AutoSamplingTheory.SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionMiddleObligation

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 cycle103GeneralMovingTargetDiscreteConditionalKernelVersionMiddleObligation :
    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_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 103 middle narrows ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary for appendix.tex lines 1368-1377 to one selected component, condC. Classification: narrows-source-cited-boundary. The lower proof-producing bridge is SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap, backed by AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap: it derives the old condDistrib sample-space equality from a measure-valued a.e. alignment of condDistrib X_k^eta hatXAtS P (hatXAtS omega) with condExpKernel P ((inferInstance : MeasurableSpace State).comap hatXAtS).map X_k^eta omega, plus the selected condExpKernel-map version of condC and the equality-set measurability consumed by ae_map_iff. The remaining exact theorem boundary is proving those measure-valued kernel alignment/version-selection facts from Mathlib condDistrib/condExpKernel, not restating hguideComp.

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. ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary
2. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample
3. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap
4. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions
5. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularity
6. AutoSamplingTheory.condDistribAeEqCondExpKernelMap
7. AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap
8. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
9. ProbabilityTheory.condDistrib_apply_ae_eq_condExpKernel_map
10. ProbabilityTheory.condExp_ae_eq_integral_condExpKernel
11. ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib
12. Mathlib.Probability.Kernel.CondDistrib
13. Mathlib.Probability.Kernel.Condexp
14. Mathlib.MeasureTheory.Integral.Bochner.Basic
15. appendix.tex:1368-1377
16. 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-to-Lean synchronization plus lower bridge registration. It consulted the local SLT EfronStein conditional-expectation/product-measure idiom as reference style but imports no SLT theorem, changes no Lake dependency, and promotes no weak-FP/KL/theorem status. Lower has narrowed the component-version theorem to measure-valued kernel a.e. equality, condExpKernel-map field version selection, and equality-set measurability.

def cycle103GeneralMovingTargetDiscreteConditionalKernelVersionMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle103_conditional_kernel_component_version_middle"
  statement := "Cycle 103 middle narrows ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary for appendix.tex lines 1368-1377 to one selected component, condC. Classification: narrows-source-cited-boundary. The lower proof-producing bridge is SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap, backed by AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap: it derives the old condDistrib sample-space equality from a measure-valued a.e. alignment of condDistrib X_k^eta hatXAtS P (hatXAtS omega) with condExpKernel P ((inferInstance : MeasurableSpace State).comap hatXAtS).map X_k^eta omega, plus the selected condExpKernel-map version of condC and the equality-set measurability consumed by ae_map_iff. The remaining exact theorem boundary is proving those measure-valued kernel alignment/version-selection facts from Mathlib condDistrib/condExpKernel, not restating hguideComp."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "ASTIS.SALD.cycle91.remaining_conditional_kernel_boundary",
    "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfSample",
    "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfSampleVersions",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularity",
    "AutoSamplingTheory.condDistribAeEqCondExpKernelMap",
    "AutoSamplingTheory.condDistribIntegralSampleAeEqOfCondExpKernelMap",
    "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
    "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",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle source-to-Lean synchronization plus lower bridge registration. It consulted the local SLT EfronStein conditional-expectation/product-measure idiom as reference style but imports no SLT theorem, changes no Lake dependency, and promotes no weak-FP/KL/theorem status. Lower has narrowed the component-version theorem to measure-valued kernel a.e. equality, condExpKernel-map field version selection, and equality-set measurability."

/-- Cycle-103 lower obligation after the compiled `condExpKernel.map` bridge. -/