Thread conditional trace-MGF into tail route#30
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Thread the S9 conditioning trace-MGF consumer into the existing quadratic-form Laplace route only under explicit tail-side measurability and event-subset premises. Record the remaining analytic/provider gaps in the assumption ledger and API docs so the wrapper cannot be mistaken for a full Matrix Bernstein theorem. Constraint: RM-LIEB-S10 permits progress-first composition but forbids proving or implying full Matrix Bernstein, Tropp/Lieb, Golden-Thompson, conditional-expectation, integrability propagation, variance-proxy hard facts, or tail-event domination. Rejected: Add an optimized public Matrix Bernstein theorem | that would hide theta optimization, dimension/rank reduction, and tail-side provider gaps not proved in this task. Confidence: high Scope-risk: narrow Directive: Keep this wrapper as an explicit-assumption bridge until separate provider theorems discharge the tail-event and conditioning assumptions. Tested: lake build HighDimProb.RandomMatrix.ConcentrationStatements; lake build HighDimProb.RandomMatrix; lake build HighDimProb.RandomMatrix.HardboneStatements; lake env lean HighDimProbTest/RandomMatrixConcentrationAPI.lean; lake env lean HighDimProbJudge/RandomMatrix/MatrixBernsteinUse.lean; lake env lean HighDimProbJudge/RandomMatrix/TraceExpUse.lean; python .github/scripts/check_text_quality.py; python scripts/judge_policy_check.py; git diff --check; lake build HighDimProbJudge; lake test Not-tested: push, PR, or external CI
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Summary
matrixBernsteinQuadraticFormUpperTail_of_conditioningTraceMGFBridgeas a thin S10 wrapper.Motivation
This advances the Lieb/Tropp stack from the conditional trace-MGF contract toward a downstream tail route without claiming a full Matrix Bernstein theorem or hiding remaining analytic assumptions.
Scope
HighDimProb/RandomMatrix/ConcentrationStatements.lean.#checkcoverage.main.Testing
git diff --checkpython .github/scripts/check_text_quality.pypython scripts/judge_policy_check.pylake build HighDimProb.RandomMatrix.ConcentrationStatementslake build HighDimProb.RandomMatrixlake build HighDimProb.RandomMatrix.HardboneStatementslake env lean HighDimProbTest/RandomMatrixConcentrationAPI.leanlake env lean HighDimProbJudge/RandomMatrix/MatrixBernsteinUse.leanlake env lean HighDimProbJudge/RandomMatrix/TraceExpUse.leanlake build HighDimProbJudgelake test