[unpaidmoon]

Change and mathematical scope

Partial negative classification. No new κ. The selected conditional exponent stays 60403/20000000 (0.00302015, #4470).

In the chart family of the uniform-commutation gap, an adjacent data line matches every character if and only if the exit chart and the next entrance chart are equal. The address space is F_2^4, and the charts are

C_u = ((1+i) I + (1-i) X_u) / 2,
X_u |z⟩ = (-1)^{u·z} |z⟩.

C_b C_a^{-1} acts by 1 on every character if and only if a = b. The 16 equal pairs match. Each of the 240 unequal pairs fails on exactly 8 characters, the odd set of a + b. The 15 entrance-I failures from #4136 are the column b = 0, a ≠ 0.

This is a finite exact classification of one chart family. It is not a multiplication theorem and not a supplier. Helper roles, an intertwiner, dirty restoration, and a hosting bill are out of scope.

Task and overlap

Base commit: fbc9ea0249746acca4f504d4fda2b84e0e36cf0d (upstream CrocSwap/integer-mult-bounds main). Package head: f8f3fb33a5d8f629ebd4b810cf1c07d21e49a0ca. The same tree is on fork draft unpaidmoon#77.

Task card: p104-side-correction (priority revision 7). Scope status: refined.

The card asks whether a changed producer/consumer contract escapes the scoped chart obstruction with a favorable full bill. Delivered P104 obstructions, including #4133, #4136, #4140, #4153, #4154, and #4370, are excluded. This package changes one hypothesis of #4136: the next entrance may be any chart C_b in the same family, not only I. That is the data-line half of #4136 open question 1 (discussion #1166 comment 19034066). It stops when every port-dependent data pair fails. It does not build the helper block or the channel bill.

This is distinct from the Π P_enc Π helper prices in fork PRs #64 and #65. This package does not use that operator. It enumerates the published C_u family only.

A port-dependent entrance was the stated way past the uniform chart obstruction. Inside this family it does not produce a data-line match, so that premise does not yet supply a cheaper P104 channel. No selected exponent is changed.

Validation

Python 3.12.3, standard library only, from the repository root. Run locally on this head:

python3 scripts/research_package.py --package research/p104-port-chart-pair --check-only
python3 -B scripts/research_package.py --package research/p104-port-chart-pair
python3 -B research/p104-port-chart-pair/verify.py
python3 -B research/p104-port-chart-pair/test_verify.py

verify.py evaluates C_u from the displayed formula, checks the four-case multiplier, and enumerates all 256 pairs. It does not import the #4136 package. Replacing the odd eigenvalue i by 1 matches all 256 pairs; that false witness is rejected.

Observed markers:

PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
PASS_P104_PORT_CHART_PAIR address=F2^4 charts=16 ordered_pairs=256 matching_pairs=16 failing_pairs=240 failures_per_unequal_pair=8 entrance_I_failures=15 data_match_iff_equal_charts=true helpers=out_of_model no_new_kappa
PASS_P104_PORT_CHART_PAIR_CONTROLS controls=counts,identity,half_fail,eigenvalues,closed_form,phase,odd_set
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-port-chart-pair outcome=partial

The multiplier table in PROOF.md is the proof argument. The scripts are a finite exhaustive check of the 256 pairs. Not run: Lean, Docker, the selected cold replay, a helper-role model, and any hosting or moment calculation.

Credit

The chart formula, the uniform-match statement, and the 15 entrance-I failures are PR #4136 (unpaidmoon), from the two-axis gate in PR #3954 (Chris R / Clear1nsight). The request for one adjacent pair is discussion #1166 comment 19034066. Predecessor lineage named in #4136 remains theirs, including Rohan Arun, Chafik Boukhalfa, and Adam Gall.

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

Open next questions

1. Does one helper block, written in this same chart family, have an exit and a next entrance that match on every helper role when the data charts already differ? First step: name the helper roles and their charts. Blocker: this package has no helper roles.
2. Is there a chart family outside {C_u}, still legal for the P104 encoding, in which two different charts transport every data character by 1? A positive example would reopen the adjacent-pair search. First step: write one alternative legal chart on the same 16 characters and test it against C_0. Blocker: no second chart family is an input of this package.

Workflow feedback (optional)

The package generator and research_package.py pin check made the catalogue card and source hashes mechanical. The fork's main is behind upstream, so the reviewable fork diff uses the existing pin branch cursor/upstream-main-fbc9ea-2eeb at the upstream commit.