[unpaidmoon]

Change and mathematical scope

Partial certificate, no new κ. On the success path of the pinned packet_engine.py, a completed packet is erased by rewind followed by Tape.clear, starting from the trailing blank. For a payload of n symbols that call has meter

reads = 3n + 4,   writes = n,   moves = 3n + 6.

The parent geometry in research/r437-carrier-integration/PHYSICAL.md is one payload

n = 9475 * 12 * 3^128 = 972 * 9475 * 3^124.

The factor 3^124 is the 124 omitted atom coordinates. The success-path rewind, the blanking scan and clear's closing rewind each step across every payload cell, so those coordinates are crossed. clear's own opening rewind only bounces off LEFT on this call. The write count meets the one-visit lower bound from research/r437-parent-spectator-blank exactly. The move count is strictly larger. The same call on the executed 972-bit fibre has moves 2922 and does not pay the parent.

This does not allocate the parent, price changed.clear() or local.clear(), or sign BILL.md's G, C or F terms. Selected κ stays 781451/250000000.

Task and overlap

Base commit: 7c49fe32c55de02c2c873655c804b16e4c3fef0a on canonical CrocSwap/integer-mult-bounds main. Priority revision 8. Selected record SHA-256 9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa.

Task card: r437-carrier-integration. Scope status: refined.

Session r85, item 8 of the ordered eligible list. The 19 October handoffs (discussion comments 19030045, 19030047, 19030049, and 19030053) are already delivered or closed. Later handoffs whose canonical artifact is an open pull request, including the H25 requests and the 2026-11-02 audits of #6348 through #6361, are excluded. The revision-8 next-decision table then supplies six rows, naming p104-side-correction, coverage-law-change and bit-helper-contract. Catalogue cards not named by those rows follow, in catalogue order:

1. Complex helpers (p104-side-correction, coverage-law-change)
2. BIT (bit-helper-contract)
3. New decoders/interfaces
4. Supplier audit
5. All-size audit/formalization
6. Verification tooling
7. bit-new-register-model
8. r437-carrier-integration (this package)
9. complex-rank-shape-decoder
10. complex-new-helper-inventory

Within the card, #4147, #4160, #5277 and #5276 are already delivered. This package answers open question 1 of research/r437-parent-spectator-blank and does not rederive the reverse coefficient.

Nearest work:

• unpaidmoon Record that the R437 parent blank-return exceeds the 972-bit child. #5276, research/r437-parent-spectator-blank: the payload ratio 9475 * 3^124. It leaves the cursor invoice open. This is that invoice.
• unpaidmoon Certify the SOURCE87 parent fibre count on the R437 carrier. #5277: SOURCE87 fibre multiplicity. Gather, routing and parking stay open.
• unpaidmoon Price the R437 child-constructor tapes inside Pi_v. #4160: one constructor term inside Pi_v, not this tape.
• unpaidmoon Derive the reverse row coefficient of the two-window R437 carrier. #4147: the reverse coefficient, reused and not recomputed.
• Chris R / Clear1nsight, research/r437-carrier-integration: the extents and the success-path call site.

No open pull request states this 3n+6 move count.

Validation

CPython 3.12, standard library, Linux. From the repository root:

python3 -B scripts/research_selected_baseline.py
python3 -B research/r437-parent-blank-cursor/verify.py
python3 -B research/r437-parent-blank-cursor/test_verify.py
python3 -B scripts/research_package.py --package research/r437-parent-blank-cursor

Orientation printed PASS_RESEARCH_BASELINE_BINDINGS_ONLY with selected κ 781451/250000000. The verifier printed PASS_R437_PARENT_BLANK_CURSOR with

parent_payload = 1340543986488876906601923244342603372287612658041763134104324465700
reads          = 4021631959466630719805769733027810116862837974125289402312973397104
writes         = 1340543986488876906601923244342603372287612658041763134104324465700
moves          = 4021631959466630719805769733027810116862837974125289402312973397106
executed_fibre_moves = 2922

Controls printed PASS_R437_PARENT_BLANK_CURSOR_CONTROLS. The registered replay printed PASS_REGISTERED_RESEARCH_PACKAGE with outcome=partial.

The general n argument is the control-flow count in PROOF.md. The checker executes the pinned Tape for n through 48, both bits, the 972-bit fibre, and miniature parents at 3^0 and 3^1. Payload-only moves, a 972-bit write count, dropping 3^124, and clear without the opening rewind are rejected.

Not run: physical.py, the pooled compiler, Lean, Docker, and make frontier6030-verify.

Credit

Parent extents and the open cursor question: Chris R / Clear1nsight, research/r437-carrier-integration, and unpaidmoon #5276. Tape machine: the retained predecessor records.Tape on the selected physical caller. Carrier lineage: ai-nanachi / PR #3647, Ali Romman / PR #1043, Sagar Thakrar / PR #3700 and PR #2423.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Where does action leave the head of changed and local before their clear calls? First step: one source-bound postcondition on a fibre of length n. Blocker: action is outside this package.
2. Can one of BILL.md's G, C or F terms be instantiated on both arms without setting the others to zero? First step: pin one tariff. Blocker: those tariffs are not inputs here.

Workflow feedback (optional)

A link to discussion #1200 is enough. The handoff index in #1166 is now mostly open-PR audit requests, so the revision-8 table plus unnamed catalogue cards is what still yields a disjoint session.