AutoSamplingTheory.SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface

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 cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface :
    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_conditional_kernel_measure_interface

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 records the blocked Mathlib measure-theory interface for appendix.tex:1368-1377: under the common probability space for (X_k^eta, hat X_s), standard-Borel/finite-measure hypotheses should allow a condExpKernel/condDistrib-style kernel whose second marginal is the named hat rho_s and whose integrals of the frozen drift summands define the measurable conditional field bar b_{k,s}. This source-cited interface is the next lower target before any claimed proof of the weak conditional Fokker-Planck identity.

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.sourceCited — 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. Mathlib.Probability.Kernel.Condexp
2. Mathlib.Probability.Kernel.CondDistrib
3. Mathlib.Probability.Kernel.Disintegration.StandardBorel
4. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
5. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
6. SALD.generalMovingTargetDiscreteConditionalDriftContract
7. SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation
8. SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
9. 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.

Source-cited Mathlib interface only. It does not import Mathlib kernel/disintegration modules into this file, construct the SALD conditional law, prove conditional expectation identities, prove density/AC, prove the weak conditional Fokker-Planck theorem, prove log-ratio admissibility, or close KL differentiation.

def cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle74_conditional_kernel_measure_interface"
  statement := "Cycle 74 records the blocked Mathlib measure-theory interface for appendix.tex:1368-1377: under the common probability space for (X_k^eta, hat X_s), standard-Borel/finite-measure hypotheses should allow a condExpKernel/condDistrib-style kernel whose second marginal is the named hat rho_s and whose integrals of the frozen drift summands define the measurable conditional field bar b_{k,s}. This source-cited interface is the next lower target before any claimed proof of the weak conditional Fokker-Planck identity."
  source := saldGeneralMovingTargetDiscreteConditionalKernelMathlibSource
  status := ProofStatus.sourceCited
  dependsOn := [
    "Mathlib.Probability.Kernel.Condexp",
    "Mathlib.Probability.Kernel.CondDistrib",
    "Mathlib.Probability.Kernel.Disintegration.StandardBorel",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "SALD.cycle70GeneralMovingTargetDiscreteConditionalLawMiddleObligation",
    "SALD.cycle71GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Source-cited Mathlib interface only. It does not import Mathlib kernel/disintegration modules into this file, construct the SALD conditional law, prove conditional expectation identities, prove density/AC, prove the weak conditional Fokker-Planck theorem, prove log-ratio admissibility, or close KL differentiation."

/-- Cycle-74 upper packet selecting the minimal cited measure interface after
cycle-73 weak-FP-to-KL substitution.
-/