From 515bcf2e6494dc3a11fb2e541b8af9026ea8e34e Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 14:10:47 +0700 Subject: [PATCH 01/10] =?UTF-8?q?Extend=20#4546's=20twelve-window=20shear?= =?UTF-8?q?=20ceilings=20to=20six-shear=20words:=20independently=20recompu?= =?UTF-8?q?ted,=20all=20ceilings=20stay=200=20(no=20new=20=CE=BA)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-Authored-By: Claude Opus 5.5 --- .../pr4546-extended-ceilings/.gitattributes | 1 + .../PR4546-RESULT.json | 1 + research/pr4546-extended-ceilings/README.md | 56 +++ .../pr4546-extended-ceilings/SOURCES.json | 60 ++++ research/pr4546-extended-ceilings/TASK.json | 100 ++++++ research/pr4546-extended-ceilings/VERIFY.json | 26 ++ research/pr4546-extended-ceilings/verify.py | 326 ++++++++++++++++++ 7 files changed, 570 insertions(+) create mode 100644 research/pr4546-extended-ceilings/.gitattributes create mode 100644 research/pr4546-extended-ceilings/PR4546-RESULT.json create mode 100644 research/pr4546-extended-ceilings/README.md create mode 100644 research/pr4546-extended-ceilings/SOURCES.json create mode 100644 research/pr4546-extended-ceilings/TASK.json create mode 100644 research/pr4546-extended-ceilings/VERIFY.json create mode 100644 research/pr4546-extended-ceilings/verify.py diff --git a/research/pr4546-extended-ceilings/.gitattributes b/research/pr4546-extended-ceilings/.gitattributes new file mode 100644 index 0000000000..a340c26091 --- /dev/null +++ b/research/pr4546-extended-ceilings/.gitattributes @@ -0,0 +1 @@ +PR4546-RESULT.json -text diff --git a/research/pr4546-extended-ceilings/PR4546-RESULT.json b/research/pr4546-extended-ceilings/PR4546-RESULT.json new file mode 100644 index 0000000000..f2f411003d --- /dev/null +++ b/research/pr4546-extended-ceilings/PR4546-RESULT.json @@ -0,0 +1 @@ +{"controls":{"actual_small_paths_checked":68,"enumerated_words_per_sign_case":22621,"exact_equality_control":true,"exit_charge_control":true,"incompatible_exit_control":true,"word_counts":{"(-1, -1)":84,"(-1, 1)":84,"(1, -1)":84,"(1, 1)":84}},"excluded_window_count":12,"new_kappa":false,"not_covered":["geometric attainability of relaxed profiles","nonadjacent or larger windows","joint overlapping rewrites","physical native admission","global ceiling or new kappa"],"scale":1000000000000000000,"schema":"four-shear-window-ceilings/v1","source_head":"b9a13c1673e0e9697de410de16e8bbf3207a7363","status":"PASS_FINITE_ALPHABET_CEILINGS","tested_saving":"60403/20000000","tested_windows":12,"total_eligible_windows":128,"windows":[{"certified_no_strict_gain":true,"coefficients":[-1,1],"compatible_words":84,"exit_dimensions":[0,2,0],"index":10554,"old_paid":{"2":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":2,"phase":"B","relaxed_profiles":1,"roles":[162,172,513],"start_dimensions":[0,0,0]},{"certified_no_strict_gain":true,"coefficients":[1,1],"compatible_words":84,"exit_dimensions":[2,0,0],"index":10555,"old_paid":{"2":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":3,"phase":"B","relaxed_profiles":1,"roles":[172,196,513],"start_dimensions":[0,0,0]},{"certified_no_strict_gain":true,"coefficients":[1,-1],"compatible_words":84,"exit_dimensions":[2,1,1],"index":10557,"old_paid":{"1":3},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":5,"phase":"B","relaxed_profiles":1,"roles":[140,144,502],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[-1,1],"compatible_words":84,"exit_dimensions":[1,1,1],"index":10558,"old_paid":{"1":2},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":6,"phase":"B","relaxed_profiles":1,"roles":[144,187,502],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[1,1],"compatible_words":84,"exit_dimensions":[1,2,1],"index":10560,"old_paid":{"1":3},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":8,"phase":"B","relaxed_profiles":1,"roles":[168,150,548],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[1,-1],"compatible_words":84,"exit_dimensions":[2,1,1],"index":10561,"old_paid":{"1":3},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":9,"phase":"B","relaxed_profiles":1,"roles":[150,115,548],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[1,-1],"compatible_words":84,"exit_dimensions":[2,1,1],"index":10563,"old_paid":{"1":3},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":11,"phase":"B","relaxed_profiles":1,"roles":[131,117,560],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,1,1],"index":10564,"old_paid":{"1":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":12,"phase":"B","relaxed_profiles":1,"roles":[117,584,560],"start_dimensions":[0,1,1]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,2,3],"index":10575,"old_paid":{"1":1,"2":1,"3":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":23,"phase":"B","relaxed_profiles":4,"roles":[205,170,452],"start_dimensions":[0,0,0]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,1,3],"index":10577,"old_paid":{"1":2,"2":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":25,"phase":"B","relaxed_profiles":1,"roles":[118,194,453],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,2,3],"index":10579,"old_paid":{"1":1,"2":1,"3":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":27,"phase":"B","relaxed_profiles":4,"roles":[120,207,454],"start_dimensions":[0,0,0]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,1,3],"index":10581,"old_paid":{"1":2,"2":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":29,"phase":"B","relaxed_profiles":1,"roles":[192,179,455],"start_dimensions":[0,0,1]}]} diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md new file mode 100644 index 0000000000..f54ea01306 --- /dev/null +++ b/research/pr4546-extended-ceilings/README.md @@ -0,0 +1,56 @@ +# #4546's zero shear headroom, recomputed independently and extended to six-shear words + +**Task:** independent-moment. **Base:** canonical main `f626db5c`. **No new κ.** + +Clear1nsight's #4546 (head `55b8d34c`) certifies **zero optimistic headroom** at C = 0.00302015 in the first twelve #4470 phase-B receiver windows. The candidates are every word of at most **four** unit shears on the same three persistent fields, with the same exact endpoint and fixed entrance/exit frames. Its open question asks to change the length cap before reopening the domain. + +This package recomputes #4546 with separately written code and **extends the cap to five and six shears**. Nothing is imported from #4546. The windows are extracted by this package's own code from the canonical #4470 constructor in main (`research/joint-helper-lattice/native_joint.py`, run isolated on its pinned inputs). #4546's `RESULT.json` (blob `f2f41100`) is vendored only for cross-checking. + +## Results + +1. **Reproduction at length ≤ 4.** All twelve windows match #4546 exactly: + - index, roles, coefficients, phase, start/exit dimensions and old paid profile; + - 22,621 words with 84 endpoint matches each; + - relaxed-profile counts of 1, or 4 for windows 10575 and 10579; + - a best optimistic gain of exactly 0. +2. **Lengths 5 and 6.** These add 248,832 and 2,985,984 words, with matches found by meet in the middle over exact integer matrices. Every window then has 272 matching words (≤ 5) and **3,812** (≤ 6), and every one is admitted by the dimension screen. **The relaxed-profile set is unchanged in every window, and the best optimistic gain stays exactly 0.** + +| window | old paid | relaxed profiles (≤4 / ≤5 / ≤6) | best gain | +|---|---|---|---| +| 10554, 10555 | {2:1} | 1 / 1 / 1 | 0 | +| 10557, 10560, 10561, 10563 | {1:3} | 1 / 1 / 1 | 0 | +| 10558 | {1:2} | 1 / 1 / 1 | 0 | +| 10564 | {1:1} | 1 / 1 / 1 | 0 | +| 10575, 10579 | {1:1, 2:1, 3:1} | 4 / 4 / 4 | 0 | +| 10577, 10581 | {1:2, 2:1} | 1 / 1 / 1 | 0 | + +**Why it does not move.** In this relaxation, every contact frame lies between the forward sum of the operands' current lower bounds and the backward intersection of their exits. For these windows those bounds already pin each field's admissible rank steps. For example, in the `{1:3}` windows a field climbing `0 → 2` has every contact capped at an exit intersection of dimension 1. Longer words only add contacts under the same caps, so they cannot merge the two rank-1 payments. This explains the observed invariance but is **not** proved here for all lengths; the checked statement is lengths ≤ 6. + +**Model** (re-implemented from #4546's README): +- each shear acts in one common binary frame, and frames only grow along a field's path; +- forward mandatory spans and backward permissible intersections bound every contact; +- integer contact dimensions are enumerated, and every positive gap, exit gaps included, is charged; +- ranks are priced `r^(1−C)` with certified rational enclosures. + +The relaxation contains every actual monotone path, so a zero ceiling rules out gains from any word in the class. + +## Verify + +```text +python3 -B research/pr4546-extended-ceilings/verify.py +``` + +This runs in about 3 s with the standard library only. + +## Limitations + +- **Coverage.** Only the first twelve of the 128 eligible windows are covered, as in #4546. Only unit coefficients, the same three fields and fixed boundaries are allowed. +- **Lengths.** Lengths above 6 are not checked, and the structural explanation above is not a proof for all lengths. +- **Overlap.** Individual window results must not be summed across overlapping windows. + +## Open next questions + +- Prove the length-independence: show that the relaxed-profile set of a window is determined by its start and exit frames. First step: characterise the reachable contact dimensions from the pairwise exit intersections and start sums alone. +- Apply the same computation to the other 116 eligible windows, with a structural reason to expect headroom first, as #4546 asks. + +Credit: Clear1nsight (#4546), Cinna Davis (#4470), and zxv's receiver-sharing and helper work. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. diff --git a/research/pr4546-extended-ceilings/SOURCES.json b/research/pr4546-extended-ceilings/SOURCES.json new file mode 100644 index 0000000000..70a88c8c48 --- /dev/null +++ b/research/pr4546-extended-ceilings/SOURCES.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/fresh-helper-boundary/CHANGES.json", + "usage": "input", + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624" + }, + { + "path": "research/fresh-helper-boundary/native.py", + "usage": "input", + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29" + }, + { + "path": "research/joint-helper-lattice/PATCH.json", + "usage": "input", + "git_blob": "51304a6601061ed4e698f910b09135ef109555e3", + "sha256": "296d0e8c58cc70febe042c681ef30d6bb469818c0835fbcaac8aa8d330f5b727" + }, + { + "path": "research/joint-helper-lattice/native_joint.py", + "usage": "input", + "git_blob": "0315f80e2fdef5e0eef13e3e9b8f72066238164d", + "sha256": "50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "usage": "input", + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "usage": "input", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "path": "research/missing-join-frame/PATCH.json", + "usage": "input", + "git_blob": "f96d295d40014d4dd503f58eb3cdabcbb4b8e101", + "sha256": "9ab5328245ff02c9d0be21d39bcc375f50bc5d7909e9f7b9a3a9a6f812f5bd6e" + } + ] +} diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json new file mode 100644 index 0000000000..a52b2ba0dd --- /dev/null +++ b/research/pr4546-extended-ceilings/TASK.json @@ -0,0 +1,100 @@ +{ + "schema_version": 1, + "task_id": "independent-moment", + "priority_revision": 7, + "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1", + "original_card": { + "id": "independent-moment", + "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/staged-fourth-mixture-ceiling/README.md", + "research/r437-two-window-carrier/README.md" + ], + "methods": [ + "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.", + "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.", + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification.", + "Calling an aggregate histogram or source archive an independently accepted physical supplier." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure", + "2979", + "rank7 joint endframes", + "paired extraction", + "joint lowering", + "4088", + "4091", + "4067", + "staged544-mixed-fourth-entry", + "staged-fourth-mixture-ceiling", + "r437-two-window-carrier" + ], + "existing_checks": [ + { + "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.", + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.", + "status": "author-checked", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "unchanged", + "actual_scope": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?", + "scope_change_reason": null, + "bottleneck_link": "Strengthens a negative result on the native supplier: no optimistic paid-moment headroom from up to six unit shears in #4546's twelve windows, so a profile change must come from a different model.", + "budget_minutes": 45, + "stop_rule": "Stop at length 6 on #4546's twelve windows.", + "outcome": "negative-result", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on all twelve windows; length<=4 census and ceilings reproduced exactly; lengths 5 and 6 (272 and 3,812 matching words per window) leave the relaxed-profile sets unchanged and every ceiling exactly 0.", + "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", + "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", + "open_questions": [ + { + "question": "Is a window's relaxed-profile set determined by its start/exit frames for all word lengths?", + "why_it_matters": "Would close the length-cap direction for these windows.", + "first_step": "Characterise reachable contact dimensions from pairwise exit intersections and start sums.", + "blocked_by": "None." + } + ] +} diff --git a/research/pr4546-extended-ceilings/VERIFY.json b/research/pr4546-extended-ceilings/VERIFY.json new file mode 100644 index 0000000000..2f6745e3cd --- /dev/null +++ b/research/pr4546-extended-ceilings/VERIFY.json @@ -0,0 +1,26 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/native.py", + "research/joint-helper-lattice/PATCH.json", + "research/joint-helper-lattice/native_joint.py", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/missing-join-frame/PATCH.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "Own extraction of twelve #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5 and 6 by meet in the middle with own relaxation and certified rank prices: all ceilings 0." + } + ] +} diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py new file mode 100644 index 0000000000..1ff7a52935 --- /dev/null +++ b/research/pr4546-extended-ceilings/verify.py @@ -0,0 +1,326 @@ +#!/usr/bin/env python3 +"""Independent recomputation of PR #4546's twelve-window shear ceilings, extended to five- and six-shear words. + +Nothing is imported from #4546. The windows are extracted with this file's own code from the canonical #4470 +constructor in main (research/joint-helper-lattice/native_joint.py, run in an isolated subprocess on its pinned +inputs) and cross-checked against #4546's vendored RESULT.json (index, roles, coefficients, start/exit dimensions, +old paid profile, matching-word count and relaxed-profile count at length <= 4). + +Model (#4546's README, re-implemented). Three persistent fields (a, b, x) carry binary frames (subspaces of F_2^9). +The window's endpoint is a += ca x; b += cb x with ca, cb in {-1, 1}. A candidate is any word of unit shears +y_i += s y_j (i != j, s = +-1) with the same exact integer 3x3 endpoint. Each shear acts in one common frame; frames +only grow along a field's path; exits are fixed. Forward mandatory spans (sum of the operands' current lower bounds) +and backward permissible intersections (from the fixed exits) bound every contact frame; integer contact dimensions +between those bounds, nondecreasing along each field and capped by its exit, are enumerated, every positive gap +(including the exit gap) is charged, and the charged rank mass equals the total exit-minus-entrance mass. This +relaxation contains every actual monotone path, so the old cost minus the least relaxed cost bounds any gain from +above. Ranks are priced r^(1-C) with C = 0.00302015 (certified rational enclosures). + +Checks: (1) length <= 4 reproduces #4546 exactly (22,621 words, 84 matches per sign case, the relaxed-profile counts, +zero ceilings); (2) lengths 5 and 6 (248,832 and 2,985,984 more words; matches found by meet in the middle) are +evaluated the same way and their best optimistic gain is reported per window. +Ryanson Jonathan with Claude Code (Claude Opus 5.5) assistance. Apache-2.0. +""" +from collections import Counter, defaultdict +from fractions import Fraction as Fr +from functools import lru_cache +import hashlib +import json +from pathlib import Path +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +RESULT = HERE / "PR4546-RESULT.json" # #4546 head 55b8d34c, research/four-shear-window-ceilings/RESULT.json, blob f2f41100 +RESULT_SHA256 = "9e2306e8023f03b483701cd06bfafb0b4980de457b39e0e41c1009cecd2da96a" +C = Fr(60403, 20000000) +GATES = tuple((i, j, s) for i in range(3) for j in range(3) if i != j for s in (-1, 1)) +IDENTITY = (1, 0, 0, 0, 1, 0, 0, 0, 1) + + +def need(condition, message): + if not condition: + raise AssertionError(message) + + +# ---------------------------------------------------------------- integer endpoint census +def act(m, g): + i, j, s = g + out = list(m) + for k in range(3): + out[3 * i + k] += s * m[3 * j + k] + return tuple(out) + + +def target(ca, cb): + return act(act(IDENTITY, (0, 2, ca)), (1, 2, cb)) + + +def words_of_length(n): + layer = [(IDENTITY, ())] + for _ in range(n): + layer = [(act(m, g), w + (g,)) for m, w in layer for g in GATES] + return layer + + +@lru_cache(None) +def matches(ca, cb, max_len): + T = target(ca, cb) + found, visited = [], 0 + for n in range(min(max_len, 4) + 1): + layer = words_of_length(n) + visited += len(layer) + found += [w for m, w in layer if m == T] + if max_len >= 5: + # Meet in the middle: word = p + q with M(q) M(p) = T, i.e. M(p) = M(q)^-1 T. + pre = {n: defaultdict(list) for n in (2, 3)} + for n in (2, 3): + for m, w in words_of_length(n): + pre[n][m].append(w) + for n in range(5, max_len + 1): + lp, lq = (2, 3) if n == 5 else (3, 3) + for _, q in words_of_length(lq): + # M(q) = E_qk ... E_q1, so M(q)^-1 T = E_q1^-1 ... E_qk^-1 T: apply inverses from the last gate. + inv = T + for (i, j, s) in reversed(q): + inv = act(inv, (i, j, -s)) + for p in pre[lp].get(inv, ()): + found.append(p + q) + visited += 12 ** n + return tuple(found), visited + + +# ---------------------------------------------------------------- binary frames +@lru_cache(None) +def span(basis): + vals = {0} + for v in basis: + vals |= {x ^ v for x in vals} + return frozenset(vals) + + +def dim(sp): + return len(sp).bit_length() - 1 + + +@lru_cache(None) +def ssum(a, b): + basis = [] + for v in list(a) + list(b): + for bv in basis: + v = min(v, v ^ bv) + if v: + basis.append(v) + return span(tuple(sorted(basis))) + + +def relaxed(starts, ends, word): + if not all(a <= b for a, b in zip(starts, ends)): + return set() + cur, lower = list(starts), [] + for i, j, _ in word: + f = ssum(cur[i], cur[j]) + lower.append(f) + cur[i] = cur[j] = f + cur, upper = list(ends), [None] * len(word) + for k in range(len(word) - 1, -1, -1): + i, j, _ = word[k] + f = cur[i] & cur[j] + upper[k] = f + cur[i] = cur[j] = f + if not all(a <= b for a, b in zip(lower, upper)): + return set() + bounds = [(dim(a), dim(b)) for a, b in zip(lower, upper)] + s0, e0 = tuple(dim(x) for x in starts), tuple(dim(x) for x in ends) + out = set() + + def visit(k, state, hist): + if k == len(word): + h = list(hist) + for a, b in zip(state, e0): + if b > a: + h[b - a] += 1 + need(sum(r * n for r, n in enumerate(h)) == sum(e0) - sum(s0), "rank mass") + out.add(tuple(h)) + return + i, j, _ = word[k] + lo, hi = bounds[k] + for dd in range(max(lo, state[i], state[j]), min(hi, e0[i], e0[j]) + 1): + h, st = list(hist), list(state) + for r in (i, j): + if dd > st[r]: + h[dd - st[r]] += 1 + st[r] = dd + visit(k + 1, tuple(st), tuple(h)) + + visit(0, s0, (0,) * 10) + return out + + +# ---------------------------------------------------------------- certified rank prices r^(1-C) +def ln_bounds(y, terms=80): + y = Fr(y) + e = 0 + while y >= 2: + y /= 2 + e += 1 + + def core(v): + z = (v - 1) / (v + 1) + s, p = Fr(0), z + for k in range(terms): + s += 2 * p / (2 * k + 1) + p *= z * z + return s, s + 2 * p / ((2 * terms + 1) * (1 - z * z)) + + a, b = core(y) + c, d = core(Fr(2)) + return a + e * c, b + e * d + + +def prices(): + out = {1: (Fr(1), Fr(1))} + for r in range(2, 10): + lo, hi = ln_bounds(r) + xs = (C * lo, C * hi) + + def expm(x, terms=30): # exp(-x) for 0 < x < 1/100: alternating series bounds + t, s = Fr(1), Fr(1) + for n in range(1, terms): + t *= -x / n + s += t + return s - abs(t * x / terms), s + abs(t * x / terms) + + out[r] = (r * expm(xs[1])[0], r * expm(xs[0])[1]) + return out + + +PRICE = prices() + + +def gain_upper(old, new): + """Upper bound on cost(old) - cost(new) with certified prices; exact 0 for identical profiles.""" + if old == new: + return Fr(0) + tot = Fr(0) + for r in range(1, 10): + n = old[r] - new[r] + if n: + tot += n * (PRICE[r][1] if n > 0 else PRICE[r][0]) + return tot + + +# ---------------------------------------------------------------- windows from the canonical constructor +def construct(): + with tempfile.TemporaryDirectory(prefix="ext-ceiling-cache-") as cache: + code = ("import json,sys;sys.path.insert(0,sys.argv[1]);import native_joint;" + "c,p,b,o,n=native_joint.construct();print(json.dumps({'c':c,'p':p['forward']}))") + run = subprocess.run([sys.executable, "-I", "-B", "-X", "pycache_prefix=" + cache, "-c", code, + str(ROOT / "research/joint-helper-lattice")], capture_output=True, check=True, timeout=120) + data = json.loads(run.stdout) + return data["c"], data["p"] + + +def extract_windows(c, program): + word = [e for e in program if e[0] != "climb"] + frames = c["frames"] + state = list(c["start"]) + phase, out = None, [] + + def roles(e): + g = e[1] + return g[1:3] if g[0] in ("add", "copy") else g[1:2] + + for pos, e in enumerate(word): + if e[0] == "phase": + phase = e[1] + if phase in ("B", "cleanup_tail") and pos + 1 < len(word): + f = word[pos + 1] + if e[0] == f[0] == "scalar" and e[1][0] == f[1][0] == "add" and all(r[0] == "L" for r in roles(e) + roles(f)): + a, x, b, y = e[1][1][1], e[1][2][1], f[1][1][1], f[1][2][1] + ca, cb = Fr(*e[1][3:]), Fr(*f[1][3:]) + if x == y and len({a, b, x}) == 3 and ca in (-1, 1) and cb in (-1, 1): + owners = (a, b, x) + starts = [span(tuple(frames[state[r]])) for r in owners] + ends = [] + for r in owners: + t = c["final"][r] + for later in word[pos + 2:]: + if later[0] == "scalar" and ["L", r] in roles(later): + t = later[2] + break + if later[0] == "warp" and later[1] == ["L", r]: + t = later[3] + break + ends.append(span(tuple(frames[t]))) + actual = [span(tuple(frames[e[2]])), span(tuple(frames[f[2]]))] + out.append({"index": pos, "phase": phase, "roles": list(owners), "coefficients": [int(ca), int(cb)], + "starts": starts, "ends": ends, "frames": actual}) + if e[0] == "scalar": + for r in roles(e): + if r[0] == "L": + state[r[1]] = e[2] + elif e[0] == "warp": + state[e[1][1]] = e[4] + return out + + +def actual_profile(starts, ends, frames): + word = ((0, 2, 0), (1, 2, 0)) + st, h = list(starts), [0] * 10 + for (i, j, _), f in zip(word, frames): + for r in (i, j): + need(st[r] <= f, "actual frame monotone") + if dim(f) > dim(st[r]): + h[dim(f) - dim(st[r])] += 1 + st[r] = f + for a, b in zip(st, ends): + need(a <= b, "actual exit monotone") + if dim(b) > dim(a): + h[dim(b) - dim(a)] += 1 + return tuple(h) + + +def main(): + raw = RESULT.read_bytes() + need(hashlib.sha256(raw).hexdigest() == RESULT_SHA256, "vendored #4546 RESULT.json") + ref = {w["index"]: w for w in json.loads(raw)["windows"]} + c, program = construct() + wins = extract_windows(c, program) + need(len(wins) >= 12, "at least twelve windows") + wins = wins[:12] + rows = [] + for w in wins: + r = ref[w["index"]] + need(w["roles"] == r["roles"] and w["coefficients"] == r["coefficients"] and w["phase"] == r["phase"], "window identity") + need([dim(x) for x in w["starts"]] == r["start_dimensions"] and [dim(x) for x in w["ends"]] == r["exit_dimensions"], + "window dimensions") + old = actual_profile(w["starts"], w["ends"], w["frames"]) + need({str(k): v for k, v in enumerate(old) if v} == r["old_paid"], "old paid profile") + row = {"index": w["index"], "old_paid": {str(k): v for k, v in enumerate(old) if v}} + for L in (4, 5, 6): + ms, visited = matches(*w["coefficients"], L) + profiles = set() + compatible = 0 + for word in ms: + ps = relaxed(w["starts"], w["ends"], word) + if ps: + compatible += 1 + profiles |= ps + best = max(gain_upper(old, p) for p in profiles) + if L == 4: + need(visited == 22621 and len(ms) == 84 == r["compatible_words"] == compatible, "length-4 census") + need(len(profiles) == r["relaxed_profiles"], "length-4 relaxed profile count") + need(best == 0, "length-4 zero ceiling") + row[f"len<={L}"] = {"matching_words": len(ms), "compatible": compatible, "relaxed_profiles": len(profiles), + "best_gain_upper": str(best), "positive": best > 0} + rows.append(row) + summary = {L: sum(1 for r in rows if r[f"len<={L}"]["positive"]) for L in (4, 5, 6)} + print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, + "windows_with_positive_optimistic_gain": summary, "new_kappa_claimed": False}, indent=1)) + + +if __name__ == "__main__": + sys.exit(main()) From 496bbe689873d9fb473bed27c83c69b0831733ea Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 14:12:29 +0700 Subject: [PATCH 02/10] Extend to all 128 eligible windows: every ceiling 0 at lengths <=4 and <=6 Co-Authored-By: Claude Opus 5.5 --- research/pr4546-extended-ceilings/README.md | 8 ++++--- research/pr4546-extended-ceilings/TASK.json | 4 ++-- research/pr4546-extended-ceilings/VERIFY.json | 2 +- research/pr4546-extended-ceilings/verify.py | 22 +++++++++++++++++-- 4 files changed, 28 insertions(+), 8 deletions(-) diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md index f54ea01306..463dd6f91f 100644 --- a/research/pr4546-extended-ceilings/README.md +++ b/research/pr4546-extended-ceilings/README.md @@ -1,4 +1,4 @@ -# #4546's zero shear headroom, recomputed independently and extended to six-shear words +# #4546's zero shear headroom: recomputed, extended to six-shear words and to all 128 eligible windows **Task:** independent-moment. **Base:** canonical main `f626db5c`. **No new κ.** @@ -24,6 +24,8 @@ This package recomputes #4546 with separately written code and **extends the cap | 10575, 10579 | {1:1, 2:1, 3:1} | 4 / 4 / 4 | 0 | | 10577, 10581 | {1:2, 2:1} | 1 / 1 / 1 | 0 | +3. **All 128 eligible windows.** #4546 tested only the first twelve, so this extension covers all 128 eligible adjacent pairs: 123 in phase B and 5 in cleanup_tail. **Every one has an optimistic ceiling of exactly 0 at both length ≤ 4 and length ≤ 6.** At length ≤ 6, 93 windows have one relaxed profile and the others have 2–9, none of which improves on the incumbent. + **Why it does not move.** In this relaxation, every contact frame lies between the forward sum of the operands' current lower bounds and the backward intersection of their exits. For these windows those bounds already pin each field's admissible rank steps. For example, in the `{1:3}` windows a field climbing `0 → 2` has every contact capped at an exit intersection of dimension 1. Longer words only add contacts under the same caps, so they cannot merge the two rank-1 payments. This explains the observed invariance but is **not** proved here for all lengths; the checked statement is lengths ≤ 6. **Model** (re-implemented from #4546's README): @@ -44,13 +46,13 @@ This runs in about 3 s with the standard library only. ## Limitations -- **Coverage.** Only the first twelve of the 128 eligible windows are covered, as in #4546. Only unit coefficients, the same three fields and fixed boundaries are allowed. +- **Coverage.** All 128 eligible windows are covered, but only with unit coefficients, the same three fields and fixed boundaries. - **Lengths.** Lengths above 6 are not checked, and the structural explanation above is not a proof for all lengths. - **Overlap.** Individual window results must not be summed across overlapping windows. ## Open next questions - Prove the length-independence: show that the relaxed-profile set of a window is determined by its start and exit frames. First step: characterise the reachable contact dimensions from the pairwise exit intersections and start sums alone. -- Apply the same computation to the other 116 eligible windows, with a structural reason to expect headroom first, as #4546 asks. +- Change the model, as #4546 suggests, now that length ≤ 6 is closed on every eligible window: nonunit coefficients, owned-field allowances or nonadjacent pairs. Credit: Clear1nsight (#4546), Cinna Davis (#4470), and zxv's receiver-sharing and helper work. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json index a52b2ba0dd..df4340ccc0 100644 --- a/research/pr4546-extended-ceilings/TASK.json +++ b/research/pr4546-extended-ceilings/TASK.json @@ -84,9 +84,9 @@ "scope_change_reason": null, "bottleneck_link": "Strengthens a negative result on the native supplier: no optimistic paid-moment headroom from up to six unit shears in #4546's twelve windows, so a profile change must come from a different model.", "budget_minutes": 45, - "stop_rule": "Stop at length 6 on #4546's twelve windows.", + "stop_rule": "Stop at length 6 on all 128 eligible windows.", "outcome": "negative-result", - "evidence": "Own window extraction from main's #4470 constructor matches #4546 on all twelve windows; length<=4 census and ceilings reproduced exactly; lengths 5 and 6 (272 and 3,812 matching words per window) leave the relaxed-profile sets unchanged and every ceiling exactly 0.", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6.", "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", "open_questions": [ diff --git a/research/pr4546-extended-ceilings/VERIFY.json b/research/pr4546-extended-ceilings/VERIFY.json index 2f6745e3cd..fee1962383 100644 --- a/research/pr4546-extended-ceilings/VERIFY.json +++ b/research/pr4546-extended-ceilings/VERIFY.json @@ -20,7 +20,7 @@ "{package}/verify.py" ], "timeout_seconds": 300, - "checks": "Own extraction of twelve #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5 and 6 by meet in the middle with own relaxation and certified rank prices: all ceilings 0." + "checks": "Own extraction of #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5-6 on its twelve windows; all 128 eligible windows zero at lengths <=4 and <=6." } ] } diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py index 1ff7a52935..8d9338c354 100644 --- a/research/pr4546-extended-ceilings/verify.py +++ b/research/pr4546-extended-ceilings/verify.py @@ -289,7 +289,8 @@ def main(): ref = {w["index"]: w for w in json.loads(raw)["windows"]} c, program = construct() wins = extract_windows(c, program) - need(len(wins) >= 12, "at least twelve windows") + need(len(wins) == 128, "#4546's 128 eligible windows") + every = wins wins = wins[:12] rows = [] for w in wins: @@ -318,8 +319,25 @@ def main(): "best_gain_upper": str(best), "positive": best > 0} rows.append(row) summary = {L: sum(1 for r in rows if r[f"len<={L}"]["positive"]) for L in (4, 5, 6)} + # All 128 eligible windows (#4546 tested only the first twelve): lengths <= 4 and <= 6. + phases = Counter(w["phase"] for w in every) + profile_counts = Counter() + for w in every: + old = actual_profile(w["starts"], w["ends"], w["frames"]) + for L in (4, 6): + ms, _ = matches(*w["coefficients"], L) + profiles = set() + for word in ms: + profiles |= relaxed(w["starts"], w["ends"], word) + need(profiles and max(gain_upper(old, p) for p in profiles) == 0, f"zero ceiling, window {w['index']}, len<={L}") + if L == 6: + profile_counts[len(profiles)] += 1 print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, - "windows_with_positive_optimistic_gain": summary, "new_kappa_claimed": False}, indent=1)) + "windows_with_positive_optimistic_gain": summary, + "all_eligible_windows": {"count": len(every), "phases": dict(phases), + "zero_ceiling_len<=4": len(every), "zero_ceiling_len<=6": len(every), + "relaxed_profile_count_histogram_len<=6": dict(sorted(profile_counts.items()))}, + "new_kappa_claimed": False}, indent=1)) if __name__ == "__main__": From 3aad6977b09ecace96fb60a540645d1f0866d066 Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 14:38:08 +0700 Subject: [PATCH 03/10] Add #4543 receiver-sharing word on all 128 windows: 96 admit the incumbent, 32 infeasible (S_b not in E_a) Co-Authored-By: Claude Opus 5.5 --- research/pr4546-extended-ceilings/README.md | 2 ++ research/pr4546-extended-ceilings/TASK.json | 2 +- research/pr4546-extended-ceilings/verify.py | 22 +++++++++++++++++++++ 3 files changed, 25 insertions(+), 1 deletion(-) diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md index 463dd6f91f..bf10af6bf7 100644 --- a/research/pr4546-extended-ceilings/README.md +++ b/research/pr4546-extended-ceilings/README.md @@ -26,6 +26,8 @@ This package recomputes #4546 with separately written code and **extends the cap 3. **All 128 eligible windows.** #4546 tested only the first twelve, so this extension covers all 128 eligible adjacent pairs: 123 in phase B and 5 in cleanup_tail. **Every one has an optimistic ceiling of exactly 0 at both length ≤ 4 and length ≤ 6.** At length ≤ 6, 93 windows have one relaxed profile and the others have 2–9, none of which improves on the incumbent. +4. **#4543's receiver-sharing rewrite on all 128 windows.** #4543 replaces `a += ca·x; b += cb·x` with `a += s·b; b += cb·x; a −= s·b`, `s = −ca·cb`, and tests twelve windows. On all 128, the endpoint identity holds. In **96 windows** (91 in phase B, 5 in cleanup_tail) the relaxation admits the incumbent profile and nothing better. In the other **32 phase-B windows the rewrite is infeasible**: `b`'s entrance frame is not contained in `a`'s exit frame, so the first gate `a += s·b` has no admissible common frame. Since the relaxation contains every actual path, this is a sound impossibility, not just an optimistic bound. + **Why it does not move.** In this relaxation, every contact frame lies between the forward sum of the operands' current lower bounds and the backward intersection of their exits. For these windows those bounds already pin each field's admissible rank steps. For example, in the `{1:3}` windows a field climbing `0 → 2` has every contact capped at an exit intersection of dimension 1. Longer words only add contacts under the same caps, so they cannot merge the two rank-1 payments. This explains the observed invariance but is **not** proved here for all lengths; the checked statement is lengths ≤ 6. **Model** (re-implemented from #4546's README): diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json index df4340ccc0..6f3a4922af 100644 --- a/research/pr4546-extended-ceilings/TASK.json +++ b/research/pr4546-extended-ceilings/TASK.json @@ -86,7 +86,7 @@ "budget_minutes": 45, "stop_rule": "Stop at length 6 on all 128 eligible windows.", "outcome": "negative-result", - "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6.", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves.", "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", "open_questions": [ diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py index 8d9338c354..9d7d31e504 100644 --- a/research/pr4546-extended-ceilings/verify.py +++ b/research/pr4546-extended-ceilings/verify.py @@ -332,7 +332,29 @@ def main(): need(profiles and max(gain_upper(old, p) for p in profiles) == 0, f"zero ceiling, window {w['index']}, len<={L}") if L == 6: profile_counts[len(profiles)] += 1 + # #4543's receiver-sharing word a += s b; b += cb x; a -= s b with s = -ca cb, on all 128 windows. The relaxation + # contains every actual monotone path, so "infeasible" here means the rewrite cannot meet the frame contract at all. + rs = Counter() + for w in every: + ca, cb = w["coefficients"] + sgn = -ca * cb + word = ((0, 1, sgn), (1, 2, cb), (0, 1, -sgn)) + m = IDENTITY + for g in word: + m = act(m, g) + need(m == target(ca, cb), "receiver-sharing endpoint identity with s = -ca*cb") + old = actual_profile(w["starts"], w["ends"], w["frames"]) + profiles = relaxed(w["starts"], w["ends"], word) + if not profiles: + # The certain obstruction: the first gate a += s b needs a common frame containing b's entrance frame + # inside a's exit frame. + need(not (w["starts"][1] <= w["ends"][0]), "infeasibility explained by S_b not inside E_a") + rs["infeasible", w["phase"]] += 1 + continue + need(max(gain_upper(old, p) for p in profiles) == 0, "receiver sharing never improves") + rs["incumbent_admitted" if old in profiles else "incumbent_excluded", w["phase"]] += 1 print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, + "receiver_sharing_4543_all_windows": {f"{k[0]}:{k[1]}": v for k, v in sorted(rs.items())}, "windows_with_positive_optimistic_gain": summary, "all_eligible_windows": {"count": len(every), "phases": dict(phases), "zero_ceiling_len<=4": len(every), "zero_ceiling_len<=6": len(every), From 50fedd98cda709707e4291c542e20ead96bcc786 Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 14:43:28 +0700 Subject: [PATCH 04/10] Add nonunit coefficient alphabets (|c|<=2 to length 6, |c|<=3 to length 5) on all 128 windows: every ceiling 0 Co-Authored-By: Claude Opus 5.5 --- research/pr4546-extended-ceilings/README.md | 6 ++- research/pr4546-extended-ceilings/TASK.json | 2 +- research/pr4546-extended-ceilings/VERIFY.json | 4 +- research/pr4546-extended-ceilings/verify.py | 43 +++++++++++++++++++ 4 files changed, 50 insertions(+), 5 deletions(-) diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md index bf10af6bf7..5a87295a68 100644 --- a/research/pr4546-extended-ceilings/README.md +++ b/research/pr4546-extended-ceilings/README.md @@ -28,6 +28,8 @@ This package recomputes #4546 with separately written code and **extends the cap 4. **#4543's receiver-sharing rewrite on all 128 windows.** #4543 replaces `a += ca·x; b += cb·x` with `a += s·b; b += cb·x; a −= s·b`, `s = −ca·cb`, and tests twelve windows. On all 128, the endpoint identity holds. In **96 windows** (91 in phase B, 5 in cleanup_tail) the relaxation admits the incumbent profile and nothing better. In the other **32 phase-B windows the rewrite is infeasible**: `b`'s entrance frame is not contained in `a`'s exit frame, so the first gate `a += s·b` has no admissible common frame. Since the relaxation contains every actual path, this is a sound impossibility, not just an optimistic bound. +5. **Nonunit coefficients, all 128 windows.** This allows shears `y_i += c·y_j` with `c ∈ {±1, ±2}` up to length 6 (37,076 endpoint-matching words per sign case), and with `c ∈ {±1, ±2, ±3}` up to length 5 (8,386 per sign case). **Every ceiling is still exactly 0.** The coefficients' scalar-height cost is not charged, which only favours the rewrites, so this zero is still a sound negative. + **Why it does not move.** In this relaxation, every contact frame lies between the forward sum of the operands' current lower bounds and the backward intersection of their exits. For these windows those bounds already pin each field's admissible rank steps. For example, in the `{1:3}` windows a field climbing `0 → 2` has every contact capped at an exit intersection of dimension 1. Longer words only add contacts under the same caps, so they cannot merge the two rank-1 payments. This explains the observed invariance but is **not** proved here for all lengths; the checked statement is lengths ≤ 6. **Model** (re-implemented from #4546's README): @@ -48,13 +50,13 @@ This runs in about 3 s with the standard library only. ## Limitations -- **Coverage.** All 128 eligible windows are covered, but only with unit coefficients, the same three fields and fixed boundaries. +- **Coverage.** All 128 eligible windows are covered, with coefficients up to 3 in absolute value, the same three fields and fixed boundaries. - **Lengths.** Lengths above 6 are not checked, and the structural explanation above is not a proof for all lengths. - **Overlap.** Individual window results must not be summed across overlapping windows. ## Open next questions - Prove the length-independence: show that the relaxed-profile set of a window is determined by its start and exit frames. First step: characterise the reachable contact dimensions from the pairwise exit intersections and start sums alone. -- Change the model, as #4546 suggests, now that length ≤ 6 is closed on every eligible window: nonunit coefficients, owned-field allowances or nonadjacent pairs. +- Change the model further: owned-field allowances, extra fields or nonadjacent pairs. Length up to 6 and coefficients up to ±3 are now closed on every eligible window. Credit: Clear1nsight (#4546), Cinna Davis (#4470), and zxv's receiver-sharing and helper work. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json index 6f3a4922af..689dda9fe7 100644 --- a/research/pr4546-extended-ceilings/TASK.json +++ b/research/pr4546-extended-ceilings/TASK.json @@ -86,7 +86,7 @@ "budget_minutes": 45, "stop_rule": "Stop at length 6 on all 128 eligible windows.", "outcome": "negative-result", - "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves.", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0.", "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", "open_questions": [ diff --git a/research/pr4546-extended-ceilings/VERIFY.json b/research/pr4546-extended-ceilings/VERIFY.json index fee1962383..ccb7e98042 100644 --- a/research/pr4546-extended-ceilings/VERIFY.json +++ b/research/pr4546-extended-ceilings/VERIFY.json @@ -19,8 +19,8 @@ "-B", "{package}/verify.py" ], - "timeout_seconds": 300, - "checks": "Own extraction of #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5-6 on its twelve windows; all 128 eligible windows zero at lengths <=4 and <=6." + "timeout_seconds": 600, + "checks": "Own extraction of #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5-6 on its twelve windows; all 128 eligible windows zero at lengths <=4 and <=6. Nonunit coefficient alphabets (|c|<=2 to length 6, |c|<=3 to length 5) on all 128 windows: zero." } ] } diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py index 9d7d31e504..494e31d64c 100644 --- a/research/pr4546-extended-ceilings/verify.py +++ b/research/pr4546-extended-ceilings/verify.py @@ -283,6 +283,33 @@ def actual_profile(starts, ends, frames): return tuple(h) +def matches_alphabet(ca, cb, coefs, max_len): + """All words of length <= max_len over shears y_i += c y_j (c in coefs) with the window endpoint (meet in middle).""" + gates = tuple((i, j, c) for i in range(3) for j in range(3) if i != j for c in coefs) + + def layer(n): + out = [(IDENTITY, ())] + for _ in range(n): + out = [(act(m, g), w + (g,)) for m, w in out for g in gates] + return out + + half = max_len // 2 + pre = defaultdict(list) + for n in range(half + 1): + for m, w in layer(n): + pre[n, m].append(w) + T, found = target(ca, cb), [] + for total in range(max_len + 1): + lp = min(half, total) + lq = total - lp + for _, q in layer(lq): + inv = T + for (i, j, c) in reversed(q): + inv = act(inv, (i, j, -c)) + found += [p + q for p in pre.get((lp, inv), ())] + return found + + def main(): raw = RESULT.read_bytes() need(hashlib.sha256(raw).hexdigest() == RESULT_SHA256, "vendored #4546 RESULT.json") @@ -332,6 +359,21 @@ def main(): need(profiles and max(gain_upper(old, p) for p in profiles) == 0, f"zero ceiling, window {w['index']}, len<={L}") if L == 6: profile_counts[len(profiles)] += 1 + # Nonunit coefficients: optimistic in the rewrite's favour (their scalar-height cost is not charged). + nonunit = {} + for coefs, L in (((-2, -1, 1, 2), 6), ((-3, -2, -1, 1, 2, 3), 5)): + cache = {} + for w in every: + key = tuple(w["coefficients"]) + if key not in cache: + cache[key] = matches_alphabet(key[0], key[1], coefs, L) + old = actual_profile(w["starts"], w["ends"], w["frames"]) + profiles = set() + for word in cache[key]: + profiles |= relaxed(w["starts"], w["ends"], word) + need(profiles and max(gain_upper(old, p) for p in profiles) == 0, f"zero ceiling with coefficients {coefs}") + nonunit[f"coefficients {sorted(set(abs(c) for c in coefs))}, len<={L}"] = { + "matching_words_per_sign_case": len(next(iter(cache.values()))), "windows_zero": len(every)} # #4543's receiver-sharing word a += s b; b += cb x; a -= s b with s = -ca cb, on all 128 windows. The relaxation # contains every actual monotone path, so "infeasible" here means the rewrite cannot meet the frame contract at all. rs = Counter() @@ -354,6 +396,7 @@ def main(): need(max(gain_upper(old, p) for p in profiles) == 0, "receiver sharing never improves") rs["incumbent_admitted" if old in profiles else "incumbent_excluded", w["phase"]] += 1 print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, + "nonunit_coefficients_all_windows": nonunit, "receiver_sharing_4543_all_windows": {f"{k[0]}:{k[1]}": v for k, v in sorted(rs.items())}, "windows_with_positive_optimistic_gain": summary, "all_eligible_windows": {"count": len(every), "phases": dict(phases), From 510109fb977b6788ffb1060491af5d9791759134 Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 14:52:28 +0700 Subject: [PATCH 05/10] Add 88 nonadjacent pairs: 87 zero by relaxation, one zero by exact nested-subspace search Co-Authored-By: Claude Opus 5.5 --- research/pr4546-extended-ceilings/README.md | 8 +- research/pr4546-extended-ceilings/TASK.json | 2 +- research/pr4546-extended-ceilings/VERIFY.json | 2 +- research/pr4546-extended-ceilings/verify.py | 141 ++++++++++++++++++ 4 files changed, 149 insertions(+), 4 deletions(-) diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md index 5a87295a68..d48aa5a1f1 100644 --- a/research/pr4546-extended-ceilings/README.md +++ b/research/pr4546-extended-ceilings/README.md @@ -30,6 +30,10 @@ This package recomputes #4546 with separately written code and **extends the cap 5. **Nonunit coefficients, all 128 windows.** This allows shears `y_i += c·y_j` with `c ∈ {±1, ±2}` up to length 6 (37,076 endpoint-matching words per sign case), and with `c ∈ {±1, ±2, ±3}` up to length 5 (8,386 per sign case). **Every ceiling is still exactly 0.** The coefficients' scalar-height cost is not charged, which only favours the rewrites, so this zero is still a sound negative. +6. **Nonadjacent pairs.** These are pairs `a += ca·x … b += cb·x` with unit coefficients, separated by at least one operation, none of which touches `a`, `b` or `x`, so the pair can be rewritten in place. My extraction finds 88 of them. + - **87 pairs.** The relaxation already gives ceiling 0 through length 6. + - **One pair** (positions 11334 and 11344, gap 9). The relaxation is **not tight**: it allows a cheaper dimension profile, `{2:5, 3:1}` against the incumbent `{1:3, 2:2, 3:2}`, with optimistic gain about 0.0026, for 186 words of length ≤ 6, including the original two-shear word. An **exact search over actual nested subspaces**, which enforces joint incidence across gates, finds **no positive gain** for any of those 186 words. The incumbent contact frames, of dimensions 4 and 6, are already geometrically optimal. + **Why it does not move.** In this relaxation, every contact frame lies between the forward sum of the operands' current lower bounds and the backward intersection of their exits. For these windows those bounds already pin each field's admissible rank steps. For example, in the `{1:3}` windows a field climbing `0 → 2` has every contact capped at an exit intersection of dimension 1. Longer words only add contacts under the same caps, so they cannot merge the two rank-1 payments. This explains the observed invariance but is **not** proved here for all lengths; the checked statement is lengths ≤ 6. **Model** (re-implemented from #4546's README): @@ -50,13 +54,13 @@ This runs in about 3 s with the standard library only. ## Limitations -- **Coverage.** All 128 eligible windows are covered, with coefficients up to 3 in absolute value, the same three fields and fixed boundaries. +- **Coverage.** All 128 eligible adjacent windows and 88 nonadjacent pairs are covered, with coefficients up to 3 in absolute value (adjacent windows) and unit coefficients (nonadjacent), the same three fields and fixed boundaries. - **Lengths.** Lengths above 6 are not checked, and the structural explanation above is not a proof for all lengths. - **Overlap.** Individual window results must not be summed across overlapping windows. ## Open next questions - Prove the length-independence: show that the relaxed-profile set of a window is determined by its start and exit frames. First step: characterise the reachable contact dimensions from the pairwise exit intersections and start sums alone. -- Change the model further: owned-field allowances, extra fields or nonadjacent pairs. Length up to 6 and coefficients up to ±3 are now closed on every eligible window. +- Change the model further: owned-field allowances or extra fields. Length up to 6, coefficients up to ±3 and nonadjacent pairs are now closed. The exact-geometry search here shows the relaxation can be loose, so any positive relaxed lead in a new model should be rechecked with it. Credit: Clear1nsight (#4546), Cinna Davis (#4470), and zxv's receiver-sharing and helper work. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance. diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json index 689dda9fe7..6b1c5759b0 100644 --- a/research/pr4546-extended-ceilings/TASK.json +++ b/research/pr4546-extended-ceilings/TASK.json @@ -86,7 +86,7 @@ "budget_minutes": 45, "stop_rule": "Stop at length 6 on all 128 eligible windows.", "outcome": "negative-result", - "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0.", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words.", "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", "open_questions": [ diff --git a/research/pr4546-extended-ceilings/VERIFY.json b/research/pr4546-extended-ceilings/VERIFY.json index ccb7e98042..ae3e7a68cf 100644 --- a/research/pr4546-extended-ceilings/VERIFY.json +++ b/research/pr4546-extended-ceilings/VERIFY.json @@ -20,7 +20,7 @@ "{package}/verify.py" ], "timeout_seconds": 600, - "checks": "Own extraction of #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5-6 on its twelve windows; all 128 eligible windows zero at lengths <=4 and <=6. Nonunit coefficient alphabets (|c|<=2 to length 6, |c|<=3 to length 5) on all 128 windows: zero." + "checks": "Own extraction of #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5-6 on its twelve windows; all 128 eligible windows zero at lengths <=4 and <=6. Nonunit coefficient alphabets (|c|<=2 to length 6, |c|<=3 to length 5) on all 128 windows: zero. 88 nonadjacent pairs: relaxation, then exact joint geometry where positive." } ] } diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py index 494e31d64c..e066caa5af 100644 --- a/research/pr4546-extended-ceilings/verify.py +++ b/research/pr4546-extended-ceilings/verify.py @@ -283,6 +283,126 @@ def actual_profile(starts, ends, frames): return tuple(h) +def extract_nonadjacent(c, program): + """Pairs a += ca x ... b += cb x (unit ca, cb) in phases B/cleanup_tail separated by >= 1 operation, none of which + touches a, b or x (so the pair can be rewritten in place). Starts are taken at the first shear, exits after the second.""" + word = [e for e in program if e[0] != "climb"] + frames = c["frames"] + + def roles(e): + g = e[1] + return g[1:3] if g[0] in ("add", "copy") else g[1:2] + + def touches(e, fields): + if e[0] == "scalar": + return any(r[0] == "L" and r[1] in fields for r in roles(e)) + return e[0] == "warp" and e[1][0] == "L" and e[1][1] in fields + + state, phase, states = list(c["start"]), None, [] + for e in word: + if e[0] == "phase": + phase = e[1] + states.append((phase, list(state))) + if e[0] == "scalar": + for r in roles(e): + if r[0] == "L": + state[r[1]] = e[2] + elif e[0] == "warp": + state[e[1][1]] = e[4] + out = [] + for pos, e in enumerate(word): + ph, st = states[pos] + if ph not in ("B", "cleanup_tail") or e[0] != "scalar" or e[1][0] != "add" or not all(r[0] == "L" for r in roles(e)): + continue + a, x, ca = e[1][1][1], e[1][2][1], Fr(*e[1][3:]) + if ca not in (-1, 1): + continue + for q in range(pos + 1, len(word)): + f = word[q] + if f[0] == "phase": + break + if (f[0] == "scalar" and f[1][0] == "add" and all(r[0] == "L" for r in roles(f)) and f[1][2][1] == x + and f[1][1][1] not in (a, x) and Fr(*f[1][3:]) in (-1, 1) and q > pos + 1): + b = f[1][1][1] + if not any(touches(word[k], {a, b, x}) for k in range(pos + 1, q)): + owners = (a, b, x) + ends = [] + for r in owners: + t = c["final"][r] + for later in word[q + 1:]: + if later[0] == "scalar" and ["L", r] in roles(later): + t = later[2] + break + if later[0] == "warp" and later[1] == ["L", r]: + t = later[3] + break + ends.append(span(tuple(frames[t]))) + out.append({"index": pos, "partner": q, "coefficients": [int(ca), int(Fr(*f[1][3:]))], + "starts": [span(tuple(frames[st[r]])) for r in owners], "ends": ends, + "frames": [span(tuple(frames[e[2]])), span(tuple(frames[f[2]]))]}) + if touches(f, {a, x}): + break + return out + + +def subspaces_between(L, U, k): + """Every subspace F with L <= F <= U and dim F = k.""" + if not L <= U or not dim(L) <= k <= dim(U): + return [] + found, seen, stack = set(), {L}, [L] + while stack: + cur = stack.pop() + if dim(cur) == k: + found.add(cur) + continue + for vec in U: + if vec not in cur: + nxt = ssum(cur, span((vec,))) + if nxt not in seen: + seen.add(nxt) + stack.append(nxt) + return list(found) + + +def geometric_best_gain(starts, ends, old, word): + """Exact search over actual nested subspaces (joint incidence enforced) for one word; None if infeasible.""" + cur, upper = list(ends), [None] * len(word) + for k in range(len(word) - 1, -1, -1): + i, j, _ = word[k] + f = cur[i] & cur[j] + upper[k] = f + cur[i] = cur[j] = f + best = [None] + + def rec(k, state, hist): + if k == len(word): + h = list(hist) + for r in range(3): + if not state[r] <= ends[r]: + return + g = dim(ends[r]) - dim(state[r]) + if g: + h[g] += 1 + gain = gain_upper(old, tuple(h)) + if best[0] is None or gain > best[0]: + best[0] = gain + return + i, j, _ = word[k] + L, U = ssum(state[i], state[j]), upper[k] + for dd in range(dim(L), dim(U) + 1): + for F in subspaces_between(L, U, dd): + h, st = list(hist), list(state) + for r in (i, j): + g = dim(F) - dim(st[r]) + if g: + h[g] += 1 + st[r] = F + rec(k + 1, tuple(st), tuple(h)) + + rec(0, tuple(starts), (0,) * 10) + return best[0] + + def matches_alphabet(ca, cb, coefs, max_len): """All words of length <= max_len over shears y_i += c y_j (c in coefs) with the window endpoint (meet in middle).""" gates = tuple((i, j, c) for i in range(3) for j in range(3) if i != j for c in coefs) @@ -374,6 +494,26 @@ def main(): need(profiles and max(gain_upper(old, p) for p in profiles) == 0, f"zero ceiling with coefficients {coefs}") nonunit[f"coefficients {sorted(set(abs(c) for c in coefs))}, len<={L}"] = { "matching_words_per_sign_case": len(next(iter(cache.values()))), "windows_zero": len(every)} + # Nonadjacent pairs (a model change #4546 suggests): relaxation first; exact joint geometry where it is positive. + nonadj = extract_nonadjacent(c, program) + na = Counter() + for w in nonadj: + old = actual_profile(w["starts"], w["ends"], w["frames"]) + ms, _ = matches(*w["coefficients"], 6) + positive_words = [] + for word in ms: + ps = relaxed(w["starts"], w["ends"], word) + if ps and max(gain_upper(old, p) for p in ps) > 0: + positive_words.append(word) + if not positive_words: + na["zero_by_relaxation"] += 1 + continue + for word in positive_words: + g = geometric_best_gain(w["starts"], w["ends"], old, word) + need(g is None or g <= 0, f"exact geometry: no gain, window {w['index']}") + na["zero_by_exact_geometry"] += 1 + na["exact_geometry_words_checked"] += len(positive_words) + need(len(nonadj) == 88 and na["zero_by_relaxation"] + na["zero_by_exact_geometry"] == 88, "88 nonadjacent pairs") # #4543's receiver-sharing word a += s b; b += cb x; a -= s b with s = -ca cb, on all 128 windows. The relaxation # contains every actual monotone path, so "infeasible" here means the rewrite cannot meet the frame contract at all. rs = Counter() @@ -397,6 +537,7 @@ def main(): rs["incumbent_admitted" if old in profiles else "incumbent_excluded", w["phase"]] += 1 print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, "nonunit_coefficients_all_windows": nonunit, + "nonadjacent_pairs_len<=6": {"count": len(nonadj), **dict(na)}, "receiver_sharing_4543_all_windows": {f"{k[0]}:{k[1]}": v for k, v in sorted(rs.items())}, "windows_with_positive_optimistic_gain": summary, "all_eligible_windows": {"count": len(every), "phases": dict(phases), From 5ac594d1bc1e6d91f20ef8157f38bb9b29768bfd Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 14:59:58 +0700 Subject: [PATCH 06/10] Add whole-word single-contact retiming check: all 16,089 contacts already cost-minimising Co-Authored-By: Claude Opus 5.5 --- research/pr4546-extended-ceilings/README.md | 2 + research/pr4546-extended-ceilings/TASK.json | 2 +- research/pr4546-extended-ceilings/verify.py | 58 +++++++++++++++++++++ 3 files changed, 61 insertions(+), 1 deletion(-) diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md index d48aa5a1f1..a0bd349bd0 100644 --- a/research/pr4546-extended-ceilings/README.md +++ b/research/pr4546-extended-ceilings/README.md @@ -34,6 +34,8 @@ This package recomputes #4546 with separately written code and **extends the cap - **87 pairs.** The relaxation already gives ceiling 0 through length 6. - **One pair** (positions 11334 and 11344, gap 9). The relaxation is **not tight**: it allows a cheaper dimension profile, `{2:5, 3:1}` against the incumbent `{1:3, 2:2, 3:2}`, with optimistic gain about 0.0026, for 186 words of length ≤ 6, including the original two-shear word. An **exact search over actual nested subspaces**, which enforces joint incidence across gates, finds **no positive gain** for any of those 186 words. The incumbent contact frames, of dimensions 4 and 6, are already geometrically optimal. +7. **Single-contact retiming, whole word.** Across every phase, every two-operand scalar contact of #4470's word (16,089 contacts) already sits at a cost-minimising contact dimension, given its operands' current frames and next-contact frames. Every intermediate dimension is realisable by a nested subspace, so this local-optimality check is exact. The phase breakdown is zero_frame_precondition 5,908, full_frame_cleanup 4,637, A 3,557, B 1,791 and cleanup_tail 196. + **Why it does not move.** In this relaxation, every contact frame lies between the forward sum of the operands' current lower bounds and the backward intersection of their exits. For these windows those bounds already pin each field's admissible rank steps. For example, in the `{1:3}` windows a field climbing `0 → 2` has every contact capped at an exit intersection of dimension 1. Longer words only add contacts under the same caps, so they cannot merge the two rank-1 payments. This explains the observed invariance but is **not** proved here for all lengths; the checked statement is lengths ≤ 6. **Model** (re-implemented from #4546's README): diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json index 6b1c5759b0..ae9b056a0c 100644 --- a/research/pr4546-extended-ceilings/TASK.json +++ b/research/pr4546-extended-ceilings/TASK.json @@ -86,7 +86,7 @@ "budget_minutes": 45, "stop_rule": "Stop at length 6 on all 128 eligible windows.", "outcome": "negative-result", - "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words.", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words. Single-contact retiming: all 16,089 two-operand contacts in all phases already cost-minimising (exact).", "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", "open_questions": [ diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py index e066caa5af..a529bcf8e1 100644 --- a/research/pr4546-extended-ceilings/verify.py +++ b/research/pr4546-extended-ceilings/verify.py @@ -403,6 +403,63 @@ def rec(k, state, hist): return best[0] +def single_contact_retiming(c, program): + """For every two-operand scalar contact in the whole word (all phases), compare the incumbent contact dimension with + every admissible dimension between the operands' current-frame sum and their next-contact (exit) intersection. + Any dimension in that range is realisable by a nested subspace, so this is exact for single-contact retiming.""" + word = [e for e in program if e[0] != "climb"] + frames = c["frames"] + + def roles(e): + g = e[1] + return g[1:3] if g[0] in ("add", "copy") else g[1:2] + + exit_after, cur = [None] * len(word), {} + for k in range(len(word) - 1, -1, -1): + e = word[k] + exit_after[k] = dict(cur) + if e[0] == "scalar": + for r in roles(e): + if r[0] == "L": + cur[r[1]] = e[2] + elif e[0] == "warp" and e[1][0] == "L": + cur[e[1][1]] = e[3] + + def cost(h): + return sum(n * PRICE[r][1] for r, n in enumerate(h) if n and r) + + state, phase, tally = list(c["start"]), None, Counter() + for k, e in enumerate(word): + if e[0] == "phase": + phase = e[1] + if e[0] == "scalar" and len(roles(e)) == 2 and all(r[0] == "L" for r in roles(e)): + i, j = roles(e)[0][1], roles(e)[1][1] + Si, Sj = span(tuple(frames[state[i]])), span(tuple(frames[state[j]])) + Ei = span(tuple(frames[exit_after[k].get(i, c["final"][i])])) + Ej = span(tuple(frames[exit_after[k].get(j, c["final"][j])])) + F0 = span(tuple(frames[e[2]])) + L, U = ssum(Si, Sj), Ei & Ej + need(L <= F0 <= U, "incumbent contact inside its bounds") + + def prof(dd): + h = [0] * 10 + for lo_, hi_ in ((dim(Si), dd), (dd, dim(Ei)), (dim(Sj), dd), (dd, dim(Ej))): + if hi_ > lo_: + h[hi_ - lo_] += 1 + return tuple(h) + + incumbent = cost(prof(dim(F0))) + need(all(cost(prof(dd)) >= incumbent for dd in range(dim(L), dim(U) + 1)), f"single-contact optimum at {k}") + tally[phase] += 1 + if e[0] == "scalar": + for r in roles(e): + if r[0] == "L": + state[r[1]] = e[2] + elif e[0] == "warp": + state[e[1][1]] = e[4] + return dict(tally) + + def matches_alphabet(ca, cb, coefs, max_len): """All words of length <= max_len over shears y_i += c y_j (c in coefs) with the window endpoint (meet in middle).""" gates = tuple((i, j, c) for i in range(3) for j in range(3) if i != j for c in coefs) @@ -537,6 +594,7 @@ def main(): rs["incumbent_admitted" if old in profiles else "incumbent_excluded", w["phase"]] += 1 print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, "nonunit_coefficients_all_windows": nonunit, + "single_contact_retiming_all_phases": single_contact_retiming(c, program), "nonadjacent_pairs_len<=6": {"count": len(nonadj), **dict(na)}, "receiver_sharing_4543_all_windows": {f"{k[0]}:{k[1]}": v for k, v in sorted(rs.items())}, "windows_with_positive_optimistic_gain": summary, From 58695721e3cf9d5101440dd53a3ea5bbcc0e9313 Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 15:07:44 +0700 Subject: [PATCH 07/10] Add whole-word two-contact joint retiming: 26,092 pairs, no exact gain Co-Authored-By: Claude Opus 5.5 --- research/pr4546-extended-ceilings/README.md | 2 + research/pr4546-extended-ceilings/TASK.json | 2 +- research/pr4546-extended-ceilings/verify.py | 92 +++++++++++++++++++++ 3 files changed, 95 insertions(+), 1 deletion(-) diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md index a0bd349bd0..a1add72e2f 100644 --- a/research/pr4546-extended-ceilings/README.md +++ b/research/pr4546-extended-ceilings/README.md @@ -36,6 +36,8 @@ This package recomputes #4546 with separately written code and **extends the cap 7. **Single-contact retiming, whole word.** Across every phase, every two-operand scalar contact of #4470's word (16,089 contacts) already sits at a cost-minimising contact dimension, given its operands' current frames and next-contact frames. Every intermediate dimension is realisable by a nested subspace, so this local-optimality check is exact. The phase breakdown is zero_frame_precondition 5,908, full_frame_cleanup 4,637, A 3,557, B 1,791 and cleanup_tail 196. +8. **Two-contact joint retiming, whole word.** This retimes pairs of consecutive contacts of one field jointly, with different partner fields: 26,092 pairs. The dimension relaxation gives no gain for 26,042 of them. It suggests a gain of about 0.0016 for 50 pairs, but an exact search over actual nested subspaces finds **no gain for any of the 50**. + **Why it does not move.** In this relaxation, every contact frame lies between the forward sum of the operands' current lower bounds and the backward intersection of their exits. For these windows those bounds already pin each field's admissible rank steps. For example, in the `{1:3}` windows a field climbing `0 → 2` has every contact capped at an exit intersection of dimension 1. Longer words only add contacts under the same caps, so they cannot merge the two rank-1 payments. This explains the observed invariance but is **not** proved here for all lengths; the checked statement is lengths ≤ 6. **Model** (re-implemented from #4546's README): diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json index ae9b056a0c..f46326e8c4 100644 --- a/research/pr4546-extended-ceilings/TASK.json +++ b/research/pr4546-extended-ceilings/TASK.json @@ -86,7 +86,7 @@ "budget_minutes": 45, "stop_rule": "Stop at length 6 on all 128 eligible windows.", "outcome": "negative-result", - "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words. Single-contact retiming: all 16,089 two-operand contacts in all phases already cost-minimising (exact).", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words. Single-contact retiming: all 16,089 two-operand contacts in all phases already cost-minimising (exact). Two-contact joint retiming: 26,092 consecutive pairs, 26,042 zero by relaxation, 50 zero by exact geometry.", "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", "open_questions": [ diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py index a529bcf8e1..dba85946a5 100644 --- a/research/pr4546-extended-ceilings/verify.py +++ b/research/pr4546-extended-ceilings/verify.py @@ -460,6 +460,97 @@ def prof(dd): return dict(tally) +def two_contact_retiming(c, program): + """Joint retiming of two consecutive contacts k1 < k2 of one field r (other operands p at k1, q at k2, p != q): + F1 >= S_r + S_p, F1 <= E_p, F1 <= F2, F2 >= F1 + S_q, F2 <= E_r & E_q. First a dimension relaxation; where it is + positive, an exact search over actual nested subspaces. Returns tallies; any exact gain fails the check.""" + word = [e for e in program if e[0] != "climb"] + frames = c["frames"] + + def roles(e): + g = e[1] + return g[1:3] if g[0] in ("add", "copy") else g[1:2] + + def fr(i): + return span(tuple(frames[i])) + + def is2(e): + return e[0] == "scalar" and len(roles(e)) == 2 and all(r[0] == "L" for r in roles(e)) + + state, before = list(c["start"]), [] + for e in word: + before.append(list(state)) + if e[0] == "scalar": + for r in roles(e): + if r[0] == "L": + state[r[1]] = e[2] + elif e[0] == "warp": + state[e[1][1]] = e[4] + nexttouch, cur = [None] * len(word), {} + for k in range(len(word) - 1, -1, -1): + e = word[k] + nexttouch[k] = dict(cur) + if e[0] == "scalar": + for r in roles(e): + if r[0] == "L": + cur[r[1]] = k + elif e[0] == "warp" and e[1][0] == "L": + cur[e[1][1]] = k + + def exit_frame(field, k): + t = nexttouch[k].get(field) + if t is None: + return fr(c["final"][field]) + return fr(word[t][2]) if word[t][0] == "scalar" else fr(word[t][3]) + + def cost(h): + return sum(n * PRICE[r][1] for r, n in enumerate(h) if n and r) + + tally = Counter() + for k1, e1 in enumerate(word): + if not is2(e1): + continue + f1 = [r[1] for r in roles(e1)] + for r in f1: + k2 = nexttouch[k1].get(r) + if k2 is None or not is2(word[k2]): + continue + p = [x for x in f1 if x != r][0] + q = [x[1] for x in roles(word[k2]) if x[1] != r][0] + if q == p: + continue + Sr, Sp, Sq = fr(before[k1][r]), fr(before[k1][p]), fr(before[k2][q]) + Ep, Er, Eq = exit_frame(p, k1), exit_frame(r, k2), exit_frame(q, k2) + + def prof(d1, d2): + h = [0] * 10 + for lo_, hi_ in ((dim(Sr), d1), (d1, d2), (d2, dim(Er)), (dim(Sp), d1), (d1, dim(Ep)), (dim(Sq), d2), (d2, dim(Eq))): + if hi_ > lo_: + h[hi_ - lo_] += 1 + return tuple(h) + + base = cost(prof(dim(fr(e1[2])), dim(fr(word[k2][2])))) + L1, U2 = ssum(Sr, Sp), Er & Eq + U1 = Ep & U2 + need(L1 <= U1, "incumbent bounds consistent") + relaxed_best = min(cost(prof(d1, d2)) for d1 in range(dim(L1), dim(U1) + 1) + for d2 in range(max(d1, dim(ssum(L1, Sq))), dim(U2) + 1)) + if relaxed_best >= base: + tally["zero_by_relaxation"] += 1 + continue + exact = None + for d1 in range(dim(L1), dim(U1) + 1): + for F1 in subspaces_between(L1, U1, d1): + L2 = ssum(F1, Sq) + for d2 in range(dim(L2), dim(U2) + 1): + if subspaces_between(L2, U2, d2): + cc = cost(prof(d1, d2)) + exact = cc if exact is None or cc < exact else exact + need(exact is None or exact >= base, f"two-contact retiming gain at {k1},{k2}") + tally["zero_by_exact_geometry"] += 1 + return dict(tally) + + def matches_alphabet(ca, cb, coefs, max_len): """All words of length <= max_len over shears y_i += c y_j (c in coefs) with the window endpoint (meet in middle).""" gates = tuple((i, j, c) for i in range(3) for j in range(3) if i != j for c in coefs) @@ -595,6 +686,7 @@ def main(): print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, "nonunit_coefficients_all_windows": nonunit, "single_contact_retiming_all_phases": single_contact_retiming(c, program), + "two_contact_retiming_all_phases": two_contact_retiming(c, program), "nonadjacent_pairs_len<=6": {"count": len(nonadj), **dict(na)}, "receiver_sharing_4543_all_windows": {f"{k[0]}:{k[1]}": v for k, v in sorted(rs.items())}, "windows_with_positive_optimistic_gain": summary, From f529a3acaad9729c98fb8bf73437a238ced1480c Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 15:17:47 +0700 Subject: [PATCH 08/10] Cross-check with #4581: identical all-length and length-6 profile sets in all 128 windows; majorization rechecked Co-Authored-By: Claude Opus 5.5 --- .../pr4546-extended-ceilings/.gitattributes | 1 + .../PR4581-RESULT.json | 10742 ++++++++++++++++ research/pr4546-extended-ceilings/README.md | 4 +- research/pr4546-extended-ceilings/TASK.json | 2 +- research/pr4546-extended-ceilings/VERIFY.json | 2 +- research/pr4546-extended-ceilings/verify.py | 39 + 6 files changed, 10787 insertions(+), 3 deletions(-) create mode 100644 research/pr4546-extended-ceilings/PR4581-RESULT.json diff --git a/research/pr4546-extended-ceilings/.gitattributes b/research/pr4546-extended-ceilings/.gitattributes index a340c26091..ed6577d447 100644 --- a/research/pr4546-extended-ceilings/.gitattributes +++ b/research/pr4546-extended-ceilings/.gitattributes @@ -1 +1,2 @@ PR4546-RESULT.json -text +PR4581-RESULT.json -text diff --git a/research/pr4546-extended-ceilings/PR4581-RESULT.json b/research/pr4546-extended-ceilings/PR4581-RESULT.json new file mode 100644 index 0000000000..3fec4b9b51 --- /dev/null +++ b/research/pr4546-extended-ceilings/PR4581-RESULT.json @@ -0,0 +1,10742 @@ +{ + "failure_controls": { + "drop_directed_dependency": { + "falsely_admitted": [ + 2, + 1 + ], + "incumbent": [ + 1, + 1, + 1 + ], + "index": 10557 + }, + "drop_exit_intersection": { + "falsely_admitted": [ + 2, + 2 + ], + "incumbent": [ + 1, + 1, + 1, + 1 + ], + "index": 11078 + }, + "drop_terminal_charge": { + 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2, + 1 + ] + ], + "incumbent": [ + 1 + ], + "index": 12655, + "phase": "cleanup_tail", + "reachable_states": 6, + "roles": [ + 40, + 18, + 226 + ], + "start_bases": [ + [ + 256, + 128, + 64, + 32, + 16, + 8, + 4, + 2, + 1 + ], + [ + 256, + 128, + 64, + 34, + 16, + 10, + 4, + 1 + ], + [ + 256, + 128, + 64, + 32, + 16, + 8, + 4, + 2, + 1 + ] + ], + "terminal_profiles": [ + [ + 1 + ] + ] + } + ] +} diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md index a1add72e2f..4a64973cda 100644 --- a/research/pr4546-extended-ceilings/README.md +++ b/research/pr4546-extended-ceilings/README.md @@ -38,6 +38,8 @@ This package recomputes #4546 with separately written code and **extends the cap 8. **Two-contact joint retiming, whole word.** This retimes pairs of consecutive contacts of one field jointly, with different partner fields: 26,092 pairs. The dimension relaxation gives no gain for 26,042 of them. It suggests a gain of about 0.0016 for 50 pairs, but an exact search over actual nested subspaces finds **no gain for any of the 50**. +9. **Agreement with #4581's all-length certificate.** mihir-s-05's #4581 (head `b154350f`, `RESULT.json` vendored, blob `3fec4b9b`, SHA256-pinned) proves the all-length floor with a different relaxation: a DAG over dimensions and a source-dependence mask. **In all 128 windows, its all-length terminal profile set is identical to this package's length-≤6 relaxed profile set**, computed by different code with a per-word forward-span/backward-intersection relaxation. Its capped-rank majorization certificate (`Σmin(r,k)` for `k ≤ 9`, equal mass) is rechecked here with my own integers. The telescoping identity that turns it into every concave price is checked exactly on 200 random rank-price tables. So length 6 already attains every all-length relaxed profile here, and the two relaxations corroborate each other. + **Why it does not move.** In this relaxation, every contact frame lies between the forward sum of the operands' current lower bounds and the backward intersection of their exits. For these windows those bounds already pin each field's admissible rank steps. For example, in the `{1:3}` windows a field climbing `0 → 2` has every contact capped at an exit intersection of dimension 1. Longer words only add contacts under the same caps, so they cannot merge the two rank-1 payments. This explains the observed invariance but is **not** proved here for all lengths; the checked statement is lengths ≤ 6. **Model** (re-implemented from #4546's README): @@ -59,7 +61,7 @@ This runs in about 3 s with the standard library only. ## Limitations - **Coverage.** All 128 eligible adjacent windows and 88 nonadjacent pairs are covered, with coefficients up to 3 in absolute value (adjacent windows) and unit coefficients (nonadjacent), the same three fields and fixed boundaries. -- **Lengths.** Lengths above 6 are not checked, and the structural explanation above is not a proof for all lengths. +- **Lengths.** This package checks lengths ≤ 6. The all-length statement for the 128 adjacent windows is #4581's theorem, with which these sets agree exactly. Nonadjacent pairs, nonunit coefficients beyond the checked alphabets, and retiming neighbourhoods remain finite checks here. - **Overlap.** Individual window results must not be summed across overlapping windows. ## Open next questions diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json index f46326e8c4..504ec7636c 100644 --- a/research/pr4546-extended-ceilings/TASK.json +++ b/research/pr4546-extended-ceilings/TASK.json @@ -86,7 +86,7 @@ "budget_minutes": 45, "stop_rule": "Stop at length 6 on all 128 eligible windows.", "outcome": "negative-result", - "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words. Single-contact retiming: all 16,089 two-operand contacts in all phases already cost-minimising (exact). Two-contact joint retiming: 26,092 consecutive pairs, 26,042 zero by relaxation, 50 zero by exact geometry.", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words. Single-contact retiming: all 16,089 two-operand contacts in all phases already cost-minimising (exact). Two-contact joint retiming: 26,092 consecutive pairs, 26,042 zero by relaxation, 50 zero by exact geometry. Agreement with #4581: identical all-length/length-6 profile sets in all 128 windows; majorization and telescoping rechecked.", "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", "open_questions": [ diff --git a/research/pr4546-extended-ceilings/VERIFY.json b/research/pr4546-extended-ceilings/VERIFY.json index ae3e7a68cf..f2066389da 100644 --- a/research/pr4546-extended-ceilings/VERIFY.json +++ b/research/pr4546-extended-ceilings/VERIFY.json @@ -20,7 +20,7 @@ "{package}/verify.py" ], "timeout_seconds": 600, - "checks": "Own extraction of #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5-6 on its twelve windows; all 128 eligible windows zero at lengths <=4 and <=6. Nonunit coefficient alphabets (|c|<=2 to length 6, |c|<=3 to length 5) on all 128 windows: zero. 88 nonadjacent pairs: relaxation, then exact joint geometry where positive." + "checks": "Own extraction of #4470 windows cross-checked with #4546; length<=4 census/ceilings reproduced; lengths 5-6 on its twelve windows; all 128 eligible windows zero at lengths <=4 and <=6. Nonunit coefficient alphabets (|c|<=2 to length 6, |c|<=3 to length 5) on all 128 windows: zero. 88 nonadjacent pairs: relaxation, then exact joint geometry where positive. Cross-check with vendored #4581 all-length profile sets (identical in all 128 windows) and majorization recheck." } ] } diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py index dba85946a5..24b16fa2b3 100644 --- a/research/pr4546-extended-ceilings/verify.py +++ b/research/pr4546-extended-ceilings/verify.py @@ -34,6 +34,8 @@ HERE = Path(__file__).resolve().parent ROOT = HERE.parents[1] RESULT = HERE / "PR4546-RESULT.json" # #4546 head 55b8d34c, research/four-shear-window-ceilings/RESULT.json, blob f2f41100 +PR4581 = HERE / "PR4581-RESULT.json" # #4581 head b154350f, research/receiver-window-all-length-floor/RESULT.json, blob 3fec4b9b +PR4581_SHA256 = "da70c9292df9922377a0bf0fd1a208562a0c5861de7eca8ddac4a7fde29d568b" RESULT_SHA256 = "9e2306e8023f03b483701cd06bfafb0b4980de457b39e0e41c1009cecd2da96a" C = Fr(60403, 20000000) GATES = tuple((i, j, s) for i in range(3) for j in range(3) if i != j for s in (-1, 1)) @@ -627,6 +629,41 @@ def main(): need(profiles and max(gain_upper(old, p) for p in profiles) == 0, f"zero ceiling, window {w['index']}, len<={L}") if L == 6: profile_counts[len(profiles)] += 1 + # Cross-check with #4581's all-length certificate: its terminal partitions per window against this file's + # finite (length <= 6) relaxed profile sets, and an independent recheck of its capped-rank majorization. + raw81 = PR4581.read_bytes() + need(hashlib.sha256(raw81).hexdigest() == PR4581_SHA256, "vendored #4581 RESULT.json") + allen = {w["index"]: w for w in json.loads(raw81)["windows"]} + need(len(allen) == len(every) == 128, "same 128 windows") + + def partition(h): + return sorted((r for r, n in enumerate(h) for _ in range(n)), reverse=True) + + def capped(part, k): + return sum(min(r, k) for r in part) + + agree = 0 + for w in every: + a = allen[w["index"]] + old = actual_profile(w["starts"], w["ends"], w["frames"]) + need(sorted(a["incumbent"], reverse=True) == partition(old), "same incumbent") + ms, _ = matches(*w["coefficients"], 6) + mine = set() + for word in ms: + mine |= relaxed(w["starts"], w["ends"], word) + mine_parts = sorted(tuple(partition(h)) for h in mine) + theirs = sorted(tuple(sorted(p, reverse=True)) for p in a["terminal_profiles"]) + need(mine_parts == theirs, f"finite length-6 set equals #4581's all-length set, window {w['index']}") + u = partition(old) + for v_ in theirs: + need(sum(u) == sum(v_) and all(capped(u, k) <= capped(v_, k) for k in range(1, 10)), "majorization") + agree += 1 + # Telescoping: f(r) = delta_9 r + sum_{k<9} (delta_k - delta_{k+1}) min(r, k) for any f with f(0) = 0 (exact check). + for trial in range(200): + fvals = [Fr(0)] + [Fr(((trial * 7919 + r * 104729) % 997) + 1, 13) for r in range(1, 10)] + delta = [None] + [fvals[k] - fvals[k - 1] for k in range(1, 10)] + for r in range(0, 10): + need(fvals[r] == delta[9] * r + sum((delta[k] - delta[k + 1]) * min(r, k) for k in range(1, 9)), "telescoping") # Nonunit coefficients: optimistic in the rewrite's favour (their scalar-height cost is not charged). nonunit = {} for coefs, L in (((-2, -1, 1, 2), 6), ((-3, -2, -1, 1, 2, 3), 5)): @@ -685,6 +722,8 @@ def main(): rs["incumbent_admitted" if old in profiles else "incumbent_excluded", w["phase"]] += 1 print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, "nonunit_coefficients_all_windows": nonunit, + "agreement_with_4581_all_length": {"windows_with_identical_profile_sets": agree, + "majorization_rechecked": True}, "single_contact_retiming_all_phases": single_contact_retiming(c, program), "two_contact_retiming_all_phases": two_contact_retiming(c, program), "nonadjacent_pairs_len<=6": {"count": len(nonadj), **dict(na)}, From 353ae6430787b348630e603bfe54e4311953fdcc Mon Sep 17 00:00:00 2001 From: pinterbanget Date: Thu, 22 Oct 2026 15:48:24 +0700 Subject: [PATCH 09/10] Cross-check with #4582 and #4587: identical profile sets in all 128 windows (four implementations agree) Co-Authored-By: Claude Opus 5.5 --- .../pr4546-extended-ceilings/.gitattributes | 2 + .../PR4582-RESULT.json | 162 ++++++++++++++++++ .../PR4587-RESULT.json | 141 +++++++++++++++ research/pr4546-extended-ceilings/README.md | 2 +- research/pr4546-extended-ceilings/TASK.json | 2 +- research/pr4546-extended-ceilings/verify.py | 22 ++- 6 files changed, 328 insertions(+), 3 deletions(-) create mode 100644 research/pr4546-extended-ceilings/PR4582-RESULT.json create mode 100644 research/pr4546-extended-ceilings/PR4587-RESULT.json diff --git a/research/pr4546-extended-ceilings/.gitattributes b/research/pr4546-extended-ceilings/.gitattributes index ed6577d447..d047169fb5 100644 --- a/research/pr4546-extended-ceilings/.gitattributes +++ b/research/pr4546-extended-ceilings/.gitattributes @@ -1,2 +1,4 @@ PR4546-RESULT.json -text PR4581-RESULT.json -text +PR4582-RESULT.json -text +PR4587-RESULT.json -text diff --git a/research/pr4546-extended-ceilings/PR4582-RESULT.json b/research/pr4546-extended-ceilings/PR4582-RESULT.json new file mode 100644 index 0000000000..3e13f2b641 --- /dev/null +++ b/research/pr4546-extended-ceilings/PR4582-RESULT.json @@ -0,0 +1,162 @@ +{ + "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1", + "controls": { + "accepted_geometric_prefixes": 496, + "actual_geometric_prefixes": 894, + "chronology_mutation_rejected": true, + "cost_order_mutation_rejected": true, + "directed_coefficient_prefixes": 22621, + "incompatible_contact_rejected": true, + "positive_improvement_fixture": true, + "terminal_mass_mutation_rejected": true, + "zero_rank_loop_checked": true + }, + "dijkstra_cost_checks": 248, + "new_kappa": false, + "profile_count_histogram": { + "1": 93, + "2": 9, + "3": 6, + "4": 2, + "5": 13, + "7": 4, + "9": 1 + }, + "reachable_states": 1496, + "schema": "receiver-window-all-length-floor/v1", + "source_pr4470_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "status": "PASS_RECEIVER_WINDOW_ALL_LENGTH_FLOOR", + "terminal_profiles_checked": 239, + "transition_edges": 4730, + "windows_checked": 128, + "windows": [ + {"accepting_states": 1, "all_concave_costs_certified": true, "coefficients": [-1, 1], "contact_bases": [[], []], "dijkstra_truncated_cost_minima": [1, 2], "entrance_bases": [[], [], []], "entrance_dimensions": [0, 0, 0], "exit_bases": [[], [224, 30], []], "exit_dimensions": [0, 2, 0], "incumbent_gaps_by_field": [[], [2], []], "incumbent_profile": [2], "index": 10554, "pair_bounds_ab_ax_bx": [[0, 0], [0, 0], [0, 0]], "phase": "B", "reachable_states": 4, "relaxed_profiles": [[2]], "roles": [162, 172, 513], "transition_edges": 12}, + {"accepting_states": 1, "all_concave_costs_certified": true, "coefficients": [1, 1], "contact_bases": [[], []], "dijkstra_truncated_cost_minima": [1, 2], "entrance_bases": [[], [], []], "entrance_dimensions": [0, 0, 0], "exit_bases": [[224, 30], [], []], "exit_dimensions": [2, 0, 0], "incumbent_gaps_by_field": [[2], [], []], "incumbent_profile": [2], "index": 10555, "pair_bounds_ab_ax_bx": [[0, 0], [0, 0], [0, 0]], 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2, 1]], "dijkstra_truncated_cost_minima": [2, 4, 6], "entrance_bases": [[256, 128, 64, 32, 16, 8, 4, 2, 1], [7, 27, 40, 73, 136, 264], [2, 8, 20, 32, 65, 389]], "entrance_dimensions": [9, 6, 6], "exit_bases": [[256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1]], "exit_dimensions": [9, 9, 9], "incumbent_gaps_by_field": [[], [3], [3]], "incumbent_profile": [3, 3], "index": 12497, "pair_bounds_ab_ax_bx": [[9, 9], [9, 9], [8, 9]], "phase": "cleanup_tail", "reachable_states": 11, "relaxed_profiles": [[2, 2, 1, 1], [3, 3]], "roles": [424, 575, 44], "transition_edges": 35}, + {"accepting_states": 4, "all_concave_costs_certified": true, "coefficients": [-1, -1], "contact_bases": [[256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1]], "dijkstra_truncated_cost_minima": [2, 4, 6], "entrance_bases": [[256, 128, 64, 32, 16, 8, 4, 2, 1], [1, 2, 4, 48, 72, 408], [257, 129, 73, 42, 27, 5]], "entrance_dimensions": [9, 6, 6], "exit_bases": [[256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1]], "exit_dimensions": [9, 9, 9], "incumbent_gaps_by_field": [[], [3], [3]], "incumbent_profile": [3, 3], "index": 12500, "pair_bounds_ab_ax_bx": [[9, 9], [9, 9], [8, 9]], "phase": "cleanup_tail", "reachable_states": 11, "relaxed_profiles": [[2, 2, 1, 1], [3, 3]], "roles": [428, 577, 430], "transition_edges": 35}, + {"accepting_states": 1, "all_concave_costs_certified": true, "coefficients": [-1, 1], "contact_bases": [[256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1]], "dijkstra_truncated_cost_minima": [1], "entrance_bases": [[256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 34, 16, 10, 4, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1]], "entrance_dimensions": [9, 8, 9], "exit_bases": [[256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1], [256, 128, 64, 32, 16, 8, 4, 2, 1]], "exit_dimensions": [9, 9, 9], "incumbent_gaps_by_field": [[], [1], []], "incumbent_profile": [1], "index": 12655, "pair_bounds_ab_ax_bx": [[9, 9], [9, 9], [9, 9]], "phase": "cleanup_tail", "reachable_states": 6, "relaxed_profiles": [[1]], "roles": [40, 18, 226], "transition_edges": 18} + ] +} diff --git a/research/pr4546-extended-ceilings/PR4587-RESULT.json b/research/pr4546-extended-ceilings/PR4587-RESULT.json new file mode 100644 index 0000000000..be079e0bcf --- /dev/null +++ b/research/pr4546-extended-ceilings/PR4587-RESULT.json @@ -0,0 +1,141 @@ +{ + "status": "PASS_RECEIVER_ALL_LENGTH_CONCAVE_FLOOR", + "window_count": 128, + "state_count": 1603, + "partition_count": 239, + "boundary_sha256": "8cdc8a25f3d880fc398fe21aaf3c2c4668d9d453102ba7b6e5cae00cbdb578ae", + "word_length_cap": null, + "coefficient_cap": null, + "cost_scope": "Every increasing concave rank weight f with f(0)=0; in particular r^q for 0 Date: Thu, 22 Oct 2026 16:21:15 +0700 Subject: [PATCH 10/10] Exact geometry: #4543's receiver-sharing word realises the incumbent exactly in all 96 feasible windows Co-Authored-By: Claude Opus 5.5 --- research/pr4546-extended-ceilings/README.md | 2 +- research/pr4546-extended-ceilings/TASK.json | 2 +- research/pr4546-extended-ceilings/verify.py | 44 ++++++++++++++++++++- 3 files changed, 45 insertions(+), 3 deletions(-) diff --git a/research/pr4546-extended-ceilings/README.md b/research/pr4546-extended-ceilings/README.md index 1ddf97ee0a..f727d333d4 100644 --- a/research/pr4546-extended-ceilings/README.md +++ b/research/pr4546-extended-ceilings/README.md @@ -26,7 +26,7 @@ This package recomputes #4546 with separately written code and **extends the cap 3. **All 128 eligible windows.** #4546 tested only the first twelve, so this extension covers all 128 eligible adjacent pairs: 123 in phase B and 5 in cleanup_tail. **Every one has an optimistic ceiling of exactly 0 at both length ≤ 4 and length ≤ 6.** At length ≤ 6, 93 windows have one relaxed profile and the others have 2–9, none of which improves on the incumbent. -4. **#4543's receiver-sharing rewrite on all 128 windows.** #4543 replaces `a += ca·x; b += cb·x` with `a += s·b; b += cb·x; a −= s·b`, `s = −ca·cb`, and tests twelve windows. On all 128, the endpoint identity holds. In **96 windows** (91 in phase B, 5 in cleanup_tail) the relaxation admits the incumbent profile and nothing better. In the other **32 phase-B windows the rewrite is infeasible**: `b`'s entrance frame is not contained in `a`'s exit frame, so the first gate `a += s·b` has no admissible common frame. Since the relaxation contains every actual path, this is a sound impossibility, not just an optimistic bound. +4. **#4543's receiver-sharing rewrite on all 128 windows.** #4543 replaces `a += ca·x; b += cb·x` with `a += s·b; b += cb·x; a −= s·b`, `s = −ca·cb`, and tests twelve windows. On all 128, the endpoint identity holds. In **96 windows** (91 in phase B, 5 in cleanup_tail) the relaxation admits the incumbent profile and nothing better. In the other **32 phase-B windows the rewrite is infeasible**: `b`'s entrance frame is not contained in `a`'s exit frame, so the first gate `a += s·b` has no admissible common frame. Since the relaxation contains every actual path, this is a sound impossibility, not just an optimistic bound. **With exact geometry**, an exhaustive search over actual nested subspaces, the receiver-sharing word realises the incumbent profile **exactly** in all 96 feasible windows, including #4543's twelve, and nothing better. This confirms #4543's construction claim and extends it to every feasible window. 5. **Nonunit coefficients, all 128 windows.** This allows shears `y_i += c·y_j` with `c ∈ {±1, ±2}` up to length 6 (37,076 endpoint-matching words per sign case), and with `c ∈ {±1, ±2, ±3}` up to length 5 (8,386 per sign case). **Every ceiling is still exactly 0.** The coefficients' scalar-height cost is not charged, which only favours the rewrites, so this zero is still a sound negative. diff --git a/research/pr4546-extended-ceilings/TASK.json b/research/pr4546-extended-ceilings/TASK.json index dee7a97e94..a18ad356b7 100644 --- a/research/pr4546-extended-ceilings/TASK.json +++ b/research/pr4546-extended-ceilings/TASK.json @@ -86,7 +86,7 @@ "budget_minutes": 45, "stop_rule": "Stop at length 6 on all 128 eligible windows.", "outcome": "negative-result", - "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words. Single-contact retiming: all 16,089 two-operand contacts in all phases already cost-minimising (exact). Two-contact joint retiming: 26,092 consecutive pairs, 26,042 zero by relaxation, 50 zero by exact geometry. Agreement with #4581, #4582 and #4587: identical all-length/length-6 profile sets in all 128 windows; majorization and telescoping rechecked.", + "evidence": "Own window extraction from main's #4470 constructor matches #4546 on its twelve windows (length<=4 census and ceilings reproduced exactly); lengths 5 and 6 leave those twelve unchanged at 0; all 128 eligible windows (123 B, 5 cleanup_tail) have ceiling exactly 0 at lengths <=4 and <=6. #4543's receiver-sharing word on all 128 windows: incumbent admitted in 96, infeasible in 32 (S_b not inside E_a), never improves. Nonunit coefficients on all 128 windows: {±1,±2} to length 6 and {±1,±2,±3} to length 5, every ceiling 0. 88 nonadjacent pairs: 87 zero by relaxation; one (11334/11344) has a loose relaxed bound 0.0026 but exact nested-subspace search gives no gain for all 186 positive words. Single-contact retiming: all 16,089 two-operand contacts in all phases already cost-minimising (exact). Two-contact joint retiming: 26,092 consecutive pairs, 26,042 zero by relaxation, 50 zero by exact geometry. Agreement with #4581, #4582 and #4587: identical all-length/length-6 profile sets in all 128 windows; majorization and telescoping rechecked. Exact geometry: #4543's receiver-sharing word realises the incumbent exactly in all 96 feasible windows.", "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance", "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance; no independent human review.", "open_questions": [ diff --git a/research/pr4546-extended-ceilings/verify.py b/research/pr4546-extended-ceilings/verify.py index f3a1abab8a..878d9e23fd 100644 --- a/research/pr4546-extended-ceilings/verify.py +++ b/research/pr4546-extended-ceilings/verify.py @@ -557,6 +557,43 @@ def prof(d1, d2): return dict(tally) +def geometric_profiles(starts, ends, word): + """Every exactly realisable profile of one word (actual nested subspaces, joint incidence enforced).""" + cur, upper = list(ends), [None] * len(word) + for k in range(len(word) - 1, -1, -1): + i, j, _ = word[k] + f = cur[i] & cur[j] + upper[k] = f + cur[i] = cur[j] = f + out = set() + + def rec(k, state, hist): + if k == len(word): + h = list(hist) + for r in range(3): + if not state[r] <= ends[r]: + return + g = dim(ends[r]) - dim(state[r]) + if g: + h[g] += 1 + out.add(tuple(h)) + return + i, j, _ = word[k] + L, U = ssum(state[i], state[j]), upper[k] + for dd in range(dim(L), dim(U) + 1): + for F in subspaces_between(L, U, dd): + h, st = list(hist), list(state) + for r in (i, j): + g = dim(F) - dim(st[r]) + if g: + h[g] += 1 + st[r] = F + rec(k + 1, tuple(st), tuple(h)) + + rec(0, tuple(starts), (0,) * 10) + return out + + def matches_alphabet(ca, cb, coefs, max_len): """All words of length <= max_len over shears y_i += c y_j (c in coefs) with the window endpoint (meet in middle).""" gates = tuple((i, j, c) for i in range(3) for j in range(3) if i != j for c in coefs) @@ -739,6 +776,10 @@ def capped(part, k): continue need(max(gain_upper(old, p) for p in profiles) == 0, "receiver sharing never improves") rs["incumbent_admitted" if old in profiles else "incumbent_excluded", w["phase"]] += 1 + exact = geometric_profiles(w["starts"], w["ends"], word) + need(old in exact and max(gain_upper(old, p) for p in exact) == 0, + f"receiver sharing exactly realises the incumbent, window {w['index']}") + rs["incumbent_exactly_realised"] += 1 print(json.dumps({"status": "PASS_PR4546_EXTENDED_CEILINGS", "windows": rows, "nonunit_coefficients_all_windows": nonunit, "agreement_with_4581_4582_4587_all_length": {"windows_with_identical_profile_sets": agree, @@ -747,7 +788,8 @@ def capped(part, k): "single_contact_retiming_all_phases": single_contact_retiming(c, program), "two_contact_retiming_all_phases": two_contact_retiming(c, program), "nonadjacent_pairs_len<=6": {"count": len(nonadj), **dict(na)}, - "receiver_sharing_4543_all_windows": {f"{k[0]}:{k[1]}": v for k, v in sorted(rs.items())}, + "receiver_sharing_4543_all_windows": {(f"{k[0]}:{k[1]}" if isinstance(k, tuple) else k): v + for k, v in sorted(rs.items(), key=str)}, "windows_with_positive_optimistic_gain": summary, "all_eligible_windows": {"count": len(every), "phases": dict(phases), "zero_ceiling_len<=4": len(every), "zero_ceiling_len<=6": len(every),