AutoSamplingTheory.SALD.cycle91GeneralMovingTargetDiscreteConditionalKernelMiddleObligation

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 cycle91GeneralMovingTargetDiscreteConditionalKernelMiddleObligation :
    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.cycle91_conditional_kernel_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 91 middle records the global phase judgment: cycle 90 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet that reduces the largest remaining proof risk is the conditional-kernel/named-law field boundary for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1368-1377. The source map targets hat rho_s = Law(hat X_s), ProbabilityTheory.condDistrib X_k^eta hat X_s P, named component fields condC_{k,s} and condScore_{k,s}, and measurable/integrable bar b_{k,s}.

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.cycle90DiscreteForwardKlMassConservationLowerObligation
2. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
3. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
4. SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents
5. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
6. sald.general_moving_target_discrete.em_interpolation_fp
7. sald.discrete_forward_kl.em_interpolation_fp
8. appendix.tex:1368-1377

note : String (explicit)

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

Middle workflow record only. It keeps theorem statements, constants, source labels, and statuses fixed; the selected proof-producing target is the concrete condDistrib-to-barB regularity theorem below.

def cycle91GeneralMovingTargetDiscreteConditionalKernelMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle91_conditional_kernel_middle"
  statement := "Cycle 91 middle records the global phase judgment: cycle 90 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet that reduces the largest remaining proof risk is the conditional-kernel/named-law field boundary for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex lines 1368-1377. The source map targets hat rho_s = Law(hat X_s), ProbabilityTheory.condDistrib X_k^eta hat X_s P, named component fields condC_{k,s} and condScore_{k,s}, and measurable/integrable bar b_{k,s}."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle90DiscreteForwardKlMassConservationLowerObligation",
    "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
    "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
    "SALD.generalMovingTargetDiscreteNamedConditionalDriftRegularityOfComponents",
    "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "appendix.tex:1368-1377"
  ]
  note := "Middle workflow record only. It keeps theorem statements, constants, source labels, and statuses fixed; the selected proof-producing target is the concrete condDistrib-to-barB regularity theorem below."

/-- Cycle-91 lower/backfill obligation for the compiled concrete
`condDistrib` drift-regularity theorem.

The new theorem removes the older supplied component regularity hypotheses for
the canonical conditional-integral route: after the SALD-specific a.e. version
equalities for `condC` and `condScore` are supplied, Mathlib regularity of
`condDistrib` integrals and the existing component-combination wrapper produce
regularity of `barB`.
-/