AutoSamplingTheory.SALD.forwardKlCoefficientChainObligation

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 forwardKlCoefficientChainObligation : 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.coefficient_chain_audit

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 coefficient bookkeeping in appendix lines 210-252: after Young and LSI, the time change yields the (1/2)*dot{s}(t)^(-1) velocity coefficient; DV contributes (1/2)*dot{s}(t)^(-1)*alpha^(-1) to the scalar a(t); Gronwall is then applied with the source a(t), b(t), followed by the exact exponent split and residual-exponent simplification in main_body.tex lines 243-246.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDependencyChainSource — 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.forward_kl.moving_target_dependency_chain
2. sald.forward_kl.endpoint_schedule_identities
3. sald.forward_kl.kl_derivative
4. sald.forward_kl.dv_energy_bound
5. sald.forward_kl.gronwall_application
6. sald.forward_kl.gronwall_side_conditions
7. probability.lsi_to_kl_fi
8. probability.dv_variational_formula
9. sald.gronwall.integrating_factor

note : String (explicit)

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

forwardKlDependencyChainAuditContract records the exact source coefficients and endpoint identifications. This is an audit obligation, not an additional theorem assumption.

def forwardKlCoefficientChainObligation : ProofObligation where
  id := "sald.forward_kl.coefficient_chain_audit"
  statement := "Formalize the coefficient bookkeeping in appendix lines 210-252: after Young and LSI, the time change yields the (1/2)*dot{s}(t)^(-1) velocity coefficient; DV contributes (1/2)*dot{s}(t)^(-1)*alpha^(-1) to the scalar a(t); Gronwall is then applied with the source a(t), b(t), followed by the exact exponent split and residual-exponent simplification in main_body.tex lines 243-246."
  source := saldForwardKlDependencyChainSource
  status := ProofStatus.obligation
  dependsOn := [
    "sald.forward_kl.moving_target_dependency_chain",
    "sald.forward_kl.endpoint_schedule_identities",
    "sald.forward_kl.kl_derivative",
    "sald.forward_kl.dv_energy_bound",
    "sald.forward_kl.gronwall_application",
    "sald.forward_kl.gronwall_side_conditions",
    "probability.lsi_to_kl_fi",
    "probability.dv_variational_formula",
    "sald.gronwall.integrating_factor"
  ]
  note := "forwardKlDependencyChainAuditContract records the exact source coefficients and endpoint identifications.  This is an audit obligation, not an additional theorem assumption."