Research: twisted helper contract absorbs three R439 helper-star restorations into A (10,492 -> 10,489 on PR1188's word; no new kappa)

[thakrarsagar]

Change and mathematical scope

Replacement-interface result with finite R439 instances. No new κ, and the
bit side does not bind. This adds one registered package,
research/r439-twisted-star-absorption-seed02/.
No selected record, supplier, pinned file or upstream/ changes.

Twisted contract (card bit-helper-contract). #1194's semantic-D contract
requires D to return every helper, (x, y, h) -> (x, y + N h, h), and keeps the
literal-reverse cleanup H4. The twisted contract makes three changes:

• H2-tw: D may leave helpers twisted by an invertible, helper-only T,
  giving (x, y + N h, T h). D stays frame-zero and source-free.
• H4-tw: C is z-only at the full frame and satisfies
  C U' diag(I_x, T) = I.
• K-tw: N = K'T.

H1, H3, H5 and J = I are kept.

• Proof. The block algebra gives the dirty boundary
  (x, y, h) -> (x, y + x, h) on every F2-module. Given the kept and structural
  clauses, the two equations are also necessary. The proof is in PROOF.md.
• Two ways it weakens Prove a semantic zero-frame D contract for a fixed R439 word #1194.
  • The cleanup is semantic even at T = I. Research: independently check semantic-D bridge for composed R439 word #1311's stale-cleanup control
    satisfies it, which is why PROOF.md states that adopting H4-tw as a general
    interface needs a chronological bridge for non-literal cleanups.
  • The helpers may stay twisted.
• The instances use neither relaxation's risk. They keep the base words'
  literal C byte for byte and are bridged cut by cut.

Helper-mixing word. Delete a D restoration a ^= b. Replace the source set
Sg of an A gate that writes a before a's first read with Sg ⊕ S, where
S is the unique register set whose current values sum to b's column. This
preserves the boundary if and only if the new set is exactly Sg ⊕ S.

• Exhaustive single-edge census. On the Finite bit construction: restored helper stars save 197 R439 ADDs (no new kappa) #967, Finite bit construction: phase-B block programs on the R439 helper-star D, 11,783 -> 11,500 ADDs (no new kappa) #1062, Finite bit construction: compose R439 A/B/star D to 10,652 ADDs #1122 and Bit construction: exact five-wire windows reduce composed R439 to 10,492 ADDs #1188 words
  it finds exactly 48/48/48/47 positive moves. Of those, 45/45/45/44 are
  frame-illegal and 3 are frame-legal, and the 3 are the same on every word.
• The three moves. 506^=374 is absorbed at A[288] (substitute 69).
  507^=355 is absorbed at A[290] (substitute 72). 514^=367 is absorbed at
  A[304] (substitute 360).

	#1062 word	absorbed	#1188 word	absorbed
ADDs	11,500	11,497	10,492	10,489
F / B	25,717 / 5,911,840	25,717 / 5,858,638	13,667 / 3,758,418	13,667 / 3,748,680
bits (caps 104/192)	95 / 182	95 / 182	91 / 175	91 / 175

Both absorbed words have:

• an exact dirty boundary on all 661 columns, forward and reverse, through the
  literal COPY/ERASE stream;
• identical per-register frame paths and exporter MOVE records;
• an unchanged paid profile, {1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19},
  with rank mass 5,129.

The unchanged owner checker reports exactly four false flags:
H2_D_frame0_targets_from_helpers, H4_C_literal_reverse_at_full,
K_equals_D and C_is_U_inverse.

Newly used premise. The instances rely on the inherited common-frame /
climb-additivity premise, now applied to helpers. Targets already rely on it,
because they climb holding y + N h. #1194 confined its own substitution to
frame-zero prefixes. Here exactly three helpers (506, 507, 514) first climb out
of frame zero holding centre + leaf, at their absorbing gates.

Not run.

• Native 5/9/11-stage C++ replay. My open Portability tooling: checked cpp_int stand-in runs the selected replay's only native step (bit589 step 4) without Boost, matching the committed Boost receipts (no new kappa) #1509 stand-in could enable it on
  hosts without Boost.
• Hosted emission and invoice, and outer assembly.

The census covers the single-edge, single-writer class only. It is not a global
minimum.

Task and overlap

• Base and track. Base 0b1cccf8. Seed 2 → bit supplier, card
  bit-helper-contract (catalogue priority revision 3), scope refined.
• Lineage.
  • Prove a semantic zero-frame D contract for a fixed R439 word #1194 (semantic-D contract, merged) and Research: independently check semantic-D bridge for composed R439 word #1311 (its bridge on Finite bit construction: compose R439 A/B/star D to 10,652 ADDs #1122's word).
  • Research audit: exclude terminal helper-star restoration on fixed R439 words #1580 and Research: exclude arbitrary terminal R439 star compensation under fixed frames #1592 (open) exclude terminal restoration moves and compensation.
    This package's absorption comes before the first read and changes A, which
    answers Research: exclude arbitrary terminal R439 star compensation under fixed frames #1592's stated next question for the centre-writer class.
• Concurrent same-card work. None of these leaves helpers twisted or
  absorbs a D restoration into A.
  • Larger scalar savings on the same Finite bit construction: phase-B block programs on the R439 helper-star D, 11,783 -> 11,500 ADDs (no new kappa) #1062 word, by other mechanisms; whether
    they compose with these three absorptions is untested:
    • Finite bit construction: two nonpositive helper moves save 11 ADDs on R439 #1543: 11,489;
    • Finite bit construction: five-helper cycle saves 12 R439 ADDs (no new kappa) #1709: 11,488;
    • Finite bit construction: two-copy scatter saves 120 ADDs (no new kappa) #1704: 11,380, under a different interface.
  • Research: H2-sem admission of the PR848 copy-path helper-sharing wrap (no new kappa) #1782 and Research: price H2-sem copy-path helper-sharing wraps (no new kappa) #1805 work under Prove a semantic zero-frame D contract for a fixed R439 word #1194's restored-helper contract.
  • Discussion CLAIM: compensated terminal helper-star deferral (seed 4bfcbdf5) #1743's terminal-deferral claim expired without a PR.
• Overlap searches for absorb, twisted, cross-cut, C_is_U_inverse, H4,
  helper-star, restoration and helper contract, run at three points through
  12:20Z, found nothing on this mechanism.

Validation

python3 scripts/research_package.py --package research/r439-twisted-star-absorption-seed02 --check-only
python3.12 scripts/research_package.py --package research/r439-twisted-star-absorption-seed02

verify.py uses only the standard library and takes about 20 s. Its checks
raise ValueError, so they also run under -O; it is registered with and
without -O.

• Inputs. It pins all 7 inputs and runs the owner checker and exporter from
  the verified bytes.
• Re-derivation. It reruns the census on four words and rebuilds both
  absorbed words, requiring an exact match with the committed payloads.
• Proof checks. It checks the twisted identities and the per-cut
  chronology: at most 3 pending centres, each at frame zero until its absorbing
  gate.
• Controls (16, all rejected or failing).
  • Omitting the restorations without the A edit: a dirty-only counterexample.
  • The A edit with literal cleanup: fails on dirty helpers 506/507/514 and
    passes on clean ones.
  • Absorption after the first centre read.
  • A wrong substitute.
  • A frame-illegal substitution.
  • The Prove a semantic zero-frame D contract for a fixed R439 word #1194-style splice with Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589's D, rejected with "helpers not restored".
  • A corrupted pin.
• Perturbations. 1,980 one-register perturbations per instance are all
  rejected.

It passes on Python 3.11–3.14.

Pre-PR review. A three-lens review found:

• Verifier lens: "ship". All data and code mutations were caught, and an
  independent re-implementation reproduced the census.
• Proof lens: confirmed the lemma by hand and with random circuits, plus the
  uniqueness, the criterion and the chronology. It corrected the
  "T = I recovers Prove a semantic zero-frame D contract for a fixed R439 word #1194" overclaim; the cleanup is weakened even at T = I,
  and that is now documented.
• Claims lens: all numbers, pins and credits check out. It added the
  concurrent-work section and fixed the notation.

Credit

• Interface lineage: woklerx (Prove a semantic zero-frame D contract for a fixed R439 word #1194), Arham Tahir (Research: independently check semantic-D bridge for composed R439 word #1311, Research audit: exclude terminal helper-star restoration on fixed R439 words #1580, Research: exclude arbitrary terminal R439 star compensation under fixed frames #1592),
  Zhihao Chen (κ = 1.048005508028206e-3: mutable-basis Hamming packets (≈2^-9.89814; conditional; complex +4.97%) #425), eumemic (Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555, xcheck_p.py), Dylan Crow (exporter).
• Lineage words: Sricharan Vagvala (Finite bit construction: restored helper stars save 197 R439 ADDs (no new kappa) #967), Sagar Thakrar (Finite bit construction: phase-B block programs on the R439 helper-star D, 11,783 -> 11,500 ADDs (no new kappa) #1062), Gareth
  Davidson (Finite bit construction: compose R439 A/B/star D to 10,652 ADDs #1122, Bit construction: exact five-wire windows reduce composed R439 to 10,492 ADDs #1188), DreamingOfClouds (Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589).
• Restoration-coalescing lineage: Research note: restoration coalescing across a recursion batch (read-free + composable-family boundary; no new kappa) #1155, Recursive interface: coalesce restoration with cancelling readers #1199, Research: noncommuting reader restoration with a paid dirty-state wrapper #1203, Research: observer-safe restoration with nonzero readers (no new kappa) #1205.

AI disclosure: prepared by Sagar Thakrar with substantial Anthropic Claude
assistance, including explorer, judge, builder and reviewer subagents. No
independent human review. New work is Apache-2.0.

Open next questions

1. Multi-gate splits of S, and chaining the gain-0 moves.
2. Native replay of the absorbed words, with Boost or the Portability tooling: checked cpp_int stand-in runs the selected replay's only native step (bit589 step 4) without Boost, matching the committed Boost receipts (no new kappa) #1509 stand-in.
3. Whether feedback or shear gains appear once the helper exit may be twisted
   (T ≠ I), complementing Finite certificate: no target-feedback saving for four-helper/four-target shears (no new kappa) #1706.
4. Whether maintainers would adopt H4-tw, which would also need a bridge for
   non-literal cleanups.

[woklerx]

Independently audit twisted helper compensation and cleanup

Intentional independent review of PR1868 at 6b222d01fee072bcd3a680e6a96ae7d22e13bcac, starting from main 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

A literal binary-matrix oracle checks all 6 helper twists and 168 raw three-coordinate invertible blocks. Its factored census validates 4,032 compensated tuples, rejects 12,096 wrong helper compensations and 168,336 wrong cleanup matrices, and detects 840 omitted-twist cleanups. Compensation and cleanup affect distinct output blocks, which is why their complete small-domain censuses can be factored. The full predecessor Python 3.12 registered replay passes on all four lineage words and both 661-column instances.

The independent finite census checks the scalar equations only; it does not extend the chronological bridge to arbitrary cleanup words. The source proof, frame work, absorption census and full-word replay are credited to PR1868; native replay is an open predecessor obligation.

Reproduce: python -O -B research/twisted-contract-independent-audit/audit.py. Source head: 6b222d01fee072bcd3a680e6a96ae7d22e13bcac.

Sagar Thakrar, PR1868; woklerx PR1194, Arham Tahir PR1311/1580/1592, Zhihao Chen PR425, eumemic PR555, Dylan Crow, Sricharan Vagvala, Gareth Davidson, Aaron Wang, Ross Richardson and DreamingOfClouds as credited in the pinned source.

Prepared by woklerx with substantial OpenAI Codex assistance.

Exact committed audit artifact. Commit 337e4908d88c622d38826357864310dd1867bf1e; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated batch, round 17.

[Mister-Meeseeks]

Batch review at 6b222d01fee072bcd3a680e6a96ae7d22e13bcac.

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

Reviewed scope: Twisted scalar helper contract and three frame-path-preserving absorption moves reduce retained1062/1188 ADD counts by3. Full661-column forward/reverse replay, lockstep frame census and strict controls pass. Physical helper-climb additivity remains inherited conditional infrastructure; the general twisted contract is not admitted as a new supplier interface.

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.