AutoSamplingTheory.SALD.cycle93GeneralMovingTargetDiscreteKlMassDerivativeMiddleObligation

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 cycle93GeneralMovingTargetDiscreteKlMassDerivativeMiddleObligation :
    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.cycle93_kl_mass_derivative_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 93 middle records the active backend judgment: cycle 92 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1358-1366. The selected boundary is the KL/log-ratio mass derivative inside eq:general_KL_derivative_0_discrete: replace the primitive hmass : massTerm=0 input behind SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction by the concrete mapped-law constant-test derivative for hat rho_s=Law(hat X_s). Classification: discharges-supplied-hypothesis for hmass; raw KL differentiability, target-time integrability, admissible llr closure, and integration-by-parts/FI identification remain source-cited boundaries.

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.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation
2. SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation
3. SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
5. SALD.generalMovingTargetDiscreteKlMassTermZeroOfLawConstantTestDerivative
6. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
7. eq:general_KL_derivative_0_discrete
8. appendix.tex:1358-1366
9. sald.general_moving_target_discrete.em_interpolation_fp
10. sald.general_moving_target_discrete.kl_derivative

note : String (explicit)

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

Middle source-to-Lean synchronization only. It selects hmass as the supplied hypothesis to discharge by a local mapped-law theorem; it does not prove raw KL differentiability, target-time derivative integrability, log-ratio admissibility closure, weak FP, integration by parts, FI, theorem closure, SLT reuse, or any Lake dependency.

def cycle93GeneralMovingTargetDiscreteKlMassDerivativeMiddleObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle93_kl_mass_derivative_middle"
  statement := "Cycle 93 middle records the active backend judgment: cycle 92 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1358-1366. The selected boundary is the KL/log-ratio mass derivative inside eq:general_KL_derivative_0_discrete: replace the primitive hmass : massTerm=0 input behind SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction by the concrete mapped-law constant-test derivative for hat rho_s=Law(hat X_s). Classification: discharges-supplied-hypothesis for hmass; raw KL differentiability, target-time integrability, admissible llr closure, and integration-by-parts/FI identification remain source-cited boundaries."
  source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle92GeneralMovingTargetDiscreteWeakFpGeneratorSplitLowerObligation",
    "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation",
    "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteKlMassTermZeroOfLawConstantTestDerivative",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "eq:general_KL_derivative_0_discrete",
    "appendix.tex:1358-1366",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  note := "Middle source-to-Lean synchronization only. It selects hmass as the supplied hypothesis to discharge by a local mapped-law theorem; it does not prove raw KL differentiability, target-time derivative integrability, log-ratio admissibility closure, weak FP, integration by parts, FI, theorem closure, SLT reuse, or any Lake dependency."

/-- Cycle-93 lower obligation for the compiled mapped-law mass handoff. -/