Price the standard-Y consumer of the encoded P104 exit.

[unpaidmoon]

Change and mathematical scope

Negative result. No new κ. Selected κ stays 0.001672660197076918.

Discussion #1166 comment 19032700 asks for one downstream consumer that keeps the PR #3943 encoded endpoint and does not pay an unaffordable source return. In the FULL-only adapter alphabet, the standard product entrance Y_i = w_i in H_i already costs 192 rank-one transports. That is the legacy return floor. The further scalar repair that restores X adds 384 unit additions and no transport.

The product defect v_N - w_N has rank 96, so none of those ports already holds the product. An explicit program attains the floor with 576 unit additions, leaves X_J = q, and replaces X_N = w_N by X_N = x_N. Both exits have frame-dimension total 2416. With the PR #3943 credit 2312, rank masses 2576 and 2768 give nine-stage gaps 1544 and 3272. The standard-Y consumer pays 352 s + 104. The scalar cleanup saving is not in that rank mass.

This is an alphabet lower bound and an exact invoice. It is not a supplier, a native-phase replay, or a multiplication theorem.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, priority revision 6).
• Head: 3f160b55ba1d83e4dbe47729d352833302ef73aa.
• Task: p104-side-correction, scope changed. The card asks for a chronological correction program. This session prices the downstream consumer left by the encoded exit.
• Handoff: Handoffs and requests for independent checks #1166 (reply in thread) (task 2; task 1 is PR Audit matched P104 source-return adapters and their 192-ADD difference #3956).
• Predecessor: PR research: consume P104 residuals in actual cleanup and price source return #3943, encoded exit, inverse, and adapter alphabet. The geometry is rebuilt from research/p104-native-channel/inputs/P104-FIXTURE.json at this base (SHA-256 516c06f6ec3cb84be588c546108de897650288576dd5fbf5fe44b9c5546ad8a4). PR research: consume P104 residuals in actual cleanup and price source return #3943's executable is not imported.

Ordered eligible handoffs, chronological on #1166 in the numbered-question order published with PR #4142, after dropping tasks delivered or refined by this round through #4157 and tasks already performed by an open PR:

1. The (7, 18) / (7, 20) functional census (comment 19021170, question 1). Question 2 is Prove codimension-one L/2 substitution soundness on double transversals. #4148.
2. The largest child rank a physical local word on the selected template can emit (comment 19021222).
3. This standard-Y consumer of the encoded exit (comment 19032700, task 2).

Dropped before that cut, among others: single-hub and third-hub tariffs (#4124, #4145); T488 ownership (#4150); the rank-8/u2 contract (#4151, #4156); the H = GQ^{-1} endpoint factor (open #4108); integer shear (#4126, #4135, #4139, #4146); the #3942 review and two-neighbour invoices (#4134, #4128, #4144); fiber tags (#4154); source-chart fusion (#4153); the K/adjoint price (#4155); the transported frame (#4157).

Nearest overlap: PR #3943 proves the 192-transport floor for restoring x while keeping w, and the equal-profile screen. This package is the different obligation that the product itself be presented on every Y_i. PR #3956 matches return adapters. PR #4006 fuses late FULL delivery with cleanup and does not price this entrance. The split read that leaves every bank in place is not this contract; section 1 of PROOF.md shows it does not put w_N on Y_N.

Validation

CPython 3.12.3, standard library. Registered replay:

python3.12 -B scripts/research_package.py --package research/p104-encoded-exit-consumer

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/p104-encoded-exit-consumer outcome=negative-result.

Direct checks, including under -O:

python3.12 -B research/p104-encoded-exit-consumer/verify.py

print PASS_P104_ENCODED_EXIT_CONSUMER with transports=192, unit_adds=576, legacy_unit_adds=960, v_minus_w_rank=96, mass=2768, progress=2312, deficit9=3272, encoded_deficit9=1544, and no_new_kappa=true.

scripts/research_package.py --check-only passed. scripts/check_research_commit.py --check-source-history passed at 3f160b55ba1d83e4dbe47729d352833302ef73aa, with source history bb4bccbf42844d2801487450727c2f63e10d1d0f.

The checker rejects a program that skips one required lift, and it records that skipping one descent leaves that Y bank in FULL. The 192-transport lower bound for every program is the argument in PROOF.md; the checker tests the witness realizability, the alphabet invoice, and the integer screen that argument uses.

Not run: the PR #3943 native prefix, Lean, Docker, and the selected cold replay.

Credit

Chris R / Clear1nsight, PR #3943, for the encoded exit, the inverse, the adapter alphabet, and the paired-chain screen. PR #3956 for the matched return-adapter audit. PR #4006 for the separate late-delivery fusion. Rohan Arun / PR #1972, Chafik Boukhalfa / PR #1991, and Adam Gall / PR #1940 for the channel and schedule retained by the fixture. Josie Elliston / PR #1071 for the fixture lineage carried on main.

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

1. Can one legal cross-chart add, or one clean scratch bank, move w_n onto Y_n for fewer than 192 transports? The bound uses the FULL-only alphabet. Blocked until that operation is shown legal on the native word and given a rank tariff.
2. Does any pinned next-stage caller accept the split entrance that reads w_N from X_N and w_J from Y_J? That entrance has no transport in this model and is not the standard Y contract. Blocked: no such caller is an input here.

Workflow feedback (optional)

#1200