7cd67214a12e972c039dd7d765fa0802de576e61677e306be177ff68bc7e", + "evidence/FRAME-TRANSFER.json": "678c21b1526d6a4908bea24c3dcff61eec636498c90f71d259b223acb872607f", "evidence/INDEPENDENT-SCALAR311.log": "42e960865be835a7b3e2598615c6077e9b6077bfc5801a5d67eca0e6c5a28854", "evidence/INTERFACE311.json": "5c48a51887b1420083015eef35da59c371b9911bfcbc5032a1dbf0993f8fe886", "evidence/MINIMUM-FRAMES.json": "c60b94107d56249887ed1d3adefb65745373f57791a0fb3c9e96e4625274de68", "evidence/SLICE.json": "de878adca9979b59a707867425b9c1450250f3a54bffa57ccde355e109a8c517", - "inputs/CANDIDATE.json.gz": "37e84d9ace34138fc0a942d7cac37c46513a952b4d8ca5384545f830cc0948c9", + "inputs/BASE-CANDIDATE.json.gz": "37e84d9ace34138fc0a942d7cac37c46513a952b4d8ca5384545f830cc0948c9", + "inputs/BASE-EXPECTED.json": "ca226880c79eddffd43556aadd01c7534b6ec8c09f897ed2eff7d73a81a1569e", + "inputs/CANDIDATE.json.gz": "3dddba9a13c96d54fa6aa3ff238711808662401a6fec7960ac34c4f885bfbf71", "inputs/ORIGINAL.json.gz": "92e399e9a486b55229b5624632ac54f800dd9e022f2aee97f1e5f264bbc0ef5c", "inputs/PR510-EXPECTED.json": "883f7a1a84f31d9e4430e348bc8d9c1ec10210b206ff602dbe126349056af13d", "inputs/PR535-EXPECTED.json": "cb734055c36681d38cf431a6926b7713351a94073cfba37d70a5384a9ef0d178", "inputs/PR539-EXPECTED.json": "e2a71c1d49c68c35fb5c4f20f10377d708f55c3d25146fa811a99c7230d6ff0c", + "inputs/PR541-ACQUISITION.json": "8520387f82956bd3ab62feeeb3f9080afee16d4ece86ef147dfc8fed64132540", + "inputs/PR541-TRACE-PROOF.md": "e24cd091820f33795aa06f3cc318d61aed6dd17dfc55b0d24d2c3285a1a8ca6a", + "inputs/PR541-WORD.json.gz": "db5cd7ab49e2e58a2924a2a9e68ee69d8165b4d5c008b6f546577f4791019dca", "inputs/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511", "scripts/minimum.py": "418f3143793ec981dbca953215f01a954c94e3097b8bc8a3833d5f726d9f5177", + "scripts/preload60.py": "105641136b565003118f362bb67086e1eeb4910aed6af593a011f60c2b2962b6", "scripts/price.py": "f00306ed546f7d515763f3e9a192d3532759cb9d78863ee8a78036757209cfad", + "scripts/profile.py": "f9d9a9e4f3dd75acaafef61d8005df6a829a7c10ebabd4006ab9698e4a03bfe5", "scripts/slice.py": "d72a4dadfc954aa51eb5b5976bbdeb661bb023201e7832fc9fe0340ef2845279", - "verify.py": "5e7e7780879e07393d86fa8f036bd9646ef0a2b98ea32e9a4c559d1e2f3ace80" + "scripts/trace_price.py": "40d8a263adf1fafd7830ae619f46422e56546bb9799775657e1106273bb6cbf7", + "scripts/trace_slice.py": "19658b829a60f827ed7488a1e6d7c18bec45aaad843e80f9d366be80f6cb8714", + "scripts/transfer.py": "1b8de34f72f6c841764b588739e522b62bd483cc5023ddfb353524601d189051", + "verify.py": "036ef52c45aa7a5c4696d9bc0415455e31548e6f82d3ed2b14b246b00870e06a" } diff --git a/research/r480-sliced-minimal-frames/NOTICE.md b/research/r480-sliced-minimal-frames/NOTICE.md index dfe09782a1..3f0b5afcd3 100644 --- a/research/r480-sliced-minimal-frames/NOTICE.md +++ b/research/r480-sliced-minimal-frames/NOTICE.md @@ -106,3 +106,5 @@ PR #442 (DaysSky): idle-axis hosting of whole residuals. Jacob Sussman introduce Complex535 is cited at25f9b7c2310d40c9efdfbe368a40ba6e74d3b0a2: icekylinx with disclosed OpenAI assistance. Literal bad-class charge follows Srikrishnabalaji461 and464/465/539. The input source note and moment/outer engines retain predecessor attribution. + +The additional60-preload trace refinement, unmodified scripts/preload60.py, pinned source word and proof are from Dugongue PR541 at6fd04b2e266b7915b69f96f27758cfce520aa40a, with disclosed OpenAI assistance. The new integration retains that event/frame schedule, then applies our observable slice and19 frozen frame reductions. Individual histogram gains are not added; the complete combined word is recounted. diff --git a/research/r480-sliced-minimal-frames/README.md b/research/r480-sliced-minimal-frames/README.md index 833ea3b11c..4c4b1793d0 100644 --- a/research/r480-sliced-minimal-frames/README.md +++ b/research/r480-sliced-minimal-frames/README.md @@ -1,29 +1,27 @@ -# Sliced R480 with causal minimum frames +# PR541 trace refinement with sliced R480 frame reductions -**Draft candidate conditional kappa = 0.001586980532763499**, about **0.1293065%** above PR539. The scalar word, frame nesting and both exact moment engines pass; the new physical template and finite invoice remain pending. This is not yet a fully admitted supplier. +**Draft combined conditional kappa = 0.001587467473762886**, above PR541's0.001587212454640692. The complex supplier now binds. The original standalone sliced-frame candidate0.001586980532763499 passed fresh physical admission; that receipt is retained as baseline evidence and does not certify this combined word. Full physical replay of the combined word is pending after this draft update. -## Change +## Complete construction -Starting from PR510's R480 word, an exact backward F2 target-response calculation identifies227 A gates with zero target response. Removing them and their227 inverse cleanup gates preserves the full scalar endpoint. This alone leaves the recursive histogram unchanged. +1. Rebuild Dugongue PR541's60-preload trace refinement on PR510's R480 word exactly, using the unmodified pinned constructor. Compare against its published word. +2. Apply our backward F2 target-response slice, removing227 A gates and their227 inverse cleanup gates. This preserves arbitrary scalar inputs and literal restoration. +3. Transfer the19 lower frames found by our causal minimum-frame construction on the original sliced R480 word. Each transfer is matched to its actual gate and independently checked for frame containment. Preserve every other PR541 frame choice. -Next process all remaining operations chronologically. At each A/B gate, replace its constructor frame by the exact rational span of the preceding operand frames. This produces the least feasible frame assignment in subspace inclusion for that fixed chronological word, with initial, center and final frames fixed. It is not a claim of global moment optimality.19 A-operation frames shrink, including three new rank-three root-closed frames. All frames remain nested, and phase B is unchanged. Source/helper inverse cleanup is literal at the full frame. +The distinction in step3 matters: recalculating the unrestricted causal minimum for the entire combined word was a losing experiment. Likewise the two separate histogram deltas do not simply add. This submission recounts the actual final word. -The paid local histogram, including nine center copies, becomes +The local paid profile, including9 center copies, is `{1:1286,2:1319,3:45,4:169,5:1,6:130,8:9}`. The complete prospective nine-stage profile is `{1:370368,2:395232,3:12960,4:64032,5:288,6:52800,7:23040,8:2592}`.480 helper residuals of width8,30720 live rows,30729 physical rows and rank deficit9984 remain. Proposed hosting uses the unchanged exact PR510 selection. -`{1:1217,2:1421,4:169,5:1,6:130,8:9}` +Two rational engines give bit c = **0.001590005077309865651707**. Cited PR535 complex b = **0.001589991533606044174031** is smaller, so six bootstrap levels and47 outer inequalities give the displayed complex-bound kappa. Literal fallback charging follows PR539 and its461/464/465 ancestry. Finite allowances are still provisional until the combined physical invoice passes. -versus `{1:1200,2:1440,4:180,6:120,8:9}`. Rank mass,480 helpers and width-eight helper intervals remain unchanged. The prospective nine-stage profile reuses PR510's whole-owner selection and adds288 copies of the local histogram difference: +## Verification -`{1:350496,2:424608,4:64032,5:288,6:52800,7:23040,8:2592}`. +`python -B verify.py /absolute/new/output` reconstructs both the original sliced-frame baseline and the full composition (Python3.11+, SymPy, no optimizer/network), checks the final candidate against pinned bytes by mathematical JSON content, and reproduces both-engine exact pricing. Output must be new and outside this package. -Its bit endpoint is **0.001589503043149746028939**. PR535's unchanged cited complex endpoint is0.001589991533606044174031, so the bit side still binds. Literal bad-class charging follows PR539 and its461/464/465 ancestry. +Completed for the combined word: independent Python3.11 scalar/frame checker,720 columns, all120 source restorations,674 nondegenerate used frames with only prime2 in determinants, and changed five-stage price. Exact global-profile arithmetic and47 outer inequalities pass under the inherited finite allowances. -## Checks and pending work +Completed for the original standalone baseline only: fresh C++ record/formal-column and mutation checks, all675 frame Grams, both local orientations, explicit138240-owner hosting, parent/hosting mutations and fresh finite invoice. The baseline prefix is191 bits charged192; two-level coefficient421 charged512; row coefficient18355. These receipts are explicitly labeled BASE and are not passed off as combined-word verification. -The inherited mutable-source independent checker passes all720 F2 columns, all120 source restorations,674 nondegenerate used frames with only prime2 in their Gram determinants, and the changed five-stage price on Python3.11.15. The PR425 interface-hypothesis audit passes. The prospective nine-stage profile passes both exact moment engines and47 strict outer inequalities; this currently assumes the preceding finite allowances remain valid. +Pending: combined physical emission, chronological prefix/finite invoice, global mutations and complete packaged admission. All inherited all-size compiler, common-label/mutable-source realization, compressed geometry, whole-call hosting, restored work, precision/tape and analytic-transfer assumptions remain conditional. No unconditional theorem, full Lean proof or measured runtime gain is claimed. -`python -B verify.py /absolute/new/output` reproduces the frozen input-to-candidate transformation and exact prospective price (Python3.11+, SymPy). Decimal arithmetic proposes an endpoint; rational intervals accept it and reject the next grid point. No optimizer or network is needed. Output must be outside this package. - -Full record-level geometry, chronological prefix bounds, explicit nine-stage whole-owner emission, mutation controls and finite invoice are being checked after draft submission. The old finite constants are not a substitute for that verification. No completed CI pass, full physical admission, all-size theorem, Lean completion or measured runtime gain is claimed. - -All inherited all-size bit/compiler, mutable-source/common-label realization, compressed geometry, whole-call hosting, restored-work, precision/tape and analytic-transfer assumptions remain conditional. See NOTICE.md for original attribution and SOURCES.json for pins. This is a new scalar/frame rewrite of the existing supplier; the complex supplier is cited rather than rebuilt. +See NOTICE.md and SOURCES.json. Dugongue541 supplies the preload transformation; our new work supplies slicing, lower frames and this compatibility-checked composition. PR535's complex operator is cited rather than rebuilt. diff --git a/research/r480-sliced-minimal-frames/SOURCES.json b/research/r480-sliced-minimal-frames/SOURCES.json index bdb539de8c..36a7d60da2 100644 --- a/research/r480-sliced-minimal-frames/SOURCES.json +++ b/research/r480-sliced-minimal-frames/SOURCES.json @@ -13,5 +13,11 @@ "pr": 539, "head": "915ca69db7f98c70b97ce96e1fcc96818517584c" }, - "scope": "Draft finite candidate. Physical emission and finite invoice pending." + "scope": "Original baseline physically admitted; combined trace/frame word pending fresh physical replay.", + "trace541": { + "pr": 541, + "head": "6fd04b2e266b7915b69f96f27758cfce520aa40a", + "author": "Dugongue", + "role": "Unmodified 60-preload constructor and source proof; exact output reconstructed against published word" + } } diff --git a/research/r480-sliced-minimal-frames/evidence/BASE-BIT-INVOICE.json b/research/r480-sliced-minimal-frames/evidence/BASE-BIT-INVOICE.json new file mode 100644 index 0000000000..cec8d4f47f --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/BASE-BIT-INVOICE.json @@ -0,0 +1,49 @@ +{ + "status": "PASS_NINE_STAGE_WHOLE_HOSTED_BIT_PRICE_AND_CITED_ASSEMBLY", + "R": 480, + "stages": 9, + "replicas": 32, + "bit_lower": "397375760308276055691/250000000000000000000000", + "bit_lower_decimal": "0.001589503041233104222764", + "next_grid_point_rejected": "317900608246620844553/200000000000000000000000", + "bit": { + "live": 30720, + "physical": 30729, + "maxchild": 8, + "rank_mass": 1956096, + "hosted_residuals": 138240, + "bank_assignments": 0, + "prefix_bits": 191, + "charged_prefix_bits": 192, + "coefficient_bits": 191, + "two_level_coefficient_bits": 421, + "charged_two_level_coefficient_bits": 512, + "row_coefficient": 18355, + "halving_depth": 2 + }, + "bit_profile": { + "1": 350496, + "2": 424608, + "4": 64032, + "5": 288, + "6": 52800, + "7": 23040, + "8": 2592 + }, + "emitted_program_sha256": "c1dcd51a6428e62d6aff160b8a4ba4ba90a5bd92289c73f3fc289465abd28ca5", + "kappa": { + "pr484": { + "complex_lower": "663394767670133/500000000000000000", + "kappa": "662515748707749/500000000000000000", + "kappa_decimal": "0.001325031497415498", + "binding_component": "complex", + "strict_outer_constraints": 47, + "outer_controls": [ + "next_grid", + "zero_eta", + "zero_beta", + "unit_beta" + ] + } + } +} diff --git a/research/r480-sliced-minimal-frames/evidence/BASE-PACKAGED314.json b/research/r480-sliced-minimal-frames/evidence/BASE-PACKAGED314.json new file mode 100644 index 0000000000..151c78aaa4 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/BASE-PACKAGED314.json @@ -0,0 +1,10 @@ +{ + "status": "PASS_PACKAGED_RECONSTRUCTION_AND_PROSPECTIVE_PRICE", + "kappa": "0.001586980532763499", + "bit": "0.001589503043149746028939", + "word_sha256": "37e84d9ace34138fc0a942d7cac37c46513a952b4d8ca5384545f830cc0948c9", + "manifest_sha256": "453ecd91c4c516880a678e2962abe0e0421d3a3c465a09cea887058eee9cf3c5", + "python": "3.14.8 (main, Sep 30 2026, 17:55:09) [Clang 21.0.0 (clang-2100.3.34.2)]", + "seconds": 4.126170333009213, + "scope": "Exact reconstruction of source slice and least frames,720 scalar columns, nesting and two rational moment engines with47 outer constraints. Prospective unchanged owner schedule and prior finite allowances; physical template and finite invoice remain pending. No completed supplier admission." +} diff --git a/research/r480-sliced-minimal-frames/evidence/BASE-PHYSICAL-ADMISSION.json b/research/r480-sliced-minimal-frames/evidence/BASE-PHYSICAL-ADMISSION.json new file mode 100644 index 0000000000..c1b013648b --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/BASE-PHYSICAL-ADMISSION.json @@ -0,0 +1,32 @@ +{ + "status": "PASS_FRESH_SLICED_MINIMUM_FRAME_RECORDS_HOSTING_AND_INVOICE", + "seconds": 79.25043887505308, + "word_sha256": "37e84d9ace34138fc0a942d7cac37c46513a952b4d8ca5384545f830cc0948c9", + "profile": { + "1": 350496, + "2": 424608, + "4": 64032, + "5": 288, + "6": 52800, + "7": 23040, + "8": 2592 + }, + "kappa": "0.001586980532763499", + "bit_invoice": { + "live": 30720, + "physical": 30729, + "maxchild": 8, + "rank_mass": 1956096, + "hosted_residuals": 138240, + "bank_assignments": 0, + "prefix_bits": 191, + "charged_prefix_bits": 192, + "coefficient_bits": 191, + "two_level_coefficient_bits": 421, + "charged_two_level_coefficient_bits": 512, + "row_coefficient": 18355, + "halving_depth": 2 + }, + "steps": 19, + "scope": "Fresh finite record/formal-column/geometry/template/whole-owner/invoice replay, with inherited mutation controls. Cited complex535 operator unchanged. Exact sharp-charge prospective profile now matches physically emitted audited profile and retained finite allowances. All-size supplier/compiler/realization/hosting/analytic assumptions remain conditional." +} diff --git a/research/r480-sliced-minimal-frames/evidence/COMBINED-PROFILE.json b/research/r480-sliced-minimal-frames/evidence/COMBINED-PROFILE.json new file mode 100644 index 0000000000..d740008344 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/COMBINED-PROFILE.json @@ -0,0 +1,11 @@ +{ + "new_chain_profile": { + "1": 1286, + "2": 1319, + "4": 169, + "3": 45, + "6": 130, + "5": 1 + }, + "scope": "Exact rank profile from every final combined-word frame transition; center copies separate and unchanged9x8. Do not add standalone histogram deltas: the frame changes interact." +} diff --git a/research/r480-sliced-minimal-frames/evidence/COMBINED-SCALAR311.log b/research/r480-sliced-minimal-frames/evidence/COMBINED-SCALAR311.log new file mode 100644 index 0000000000..b42d23cf03 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/COMBINED-SCALAR311.log @@ -0,0 +1,7 @@ +labels: 120 distinct lines of norm 2 (pairwise |ip| <= 1), spanning rank 8 +legality + exact F2 on all 720 columns: PASS (gates D/A/B/C = 120/2541/240/2541) +relaxed check: 712 gates have a source register as destination; all 120 sources restored exactly +nondegeneracy: 674 used frames, all Gram dets > 0 (positive-definite form); primes in dets: [2] +histogram {1: 6430, 2: 6595, 3: 225, 4: 1085, 5: 5, 6: 650, 7: 240, 8: 45, 14: 240, 18: 240} m 40 W 960 mass 38280 deficit 120 (4v-5L = 120 ) maxchild 18 +no envelope saving in [0.00128924129269366504, 0.00128924129269366504] +bad envelope saving in [0.00128924129182445790, 0.00128924129182445790] diff --git a/research/r480-sliced-minimal-frames/evidence/FRAME-TRANSFER.json b/research/r480-sliced-minimal-frames/evidence/FRAME-TRANSFER.json new file mode 100644 index 0000000000..3293cb957f --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/FRAME-TRANSFER.json @@ -0,0 +1,26 @@ +{ + "status": "PASS_FROZEN_FRAME_TRANSFER_CONTAINMENTS", + "accepted_indices": [ + 2176, + 2270, + 2296, + 2331, + 2360, + 2390, + 2418, + 2419, + 2420, + 2427, + 2430, + 2455, + 2456, + 2457, + 2464, + 2494, + 2495, + 2496, + 2503 + ], + "rejected_indices": [], + "scope": "Only previously beneficial19 operation-frame changes transferred to sliced PR541 by exact gate identity; full scalar/geometry/profile/physical checks follow." +} diff --git a/research/r480-sliced-minimal-frames/inputs/BASE-CANDIDATE.json.gz b/research/r480-sliced-minimal-frames/inputs/BASE-CANDIDATE.json.gz new file mode 100644 index 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Same480 width8 helpers and original owner schedule proposed. Physical template, chronological finite invoice and changed-frame geometric checks remain required; old outer finite constants used prospectively." +} diff --git a/research/r480-sliced-minimal-frames/inputs/CANDIDATE.json.gz b/research/r480-sliced-minimal-frames/inputs/CANDIDATE.json.gz index fcdfbb303931d7a872a80df86a76c4665712cc4c..268fbbd46bf9dea1cc210d74fe4b1cff5ac52cc6 100644 GIT binary patch literal 48424 zcmZ6y2T)V(^9HIQ(nW;;3Ir99-UJ1tDM||^5PB~nRX}MsC8@rg+cjk@^1Z=C zEJV9-y^f)4MwtXJC@z>>r6jNVvWqQ}8`5L0UJljf>&}WR`S2eu{oBicH%l^j*LWme z885#&85%pyqin9CXqF-NwtD0^tZ_JXz_Zfa{*AjyDDoWrDR@C|-6v?)8&Ne-yJ7w2 zfM?Pth}`~Qcg5Q$)7r<18B@qlp2U10>@i7B*gP(Az~*51uldCDgz_Ks(AZnz!u*hI zJBiO zR^v(}4wv5fUM8#9i^CXbzRiX0$f;lUIidvG0P{#KE5Ez4KxO5Q6S>_KM`3uI&Ns{L zp5MzetCr!{?8cP9Yh1-T*7Q0(c)^CRIj!RYL2Yyq^NZ>rV`I$jjPBImLqpm){>e%HozLb!Lo2UZQrpgV#`w?C3m9@RPE(m6 znr`9Z*J04rYwSY~oWbP*`l|H$>!}B-1&j6YfQ`3=TuUyr9JLrP>6;>+yw_-}YCYXS z#`yLS{A$I0by2MNTGNX9in-9Br6+F!`$p5a%IZAv`T=Txut|C%RRj9YPa4iTg5A6r 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100644 index 0000000000..62096bee18 --- /dev/null +++ b/research/r480-sliced-minimal-frames/inputs/PR541-TRACE-PROOF.md @@ -0,0 +1,92 @@ +# Frame-sensitive trace refinement and the preload60 construction + +## Sufficient meta-theorem + +Let a finite reversible scalar program act on registers indexed by I over a field K. A scalar addition is T(t,s,q)=I+q e_t e_s^T, with t != s. Each register has an explicit initial frame, an explicit terminal frame, and a monotone chain of finite subspaces at its actual uses. Certain observation checkpoints (for example retained totals at a scatter) are fixed. + +Construct another program by the following certified operations: + +1. Factor a multi-source addition into elementary additions with the same destination and unchanged coefficients. +2. Permute elementary additions only through explicitly checked commuting gates, without crossing protected observation checkpoints. +3. Assign a new common frame to each relocated addition. Require that every touched register's predecessor frame is contained in it and that it is contained in that register's successor frame, including fixed initial, terminal and observation frames. +4. Rebuild the inverse background cleanup literally. Recompute every actual frame transition, retained-copy rank, scalar prefix bound and finite realization invoice. + +Then the new scalar program has exactly the same complete arbitrary-input endpoint. Its framed program satisfies the retained native frame-realization interface, and its exact recursive profile is the profile recomputed from those new chains, together with all retained-copy children. If the entrance and terminal signatures stay fixed, every old whole-owner allocation remains usable with unchanged residual-width and idle-remainder accounting. The changed physical finite realization still requires its actual phase/compiler and prefix checks; the theorem does not make those checks or inherited all-size hypotheses disappear. + +This is a calculus of representations of the SAME scalar word: it searches the trace-equivalence class and then selects a different legal frame labeling. A fixed event-order frame optimizer cannot expose every member of that class. A scalar-only optimizer cannot see the cost of its frame chains. Their joint finite certificate is the sufficient object. + +## Algebraic proof + +For t distinct from all s_i, the elementary additions to destination t commute, since e_(s_i)^T e_t=0. Hence + + I + sum_i q_i e_t e_(s_i)^T = product_i T(t,s_i,q_i). + +For distinct-source/destination elementary additions T(t,s,q) and T(u,v,r), the sufficient commuting condition is t != v and u != s. Expanding both products gives the same identity, two linear terms and zero cross terms. (There are further special commuting cases; they are not needed.) A scale on register u commutes with T(t,s,q) when u is neither t nor s. + +Every allowed adjacent exchange therefore preserves the entire linear operator. Induction on the explicit exchange list proves equality of the reordered body. It holds on arbitrary source, target and dirty-helper columns, not merely clean inputs. A word can be moved through a whole interval if it commutes with every gate crossed. Protected checkpoints are preserved because no move crosses them. + +If background updates do not read target registers, the background transformation is independent of targets. Reversing the order and inverting each actual new background gate gives its exact inverse, restoring all source/helper inputs. For an addition this negates its coefficient; over F2 the coefficient is unchanged. The body's target output is unchanged by the trace identity. Thus the full dirty-register endpoint is unchanged. Existing compensation can be retained because the body map itself, on every column, is unchanged. + +At a relocated instruction, the explicit predecessor/common/successor inclusions establish native frame legality. All other chains retain their previous inclusions. Applying the existing compiler interface to the actual changed word gives the same final labeled endpoint, with exactly the newly listed transition ranks. This last statement is conditional on that pre-existing all-size compiler interface; finite column replay is not an independent proof of the all-size interface. + +## Critical pair: splitting plus scheduling plus reframing + +Consider a two-source cell h += x+y first formed at a rank2 frame containing the rank1 source frames. Suppose its x addition commutes through the entire prefix, h initially has frame0, and the prefix does not observe h. Factor the gate into h += x followed by h += y. Move h += x to the beginning and perform it at x's rank1 frame. The later h += y remains at the original rank2 frame. + +The scalar map is identical. In the actual selected instance, the helper's former rank2 climb splits into two rank1 climbs. Meanwhile x no longer needs a formerly unique intermediate rank2 use between rank1 and rank4: its two climbs of ranks1 and2 coalesce into a rank3 climb. Therefore the net child-profile change is + + +delta1 - 2 delta2 + delta3. + +This is why neither a fixed-position scalar rewrite nor a fixed-order frame-coalescing pass alone finds the gain. The seam is moved before the frame assignment is simplified. 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Fresh physical invoice separately establishes charged two-level coefficient<=512 and row bound18355; complex535 operator cited. All-size contracts remain conditional." +} diff --git a/research/r480-sliced-minimal-frames/evidence/FULL311-TESTED-MANIFEST.json b/research/r480-sliced-minimal-frames/evidence/FULL311-TESTED-MANIFEST.json new file mode 100644 index 0000000000..47f5de33fb --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/FULL311-TESTED-MANIFEST.json @@ -0,0 +1,45 @@ +{ + "EXPECTED.json": "29e445acd36fd8bbe899e556e1ba9dfcb4d78ebbd65ee6c48611685196e5cac1", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE.md": "c073cd776c23e35407efa41f97a5b95e88a242efdddad2b8376a397682de6def", + "README.md": "e0cc67c02a16a7f39bca8304aecbcbad6b80c438f892ecaafec89f7ea709ff48", + "SOURCES.json": "ff07b94d6d4d416571dd3f886e499e9e165f7bd11715cca42fb4418880b98475", + "dependencies/source493.tar.gz": "194addabc3054ab2ea0f98e92f2343d032f6e7f8bcdc68013857fabeef68f446", + "dependencies/source510.tar.gz": "ae1f71ba91a57f4fa4dee2a7ca4e113086ee2a6a55b6631fa16ab112b271ded3", + 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"inputs/PR510-EXPECTED.json": "883f7a1a84f31d9e4430e348bc8d9c1ec10210b206ff602dbe126349056af13d", + "inputs/PR535-EXPECTED.json": "cb734055c36681d38cf431a6926b7713351a94073cfba37d70a5384a9ef0d178", + "inputs/PR539-EXPECTED.json": "e2a71c1d49c68c35fb5c4f20f10377d708f55c3d25146fa811a99c7230d6ff0c", + "inputs/PR541-ACQUISITION.json": "8520387f82956bd3ab62feeeb3f9080afee16d4ece86ef147dfc8fed64132540", + "inputs/PR541-TRACE-PROOF.md": "e24cd091820f33795aa06f3cc318d61aed6dd17dfc55b0d24d2c3285a1a8ca6a", + "inputs/PR541-WORD.json.gz": "db5cd7ab49e2e58a2924a2a9e68ee69d8165b4d5c008b6f546577f4791019dca", + "inputs/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511", + "scripts/minimum.py": "418f3143793ec981dbca953215f01a954c94e3097b8bc8a3833d5f726d9f5177", + "scripts/physical.py": "a7588a357d9bbabc69f8375fbfc129bde894165c2e95087222c3b1c82f2b9c59", + "scripts/preload60.py": "105641136b565003118f362bb67086e1eeb4910aed6af593a011f60c2b2962b6", + "scripts/price.py": "f00306ed546f7d515763f3e9a192d3532759cb9d78863ee8a78036757209cfad", + "scripts/profile.py": "f9d9a9e4f3dd75acaafef61d8005df6a829a7c10ebabd4006ab9698e4a03bfe5", + "scripts/slice.py": "d72a4dadfc954aa51eb5b5976bbdeb661bb023201e7832fc9fe0340ef2845279", + "scripts/trace_price.py": "40d8a263adf1fafd7830ae619f46422e56546bb9799775657e1106273bb6cbf7", + "scripts/trace_slice.py": "19658b829a60f827ed7488a1e6d7c18bec45aaad843e80f9d366be80f6cb8714", + "scripts/transfer.py": "1b8de34f72f6c841764b588739e522b62bd483cc5023ddfb353524601d189051", + "verify.py": "e9a1dea264ee2e781000d4a23b89dfcca15cd606e11814215ac9656723c82450" +} diff --git a/research/r480-sliced-minimal-frames/evidence/HOSTED-AUDIT314.json b/research/r480-sliced-minimal-frames/evidence/HOSTED-AUDIT314.json new file mode 100644 index 0000000000..0a04cbde0d --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/HOSTED-AUDIT314.json @@ -0,0 +1,41 @@ +{ + "status": "PASS_INDEPENDENT_REPLICATED_HOSTING_AUDIT", + "template_sha256": "aa07bfa63393dba62a03bc98f2c82d2fbe2dc9cc24a59c92d977681631d34a15", + "emitted_program_sha256": "e4e1a89c55925d0421c882df31426fe939ab5fa98e9828155e711aea0b6532c8", + "emitted_events": 10500480, + "profile": { + "1": 370368, + "2": 395232, + "3": 12960, + "4": 64032, + "5": 288, + "6": 52800, + "7": 23040, + "8": 2592 + }, + "live": 30720, + "physical": 30729, + "hosted_residuals": 138240, + "bank_assignments": 0, + "rank_mass": 1956096, + "deficit": 9984, + "maxchild": 8, + "mutations_rejected": [ + "slot outside window", + "copy index outside family", + "negative slot offset", + "wrong residual width", + "duplicate helper", + "omitted helper", + "hosted owner in another replica or outside the data stock", + "hosted owner on a wrong data family", + "wrong call orientation", + "duplicate call", + "changed idle rank", + "understated live stock", + "missing remainder summary", + "stale stage count", + "hosted coordinate beyond the pending set", + "overlapping hosted coordinates" + ] +} diff --git a/research/r480-sliced-minimal-frames/evidence/INITIAL-311-DIAGNOSTIC-MISMATCH.json b/research/r480-sliced-minimal-frames/evidence/INITIAL-311-DIAGNOSTIC-MISMATCH.json new file mode 100644 index 0000000000..a092d03fc5 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/INITIAL-311-DIAGNOSTIC-MISMATCH.json @@ -0,0 +1,8 @@ +{ + "status": "PRESERVED_REPLAY_METADATA_FAILURE", + "field": "fee_delta", + "expected": -0.04495826477563014, + "actual": -0.044958264775633694, + "all_other_nontiming_fields_identical": true, + "repair": "Exclude only floating discovery fee diagnostic from frozen receipt equality; require all actual frames, exact profiles, candidate word and rational moments unchanged." +} diff --git a/research/r480-sliced-minimal-frames/evidence/INITIAL-311-DIAGNOSTIC-MISMATCH.log b/research/r480-sliced-minimal-frames/evidence/INITIAL-311-DIAGNOSTIC-MISMATCH.log new file mode 100644 index 0000000000..f6e9a07a4a --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/INITIAL-311-DIAGNOSTIC-MISMATCH.log @@ -0,0 +1,8 @@ +slice PASS +minimum PASS +price PASS +Traceback (most recent call last): + File "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/r480-minimal-publication/research/r480-sliced-minimal-frames/verify.py", line 20, in + m=json.loads((O/'bit510-sliced-minimal-frames/RESULT.json').read_text());e=json.loads((P/'evidence/MINIMUM-FRAMES.json').read_text());assert {k:v for k,v in m.items()if k!='seconds'}=={k:v for k,v in e.items()if k!='seconds'} + ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +AssertionError diff --git a/research/r480-sliced-minimal-frames/evidence/NATIVE-LEGALITY314.json b/research/r480-sliced-minimal-frames/evidence/NATIVE-LEGALITY314.json new file mode 100644 index 0000000000..2efae837e5 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/NATIVE-LEGALITY314.json @@ -0,0 +1,50 @@ +{ + "all_final_frames_pass": true, + "common_frame_ADDs": 33492, + "containment_pairs_checked": 2412, + "copies": 9, + "donor_intersections": 0, + "erasures": 9, + "max_inherited_integer_abs": 2, + "nested_MOVEs": 2950, + "new_frame_ids_collision": false, + "nondegeneracy_checked_by_separate_exact_bank_audit": true, + "old_max_frame_id": 674, + "paid_histogram": [ + [ + 1, + 1286 + ], + [ + 2, + 1319 + ], + [ + 3, + 45 + ], + [ + 4, + 169 + ], + [ + 5, + 1 + ], + [ + 6, + 130 + ], + [ + 8, + 9 + ] + ], + "rank_mass": 5592, + "records": 36460, + "scope": "Independent chronological geometry/copy/source-owner audit. F2 all-column replay is in the separately freshly compiled transform receipt; address transform theorem and bank completion remain separate.", + "selected_helpers": 0, + "selected_pairs": 0, + "source_owner_intersections": 0, + "status": "PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE" +} diff --git a/research/r480-sliced-minimal-frames/evidence/NINE-COLUMNS314.json b/research/r480-sliced-minimal-frames/evidence/NINE-COLUMNS314.json new file mode 100644 index 0000000000..cb973e9e83 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/NINE-COLUMNS314.json @@ -0,0 +1,196 @@ +{ + "bridge_additions": 2160, + "copied_center_original_source_immutable": true, + "formal_columns_checked": 1440, + "fresh_center_copies": 81, + "global_live_registers": 1440, + "independent_dirty_registers": 480, + "local_odd_scalar_additions": 33492, + "local_raw_H": [ + [ + 1, + 1286 + ], + [ + 2, + 1319 + ], + [ + 3, + 45 + ], + [ + 4, + 169 + ], + [ + 5, + 1 + ], + [ + 6, + 130 + ], + [ + 8, + 9 + ] + ], + "local_registers": 720, + "local_scalar_additions": 33492, + "local_scalar_stream": "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/trace541-frozen-admission/cout/COHORT249-RECORDS.bin", + "negative_controls": [ + { + "omit_bridge": 0, + "rejected": true + }, + { + "omit_bridge": 1, + "rejected": true + }, + { + "omit_bridge": 2, + "rejected": true + }, + { + "omit_bridge": 3, + "rejected": true + }, + { + "omit_bridge": 4, + "rejected": true + }, + { + "omit_bridge": 5, + "rejected": true + }, + { + "omit_bridge": 6, + "rejected": true + }, + { + "omit_bridge": 7, + "rejected": true + }, + { + "omit_bridge": 8, + "rejected": true + }, + { + "omit_bridge": 9, + "rejected": true + }, + { + "omit_bridge": 10, + "rejected": true + }, + { + "omit_bridge": 11, + "rejected": true + }, + { + "omit_bridge": 12, + "rejected": true + }, + { + "omit_bridge": 13, + "rejected": true + }, + { + "omit_bridge": 14, + "rejected": true + }, + { + "omit_bridge": 15, + "rejected": true + }, + { + "omit_bridge": 16, + "rejected": true + }, + { + "omit_bridge": 17, + "rejected": true + } + ], + "new_Q_categories": [ + 28, + 29 + ], + "payload_prefix_bits": 101, + "payload_prefix_upper": "2245964444139092419234253795328", + "reverse_fresh_center_copies": 36, + "scope": "All independent physical input columns over F2, including all arbitrary helper dirt, restored; external copied-center work closes to zero. New cohort scalar lift uses actual signed coefficients and computed cancellation-free bounds; unchanged source527 signed decoder remains separate defining evidence. Physical projector routing and paid rank/bank receipts are independently bound, not inferred from scalar check.", + "seconds": 0.005357833, + "signed_lift_prefix": [ + { + "bits": 18, + "cancellation_free_signed_row_l1_upper": "167007", + "reverse": false + }, + { + "bits": 22, + "cancellation_free_signed_row_l1_upper": "2744792", + "reverse": true + } + ], + "signed_reverse_semantics": "Reverse ADD coefficient negated; reverse DISCARD is fresh COPY from recorded unchanged original center; reverse COPY is DISCARD. Each such block is inverse over every commutative coefficient ring, by elementary-shear induction.", + "stage_additions": 301428, + "stages": [ + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": false, + "stage": 0 + }, + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": true, + "stage": 1 + }, + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": false, + "stage": 2 + }, + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": true, + "stage": 3 + }, + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": false, + "stage": 4 + }, + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": true, + "stage": 5 + }, + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": false, + "stage": 6 + }, + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": true, + "stage": 7 + }, + { + "fresh_copies": 9, + "scalar_additions": 33492, + "signed_inverse": false, + "stage": 8 + } + ], + "status": "PASS_NEW_COHORT249_ALL_BRIDGED_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL" +} \ No newline at end of file diff --git a/research/r480-sliced-minimal-frames/evidence/PACKAGED-FULL311.json b/research/r480-sliced-minimal-frames/evidence/PACKAGED-FULL311.json new file mode 100644 index 0000000000..1d4ded07d0 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/PACKAGED-FULL311.json @@ -0,0 +1,11 @@ +{ + "status": "PASS_PACKAGED_CONSTRUCTION_PHYSICAL_ADMISSION_AND_EXACT_PRICE", + "kappa": "0.001587467473762886", + "bit": "0.001590005077309865651707", + "word_sha256": "2928c90b7a90a8ba733a1dbf4eec3de064c3bc9f91dbde6cdb6392913cdf556a", + "manifest_sha256": "df123ccbeb5ad0b46cc58ec6a8a53e83d2ba0b1fe4758947170e1052279fdbcc", + "python": "3.11.15 (main, Mar 3 2026, 00:52:57) [Clang 17.0.0 (clang-1700.6.3.2)]", + "seconds": 101.19323466706555, + "scope": "Fresh complete finite record, geometry, owner and invoice replay plus exact source reconstruction and two-engine pricing. Complex535 cited rather than rebuilt; inherited all-size assumptions remain conditional.", + "physical_receipt": "trace541-frozen-admission/RESULT.json" +} diff --git a/research/r480-sliced-minimal-frames/evidence/PARENT-AUDIT314.json b/research/r480-sliced-minimal-frames/evidence/PARENT-AUDIT314.json new file mode 100644 index 0000000000..b6924fca09 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/PARENT-AUDIT314.json @@ -0,0 +1,44 @@ +{ + "status": "PASS_INDEPENDENT_COMPRESSED_BIT_TEMPLATE_AUDIT", + "template_sha256": "96841716c7901ae12d572113ffa3b7c14c1c3c9568a7c044f114941e7b5213e3", + "source_frames": 675, + "exact_nested_frame_pairs": 2412, + "exact_reflected_pairs": 2412, + "orthogonal_lift_argument": "Adding the same orthogonal E_s leaves P_V-P_U unchanged; each audited projector is therefore the literal child projector in every one of the nine windows.", + "exact_bank_families": 17280, + "residual_isometries": 1, + "entrance_rank_total": 0, + "mutations_rejected": [ + "omit an idle child", + "omit a bridge", + "omit terminal exchange", + "remove a local invocation", + "understate live stock", + "omit a local paid move", + "wrong reflected copy charge", + "alter residual orthogonal basis", + "misstate replication count", + "misstate stage count", + "alias data across stages", + "delay an idle advance past its level", + "truncate the last idle advance", + "re-use a helper bank slot", + "wrong residual frame", + "alias data across replica groups", + "omit the fourth replica group" + ], + "profile": { + "1": 370368, + "2": 379872, + "3": 12960, + "4": 48672, + "5": 288, + "6": 37440, + "7": 23040, + "8": 2592, + "14": 15360, + "28": 15360, + "42": 15360 + }, + "seconds": 8.728064374998212 +} diff --git a/research/r480-sliced-minimal-frames/evidence/PHYSICAL311.json b/research/r480-sliced-minimal-frames/evidence/PHYSICAL311.json new file mode 100644 index 0000000000..6f1be6e126 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/PHYSICAL311.json @@ -0,0 +1,33 @@ +{ + "status": "PASS_FRESH_TRACE_AND_FROZEN_FRAMES_RECORDS_HOSTING_AND_INVOICE", + "seconds": 91.31745012500323, + "word_sha256": "2928c90b7a90a8ba733a1dbf4eec3de064c3bc9f91dbde6cdb6392913cdf556a", + "profile": { + "1": 370368, + "2": 395232, + "3": 12960, + "4": 64032, + "5": 288, + "6": 52800, + "7": 23040, + "8": 2592 + }, + "kappa": "0.001587467473762886", + "bit_invoice": { + "live": 30720, + "physical": 30729, + "maxchild": 8, + "rank_mass": 1956096, + "hosted_residuals": 138240, + "bank_assignments": 0, + "prefix_bits": 191, + "charged_prefix_bits": 192, + "coefficient_bits": 191, + "two_level_coefficient_bits": 421, + "charged_two_level_coefficient_bits": 512, + "row_coefficient": 18355, + "halving_depth": 2 + }, + "steps": 19, + "scope": "Fresh finite record/formal-column/geometry/template/whole-owner/invoice replay, with inherited mutation controls. Cited complex535 operator unchanged. Exact sharp-charge prospective profile now matches physically emitted audited profile and retained finite allowances. All-size supplier/compiler/realization/hosting/analytic assumptions remain conditional." +} diff --git a/research/r480-sliced-minimal-frames/evidence/PHYSICAL314.json b/research/r480-sliced-minimal-frames/evidence/PHYSICAL314.json new file mode 100644 index 0000000000..22b082d1c6 --- /dev/null +++ b/research/r480-sliced-minimal-frames/evidence/PHYSICAL314.json @@ -0,0 +1,33 @@ +{ + "status": "PASS_FRESH_TRACE_AND_FROZEN_FRAMES_RECORDS_HOSTING_AND_INVOICE", + "seconds": 75.72498749999795, + "word_sha256": "3dddba9a13c96d54fa6aa3ff238711808662401a6fec7960ac34c4f885bfbf71", + "profile": { + "1": 370368, + "2": 395232, + "3": 12960, + "4": 64032, + "5": 288, + "6": 52800, + "7": 23040, + "8": 2592 + }, + "kappa": "0.001587467473762886", + "bit_invoice": { + "live": 30720, + "physical": 30729, + "maxchild": 8, + "rank_mass": 1956096, + "hosted_residuals": 138240, + "bank_assignments": 0, + "prefix_bits": 191, + "charged_prefix_bits": 192, + "coefficient_bits": 191, + "two_level_coefficient_bits": 421, + "charged_two_level_coefficient_bits": 512, + "row_coefficient": 18355, + "halving_depth": 2 + }, + "steps": 19, + "scope": "Fresh finite record/formal-column/geometry/template/whole-owner/invoice replay, with inherited mutation controls. Cited complex535 operator unchanged. Exact sharp-charge prospective profile now matches physically emitted audited profile and retained finite allowances. All-size supplier/compiler/realization/hosting/analytic assumptions remain conditional." +} diff --git a/research/r480-sliced-minimal-frames/scripts/final_arithmetic.py b/research/r480-sliced-minimal-frames/scripts/final_arithmetic.py new file mode 100644 index 0000000000..103d9c887f --- /dev/null +++ b/research/r480-sliced-minimal-frames/scripts/final_arithmetic.py @@ -0,0 +1,38 @@ +"""Two exact moments, explicit six-level cutoffs and invalid-assembly controls. +Prepared for rohanarun with OpenAI Codex assistance. Apache-2.0. +""" +from pathlib import Path +from fractions import Fraction as Q +import json,sys,importlib.util +P=Path(sys.argv[1]).resolve();out=Path(sys.argv[2]).resolve();assert not out.exists() +def load(n): + s=importlib.util.spec_from_file_location('final_'+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']] +e=json.loads((P/'EXPECTED.json').read_text());baseline=json.loads((P/'inputs/PR510-EXPECTED.json').read_text())['nine'];cp=json.loads((P/'inputs/PR535-EXPECTED.json').read_text());H={int(r):n for r,n in e['profile'].items()};m=baseline['m'];W=baseline['bit']['live'];c=Q(e['bit_lower']);b=Q(e['complex_lower']);N=2*m +assert sum(r*n for r,n in H.items())==baseline['bit']['rank_mass'] +factor=Q(2*m**3,2**80)*(6*N*(N-1)+3*N+6*(N-1))*sum(H.values()) +moments=[] +for a,ok in [(c,True),(c+Q(1,10**24),False)]: + l,u=M.moment(H,m,W,a,False);g,h=M.moment({1:1},m,W,a,False);l+=factor*g;u+=factor*h + ll,uu=B.moment(m,W,list(H.items()),a);gg,hh=B.moment(m,W,[(1,1)],a);ll+=factor*gg;uu+=factor*hh + assert (u<1 and uu<1)if ok else(l>1 and ll>1) + moments.append(dict(endpoint=str(a),accept=ok,mercator=[str(l-1),str(u-1)],base_two=[str(ll-1),str(uu-1)])) +CP={int(r):n for r,n in cp['global_profile'].items()} +for a,ok in [(b,True),(b+Q(1,10**24),False)]: + l,u=M.moment(CP,73,cp['live'],a,True);ll,uu=B.moment(73,cp['live'],list(CP.items()),a);gg,hh=B.moment(73,cp['live'],[(1,32*73**2*sum(CP.values()))],a);ll+=gg/10**16;uu+=hh/10**16 + assert (u<1 and uu<1)if ok else(l>1 and ll>1) +eta=beta=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24);assert s0 + 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);assert k==Q(e['kappa']) +bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}} +a=A.assembly(chain[-1],b,bridge,k,eta=eta,beta=beta);assert len(a['strict_constraints'])==47 and all(v>0 for v in a['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) +res=dict(status='PASS_TWO_ENGINE_MOMENTS_EXPLICIT_BOOTSTRAP_AND_47_OUTER_CONSTRAINTS',kappa=str(k),bit=str(c),complex=str(b),binding='complex'if (1-beta)*b