AutoSamplingTheory.SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperObligation

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 cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperObligation :
    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.cycle75_conditional_law_upper

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 75 upper records that cycle 74 passed and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active lower packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower work is the conditional-law/measurability and named conditional drift construction interface for appendix.tex:1368-1377: instantiate or sharpen the cycle-74 condDistrib/condExpKernel source-cited interface for the joint law of (X_k^eta,hat X_s), the named hat rho_s marginal, and the component conditional drift integrals, or record the exact missing Mathlib theorem.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperPacket
2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
3. SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation
4. SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceLowerObligation
5. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents
6. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
7. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
8. SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents
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.

Upper workflow obligation only. It fixes the next lower packet and status discipline, adds no theorem assumptions, imports no SLT or Mathlib module, and proves no weak Fokker-Planck, KL derivative, density, or conditional-law theorem.

def cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle75_conditional_law_upper"
  statement := "Cycle 75 upper records that cycle 74 passed and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active lower packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower work is the conditional-law/measurability and named conditional drift construction interface for appendix.tex:1368-1377: instantiate or sharpen the cycle-74 condDistrib/condExpKernel source-cited interface for the joint law of (X_k^eta,hat X_s), the named hat rho_s marginal, and the component conditional drift integrals, or record the exact missing Mathlib theorem."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperPacket",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceLowerObligation",
    "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Upper workflow obligation only. It fixes the next lower packet and status discipline, adds no theorem assumptions, imports no SLT or Mathlib module, and proves no weak Fokker-Planck, KL derivative, density, or conditional-law theorem."

/-- Cycle-75 middle source-to-Lean map for the conditional-law orientation and
measurability handoff.

Mathlib's `condDistrib Y X μ` is oriented by the conditioning variable first:
for `X_k^eta | hat X_s`, the generated joint law is `(hat X_s, X_k^eta)`.
The existing cycle-71 SALD endpoint compatibility is oriented as
`(X_k^eta, hat X_s)`.  This middle obligation records that the lower packet must
bridge that orientation using only `Measure.map` bookkeeping before consuming
the conditional-kernel and integral-measurability theorems.
-/