AutoSamplingTheory.SALD.discreteForwardKlEmConditionalFpObligation

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 discreteForwardKlEmConditionalFpObligation : 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_conditional_fokker_planck

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 347-385: define the conditional frozen drift bar b_{k,s} and derive the interpolation Fokker--Planck equation partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + Delta hat rho_s, including the Laplacian split relative to tilde pi_s.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteConditionalFpSource — 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.cycle15DiscreteForwardKlUpperPacket
2. SALD.cycle35DiscreteForwardKlEmFpUpperPacket
3. SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract
4. sald.discrete_forward_kl.cycle35_em_fp_upper
5. sald.discrete_forward_kl.conditional_drift_density
6. sald.discrete_forward_kl.em_endpoint_laws
7. FokkerPlanckContract
8. KLContract
9. FIContract

note : String (explicit)

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

The cycle-15 upper/middle packets and cycle-35 proof-closure packet select this as the lower slice. The source invokes it as the Fokker--Planck equation associated with the frozen interpolation; Lean still needs a conditional-expectation, density, Laplacian-split, and integration-by-parts backend.

def discreteForwardKlEmConditionalFpObligation : ProofObligation where
  id := "sald.discrete_forward_kl.em_conditional_fokker_planck"
  statement := "Formalize appendix lines 347-385: define the conditional frozen drift bar b_{k,s} and derive the interpolation Fokker--Planck equation partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + Delta hat rho_s, including the Laplacian split relative to tilde pi_s."
  source := saldForwardKlDiscreteConditionalFpSource
  status := ProofStatus.obligation
  dependsOn := ["SALD.cycle15DiscreteForwardKlUpperPacket", "SALD.cycle35DiscreteForwardKlEmFpUpperPacket", "SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract", "sald.discrete_forward_kl.cycle35_em_fp_upper", "sald.discrete_forward_kl.conditional_drift_density", "sald.discrete_forward_kl.em_endpoint_laws", "FokkerPlanckContract", "KLContract", "FIContract"]
  note := "The cycle-15 upper/middle packets and cycle-35 proof-closure packet select this as the lower slice. The source invokes it as the Fokker--Planck equation associated with the frozen interpolation; Lean still needs a conditional-expectation, density, Laplacian-split, and integration-by-parts backend."