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Expose natural-state provider tail route#33

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freezed-corpse-143 wants to merge 1 commit into
rm-lieb-provider-theorem-pushfrom
rm-lieb-next-frontiers-s14-s16
Closed

Expose natural-state provider tail route#33
freezed-corpse-143 wants to merge 1 commit into
rm-lieb-provider-theorem-pushfrom
rm-lieb-next-frontiers-s14-s16

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@freezed-corpse-143

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Summary

  • Add matrixBernsteinQuadraticFormUpperTail_of_naturalStateProviderAssumptions as a public-friendly S16 wrapper over the existing conditioning-trace-MGF provider assumptions.
  • Wire the new route into the provider API/judge #check surfaces.
  • Document the boundary in docs/STATEMENTS.md, docs/RandomMatrixAPI.md, docs/Status.md, and docs/TestPlan.md.

Scope

This is an API/assumption-compression route only. It keeps the hard conditioning assumptions explicit and does not claim full Matrix Bernstein, Epstein affine-line concavity, Lieb, or Tropp one-step closure.

Stacking

Stacked on rm-lieb-provider-theorem-push / PR #32.

Testing

  • lake build HighDimProb.RandomMatrix.ConcentrationStatements
  • lake env lean HighDimProbTest/RandomMatrixLiebProviderAPI.lean
  • lake env lean HighDimProbJudge/RandomMatrix/LiebProviderUse.lean
  • python scripts/judge_policy_check.py
  • python .github/scripts/check_text_quality.py
  • git diff --check
  • Lean source placeholder scan
  • lake test
  • lake build
  • lake build HighDimProbJudge

Package the S16 tail wrapper as a public route over the existing provider-assumption record while keeping the S15 conditioning contract explicit.

Constraint: S15 audit leaves history/current conditioning as explicit assumptions until a sigma-algebra independence bridge is proved.

Rejected: compress ordinary iIndepFun into the conditional step contract | it would overstate the available conditioning theorem.

Confidence: high

Scope-risk: moderate

Directive: Do not market this wrapper as full Matrix Bernstein or as closing Epstein/Lieb/Tropp one-step.

Tested: lake build HighDimProb.RandomMatrix.ConcentrationStatements; lake env lean HighDimProbTest/RandomMatrixLiebProviderAPI.lean; lake env lean HighDimProbJudge/RandomMatrix/LiebProviderUse.lean; python scripts/judge_policy_check.py; python .github/scripts/check_text_quality.py; git diff --check; lake test; lake build; lake build HighDimProbJudge.

Not-tested: Provider S14 derivative primitives live in the separate HighDimProbLiebProvider repository.
@dududuguo

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Thanks for the careful provider-route work here. The useful S16 natural-state tail wrapper surface has now been manually integrated and refactored into main in 7413583 (Integrate Lieb provider bridge layer), along with the corresponding tests, judge check, and docs. I'm closing this stacked PR rather than merging the old branch because the final main version keeps the provider/core API split and avoids reintroducing older abstraction/doc structure.

@dududuguo dududuguo closed this Jun 27, 2026
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