Compose conditional trace-MGF assumptions#29
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Compose the existing conditioning bridge into the natural-state finite-family trace-MGF route while keeping every hard probabilistic and analytic ingredient explicit and ledgered for provider work.\n\nConstraint: Progress-first theory mode allows missing hard ingredients as explicit assumptions recorded in docs/STATEMENTS.md.\nRejected: Waiting for history, independence, conditional-expectation, integrability, or Lieb providers | current strategy is to unblock downstream composition first.\nConfidence: high\nScope-risk: narrow\nDirective: Do not treat this as an unconditional Matrix Bernstein or Tropp/Lieb proof; it is an assumption-composition consumer.\nTested: lake build HighDimProb.RandomMatrix.HardboneStatements; lake env lean HighDimProbTest/RandomMatrixHardboneStatementsAPI.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; lake build\nNot-tested: GitHub CI and PR checks not run locally
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Summary
traceMGFBernsteinVarianceProxyBound_of_conditioningBridge.Motivation
This keeps theory progress moving by packaging the S9 conditional step as a reusable contract, with unresolved analytic obligations exposed as explicit assumptions rather than hidden in the wrapper.
Scope
HighDimProb/RandomMatrix/HardboneStatements.lean.main.Testing
git diff --checkpython .github/scripts/check_text_quality.pypython scripts/judge_policy_check.pylake build HighDimProb.RandomMatrix.HardboneStatementslake env lean HighDimProbTest/RandomMatrixHardboneStatementsAPI.leanlake env lean HighDimProbJudge/RandomMatrix/TraceExpUse.leanlake test