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…uction Explicit arbitrary-input root family, transported-idle obstruction, and exact complete caller lower invoice. No new kappa. Prepared for @CubeJerry with substantial OpenAI GPT-6 assistance and independent construction/accounting checks.
… certificates Certify all feasible relaxed idle supports and complete costs, with independent nullspace/pricing checks and a uniform no-reentry bound through kappa .01. No new kappa. Prepared for @CubeJerry with substantial OpenAI assistance.
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Change and mathematical scope
No new κ. Construct the even-L root and correct one excess physical idle incidence in #6868's proxy. All 90 specified L18/pivot8 enlargements lose at κ=.00337180, with no reentry through .01 under the fixed-word, unchanged-native, whole-idle contract. Frames must be data-independent or nondegenerate at D=1,S=-1.
Task and sources
Base 7c49fe3. #6868: 5a4f80e; #6833: 51f54e3. Distinct from #6858.
Validation
python3 -B scripts/research_package.py --package research/p104-uncovered-pivot-rootExpected: PASS_REGISTERED_RESEARCH_PACKAGE. Eight registered checks, independent geometry/pricing, normal/-O and read-only exports passed. Controls reject missing thin/pivot terms, corrupt inputs and infeasible prices. Complete remote tree matches tested files.
Limitations and credit
All five assumptions remain. Optimistic covers need not be attainable; other masks, dense duals and changed words remain open. No native/compiler admission. Full-history preflight unrun on shallow checkout. @CubeJerry with substantial OpenAI assistance and separate review; credit DreamingOfClouds, Ali Romman and retained lineage.
Proofs, exact byte pins, receipts and remaining questions.