Repository navigation
Finite bit construction: two-sided R439 compensation saves 1,228 more ADDs beyond PR915 - #926
Merged
Mister-Meeseeks merged 2 commits intoOct 13, 2026
Conversation
thakrarsagar
added a commit
to thakrarsagar/integer-mult-bounds
that referenced
this pull request
Oct 14, 2026
- The synthetic witness is described exactly: its post-scatter reads undo W_syn's moved compensation, so after B it equals CrocSwap#1179's prefix entrance on PR589; it now also fails without its late reads (new control). - The open triple's obstacle is scoped to A6R (B++C fixed); LC-fav also allows a rewritten B/C. 'Settles/decides' becomes 'narrows to one open triple'. - PROOF.md: cone lemma is CrocSwap#1128 section 1 (Lemma 2 is the dual of section 2); Lemma 1 states only x-free, pivot-free D' contributions; Step 4 folds scatter-extension snapshot terms into u; frames at sigma equal raw frames; reads during C reduce to the end of B (asserted: C at FULL, no target). - Donors: 5,212 enumerated, 5,059 placeable. W_t are coordinate subspaces (recorded); the structural reason is restated accordingly. - Relaxation checked to contain every admission; census sanity checks are labelled as such; flipped-byte control recorded; engine-2 coverage stated precisely; credits for eumemic, DreamingOfClouds, CrocSwap#967, CrocSwap#915/CrocSwap#926, CrocSwap#1043, CrocSwap#1079, CrocSwap#1256.
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Finite bit-circuit construction: 192 disjoint helper pairs around the frozen PR915 target basis reduce the complete R439 word from 13,208 to 11,980 ADDs, saving 1,228 further ADDs after paying preparation and restoration. Against selected PR589, the reduction is 24,305 to 11,980, or 12,325 ADDs. No new kappa is claimed.
The complete D bill is 192 + 306 + 4,764 + 306 + 192 = 5,760 ADDs. The actual two-sided middle matrix is rebuilt, including its 7,031-entry mixed term. Helpers are restored before A. All non-D fields, every register's ordered MOVE path, all COPY/ERASE records, nine rank-seven totals and rank mass 5,129 are retained.
The precision tradeoff is explicit: forward/reverse positive bounds become 71,907 / 10,562,318. The local payload estimate is 102 bits; the nine-stage estimate is 192 bits, strictly below the existing ceiling and using about 99.925% of it. Both bounds are recomputed on every admitted complete partial word. Standalone savings and predecessor bounds are not added or inherited.
Reproduce from the repository root with Python 3.12+, C++17 and Boost headers:
The full verifier passed on ordinary CPython 3.14.4 and isolated optimized CPython 3.12.3 from a minimal read-only source tree. Every receipt field agrees. Coverage includes all 192,282 pair scores, independent set-valued reconstruction, 48,729 direct four-term coefficients, 661 input columns in both D directions for all three words, original E8/frame/endpoint checks, and fresh unchanged C++ 5/9/11-stage checks on 883/1,327/1,549 formal columns per word. All 144 omitted-bridge controls, 19 local controls and 8 package tests pass. The selected-record and staged whitespace checks pass. Full repository and selected-supplier cold suites are not claimed.
The original H2 and literal K extraction remain false for the changed word; their predicates are unchanged and explicitly reported. This requires the semantic D-boundary contract already used by PR915: arbitrary
(x,y,s)maps to(x,y+Ks,s)with restored helpers. Remaining integration work is acceptance of that interface, changed whole-hosted emission and audit, full finite/precision invoice reconstruction, and outer assembly. The common-label realization and analytic assumptions remain inherited.Base 91a2094; OS assignment seed 5, bit-supplier track. The declared search completes one sorted disjoint greedy pass: 2,298 positive pairs, 192 accepted, 2,106 overlap skips and no bound rejects. No optimal-matching or global-circuit claim is made. A 714-open-PR refresh through #924 found no new R439 two-sided D construction. #917 concerns historical complex CK; #923 changes R439 frame520 and cleanup. Their savings are not composed here. Only
research/r439-two-sided-compensation/is added; the frozen review batch is not edited or treated as approval.Credit Scott Woolsey Biggart / @swbiggart, PR733 (
dfe84e09298abc5c5e0074afda59a821e10abfb4) for the prior two-sided method and mixed-term obligation, and PR915 (e9daefe320a0043000bd9746664ed02c3287d056) for the frozen target basis. The package preserves source snapshots and notices. Credit also remains with DreamingOfClouds, eumemic, commdata2338, Mikhail R. Gadelha, Greer Guthrie, Sagar Thakrar, and the native verification lineage; Ross Richardson's concurrent PR917 is acknowledged. Prepared for Gareth Davidson (@bitplane) with substantial OpenAI Codex assistance. Apache-2.0; no independent human review claimed.Published head: 0f216a3. Mathematical implementation: 1e9c43e; the final commit changes only the local claim to record the result and PR link. The remote OPEN state, exact head and 24-file package scope were verified. All five hosted workflows at the published head report
action_required; no hosted CI pass is claimed. Research-artifact workflow. An immediate post-submission refresh also found #925 (R439 phase-A frame267) and #927 (historical ranking reconciliation), both distinct from this D construction.