AutoSamplingTheory.SALD.cycle32DvVariationLowerObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle32DvVariationLowerObligation : ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

This Lean definition constructs provenance or workflow data. It does not prove the mathematical statements stored as text. Status labels, named dependencies and citations are data, not compilation, proof or source certificates.

id : String (explicit)

Stable obligation identifier.

sald.dv_variation.cycle32_lower_supremum_bridge

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Maintain the lower scalar bridge for appendix.tex lines 73-79: once the cited DV formula identifies KL(nu||mu) with the supremum over admissible finite-log-mgf test values, and the selected test value E_nu[Z]-logMgf is in that bounded admissible set, AutoSamplingTheory.dvVariationalOneSidedFromSupremumScalar derives E_nu[Z] <= KL(nu||mu)+logMgf.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldDvVariationSource — audited data reference, not expanded and not a compiled dependency edge

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. SALD.cycle32DvVariationUpperPacket
2. SALD.cycle32DvVariationInterfaceObligation
3. SALD.cycle32DvVariationMiddleAuditContract
4. SALD.cycle32DvVariationMiddleObligation
5. AutoSamplingTheory.dvVariationalOneSidedConsequenceScalar
6. AutoSamplingTheory.dvVariationalOneSidedFromSupremumScalar
7. probability.dv_variational_formula
8. dvVariationalFormulaInterface saldDvVariationSource
9. SALD.saldDvFiniteLogMgfContract
10. sald.dv_variation.finite_log_mgf_interface

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

The compiled theorem proves only the order-theoretic supremum-to-one-sided consequence over Real values. The bounded admissible-value set, common probability space, measurability, finite log-mgf, and the Boucheron DV equality itself are still explicit cited/obligation inputs.

def cycle32DvVariationLowerObligation : ProofObligation where
  id := "sald.dv_variation.cycle32_lower_supremum_bridge"
  statement := "Maintain the lower scalar bridge for appendix.tex lines 73-79: once the cited DV formula identifies KL(nu||mu) with the supremum over admissible finite-log-mgf test values, and the selected test value E_nu[Z]-logMgf is in that bounded admissible set, AutoSamplingTheory.dvVariationalOneSidedFromSupremumScalar derives E_nu[Z] <= KL(nu||mu)+logMgf."
  source := saldDvVariationSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle32DvVariationUpperPacket",
    "SALD.cycle32DvVariationInterfaceObligation",
    "SALD.cycle32DvVariationMiddleAuditContract",
    "SALD.cycle32DvVariationMiddleObligation",
    "AutoSamplingTheory.dvVariationalOneSidedConsequenceScalar",
    "AutoSamplingTheory.dvVariationalOneSidedFromSupremumScalar",
    "probability.dv_variational_formula",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "sald.dv_variation.finite_log_mgf_interface"
  ]
  note := "The compiled theorem proves only the order-theoretic supremum-to-one-sided consequence over Real values. The bounded admissible-value set, common probability space, measurability, finite log-mgf, and the Boucheron DV equality itself are still explicit cited/obligation inputs."

/-- Cycle-37 upper packet for the cited Donsker--Varadhan proof target.

This packet follows the current proof-closure order after cycle 36 advanced
the Gronwall assembly under explicit Mathlib side conditions.  It selects
`lem:dv_variation` as item (2), keeps Boucheron Corollary 4.15 source-cited,
and asks middle/lower work to sharpen the Lean theorem interface or prove only
backend sublemmas that genuinely build locally.
-/