AutoSamplingTheory.SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation

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 cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation :
    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.cycle74_measure_interface_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 74 middle synchronizes appendix.tex:1368-1377 with the cited Mathlib conditional-kernel candidates: the paper conditions X_k^eta on hat X_s=x under the joint law of (X_k^eta,hat X_s), so the next proof-producing audit should look for a condDistrib/condExpKernel backend whose compProd law recovers the joint law, whose second marginal is the named hat rho_s from cycle 71, and whose integral_condDistrib or integral_condExpKernel measurability/integrability theorems can define the two frozen drift summands and their linear combination bar b_{k,s}. This is a middle source map only, not a proof of the conditional law or weak FP theorem.

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.cycle74GeneralMovingTargetDiscreteMeasureInterfaceUpperObligation
2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
3. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
4. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
5. SALD.generalMovingTargetDiscreteConditionalDriftContract
6. SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation
7. SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
8. SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation
9. Mathlib.Probability.Kernel.CondDistrib.compProd_map_condDistrib
10. Mathlib.Probability.Kernel.CondDistrib.condDistrib_ae_eq_iff_measure_eq_compProd
11. Mathlib.Probability.Kernel.CondDistrib.condExp_prod_ae_eq_integral_condDistrib
12. Mathlib.Probability.Kernel.Condexp.condExp_ae_eq_integral_condExpKernel
13. 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 synchronization only. The cited Mathlib declarations are audit targets, not imported or locally instantiated here. Standard-Borel/nonempty state, finite/probability measure, joint-law equality, marginal compatibility, measurability, integrability, vector-valued conditional expectation, density/AC, weak FP, and KL differentiation remain explicit obligations.

def cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle74_measure_interface_middle"
  statement := "Cycle 74 middle synchronizes appendix.tex:1368-1377 with the cited Mathlib conditional-kernel candidates: the paper conditions X_k^eta on hat X_s=x under the joint law of (X_k^eta,hat X_s), so the next proof-producing audit should look for a condDistrib/condExpKernel backend whose compProd law recovers the joint law, whose second marginal is the named hat rho_s from cycle 71, and whose integral_condDistrib or integral_condExpKernel measurability/integrability theorems can define the two frozen drift summands and their linear combination bar b_{k,s}. This is a middle source map only, not a proof of the conditional law or weak FP theorem."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceUpperObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation",
    "SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
    "SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpMiddleObligation",
    "Mathlib.Probability.Kernel.CondDistrib.compProd_map_condDistrib",
    "Mathlib.Probability.Kernel.CondDistrib.condDistrib_ae_eq_iff_measure_eq_compProd",
    "Mathlib.Probability.Kernel.CondDistrib.condExp_prod_ae_eq_integral_condDistrib",
    "Mathlib.Probability.Kernel.Condexp.condExp_ae_eq_integral_condExpKernel",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle synchronization only. The cited Mathlib declarations are audit targets, not imported or locally instantiated here. Standard-Borel/nonempty state, finite/probability measure, joint-law equality, marginal compatibility, measurability, integrability, vector-valued conditional expectation, density/AC, weak FP, and KL differentiation remain explicit obligations."

/-- Cycle-74 lower obligation for the supplied-kernel regularity handoff. -/