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Prove positive common-covector correlation over every finite field (no κ) #6703

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Mister-Meeseeks merged 1 commit into from
Nov 10, 2026
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Prove positive common-covector correlation over every finite field (no κ) #6703

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834 changes: 834 additions & 0 deletions research/common-covector-all-field-positive/CASES.json
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19 changes: 19 additions & 0 deletions research/common-covector-all-field-positive/NOTICE
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Common-covector all-field positive sign corollary
Prepared for ToikY with substantial OpenAI Codex assistance; Apache-2.0.
Separate AI primary, independent oracle and static review are not independent
human acceptance or formal proof-kernel checking.

Nick Petalas, PR4807: exact all-field common-covector count, orbit and dependent-
pair subtraction; binary strict-positive theorem; explicit odd-field sign
question and suggested q*delta-alpha^2=q-1 identity. This package adds only the
quantified remaining sign proof, not a new count or generic correlation principle.
Nick Petalas PR4227: marginal law; PR4261: partial-sum/header counting method;
PR4778: two-way-coupling question; PR4769/4274: one-way comparison context.
Cinna Davis: BIT request context. source527, commdata2338, Jose Manuel and all
retained normalizer/recursive-closure lineage retain predecessor credit.
Two exact source prose objects and their original notices remain in inputs/.
No predecessor program is copied, imported or executed.

Classical elementary polynomial identities and rational inequalities are used.
Douglas Colkitt and other repository contributors retain task/replay-framework
credit. No supplier, physical caller, kappa or selected-frontier change follows.
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