AutoSamplingTheory.SALD.forwardKlDensityBoundaryObligation

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 forwardKlDensityBoundaryObligation : 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.forward_kl.density_boundary_regular

statement : String (explicit)

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

Formalize the density regularity, mass conservation, differentiation-under-the-integral, and boundary/integration-by-parts conditions used in appendix lines 168-208 for the KL derivative computation.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDerivativeSource — 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.cycle30ForwardKlUpperPacket
2. SALD.cycle30ForwardKlMiddleContract
3. sald.forward_kl.cycle30_derivative_side_upper
4. sald.forward_kl.cycle30_derivative_side_middle
5. SALD.forwardKlDerivativeSideConditionContract
6. SALD.forwardKlFirstTermFisherSubstitutionScalar
7. KLContract
8. FIContract
9. eq:FP-eq
10. TransportVelocityContract

note : String (explicit)

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

The paper uses these analytic side conditions implicitly; forwardKlDerivativeSideConditionContract and the cycle 30 middle packet record them before any attempt to prove the derivative inequality.

def forwardKlDensityBoundaryObligation : ProofObligation where
  id := "sald.forward_kl.density_boundary_regular"
  statement := "Formalize the density regularity, mass conservation, differentiation-under-the-integral, and boundary/integration-by-parts conditions used in appendix lines 168-208 for the KL derivative computation."
  source := saldForwardKlDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle30ForwardKlUpperPacket",
      "SALD.cycle30ForwardKlMiddleContract",
      "sald.forward_kl.cycle30_derivative_side_upper",
      "sald.forward_kl.cycle30_derivative_side_middle",
      "SALD.forwardKlDerivativeSideConditionContract",
      "SALD.forwardKlFirstTermFisherSubstitutionScalar",
      "KLContract",
      "FIContract",
      "eq:FP-eq",
    "TransportVelocityContract"
  ]
  note := "The paper uses these analytic side conditions implicitly; forwardKlDerivativeSideConditionContract and the cycle 30 middle packet record them before any attempt to prove the derivative inequality."