Thread explicit Tropp assumptions forward#28
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Constraint: Hard Lieb/Jensen, log-order, and trace-exp monotonicity providers are being filled separately, so this leaf must consume them explicitly rather than prove them. Rejected: Waiting for all hard assumptions before composing the one-step route | the current strategy is progress-first with assumptions recorded in docs/STATEMENTS.md Confidence: high Scope-risk: narrow Directive: Keep future high-level Tropp progress assumption-consuming unless a separate provider theorem actually discharges the analytic input. Tested: 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 Not-tested: Provider proofs for Lieb concavity, Jensen, operator-log monotonicity, trace-exp monotonicity, conditional expectation, integrability propagation, and full Matrix Bernstein remain open.
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Summary
HardboneStatements.Motivation
This advances the Lieb/Tropp roadmap by exposing the next conditional trace-MGF composition layer while keeping the hard analytic steps as explicit assumptions rather than overstating proved results.
Scope
HighDimProb/RandomMatrix/HardboneStatements.lean.main; this is stacked on the S6 CStar transport branch.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