Prove honest real-to-CStar positivity transport leaf#27
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Prove honest real-to-CStar positivity transport leaf#27freezed-corpse-143 wants to merge 1 commit into
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Constraint: Real PSD-to-complex positivity and CFC log-back compatibility are not proved in this leaf. Rejected: Proving the existing real MatrixLE statement directly | it would require a separate real-to-complex positivity bridge not established here Confidence: high Scope-risk: narrow Directive: Do not replace explicit complexified premises with real MatrixLE/IsPSDMatrix assumptions without a proved complexification bridge. Tested: lake build HighDimProb.RandomMatrix.CStarBridge; lake env lean HighDimProbTest/RandomMatrixCStarBridgeAPI.lean; python .github/scripts/check_text_quality.py; python scripts/judge_policy_check.py; git diff --check; lake build HighDimProbJudge; lake test; lake build Not-tested: Direct real PSD/MatrixLE-to-complex positivity and unconditional CFC.log transport remain open.
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Closing this PR under the current repository strategy. The real-to-CStar transport direction is mathematically useful, but this layer should move to the independent finite-dimensional matrix inequalities/proof-provider line rather than becoming part of HighDimProb's long-term public API surface. HighDimProb should keep clean statement targets and adapters, while hard CStar/functional-calculus proofs are developed outside the main user-facing route. |
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Summary
CStarMatrixCStar-side transport lemmas from explicit complexified nonnegativity, Loewner-order, and strict-positivity premises.CFC.logcompatibility.Boundary
MatrixLE, or strict-positivity facts automatically supply the complexified premises.CFC.loglog-back compatibility.Test Plan
lake build HighDimProb.RandomMatrix.CStarBridgelake env lean HighDimProbTest/RandomMatrixCStarBridgeAPI.leanpython .github/scripts/check_text_quality.pypython scripts/judge_policy_check.pygit diff --checklake build HighDimProbJudgelake testlake build