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Research: extend R439 frame obstruction to dirty workspace - #1810
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Batch review at Merged to Reviewed scope: Semantic forward/inverse dependency invariant extends the fixed common-frame B-block obstruction to reversible nonlinear gates and arbitrary independent dirty workspace. Exact114-wire reconstruction, separate truth-table/Gram oracle and mutation tests validate93H2+10H3. Changed entries, role normalization or COPY contracts remain outside. 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. |
Source-bound consolidation receipt (card overlap-receipt, scope refined to one existing integration receipt). Re-derives from Git that all 77 changed paths of the nine reviewed heads (#1805, #1806, #1808, #1810, #1811, #1812, #1814, #1815, #1827) are retained byte-identically in merge 5112234, that no head changed since review, and that all authors are credited in CONTRIBUTORS.md. Records the still-partial ledger dispositions without changing them. No kappa, disposition, closure or frontier change. Aaron Wang, with help from opencode.
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The fixed R439 B-block interfaces explicitly left added wires outside their obstruction. This package proves that independent dirty workspace cannot lower their original-wire frame invoice, even with arbitrary reversible nonlinear Boolean gates and arbitrary auxiliary garbage at exit. All 114 original exits still equal their rank-four block frames; the exact minimum is 93H2 + 10H3 (rank mass 216).
The proof extends the credited forward/inverse dependency invariant to essential dependence of bijections. For an endpoint (x,z) -> (Mx,G(x,z)), the inverse original coordinates remain M^-1 y for every workspace output. Exact rational span witnesses instantiate the result on all ten source-pinned blocks. The written induction covers arbitrary finite circuit lengths and workspace sizes; finite checks corroborate it.
Scope: independent arbitrary inputs; exact original block maps and entry labels; all operands share a monotone frame inside the block frame; fixed outside visits. Every auxiliary climb and continuation is charged. The complete frame-moment comparison keeps caller width, role denominator W and other charges fixed. Changed W, hosting, precision or cross-block entry contracts require separate pricing. No new κ, supplier adoption or selected-frontier change.
Credit and delta: PR1368 supplies the ten interfaces and forward witnesses. PR1511 already closes B508 by the XOR inverse-column invariant; PR1535/1576 close B509, with PR1778 later corroborating B508. PR1128 already allows restored dirty extras in its linear helper-boundary theorem. This adds the nonlinear/garbage-workspace closure and exact ten-block application, not priority for those results. The fixed-prefix nonlinear cleanup and PR1757 common-flag bounds are separately credited. Exact predecessor heads, licenses and substantial OpenAI Codex assistance are recorded. No subagents or independent human review.
Validation:
Reproduce:
Base: 0b1cccf.
Verified contribution head: aed73d5.
Discussion 1795.
Final overlap at 10:26–10:27 UTC covered 465 open PRs and 444 Discussion records with complete pagination and no warnings; 67 matches were inspected. No global novelty claim.
Next: an exact cross-block interval changing donor 466 before B508 or donor 17/468 before B509, with both dependency directions and a favorable complete budget. Further synthesis inside the closed interface is not proposed.