AutoSamplingTheory.SALD.discreteForwardKlEmInterpolationObligation

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 discreteForwardKlEmInterpolationObligation : 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_interpolation_fp

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Assemble appendix lines 260-385: the continuous Euler--Maruyama interpolation hat X_s has endpoint laws rho_k^eta and satisfies the conditional-drift Fokker--Planck equation used in the discrete KL derivative block.

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. SALD.cycle15DiscreteForwardKlUpperPacket
2. SALD.cycle35DiscreteForwardKlEmFpUpperPacket
3. sald.discrete_forward_kl.cycle35_em_fp_upper
4. sald.discrete_forward_kl.em_endpoint_laws
5. sald.discrete_forward_kl.em_conditional_fokker_planck
6. EulerMaruyamaContract
7. FokkerPlanckContract
8. KLContract
9. FIContract

note : String (explicit)

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

The source uses the interpolation Fokker--Planck equation as a standard fact; discreteForwardKlEmInterpolationSideConditionContract keeps the endpoint, conditional-drift, and stitched-interval interfaces explicit for the cycle-15 lower packet and the cycle-35 proof-closure handoff.

def discreteForwardKlEmInterpolationObligation : ProofObligation where
  id := "sald.discrete_forward_kl.em_interpolation_fp"
  statement := "Assemble appendix lines 260-385: the continuous Euler--Maruyama interpolation hat X_s has endpoint laws rho_k^eta and satisfies the conditional-drift Fokker--Planck equation used in the discrete KL derivative block."
  source := saldForwardKlDiscreteInterpolationSource
  status := ProofStatus.obligation
  dependsOn := ["SALD.cycle15DiscreteForwardKlUpperPacket", "SALD.cycle35DiscreteForwardKlEmFpUpperPacket", "sald.discrete_forward_kl.cycle35_em_fp_upper", "sald.discrete_forward_kl.em_endpoint_laws", "sald.discrete_forward_kl.em_conditional_fokker_planck", "EulerMaruyamaContract", "FokkerPlanckContract", "KLContract", "FIContract"]
  note := "The source uses the interpolation Fokker--Planck equation as a standard fact; discreteForwardKlEmInterpolationSideConditionContract keeps the endpoint, conditional-drift, and stitched-interval interfaces explicit for the cycle-15 lower packet and the cycle-35 proof-closure handoff."