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Research: four signed-connector transfers force unit coefficients - #1983
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Batch review at Merged to Reviewed scope: Written reduction forces unit coefficients and fixed ports for exactly twelve signed queries and four nonzero one-way restoring transfers, even allowing arbitrary rational/complex transfer coefficients. Independent cube-walk and exact linear-system checks corroborate the proof. Other query counts, bidirectional alphabets and supplier implementations are excluded from the claim. 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. |
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The signed 3×3 connector's port theorem in #1682 excludes nonunit transfers. This contribution proves that its entire enlarged coefficient alphabet collapses to the unit class: with exactly twelve ordinary signed child queries and four nonzero one-way root transfers over Q or C, every transfer coefficient must be +1 or −1. The six operator ports and complete fixed additive tariff are therefore unchanged.
Status: scoped theorem / research note; no new κ. The proof retains arbitrary independent dirty roots, immutable sources, unread outputs, and uniform correctness for arbitrary linear Ai/Bj. Equal-height readouts force one transfer pair to be unit; restoration of the same source coefficient forces the other pair. The included proof independently establishes the port reduction and then forces all four coefficients to be units.
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research/nonunit-signed-connector-rigidity/is added. Reproduce:Expected:
PASS_NONUNIT_SIGNED_CONNECTOR_RIGIDITY.A six-vertex/two-leaf cube argument supplies a direct written proof of the inherited one-root obstruction, with finite checks as corroboration. Verification includes generic exact elimination versus a separate difference formula on all 192 coefficient systems; event permutations versus cube-state dynamic programming on the inherited 720-walk obstruction; free noncommutative forward/inverse maps; and separate dense block-matrix checks on all 16 dirty basis columns. All 48 consistent coefficient systems have unit solutions. Seventeen semantic program mutations fail. Valid scaled-query and six-transfer controls show that the named restrictions matter. Read-only relocation and two actual source-corruption controls pass.
Primary checks pass on stable CPython 3.15.0 through the research wrapper. The repository's explicitly pinned Python 3.12 registered replay also passes on 3.12.12. Metadata/source pins, selected-record verification, five selected-record tests, binding-only baseline and diff checks pass. Hosted CI is separate. The written program-to-equation reduction is not proof-assistant or independently human-reviewed evidence; the distinct models were written by the same assistant.
Credit Ross Richardson's #944 target/one-root obstruction, #1651 attaining word and #1682 unit-port argument; Charles Bethin's #1637 dirty two-root interface; Cinna Davis's #1675 distinct bidirectional short-transfer obstruction; and the predecessor notices retained in NOTICE.md. Exact heads and source hashes are supplied. The 7,257,600-trace unit census is not repeated or claimed as a new result. This closes its excluded coefficient freedom rather than adding a small tested coefficient neighborhood.
No selected-supplier seam, physical admission, new recursive schedule, full cold replay, selected-frontier change or new multiplication exponent is claimed. Complete child/source/frame/restoration/transfer/control costs remain in the conditional tariff. Substantial OpenAI Codex assistance is disclosed. Apache-2.0.