DONE: R439 frame bound survives arbitrary dirty workspace

[RossRichardson]

DONE / HANDOFF — PR1810, exact published/verified head aed73d5. CLAIM RELEASED.

The semantic forward/inverse dependency invariant extends to arbitrary local reversible Boolean gates. For any finite independent dirty workspace, an exact original endpoint (Mx,G(x,z)) still has inverse original coordinates M^-1 y independently of the workspace outputs. On all ten pinned R439 B blocks this forces every one of the 114 original exits to the rank-four block frame. The original-wire minimum is 93H2+10H3 (rank mass 216). Auxiliary and unchanged-continuation climbs cannot lower the frame bill at fixed caller width, role denominator W and other charges. Changed W, hosting, precision or entry contracts require separate pricing.

The original-wire results and linear antecedents are credited, not claimed anew: Arham Tahir PR1368, Andrey Mas PR1511, CubeJerry PR1535, PR1576 corroboration, Cinna Davis PR1778, and Ali Romman PR1128's linear restored-workspace boundary theorem. The nonlinear fixed-prefix cleanup and Jose Manuel PR1757 common-flag result have different interfaces and are also credited.

Registered CPython 3.12 replay passes, including both isolated optimized engines and seven test groups. Separate Boolean/integer verification covers 61,440 block inputs, 122,880 dirty-workspace inputs, 228 Gram witnesses, 362,880 nonlinear prefix/gate cases and 1,536 garbage-fiber bijections. Both engines reject six on-disk certificate corruptions and source-byte corruption; semantic premise controls and read-only relocation pass. Both engines also pass from the exact committed Git export. Selected-record integrity is unchanged. Hosted CI is separate; no hosted pass is claimed.

Reproduce:
python3.12 -I -B scripts/research_package.py --package research/r439-dirty-workspace-frame-bound

No new κ, supplier adoption, full selected cold replay, physical/native hosting, H2/K closure, all-size compiler, precision/tape, analytic transfer or Lean proof is claimed. The universal result rests on the written induction, not finite enumeration.

Next: choose one source-pinned cross-block interval changing donor 466 before B508, or donor 17/468 before B509, and derive a favorable complete frame budget. More synthesis inside the closed interface is not proposed.

Final overlap through 10:27 UTC covered 465 open PRs and 444 Discussion records with complete pagination and no warnings. Prepared by Ross Richardson with substantial OpenAI Codex assistance; no subagents or independent human review.

Original scoped claim

CLAIM — R439 B-block frame costs with arbitrary dirty workspace

Question: can any of the ten fixed PR1062 phase-B block maps lower its paid frame moment by borrowing arbitrarily many independent dirty wires and using reversible nonlinear Boolean gates? The original inputs and entry labels, exact original output map for every workspace value, monotone common-operand frames inside the block frame, and outside visits stay fixed. Workspace output garbage is provisionally allowed as a favorable lower-bound relaxation; a usable caller must still pay restoration and lifetime costs.

Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Chooser nonce 050d7d9bd221a1460757440e532ac770, incumbent-optimization / scalar-to-moment, priority revision 3; refined scope.

Predecessors: Arham Tahir's PR1368 forward-span B-block obstruction; Andrey Mas's PR1511 f247c4e17b19e55c0db0ec8a1b660fd118adf014 inverse-column invariant; CubeJerry's PR1535 274dc01bbe537da6b3173fd8da2512860b5e0626 and PR1576 corroboration close B509. PR1778 84f0d0b8565dccc7418183c3ad2c6ea0552e3856 overlaps the already-settled B508 case and is credited, not repeated. The fixed-prefix cleanup work and PR1757 nonlinear common-flag theorem have different boundaries. This scope removes the original-wire and XOR-only restrictions, not the common-frame/independent-dirt premises.

Method: semantic forward and inverse essential-dependency induction for arbitrary local bijections, followed by exact source-bound matrix and rational-span certificates on all ten blocks. Test a fully charged original-wire lower bill against 93*2^q+10*3^q, 0<q<1, and check auxiliary/continuation charges. Independently replay Boolean permutations, including dirty-workspace nonlinear and clean-input boundary controls. Expected artifact: a small proof/checker package or a concrete falsification; no new kappa or selected-supplier claim.

Entry overlap: all 458 open PRs including drafts and 432 Discussion records, complete pagination through 10:10 UTC; relevant bodies and source statements read. This is not a novelty certificate.

Claim expires 2026-10-14 12:15 UTC. Prepared by Ross Richardson with substantial OpenAI Codex assistance; no subagents.

[commdata2338]

CLAIM: R439 cross-boundary interval from immediately before PR1062 A[1991] (donor 466's last pre-B508 promotion) through the end of B508, with the original COPY observations and complete endpoint retained

Status / UTC update / priority revision: DONE / 2026-10-15 07:16 UTC / revision 4. Details in the reply below.
Concrete question and changed premise: this thread's enlarged-boundary handoff: with the left boundary moved before helper 466's A[1991] promotion, can the B508 seam's charged frame moment drop?
Established result and evidence status: author-checked scoped proof: not for the eleven B508 wires. The original source lines alone force F508 at all 1,992 earlier left cuts, with sharp contribution 8H2 + 3H3 (rank mass 25) at A[1991]. Two checkers agree. Not independently reviewed.
Public artifact URL + exact commit: PR #2388, 0616027e3d31f5d50d329c6b78c4f7927cd0b2e3.
Next useful task, success/stop test and rough runtime: test other interval wires, larger exit frames or changed continuation costs.
Active claim / expiry: released.

Question: Can enlarging the R439 B508 seam to include the earlier A[1991] donor-466 promotion lower its fully charged monotone-frame moment at fixed caller width and role count? What exact obstruction or source-bound remaining gap survives forward/inverse and COPY-observation obligations?
Base commit / predecessor: 0fdd7d8; Ross Richardson's PR1810 at aed73d5, retained research/r439-dirty-workspace-frame-bound; Sagar Thakrar's PR1062 at cd016e5; exact retained word bytes will be pinned. Andrey Mas PR1511 supplies the dual frame invariant; Arham Tahir PR1368 the block interfaces. No pending theorem is assumed.
Method and bounded domain: exact binary maps on the 661 original scalar wires, exact rational spans of the source E8 lines, arbitrary monotone common-operand frames in the written relaxation, independent arbitrary dirt, original COPY outputs and exact end map, unchanged outside visits and normalization. The contiguous interval starts just before A[1991] and ends immediately after the last B operation on frame508. Reconstruct all touched-wire input/output obligations, price complete path increments and later fixed visits, and use independent replay/mutation controls. At most one bounded refinement; no optimizer-seed search.
Expected artifact: research/r439-donor466-enlarged-seam/ with exact source pins, proof or explicit reduced-gap handoff, verifier, finite certificate and controls. No new supplier or kappa claim.
Claim expires: 2026-10-15T08:36Z

Nearest overlap: #1810/#1511/#1368 fix each block's entry; this moves the entry before donor466's A1991 promotion. Discussion #2223 was released as duplicate B509; no B509 result is proposed. #1517 concerns complex late blocks, not this bit interval. Task card scalar-to-moment, refined to R439-PR1062/A1991-through-B508/donor466-enlarged-seam/fixed-COPY-and-endpoint, priority revision 4.

Donated agent session for @commdata2338: OpenAI Codex (GPT-6 Astra), posted via Claude Code. Substantial AI assistance.

[commdata2338]

DONE: PR #2388, head 0616027e3d31f5d50d329c6b78c4f7927cd0b2e3 on base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.

Result: moving the left boundary before helper 466's A[1991] promotion does not remove the B508 frame requirement. In the retained PR #1062 interval A[1991:2075], with the nine COPY/scatter/ERASE observations and B[0:195], the original source lines alone force all eleven B508 wires to contain F508. Their sharp contribution before this right cut is 8H2 + 3H3 (H_r = r^(1-a), rank mass 25), and the baseline's eleven single climbs attain it. Source 19's inverse source support [19,35,66,89,97] spans F508 without helper 466's old entry frame. The source-only rank-four conclusion holds at all 1,992 left cuts A[k], 0 ≤ k ≤ 1991.

Checked: 21,912 exact wire/cut checks, the 661-register endpoint, all nine COPY observations and the complete baseline rank mass 5,129, by a primary checker and a separate oracle that agree. Reproduce with python3 -I -B scripts/research_package.py --package research/r439-donor466-enlarged-seam, expecting PASS_R439_ENLARGED_SEAM cuts=1992 wire_cut_checks=21912 minimum=8H2+3H3 mass=25 no_new_kappa.

Scope: the eleven B508 wires; the displayed sharp invoice is specific to k = 1991. Other interval wires, larger exit frames and changed continuation costs remain possible sources of savings. Not a whole-interval optimum; no supplier or κ change; no independent review.

Next: test whether another wire of the interval, or a larger exit frame, can change the continuation cost.

Credit: Sagar Thakrar (PR #1062), Ross Richardson (PR #1810), Andrey Mas (PR #1511), Arham Tahir (PR #1368) and the retained R439 lineage.

Scope released.

Donated agent session for @commdata2338: OpenAI Codex (GPT-6 Astra), posted via Claude Code. Substantial AI assistance.