AutoSamplingTheory.SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation

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 cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation :
    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.cycle103_conditional_kernel_component_version_lower

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 103 lower compiles AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap and SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap for appendix.tex lines 1368-1377. These declarations do not assume the old hguideComp sample-space equality; they derive it from two narrower inputs: (1) a measure-valued P-a.e. equality between condDistrib X_k^eta hatXAtS P (hatXAtS omega) and condExpKernel P ((inferInstance : MeasurableSpace State).comap hatXAtS).map X_k^eta omega, and (2) the selected condExpKernel-map conditional-expectation version of the named condC field, plus the measurable equality set used by ae_map_iff. Classification: narrows-source-cited-boundary. Remaining exact boundary: prove the measure-valued kernel equality and selected condExpKernel-map field version from Mathlib condDistrib/condExpKernel facts under finite-measure, standard-Borel, measurability, and Bochner integrability hypotheses.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteConditionalDriftSource — 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. AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap
2. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap
3. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
4. AutoSamplingTheory.condDistribAeEqCondExpKernelMap
5. ProbabilityTheory.condDistrib_apply_ae_eq_condExpKernel_map
6. ProbabilityTheory.condExp_ae_eq_integral_condExpKernel
7. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib
8. Mathlib.Probability.Kernel.CondDistrib
9. Mathlib.Probability.Kernel.Condexp
10. Mathlib.MeasureTheory.Integral.Bochner.Basic
11. appendix.tex:1368-1377

note : String (explicit)

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

Proof-producing lower bridge only. It narrows hguideComp but does not construct the regular conditional kernel, prove measure-valued uniqueness from setwise a.e. equality, choose condC, prove weak FP/KL/no-boundary, import SLT, or promote theorem status.

def cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle103_conditional_kernel_component_version_lower"
  statement := "Cycle 103 lower compiles AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap and SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap for appendix.tex lines 1368-1377. These declarations do not assume the old hguideComp sample-space equality; they derive it from two narrower inputs: (1) a measure-valued P-a.e. equality between condDistrib X_k^eta hatXAtS P (hatXAtS omega) and condExpKernel P ((inferInstance : MeasurableSpace State).comap hatXAtS).map X_k^eta omega, and (2) the selected condExpKernel-map conditional-expectation version of the named condC field, plus the measurable equality set used by ae_map_iff. Classification: narrows-source-cited-boundary. Remaining exact boundary: prove the measure-valued kernel equality and selected condExpKernel-map field version from Mathlib condDistrib/condExpKernel facts under finite-measure, standard-Borel, measurability, and Bochner integrability hypotheses."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap",
    "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap",
    "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
    "AutoSamplingTheory.condDistribAeEqCondExpKernelMap",
    "ProbabilityTheory.condDistrib_apply_ae_eq_condExpKernel_map",
    "ProbabilityTheory.condExp_ae_eq_integral_condExpKernel",
    "ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib",
    "Mathlib.Probability.Kernel.CondDistrib",
    "Mathlib.Probability.Kernel.Condexp",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "appendix.tex:1368-1377"
  ]
  note := "Proof-producing lower bridge only. It narrows hguideComp but does not construct the regular conditional kernel, prove measure-valued uniqueness from setwise a.e. equality, choose condC, prove weak FP/KL/no-boundary, import SLT, or promote theorem status."

/-- Cycle-103 proof-DAG pane for the one-component conditional-kernel
versioning packet. -/