Implement framed XOR endpoint corrections on two tapes

[Dugongue]

PR3480's 23 residual P112 translations cancel only under its shared-register condition. This package supplies a separately paid alternative: explicit two-tape machines that implement each framed XOR endpoint correction, with natural output order, genuine halt, restored heads and arbitrary exterior frames.

The copy variant preserves its borrowed input and uses a full owned destination. Its exact time is 2NB+4N+(B+2)Q, with Q=V_h(delta)+1+2 rev_h(delta) <= (h+1)N. The in-place variant swaps each XOR pair through one arbitrary dirty B-bit record and restores that record exactly; its larger seek bill is fully charged. All programs use four symbols and literal finite transition tables. They make zero recursive Fourier calls; compilation/control size and all tape movements remain explicit.

For the literal 23 PR3480 masks at N=512, sums of isolated copy costs are 82,936 B + 165,872 unit transitions. The in-place formulas sum to 2,033,554 B + 4,049,444. These are tape invoices, not rank-one-equivalent prices or a new κ. The native owner/layout/framing map, buffer lifetimes, acquisition and complete caller bill remain open. Separate two-tape instances do not silently provide a free native batch scheduler.

The complete informal proof covers every fixed address dimension/mask and every payload width, including exact travel formulas, dirty-record restoration, C_E² endpoint composition and norm/error preservation. A uniform compiler generates each finite controller; no single unpriced fixed-control interpreter for unbounded online h is assumed. No new Lean kernel or independent human review is claimed.

Registered Python 3.12 replay passes: 252 copy cases, 85 complete small-space basis cases, all 23 literal h=9 masks, 94 in-place cases and 1,168,046 executed unit transitions. Eight semantic control groups pass normally and with assertions disabled, including separate complex block endpoints, missing dirty-scratch restoration, wrong masks, missing head restoration, invalid moves/writes, malformed framing, bounded failure and actual Git-free CLI/source/receipt corruption. The other large in-place entries are proved formulas, not claimed executions.

Credit Gonzalo Mier/PR3480 for the immediate handoff and mask source, Cinna Davis/PR2297 for the five-plane operator and retained decoder lineage, Sagar Thakrar/PR3876 for the separate scalar-contract boundary, Tekalign's merged high-route permutation-frame compiler and its native route lineage, Gareth Davidson's coordinate-CNOT work, ywz65's integer-address work, and the shared MathProof commuting-phase/locality/frame modules. Original notices and source bytes are preserved. Prepared by Dugongue with substantial OpenAI Codex assistance.

Base 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. This round fetched canonical main and checked 583 open PR bodies plus refreshed recent/updated records through PR3878, relevant actual sources, merged scope comparisons and partial Discussion HTML. The latest Gaussian expansion submission is recorded as a different pending route. No exhaustive novelty or predecessor-admission claim. The selected baseline binding check passes; the unrelated selected cold replay was not run.

Reproduce:

python3.12 -B scripts/research_package.py --package research/xor-endpoint-tapes