Prove trace-exp rank/support hardbone leaf#18
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Prove the local trace-exponential dimension-factor bounds from explicit support certificates and expose the witnesses through API, judge, example, and status docs without broadening the hardbone boundary. Constraint: Keep Tropp/Lieb, Golden-Thompson, trace-exp integrability, variance-proxy, support construction, effective-rank, full Matrix Bernstein, and unconditional concentration outside this leaf. Rejected: Cherry-picking later worker auto-checkpoints | they duplicated the leader-integrated proof/coverage and conflicted after canonical validation. Confidence: high Scope-risk: narrow Directive: Treat these theorems as support-certificate consumers only; do not cite them as support construction or effective-rank proofs. Tested: lake build HighDimProb.RandomMatrix.HardboneStatements; lake env lean HighDimProbTest/RandomMatrixHardboneStatementsAPI.lean; lake env lean HighDimProbJudge/RandomMatrix/TraceExpUse.lean; lake env lean HighDimProb/Examples/RandomMatrix/HardboneStatementAtlasUsage.lean; lake build HighDimProbJudge; lake build HighDimProb.Examples; lake test; lake build; python scripts/judge_policy_check.py; python .github/scripts/check_text_quality.py; git diff --check Not-tested: GitHub PR checks; PR creation/push intentionally not performed.
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Summary
traceMatrixExp_le_rank_exp_lambdaMaxtraceMatrixExp_le_supportDim_exp_lambdaMaxMotivation
This discharges the RM-HB12 rank/support hardbone leaf on top of the current sample-covariance CFC-free wrapper baseline. It turns two previously typed statement targets into checked theorem witnesses without widening the Matrix Bernstein theorem boundary.
Scope
upstream/main@f900a0c; PR head isc215c12.Testing
git diff --check upstream/main...HEADlake build HighDimProb.RandomMatrix.HardboneStatementslake env lean HighDimProbTest/RandomMatrixHardboneStatementsAPI.leanlake env lean HighDimProbJudge/RandomMatrix/TraceExpUse.leanlake env lean HighDimProb/Examples/RandomMatrix/HardboneStatementAtlasUsage.leanpython scripts/judge_policy_check.pypython .github/scripts/check_text_quality.pylake build HighDimProbJudgelake build HighDimProb.Exampleslake testlake build