Add centered operator norm boundedness bridge#9
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Expose the centered random-matrix bound as a small algebraic wrapper around the deterministic operator-norm triangle inequality, while keeping the stronger analytic obligations out of scope. Constraint: stacked on PR #8 because the centered bridge reuses the rank-one operator-norm API branch as its clean base. Rejected: proving expectation contraction or measurability/integrability here | those are separate next safe tasks and would broaden the review surface. Confidence: high Scope-risk: narrow Directive: Keep this PR framed as explicit-bound algebra only; do not present it as a full centered Matrix Bernstein prerequisite closure. Tested: lake build; lake test; lake build HighDimProbJudge; python scripts/judge_policy_check.py; git diff --check; forbidden-token and conflict-marker scans Not-tested: GitHub PR CI, because the branch has not been pushed or opened in this local preparation step.
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Summary
deterministicOperatorNorm_sub_le_addfrom the deterministic operator-norm API.BoundedOperatorNorm/PointwiseOperatorNormBoundwrappers forcenteredRandomMatrixusing an explicit bound onmatrixExpect P X.Motivation
This is the next small prerequisite after the rank-one operator-norm bound bridge. Matrix Bernstein setup often needs a centered summand bound, but this PR intentionally keeps the result algebraic and explicit: it uses the triangle inequality and a supplied expectation-norm bound, without proving expectation contraction or vector-to-matrix integrability.
Scope
HighDimProb.RandomMatrix.OperatorNormHighDimProb.RandomMatrix.AssumptionsHighDimProbJudge.RandomMatrix.OperatorNormUseThis PR does not prove:
matrixExpectStacking
This PR is intended to be stacked on #8 (
rm-rank-one-operator-norm-bound) so the review diff contains only the centered operator-norm increment. After #8 lands, this PR can be retargeted tomainif needed.Review gates
git diff --checkpassed.Testing
HighDimProb,HighDimProbTest,HighDimProbJudgegit diff --checklake buildlake testlake build HighDimProbJudgepython scripts/judge_policy_check.py