AutoSamplingTheory.SALD.cycle32DvVariationMiddleObligation

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 cycle32DvVariationMiddleObligation : 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_middle_source_to_lean

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 middle source-to-Lean map for appendix.tex lines 73-79 after the local Mathlib audit: DV equality remains Boucheron-source-cited, while the one-sided consequence uses only the compiled scalar rearrangement from E_nu[Z]-logMgf <= KL to E_nu[Z] <= KL+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. AutoSamplingTheory.dvVariationalOneSidedConsequenceScalar
5. probability.dv_variational_formula
6. dvVariationalFormulaInterface saldDvVariationSource
7. SALD.saldDvFiniteLogMgfContract

note : String (explicit)

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

The only new compiled proof is real-order algebra. The analytic entropy-duality theorem, common-space witness, measurable-test witness, and finite-log-mgf witness are not closed.

def cycle32DvVariationMiddleObligation : ProofObligation where
  id := "sald.dv_variation.cycle32_middle_source_to_lean"
  statement := "Maintain the middle source-to-Lean map for appendix.tex lines 73-79 after the local Mathlib audit: DV equality remains Boucheron-source-cited, while the one-sided consequence uses only the compiled scalar rearrangement from E_nu[Z]-logMgf <= KL to E_nu[Z] <= KL+logMgf."
  source := saldDvVariationSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle32DvVariationUpperPacket",
    "SALD.cycle32DvVariationInterfaceObligation",
    "SALD.cycle32DvVariationMiddleAuditContract",
    "AutoSamplingTheory.dvVariationalOneSidedConsequenceScalar",
    "probability.dv_variational_formula",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract"
  ]
  note := "The only new compiled proof is real-order algebra. The analytic entropy-duality theorem, common-space witness, measurable-test witness, and finite-log-mgf witness are not closed."

/-- Cycle-32 lower scalar bridge for the cited DV formula.

This records the proof-producing lower slice: from a bounded set of admissible
variational values, membership of the selected test, and the source-cited
supremum identity, Lean derives the one-sided real inequality used downstream.
The cited entropy-duality theorem and theorem-specific admissibility witnesses
remain obligations.
-/