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Scoped negative result: R439 source-substitution census has one known survivor - #1079

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Mister-Meeseeks merged 1 commit into
CrocSwap:mainfrom
bbMisk:research/source-substitution-seed11-20261013-1719
Oct 14, 2026
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Mister-Meeseeks merged 1 commit into
CrocSwap:mainfrom
bbMisk:research/source-substitution-seed11-20261013-1719

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@bbMisk

@bbMisk bbMisk commented Oct 13, 2026

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Scoped negative result; no new kappa. In the class defined below, the only removable helper in PR589's tuned R439 word is helper 470, the source 77 boundary already constructed by Ali Romman in PR1043. This package adds a complete finite census and six exact frame obstructions. It does not claim that helper deletion, other circuits, or the bit supplier are globally optimal.

Classification Helpers
Retained decoder totals, outside the deletion class 9
A read has no eligible source with the same clean response 423
All reads have unique source matches, but frames forbid substitution 6
Admitted, already known from PR1043 1
Total 439

Choose one non-retained helper q. Delete every A/B gate whose destination is q. At each surviving A/B read of q, replace that occurrence by one current source register s, distinct from the destination. Cancel repeated operands over F2. Require that q and s have equal clean-source response rows immediately before that gate in the original word. Helper inputs and target inputs are set to zero only for this response screen; they remain arbitrary in the final construction checks.

Keep all other A/B gates, their order and frames fixed. Keep start/final frames, retained totals and COPY frames fixed. A changed read may use any common frame; the six exclusions below do not restrict it to the shipped catalogue. Rebuild C as the literal full-frame inverse of the surviving z-gates. Rebuild frame-zero D from the complete dirty-helper response. Source access, restoration and compensation are not free.

python3 -I -B research/bit-source-substitution-seed11/check.py

Expected final line:

PASS_SOURCE_SUBSTITUTION_INDEPENDENT helpers=439 retained=9 clean_blocked=423 frame_blocked=6 survivor=470 reads=2102 controls=10 no_new_kappa

The base is 2921874911956718fcaaaf9396fe8267b3cfa9f0, whose selected conditional kappa is 1661960547713947/1000000000000000000, from PR942 with unchanged PR589 on PR555. The selected record is context, not a moving runtime input. The two consumed files and their exact SHA256 pins are in SOURCES.json.

Prepared for Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance in research, mathematics, implementation, verification and writing. Apache-2.0. Credit Ali Romman for PR1043; DreamingOfClouds for PR589/545/510; eumemic for PR555/543 and the owning checker; Zhihao Chen for the interleaved-interface lineage; Dylan Crow, chafreaky, DaysSky, Jacob Sussman and the retained E8 supplier contributors. The original dependency packages and their notices are unchanged. Separate implementations here do not imply independent human review.

@Mister-Meeseeks

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100-PR batch review at bb20dab261884412f2d2a7955cdb2fd8e2e64a16.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Complete direct-source substitution census in a precisely fixed R439 deletion class; confirms #1043's unique surviving candidate in that class.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.

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.
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