AutoSamplingTheory.SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation

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 cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation :
    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.cycle80_conditional_law_middle

statement : String (explicit)

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

Cycle 80 middle synchronizes appendix.tex lines 1368-1377 with the existing cycle-70/74/75 conditional-law interfaces after checking the SLT reference style. The lower theorem boundary is: on the common EM probability space, instantiate a regular conditional kernel for X_k^eta given hat X_s=x; identify the named marginal hat rho_s=Law(hat X_s) in the orientation required by condDistrib/condExpKernel; supply component conditional-integral fields for c_{t_k}(X_k^eta) and nabla log pi_{t_k}(X_k^eta); prove or cite their measurability and integrability; then feed SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents and SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents or its swapped-orientation variant to obtain the source field bar b_{k,s}. This keeps the weak FP and KL derivative wrappers as consumers only.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource — 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.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityUpperObligation
2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
3. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation
4. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
5. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
6. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
7. SALD.generalMovingTargetDiscreteConditionalDriftContract
8. SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents
9. SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents
10. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents
11. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfSwappedComponents
12. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
13. AutoSamplingTheory.lawMapProdSwap
14. ProbabilityTheory.compProd_map_condDistrib
15. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib
16. ProbabilityTheory.condExp_ae_eq_integral_condExpKernel
17. Mathlib.Probability.Kernel.Condexp
18. Mathlib.Probability.Kernel.CondDistrib
19. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

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

Middle source map only. It records the lower-ready conditional-law/measurability theorem boundary and the Mathlib candidate facts; it imports no Mathlib kernel module, adds no Lake dependency, constructs no conditional law, proves no vector-valued conditional expectation theorem, and does not promote weak FP, generator-to-law, KL derivative, density/AC, LSI/KL/FI, DV, Gronwall, or theorem contracts.

def cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle80_conditional_law_middle"
  statement := "Cycle 80 middle synchronizes appendix.tex lines 1368-1377 with the existing cycle-70/74/75 conditional-law interfaces after checking the SLT reference style. The lower theorem boundary is: on the common EM probability space, instantiate a regular conditional kernel for X_k^eta given hat X_s=x; identify the named marginal hat rho_s=Law(hat X_s) in the orientation required by condDistrib/condExpKernel; supply component conditional-integral fields for c_{t_k}(X_k^eta) and nabla log pi_{t_k}(X_k^eta); prove or cite their measurability and integrability; then feed SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents and SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents or its swapped-orientation variant to obtain the source field bar b_{k,s}. This keeps the weak FP and KL derivative wrappers as consumers only."
  source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityUpperObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation",
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents",
    "SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents",
    "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents",
    "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfSwappedComponents",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "AutoSamplingTheory.lawMapProdSwap",
    "ProbabilityTheory.compProd_map_condDistrib",
    "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib",
    "ProbabilityTheory.condExp_ae_eq_integral_condExpKernel",
    "Mathlib.Probability.Kernel.Condexp",
    "Mathlib.Probability.Kernel.CondDistrib",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle source map only. It records the lower-ready conditional-law/measurability theorem boundary and the Mathlib candidate facts; it imports no Mathlib kernel module, adds no Lake dependency, constructs no conditional law, proves no vector-valued conditional expectation theorem, and does not promote weak FP, generator-to-law, KL derivative, density/AC, LSI/KL/FI, DV, Gronwall, or theorem contracts."

/-- Cycle-80 lower obligation for the endpoint/conditional drift-regularity
wrapper. -/