[unpaidmoon]

Change and mathematical scope

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

PR CrocSwap#4086 (head cd0f22abce2b74d7d080a2e640c0f495d3d2c3aa) already proves that the q2 event58 separable suffix costs at least 22f for every f ≥ 2, and that the existing word attains 22f. A 16f suffix is impossible in that class. There is no open gap between 20 and 22.

This package records a weaker independent count in the same gate set: paid natives restricted to K, T, W and their inverses, plus ADD, rational SCALE, and BANK_SWAP. Six fresh queries, two K queries, and one W are disjoint, so the native mass is at least 20. That already excludes 16. It does not see PR CrocSwap#4086's chi_KW defect of rank 4D, which is what forces the third K and lifts the tariff to 22f. The mass-22 neutral rewrite is replayed. This is not a paid-profile or κ improvement, and it is not a multiplication theorem.

Task and overlap

Base commit bb4bccbf42844d2801487450727c2f63e10d1d0f (upstream main, priority revision 6).

Task card joint-query-controller, scope changed. The card asks for a literal producer magnitude ledger. Discussion CrocSwap#1166 comment 19039339, quoting PR CrocSwap#4082 (head ff277e8a958829954f371c85bdc447672266edbd), left a local16 suffix open. PR CrocSwap#4086 later closed it at 22f. A later address-swap menu prices the rank-0 source swap P and does not undercut 22f. This package does not reopen either result.

The three monomials are vendored from the CrocSwap#4082 head because that head is not a Git object of this checkout. verify.py checks SHA-256 057a8d5de8c64e63d37db78b26d83164fe1b64d71ce322b1d2cecadcccffd079 of operators.json.

Validation

Python 3.12, from commit 9a8b8de7f3cd0f8c36c02d49a48fc40ea420f652.

python3.12 -B scripts/research_package.py --package research/cut58-local16-native-floor

Observed:

PASS_CUT58_LOCAL16_NATIVE_FLOOR lower_bound=20 replayed_rewrite=22 target16=impossible_by_this_bound sharp_floor_not_reproved=pr4086 fresh_queries=6 k_queries=2 w_queries=1 group=256 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/cut58-local16-native-floor outcome=partial

verify.py checks the 256-element splitting, centrality of T, the one-K bimodule obstruction, the address-row obstruction, the low-bit representation of all 128 even monomials, representation rank 96 of the six cores, and equality of the mass-22 gate list with T on those cores. A duplicate-core control drops the rank to 80. The generator invariant is the written argument in PROOF.md. The sharp 22f character proof is not rerun.

Not run: Lean, Docker, the selected cold replay, the CrocSwap#4086 Gram and minor certificates, owner/scan/supplier pricing, and any outside-group adapter.

Credit

Ross Richardson, PR CrocSwap#4082, for the entrance, the matrix, and the mass-22 rewrite. Ross Richardson, PR CrocSwap#4086, for the sharp 22f separable tariff. Discussion CrocSwap#3606 carries both findings. The monomial multiplication is trimmed from the CrocSwap#4082 quadratic-chart code. Apache-2.0.

Substantial Cursor Grok 4.7 assistance for the algebra check and the writeup. This is not independent human or formal-kernel review.

Open next questions

None justified from this package. The sharp separable tariff is PR CrocSwap#4086, and the source ADDRESS swap was priced afterward without lowering 22f.

Workflow feedback

Comment 19039339 still says the local16 target is open, while PR CrocSwap#4086, later the same day, already closed it. A handoff line that names the closing PR would have avoided a weaker recount.