AutoSamplingTheory.SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation

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 cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation :
    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.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_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.

Sharpen the appendix.tex:1354-1387 backend for sald.general_moving_target_discrete.kl_derivative: hat X_s, X_k^eta, and X_{k+1}^eta live on a common filtered probability space; the compiled named-interpolation handoff proves hat rho_s endpoint laws rho_k^eta and rho_{k+1}^eta from pointwise endpoint identities and law representations; bar b_{k,s}(x) is a measurable integrable regular-conditional expectation given hat X_s=x; hat rho_s admits a density and is absolutely continuous with tilde pi_s where KL and FI are evaluated; and the weak conditional-drift Fokker-Planck equation holds before the KL derivative identity is differentiated.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.generalVaSaldEulerMaruyamaContract
2. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
3. SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff
4. SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation
5. sald.general_moving_target_discrete.em_interpolation_fp
6. sald.general_moving_target_discrete.derivative_side_conditions
7. EulerMaruyamaContract
8. FokkerPlanckContract
9. KLContract
10. FIContract

note : String (explicit)

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

This is the promised narrow middle backfill after the theorem-level route is wired. It is a source-dependency audit of local SDE/measure assumptions, guided only by local SLT one-step/disintegration patterns as reference; no SLT theorem is imported or marked formalized.

def cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit"
  statement := "Sharpen the appendix.tex:1354-1387 backend for sald.general_moving_target_discrete.kl_derivative: hat X_s, X_k^eta, and X_{k+1}^eta live on a common filtered probability space; the compiled named-interpolation handoff proves hat rho_s endpoint laws rho_k^eta and rho_{k+1}^eta from pointwise endpoint identities and law representations; bar b_{k,s}(x) is a measurable integrable regular-conditional expectation given hat X_s=x; hat rho_s admits a density and is absolutely continuous with tilde pi_s where KL and FI are evaluated; and the weak conditional-drift Fokker-Planck equation holds before the KL derivative identity is differentiated."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalVaSaldEulerMaruyamaContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscreteEmEndpointLawPairHandoff",
    "SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.derivative_side_conditions",
    "EulerMaruyamaContract",
    "FokkerPlanckContract",
    "KLContract",
    "FIContract"
  ]
  note := "This is the promised narrow middle backfill after the theorem-level route is wired. It is a source-dependency audit of local SDE/measure assumptions, guided only by local SLT one-step/disintegration patterns as reference; no SLT theorem is imported or marked formalized."

/-- Cycle-48 middle obligation tying the route audit and the narrow EM
endpoint/conditional-law interface to lower work. -/