AutoSamplingTheory.SALD.cycle89DiscreteForwardKlClosurePressureMiddleObligation

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 cycle89DiscreteForwardKlClosurePressureMiddleObligation :
    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_closure_pressure_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 89 middle synchronizes the pressure-test route for thm:forward-KL-discrete. The current EM/KL handoffs from cycles 85--88 and the existing LSI, DV, Gronwall, and accumulated-error interfaces route the theorem skeleton up to SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative. The next lower packet is the non-wrapper derivative boundary at appendix.tex lines 388-413, with target-transport companion appendix.tex lines 414-436: prove or isolate the integration-by-parts and Fisher-information theorem turning the weak-FP log-ratio action and target transport action into eq:KL-derivative-1-discrete and eq:KL-derivative-2-discrete. 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.cycle89DiscreteForwardKlClosurePressureUpperObligation
SALD.discreteForwardKlStatementContract
SALD.discreteForwardKlDerivativeObligation
SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
SALD.cycle56DiscreteForwardKlGronwallLowerObligation
SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation
SALD.cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation
SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation
SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
sald.discrete_forward_kl.em_interpolation_fp
sald.discrete_forward_kl.em_conditional_fokker_planck
sald.discrete_forward_kl.kl_derivative
sald.discrete_forward_kl.dv_velocity_bound
sald.discrete_forward_kl.gronwall_accumulation
sald.discrete_forward_kl.accumulated_error_bridge
sald.general_moving_target_discrete.em_interpolation_fp
sald.general_moving_target_discrete.kl_derivative
eq:KL-derivative-1-discrete
eq:KL-derivative-2-discrete
eq:general_KL_derivative_0_discrete
eq:LSI-KL-FI
lem:dv_variation
lem:gronwall

note : String (explicit)

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

Middle source-map record only. It preserves the theorem statement and constants, keeps the shared EM backend active, and selects the appendix.tex:388-413 IBP/FI boundary as lower work; no new supplied-hypothesis wrapper or formalized analytic closure is introduced.

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 cycle89DiscreteForwardKlClosurePressureMiddleObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle89_closure_pressure_middle"
  statement := "Cycle 89 middle synchronizes the pressure-test route for thm:forward-KL-discrete. The current EM/KL handoffs from cycles 85--88 and the existing LSI, DV, Gronwall, and accumulated-error interfaces route the theorem skeleton up to SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative. The next lower packet is the non-wrapper derivative boundary at appendix.tex lines 388-413, with target-transport companion appendix.tex lines 414-436: prove or isolate the integration-by-parts and Fisher-information theorem turning the weak-FP log-ratio action and target transport action into eq:KL-derivative-1-discrete and eq:KL-derivative-2-discrete. Classification: narrows-source-cited-boundary."
  source := saldForwardKlDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle89DiscreteForwardKlClosurePressureUpperObligation",
    "SALD.discreteForwardKlStatementContract",
    "SALD.discreteForwardKlDerivativeObligation",
    "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
    "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
    "SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation",
    "SALD.cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation",
    "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "sald.discrete_forward_kl.em_conditional_fokker_planck",
    "sald.discrete_forward_kl.kl_derivative",
    "sald.discrete_forward_kl.dv_velocity_bound",
    "sald.discrete_forward_kl.gronwall_accumulation",
    "sald.discrete_forward_kl.accumulated_error_bridge",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative",
    "eq:KL-derivative-1-discrete",
    "eq:KL-derivative-2-discrete",
    "eq:general_KL_derivative_0_discrete",
    "eq:LSI-KL-FI",
    "lem:dv_variation",
    "lem:gronwall"
  ]
  note := "Middle source-map record only. It preserves the theorem statement and constants, keeps the shared EM backend active, and selects the appendix.tex:388-413 IBP/FI boundary as lower work; no new supplied-hypothesis wrapper or formalized analytic closure is introduced."

/-- Cycle-89 lower handoff for the discrete derivative IBP/FI split. -/

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