AutoSamplingTheory.SALD.cycle37DvVariationUpperObligation

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 cycle37DvVariationUpperObligation : 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.cycle37_upper_packet

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 cycle 37 upper packet for appendix.tex lines 73-79: after the cycle 36 Gronwall assembly, return to proof-closure priority item (2), lem:dv_variation, and direct middle/lower work toward either a genuinely compiling Mathlib-backed entropy-duality interface or a sharper source-cited theorem interface for the paper's Boucheron Corollary 4.15 display.

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.sourceCited — 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.cycle37DvVariationUpperPacket
2. SALD.dvContract
3. SALD.cycle32DvVariationUpperPacket
4. SALD.cycle32DvVariationInterfaceObligation
5. SALD.cycle32DvVariationMiddleObligation
6. SALD.cycle32DvVariationLowerObligation
7. AutoSamplingTheory.dvVariationalOneSidedConsequenceScalar
8. AutoSamplingTheory.dvVariationalOneSidedFromSupremumScalar
9. dvVariationalFormulaInterface saldDvVariationSource
10. probability.dv_variational_formula
11. SALD.saldDvFiniteLogMgfContract
12. sald.dv_variation.finite_log_mgf_interface
13. Mathlib InformationTheory.KullbackLeibler.Basic
14. Mathlib MeasureTheory.Measure.Tilted

note : String (explicit)

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

This is an upper-role assignment packet, not a proof of Donsker--Varadhan. The cited equality remains source-cited unless a local Lean theorem builds; the existing scalar lemmas are only post-DV order consequences.

def cycle37DvVariationUpperObligation : ProofObligation where
  id := "sald.dv_variation.cycle37_upper_packet"
  statement := "Maintain the cycle 37 upper packet for appendix.tex lines 73-79: after the cycle 36 Gronwall assembly, return to proof-closure priority item (2), lem:dv_variation, and direct middle/lower work toward either a genuinely compiling Mathlib-backed entropy-duality interface or a sharper source-cited theorem interface for the paper's Boucheron Corollary 4.15 display."
  source := saldDvVariationSource
  status := ProofStatus.sourceCited
  dependsOn := [
    "SALD.cycle37DvVariationUpperPacket",
    "SALD.dvContract",
    "SALD.cycle32DvVariationUpperPacket",
    "SALD.cycle32DvVariationInterfaceObligation",
    "SALD.cycle32DvVariationMiddleObligation",
    "SALD.cycle32DvVariationLowerObligation",
    "AutoSamplingTheory.dvVariationalOneSidedConsequenceScalar",
    "AutoSamplingTheory.dvVariationalOneSidedFromSupremumScalar",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "probability.dv_variational_formula",
    "SALD.saldDvFiniteLogMgfContract",
    "sald.dv_variation.finite_log_mgf_interface",
    "Mathlib InformationTheory.KullbackLeibler.Basic",
    "Mathlib MeasureTheory.Measure.Tilted"
  ]
  note := "This is an upper-role assignment packet, not a proof of Donsker--Varadhan. The cited equality remains source-cited unless a local Lean theorem builds; the existing scalar lemmas are only post-DV order consequences."

/-- Cycle-37 middle source-to-Lean map for the cited DV theorem.

This records the proof-producing Mathlib-backed sublemma now available for the
one-sided admissible-test inequality.  It does not promote the paper-cited
supremum equality to a local theorem.
-/