AutoSamplingTheory.SALD.cycle120GeneralMovingTargetDiscreteEmPathDerivativeDominationLowerObligation

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 cycle120GeneralMovingTargetDiscreteEmPathDerivativeDominationLowerObligation :
    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.cycle120_em_path_derivative_domination_lower_ready

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 120 lower-ready packet narrows ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions to ASTIS.SALD.cycle120.lower_ready.em_sample_path_derivative_domination. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalDominated now discharges the local-neighborhood input hsampleNeighborhood by specializing to the source EM interval. The remaining lower-ready facts are, for each admissible weak test, sample measurability, sample integrability, derivative measurability, local derivative bound, bound integrability, and pointwise HasDerivAt inputs for the frozen EM interpolation. The expected source route is the path formula eq:general_moving_target_SALD_frozen_interp and appendix.tex:1379-1387, with test regularity and common-space assumptions exposed. Remaining exact boundary after this packet: hderivValue identifying the sample-derivative integral with driftAction + diffusionAction, canonical barB drift weak-action/pairing measurability and gradient bound, no-boundary divergence, diffusion source action, and law-derivative/partialS uniqueness if the normalized consumer is used.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — 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.cycle120GeneralMovingTargetDiscreteEmPathDerivativeDominationMiddleObligation
2. ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions
3. ASTIS.SALD.cycle120.lower_ready.em_sample_path_derivative_domination
4. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated
5. AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndDominated
6. Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le
7. eq:general_moving_target_SALD_frozen_interp
8. appendix.tex:1379-1387
9. sald.general_moving_target_discrete.em_interpolation_fp
10. sald.discrete_forward_kl.em_interpolation_fp

note : String (explicit)

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

Lower-ready source-cited theorem boundary only. It rejects wrapper churn around the already consumed canonical barB witness and leaves source-action equalities outside this packet.

def cycle120GeneralMovingTargetDiscreteEmPathDerivativeDominationLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle120_em_path_derivative_domination_lower_ready"
  statement := "Cycle 120 lower-ready packet narrows ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions to ASTIS.SALD.cycle120.lower_ready.em_sample_path_derivative_domination. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalDominated now discharges the local-neighborhood input hsampleNeighborhood by specializing to the source EM interval. The remaining lower-ready facts are, for each admissible weak test, sample measurability, sample integrability, derivative measurability, local derivative bound, bound integrability, and pointwise HasDerivAt inputs for the frozen EM interpolation. The expected source route is the path formula eq:general_moving_target_SALD_frozen_interp and appendix.tex:1379-1387, with test regularity and common-space assumptions exposed. Remaining exact boundary after this packet: hderivValue identifying the sample-derivative integral with driftAction + diffusionAction, canonical barB drift weak-action/pairing measurability and gradient bound, no-boundary divergence, diffusion source action, and law-derivative/partialS uniqueness if the normalized consumer is used."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle120GeneralMovingTargetDiscreteEmPathDerivativeDominationMiddleObligation",
    "ASTIS.SALD.cycle119.remaining_em_path_derivative_domination_and_source_actions",
    "ASTIS.SALD.cycle120.lower_ready.em_sample_path_derivative_domination",
    "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfDominated",
    "AutoSamplingTheory.lawIntegralHasDerivAtOfMeasureMapEqAndDominated",
    "Mathlib.Analysis.Calculus.ParametricIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le",
    "eq:general_moving_target_SALD_frozen_interp",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "Lower-ready source-cited theorem boundary only. It rejects wrapper churn around the already consumed canonical barB witness and leaves source-action equalities outside this packet."

/-- Cycle-120 proof-DAG pane for the EM sample-path derivative/domination
subboundary. -/