Independent verification: complete minimum-word census for dirty fanout stars (no new kappa)

[RossRichardson]

Independent verification / scoped equality-count result; no new κ.

PR889 proves that its one-connector, one-source dirty fanout needs 2k+2 signed queries. This package independently checks that minimum for k=1..5 and counts every minimum-length labelled word: 4, 24, 288, 5,760, 172,800. A written proof characterizes the equality cases and gives 2(k+1)(k!)² for every k>=1 within that alphabet.

The new checker uses exact integer coefficient states and a symmetry quotient retaining labelled-word multiplicities, with proved safe pruning. An unquotiented, unpruned implementation agrees at every length for k=1,2. A separate free-associative-algebra interpreter checks all arbitrary dirty input columns of 60 actual emitted recursive programs and their literal inverses; five one-factor batches additionally pass strict star-alphabet and single-connector admission. Only the predecessor's emitter is executed; no predecessor interpreter, census or invoice is imported.

Reproduce offline with Python 3.10+ and the standard library:

python3 -I -B research/dirty-fanout-star-census/verify.py
python3 -I -O -B research/dirty-fanout-star-census/test_package.py

Expected marker: PASS_STAR_CENSUS k=1..5 minima=4,6,8,10,12 counts=4,24,288,5760,172800 emitter_cases=60 star_cases=5 controls=6 no_new_kappa; all 10 package tests pass. Normal/optimized runs agree. Six built-in controls and package mutations detect restoration/sign/order/alias failures, lost label multiplicity, invalid model ports, omitted source pins, source drift and receipt corruption. Standalone relocation and unchanged default-output bytes pass. Selected-record integrity and all five existing selected-result tests pass on both bases.

Original base: 91a2094f2e022930069e8cfdc810a3ea1b81cd09. Refreshed submission base: 47481c89fd30a43f8f882eb4b391e89c29273fd0. Subject PR889: e2021d1c9e06948528cbc0a8fd7079b671da981d; three verbatim files have SHA256/Git-blob pins. During verification main selected PR890 at κ=1661957774647029/10^18; this package leaves that selection and upstream/ unchanged. Only research/dirty-fanout-star-census/ differs from refreshed main.

Seed 79, independent-verification track. No pinned coordination issue exists; the local claim records three candidates, fixed coverage and stopping rule. The final queue refresh includes PR937. Concurrent PR934 extends PR889 to multiple sources and supplies optimal witnesses; this contribution adds the complete minimizer count for the one-source alphabet. PR896's nonlinear binary evaluator formalization is distinct. No superseded frontier or pending title is used as the accepted bound.

Credit CubeJerry / PR889 for the batched interface and original restricted-query minimum, and Chafik Boukhalfa / PR628 for the dirty-commutator lineage. Prepared for @RossRichardson with substantial OpenAI Codex assistance, including a delegated proof derivation/code review. Original notices and Apache-2.0 license are retained; no independent human review claimed.

The universal argument is a written mathematical proof, not proof-assistant formalization. Finite emitter checks do not establish all-size compilation, physical hosting/tape, rounded-leaf accuracy, supplier admission or the full multiplication theorem. No full repository regeneration, selected cold replay or hosted-CI success is claimed. There is no new supplier or exponent saving.

[Mister-Meeseeks]

100-PR batch review at df645942469e6a739ec94010a6068c398f4a6c86.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent dirty fanout minimizer census and equality-count proof in the signed one-connector star alphabet.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.