AutoSamplingTheory.SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation

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 cycle54GeneralMovingTargetDiscreteEmFpLowerObligation :
    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.cycle54_em_fp_lower

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 54 lower compiles the source-shaped sigma-weighted Fokker--Planck regrouping from appendix.tex lines 1380-1387: from partial_s hat rho_s = -div(hat rho_s*bar b_{k,s})+(sigma_eta^2/2)*Delta hat rho_s and Delta hat rho_s = div(hat rho_s*A_s)+div(hat rho_s*nabla log tilde pi_s), SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff derives the regrouped divergence form with (sigma_eta^2/2)*div(hat rho_s*A_s)+div(hat rho_s*((sigma_eta^2/2)*nabla log tilde pi_s-bar b_{k,s})).

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff
2. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.general_moving_target_discrete.kl_derivative
5. FokkerPlanckContract

note : String (explicit)

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

Proof-producing algebra only. Common-space construction, regular conditional drift, density/absolute-continuity, weak Fokker-Planck identity, KL differentiation under the integral, mass conservation, boundary integration by parts, and endpoint stitching remain analytic obligations.

def cycle54GeneralMovingTargetDiscreteEmFpLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle54_em_fp_lower"
  statement := "Cycle 54 lower compiles the source-shaped sigma-weighted Fokker--Planck regrouping from appendix.tex lines 1380-1387: from partial_s hat rho_s = -div(hat rho_s*bar b_{k,s})+(sigma_eta^2/2)*Delta hat rho_s and Delta hat rho_s = div(hat rho_s*A_s)+div(hat rho_s*nabla log tilde pi_s), SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff derives the regrouped divergence form with (sigma_eta^2/2)*div(hat rho_s*A_s)+div(hat rho_s*((sigma_eta^2/2)*nabla log tilde pi_s-bar b_{k,s}))."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative",
    "FokkerPlanckContract"
  ]
  note := "Proof-producing algebra only. Common-space construction, regular conditional drift, density/absolute-continuity, weak Fokker-Planck identity, KL differentiation under the integral, mass conservation, boundary integration by parts, and endpoint stitching remain analytic obligations."