AutoSamplingTheory.SALD.guidedResidualIdentityObligation

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 guidedResidualIdentityObligation : 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.guided_path_residual.identity

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 658-704: differentiate pi_t=Z_t^(-1)*p_t*exp(-f_t), add div(pi_t*u_t), cancel the divergence terms, substitute dot Z_t/Z_t, and prove the residual identity plus mean-zero property.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGuidedResidualSource — 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.guided_path_residual.normalizer_derivative
2. TransportVelocityContract
3. GuidedTiltContract

note : String (explicit)

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

This proposition supports thm:unified-forward-KL; do not replace the centered residual with an uncentered guide derivative.

def guidedResidualIdentityObligation : ProofObligation where
  id := "sald.guided_path_residual.identity"
  statement := "Formalize appendix lines 658-704: differentiate pi_t=Z_t^(-1)*p_t*exp(-f_t), add div(pi_t*u_t), cancel the divergence terms, substitute dot Z_t/Z_t, and prove the residual identity plus mean-zero property."
  source := saldGuidedResidualSource
  status := ProofStatus.obligation
  dependsOn := ["sald.guided_path_residual.normalizer_derivative", "TransportVelocityContract", "GuidedTiltContract"]
  note := "This proposition supports thm:unified-forward-KL; do not replace the centered residual with an uncentered guide derivative."