AutoSamplingTheory.SALD.discreteForwardKlEmEndpointObligation

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 discreteForwardKlEmEndpointObligation : 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.discrete_forward_kl.em_endpoint_laws

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 appendix lines 260-266 and 334-335: the continuous EM interpolation hat X_s has endpoint laws hat rho_{s_k}=rho_k^eta and hat rho_{s_{k+1}}=rho_{k+1}^eta on each step.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteInterpolationSource — 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. EulerMaruyamaContract
2. SALD.discreteForwardKlEmEndpointLawPairHandoff

note : String (explicit)

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

This is endpoint law bookkeeping for stitching local EM intervals; cycle 40 lower proves the endpoint law pair once explicit named-law representations for hat rho_s and rho_k^eta are supplied. It does not construct Brownian laws, densities, or any KL inequality.

def discreteForwardKlEmEndpointObligation : ProofObligation where
  id := "sald.discrete_forward_kl.em_endpoint_laws"
  statement := "Formalize appendix lines 260-266 and 334-335: the continuous EM interpolation hat X_s has endpoint laws hat rho_{s_k}=rho_k^eta and hat rho_{s_{k+1}}=rho_{k+1}^eta on each step."
  source := saldForwardKlDiscreteInterpolationSource
  status := ProofStatus.obligation
  dependsOn := ["EulerMaruyamaContract", "SALD.discreteForwardKlEmEndpointLawPairHandoff"]
  note := "This is endpoint law bookkeeping for stitching local EM intervals; cycle 40 lower proves the endpoint law pair once explicit named-law representations for hat rho_s and rho_k^eta are supplied. It does not construct Brownian laws, densities, or any KL inequality."