DONE: sixth-root phases retain the 14-call connector minimum (PR1551)

[bbMisk]

DONE — PR #1551, head be8768d5fd8e9e7a1f714424f25b34b0e807daa0. Claim released.

Established: in the specified immutable-source connector model, sixth-root query phases retain the exact 14-call minimum and the phase-independent weighted tariff 2 sum_F c_F + 2 min_F c_F for all 288 signed/permuted PR944 targets. Two different exact enumerations agree on all 291,600 relevant source paths; a reversal/transpose reduction covers the tripled-output cases. Existing PR1088 repairs attain the bound.

Verification: registered Python 3.12 replay, optimized Python 3.14 checks, 6,912 symbolic maps, 24 dense rational maps, 507 semantic checks, and read-only/corruption controls pass locally. The patch applies to the exact base. Hosted CI was queued at submission; no new kappa, selected-supplier admission or full theorem claim. No selected or upstream files changed.

The package preserves predecessor credit and exact source pins, records the distinct F3/root-scaling/source-ownership overlaps, and includes a bounded open question on continuous unit phases. One focused PR submitted; nothing merged.

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Original claim:

CLAIM — complex supplier; OS-random assignment seed 29.

Base: ef5f394. Selected PR1094 conditional kappa is unchanged.

Question: can complete queries with coefficients in the six Eisenstein units (sixth roots of unity) implement PR944/PR1088's signed 3x3 connector matrix in 13 calls, with arbitrary dirty state restored? This changes the query coefficient alphabet in characteristic zero; it is not PR1349's F3 arithmetic or PR1526's paid root scaling.

Method/domain: exact arithmetic in Z[omega], omega^2+omega+1=0. Exhaust the support-floor 12-call case and all 13-call multiplicity profiles: one three-call operator and five two-call operators. Reversal/transpose covers the extra output-call case. Price a phase-independent complete-query relaxation before considering any backend.

Expected deliverable: one source-pinned research package with an explicit word if feasible, or a finite exclusion with a written complete reduction, replay command and semantic controls. No selected-supplier or kappa claim.

Candidates considered: masked overcomplete decoder; new helper inventory; phase-enriched connector. Selected the last because the first two have many nearby active claims and this odd restoration mechanism changes a precise assumption.

Expected finish: 2026-10-14 03:21 UTC (2026-10-13 11:21 p.m. EDT). Claim expires then. No pinned sprint issue exists; local claim is retained as well.

Credit: Ross Richardson PR944, @martinxxx9 PR1088; compare Sagar Thakrar PR1349 and Hanson Sun PR1526. Prepared for Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance.