AutoSamplingTheory.SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryUpperObligation

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 cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryUpperObligation :
    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.cycle85_conditional_kernel_boundary_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 85 upper records that cycle 84 passed reviewer/build and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower packet is the conditional-kernel/conditional-expectation theorem boundary at appendix.tex:1368-1377: instantiate or precisely block the Mathlib condDistrib/condExpKernel orientation for X_k^eta | hat X_s=x, the named marginal hat rho_s=Law(hat X_s), component conditional-integral fields, and measurability/integrability of bar b_{k,s}. Lower must classify the packet as discharges-supplied-hypothesis, narrows-source-cited-boundary, or rejected-wrapper-churn.

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.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryUpperPacket
2. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation
3. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation
4. SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
5. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation
6. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
7. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
8. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents
9. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfSwappedComponents
10. SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff
11. Mathlib.Probability.Kernel.Condexp
12. Mathlib.Probability.Kernel.CondDistrib
13. 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 lower packet and anti-wrapper-churn review discipline; it proves no conditional law, conditional expectation theorem, weak FP theorem, KL derivative, or theorem closure.

def cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryUpperObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle85_conditional_kernel_boundary_upper"
  statement := "Cycle 85 upper records that cycle 84 passed reviewer/build and needs no recovery, confirms that Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill, and keeps the active packet on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The selected lower packet is the conditional-kernel/conditional-expectation theorem boundary at appendix.tex:1368-1377: instantiate or precisely block the Mathlib condDistrib/condExpKernel orientation for X_k^eta | hat X_s=x, the named marginal hat rho_s=Law(hat X_s), component conditional-integral fields, and measurability/integrability of bar b_{k,s}. Lower must classify the packet as discharges-supplied-hypothesis, narrows-source-cited-boundary, or rejected-wrapper-churn."
  source := saldGeneralMovingTargetDiscreteConditionalDriftSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryUpperPacket",
    "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation",
    "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityMiddleObligation",
    "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation",
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation",
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents",
    "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfSwappedComponents",
    "SALD.generalMovingTargetDiscreteEndpointConditionalDriftRegularityHandoff",
    "Mathlib.Probability.Kernel.Condexp",
    "Mathlib.Probability.Kernel.CondDistrib",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Upper workflow obligation only. It fixes the lower packet and anti-wrapper-churn review discipline; it proves no conditional law, conditional expectation theorem, weak FP theorem, KL derivative, or theorem closure."

/-- Cycle-85 middle boundary narrowing using local Mathlib conditional-kernel
helpers.

This is not another supplied-hypothesis wrapper.  The local declarations in
`AutoSamplingTheory/Probability.lean` compile the Mathlib orientation from
`condDistrib` to `condExpKernel.map`, plus the vector-valued
conditional-integral measurability/integrability handoff.  The remaining lower
boundary is now the source-specific versioning step: turn those sample-space
a.e. conditional-integral facts into the named `hat rho_s` component fields
used by the existing `bar b_{k,s}` wrappers.
-/