AutoSamplingTheory.SALD.cycle89DiscreteForwardKlClosurePressureLowerObligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle89DiscreteForwardKlClosurePressureLowerObligation :
    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.discrete_forward_kl.cycle89_derivative_ibp_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 89 lower narrows the selected derivative blocker by compiling SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar and SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar. The old opaque scalar input dK=-FI+frozenCross+movingCross is replaced by a raw KL derivative split with an explicit mass term, a named first-term IBP/FI identity for eq:KL-derivative-1-discrete, and a named target-transport IBP identity for eq:KL-derivative-2-discrete. The remaining analytic theorem boundary is exactly: prove hfirst from weak-FP log-ratio action plus divergence integration by parts and Fisher identification, prove htarget from target transport integration by parts, and prove hmass from mass conservation under the density/boundary hypotheses. Classification: narrows-source-cited-boundary.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — 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

SALD.cycle89DiscreteForwardKlClosurePressureMiddleObligation
SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar
SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar
SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar
SALD.discreteForwardKlPostLsiDerivativeBoundScalar
SALD.discreteForwardKlDerivativeObligation
SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
sald.discrete_forward_kl.em_interpolation_fp
sald.discrete_forward_kl.em_conditional_fokker_planck
sald.discrete_forward_kl.kl_derivative
sald.general_moving_target_discrete.em_interpolation_fp
sald.general_moving_target_discrete.kl_derivative
eq:KL-derivative-0-discrete
eq:KL-derivative-1-discrete
eq:KL-derivative-2-discrete
eq:KL-derivative-5-discrete
eq:LSI-KL-FI

note : String (explicit)

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

The compiled theorem is local scalar bookkeeping only. It removes the older supplied post-IBP derivative display as a single hypothesis and exposes the smaller missing analytic facts: mass conservation, first-term divergence IBP/FI identification, and target-transport IBP. It does not prove weak FP, log-ratio admissibility, integration by parts, Fisher information, LSI, DV, Gronwall, or theorem closure.

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle89DiscreteForwardKlClosurePressureLowerObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle89_derivative_ibp_lower"
  statement := "Cycle 89 lower narrows the selected derivative blocker by compiling SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar and SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar. The old opaque scalar input dK=-FI+frozenCross+movingCross is replaced by a raw KL derivative split with an explicit mass term, a named first-term IBP/FI identity for eq:KL-derivative-1-discrete, and a named target-transport IBP identity for eq:KL-derivative-2-discrete. The remaining analytic theorem boundary is exactly: prove hfirst from weak-FP log-ratio action plus divergence integration by parts and Fisher identification, prove htarget from target transport integration by parts, and prove hmass from mass conservation under the density/boundary hypotheses. Classification: narrows-source-cited-boundary."
  source := saldForwardKlDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle89DiscreteForwardKlClosurePressureMiddleObligation",
    "SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar",
    "SALD.discreteForwardKlPostLsiDerivativeBoundScalar",
    "SALD.discreteForwardKlDerivativeObligation",
    "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "sald.discrete_forward_kl.em_conditional_fokker_planck",
    "sald.discrete_forward_kl.kl_derivative",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative",
    "eq:KL-derivative-0-discrete",
    "eq:KL-derivative-1-discrete",
    "eq:KL-derivative-2-discrete",
    "eq:KL-derivative-5-discrete",
    "eq:LSI-KL-FI"
  ]
  note := "The compiled theorem is local scalar bookkeeping only. It removes the older supplied post-IBP derivative display as a single hypothesis and exposes the smaller missing analytic facts: mass conservation, first-term divergence IBP/FI identification, and target-transport IBP. It does not prove weak FP, log-ratio admissibility, integration by parts, Fisher information, LSI, DV, Gronwall, or theorem closure."

/-- Cycle-89 proof-DAG pane for the discrete theorem closure pressure test. -/

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