AutoSamplingTheory.SALD.cycle109GeneralMovingTargetDiscreteNamedBarBSourceDefMiddleObligation

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 cycle109GeneralMovingTargetDiscreteNamedBarBSourceDefMiddleObligation :
    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.cycle109_named_barB_source_def_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 109 middle keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to the named barB source-definition boundary at appendix.tex:1368-1377. Classification: narrows-source-cited-boundary. The compiled local theorem SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpKernelSourceDef replaces a direct hbarBAe equality for barB with two smaller source-facing inputs: the measure-valued sample-space alignment between condDistrib XkEta hatXAtS P and condExpKernel P (mState.comap hatXAtS).map XkEta, and the source conditional-expectation definition of barB using that condExpKernel.map representative. The remaining exact theorem is SALD.cycle109GeneralMovingTargetDiscreteNamedBarBSourceDefBoundary, with imports and hypotheses listed explicitly.

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. SALD.cycle109GeneralMovingTargetDiscreteNamedBarBSourceDefBoundary
2. SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpKernelSourceDef
3. SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq
4. SALD.generalMovingTargetDiscreteCondDistribCanonicalDriftRegularity
5. SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap
6. SALD.cycle106GeneralMovingTargetDiscreteCanonicalCondDistribDriftLowerObligation
7. SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation
8. AutoSamplingTheory.condDistribAeEqCondExpKernelMap
9. Mathlib.Probability.Kernel.CondDistrib
10. Mathlib.Probability.Kernel.Condexp
11. appendix.tex:1368-1377
12. 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 plus one compiled source-definition bridge. Local SLT/EfronStein.lean was consulted for conditional-expectation and product-measure proof style only; no SLT theorem is imported or marked formalized.

def cycle109GeneralMovingTargetDiscreteNamedBarBSourceDefMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle109_named_barB_source_def_middle"
  statement := "Cycle 109 middle keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to the named barB source-definition boundary at appendix.tex:1368-1377. Classification: narrows-source-cited-boundary. The compiled local theorem SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpKernelSourceDef replaces a direct hbarBAe equality for barB with two smaller source-facing inputs: the measure-valued sample-space alignment between condDistrib XkEta hatXAtS P and condExpKernel P (mState.comap hatXAtS).map XkEta, and the source conditional-expectation definition of barB using that condExpKernel.map representative. The remaining exact theorem is SALD.cycle109GeneralMovingTargetDiscreteNamedBarBSourceDefBoundary, with imports and hypotheses listed explicitly."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle109GeneralMovingTargetDiscreteNamedBarBSourceDefBoundary",
    "SALD.generalMovingTargetDiscreteCondDistribNamedBarBAeEqOfCondExpKernelSourceDef",
    "SALD.generalMovingTargetDiscreteCondDistribNamedDriftRegularityOfCanonicalAeEq",
    "SALD.generalMovingTargetDiscreteCondDistribCanonicalDriftRegularity",
    "SALD.generalMovingTargetDiscreteCondDistribNamedFieldAeEqOfCondExpKernelMap",
    "SALD.cycle106GeneralMovingTargetDiscreteCanonicalCondDistribDriftLowerObligation",
    "SALD.cycle103GeneralMovingTargetDiscreteConditionalKernelVersionLowerObligation",
    "AutoSamplingTheory.condDistribAeEqCondExpKernelMap",
    "Mathlib.Probability.Kernel.CondDistrib",
    "Mathlib.Probability.Kernel.Condexp",
    "appendix.tex:1368-1377",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Middle synchronization plus one compiled source-definition bridge. Local SLT/EfronStein.lean was consulted for conditional-expectation and product-measure proof style only; no SLT theorem is imported or marked formalized."

/-- Cycle-109 lower packet using Mathlib's product conditional-expectation
identity for the named `barB` source definition. -/