Price the cut58 ADDRESS swap against the separable response menu.

[unpaidmoon]

Change and mathematical scope

The source ADDRESS swap P from the q2 event58 suffix does not undercut the separable per-response tariff. For every g in G=<K,W,T> and every placement P^a g P^b, the monomial inherits one (K-parity, W-parity, T-parity) label and has the same one-coordinate polar rank as g. That rank still meets 2(q + (p xor q) + e).

The menu has 1008 monomials. 752 lie outside G, including P T P, P K P and P W P, and 40 extra polar-rank-zero monomials. All 40 inherit the zero label. This is a finite menu certificate. It is not a word-length bound, a scalar saving, a paid-profile improvement, or a κ change. Selected conditional κ stays 836330098538459/500000000000000000 (0.001672660197076918).

PR #4086 already proves native mass at least 22f inside the separable class and excludes a 16f suffix there. This package does not extend that word bound. A same-rank outside sandwich, or one of the extra free monomials, might still shorten a full six-bank word. No such word is constructed or ruled out.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, priority revision 6).
• Task: joint-query-controller, scope refined. The card asks for a QQ16 producer and consumer. Discussion Handoffs and requests for independent checks #1166 comment 19039339 asks for the event58 local-16 suffix. Open PR Prove a sharp native cost floor for six-bank cleanup #4086, head cd0f22abce2b74d7d080a2e640c0f495d3d2c3aa, answers that question for separable responses h T^e and names one outside adapter as the next test. This package prices the source ADDRESS swap, which Prove a sharp native cost floor for six-bank cleanup #4086 places outside its alphabet.
• Ordered eligible Handoffs and requests for independent checks #1166 handoffs for this session, after dropping delivered work, open-PR matches, and the parallel-session exclusions: (1) 19016699 typed physical H, (2) 19021149 two-bearing factorization, (3) 19031016 integer-shear recurrence, (4) 19034066 adjacent completed-call pair, (5) 19034741 chronological caller, (6) 19035513 source-normalization fusion, (7) 19035716 literal-index bridge, (8) 19036235 K/adjoint frame, (9) 19037887 fixed-tape producer, (10) 19039339 event58 local-16. Item 10 is the handoff taken. Because Prove a sharp native cost floor for six-bank cleanup #4086 already excludes 16f in-class, the distinct remaining piece is this adapter.
• Predecessor operators and the displayed matrix: PR Bound late-tail cleanup and expose the earlier exact interface #4082, head ff277e8a958829954f371c85bdc447672266edbd. Those bytes are vendored in operators.json and checked by SHA256 9704ae3c0c1fbb93526970b05a63f486f376961edd019ba526249477d2aa0ab3. That head is not a git object in this clone.
• Domain: the 1024 writings P^a (h T^e) P^b on the fixed 12-bit monomials. Not a new operation alphabet beyond this one adapter, and not a search below 22f.

Validation

CPython 3.12. Registered replay:

python3.12 -B scripts/research_package.py --package research/cut58-address-swap-menu

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/cut58-address-swap-menu outcome=completed.

Direct check:

python3.12 -I -B research/cut58-address-swap-menu/verify.py

prints PASS_CUT58_ADDRESS_SWAP_MENU distinct_sandwiches=1008 outside_group=752 extra_rank_zero=40 rank_preserved=true tariff_not_undercut=true extends_22_word_bound=false no_new_kappa=true.

The same line passed under -O. Metadata pins passed with --check-only. The checker rebuilds H (order 128, census matching the #4086 table) and G (order 256), enumerates every writing, and rejects a forced label conflict, a K rank tampered to 0, and the claim that the identity adapter transports T outside G.

Not run: the PR #4086 Gram and endpoint oracles, closure of the full group generated by the menu (it was still growing past 20,000 elements), a word below 22f, Lean, Docker, and the selected cold replay. The physical factor f is the disjoint-support multiplier proved in PR #4086; this package certifies the one-coordinate ranks that multiply it. The first catalogue command python3 -B scripts/research_baseline.py returned PASS_RESEARCH_BASELINE_BINDINGS_ONLY only.

Credit

Ross Richardson for PR #4082 and PR #4086, including the separable rank table and the request for one outside adapter. Preserve icekylinx/PR531, Rohan Arun/kernel92, Chris R/Clear1nsight, and ToikY as credited there. The mod-2 K/W tagging is recomputed here on the 12-bit monomials rather than imported.

Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent human or formal-kernel review is claimed. New work is Apache-2.0.

Open next questions

Linked from research/cut58-address-swap-menu/TASK.json:

1. Can a word in this 1008-element menu realize the cut58 matrix below 22f? That is the only way this adapter could still undercut stock. First step: extend one Prove a sharp native cost floor for six-bank cleanup #4086 character to <K,W,T,P>, or give an explicit cheaper word. Blocker: the generated subgroup did not close in a direct enumeration, and the separable characters are not claimed outside G.
2. Is there a phase-correct monomial outside this double coset cheaper than the separable tariff of the defect it replaces? First step: one explicit monomial not among the 1008. Blocker: no such monomial is priced here.

Workflow feedback (optional)

The event58 local-16 handoff on #1166 was still the tenth open item in chronological order, but its separable case was already closed by PR #4086 under a title that does not contain “cut58”. A handoff index that drops a request once an open PR states the same bound would have made that overlap visible before the menu calculation.