AutoSamplingTheory.SALD.discreteForwardKlDvFiniteLogMgfWitnessObligation

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 discreteForwardKlDvFiniteLogMgfWitnessObligation : 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.dv_finite_log_mgf_witness

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 discrete DV side interface for appendix lines 493-523: with nu=hat rho_s, mu=tilde pi_s=pi_{t(s)}, and Z=alpha*||v_{t(s)}||^2, derive the finite log-mgf condition from the continuous alpha0-complexity assumption, expose common-space and absolute-continuity for the EM interpolation law, divide by alpha>0, and preserve the dot t(s)^2 scaling before the time-change step.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteDvVelocitySource — 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. probability.dv_variational_formula
2. def:alpha-complexity
3. SALD.saldDvFiniteLogMgfContract
4. sald.dv_variation.finite_log_mgf_interface
5. sald.forward_kl.dv_alpha_mgf_monotonicity
6. sald.forward_kl.dv_finite_log_mgf_witness
7. sald.discrete_forward_kl.em_endpoint_laws
8. sald.discrete_forward_kl.em_interpolation_fp

note : String (explicit)

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

discreteForwardKlDvFiniteLogMgfWitnessContract narrows the Cycle 11 upper target to the theorem-specific EM-interpolation DV witness. It is not a new theorem assumption and does not mark DV or exponential-moment monotonicity formalized.

def discreteForwardKlDvFiniteLogMgfWitnessObligation : ProofObligation where
  id := "sald.discrete_forward_kl.dv_finite_log_mgf_witness"
  statement := "Formalize the discrete DV side interface for appendix lines 493-523: with nu=hat rho_s, mu=tilde pi_s=pi_{t(s)}, and Z=alpha*||v_{t(s)}||^2, derive the finite log-mgf condition from the continuous alpha0-complexity assumption, expose common-space and absolute-continuity for the EM interpolation law, divide by alpha>0, and preserve the dot t(s)^2 scaling before the time-change step."
  source := saldForwardKlDiscreteDvVelocitySource
  status := ProofStatus.obligation
  dependsOn := [
    "probability.dv_variational_formula",
    "def:alpha-complexity",
    "SALD.saldDvFiniteLogMgfContract",
    "sald.dv_variation.finite_log_mgf_interface",
    "sald.forward_kl.dv_alpha_mgf_monotonicity",
    "sald.forward_kl.dv_finite_log_mgf_witness",
    "sald.discrete_forward_kl.em_endpoint_laws",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "discreteForwardKlDvFiniteLogMgfWitnessContract narrows the Cycle 11 upper target to the theorem-specific EM-interpolation DV witness. It is not a new theorem assumption and does not mark DV or exponential-moment monotonicity formalized."