AutoSamplingTheory.SALD.cycle89DiscreteForwardKlClosurePressureUpperObligation

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 cycle89DiscreteForwardKlClosurePressureUpperObligation :
    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_upper

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 upper pressure-tests thm:forward-KL-discrete through the current compiled EM/KL handoffs and existing LSI, DV, Gronwall, and accumulated-error interfaces. The route reaches SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative, where the first non-wrapper blocker is appendix.tex lines 388-413: turn the weak-FP log-ratio action and target transport action into eq:KL-derivative-1-discrete and eq:KL-derivative-2-discrete by integration by parts and Fisher-information identification. Upstream raw KL differentiation, mass conservation, log-ratio admissibility, target-time integrability, and weak conditional FP remain source-cited under appendix.tex lines 1358-1387. 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.cycle89DiscreteForwardKlClosurePressureUpperPacket
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
probability.lsi_to_kl_fi
lem:dv_variation
lem:gronwall
eq:LSI-KL-FI

note : String (explicit)

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

Upper pressure-test record only. It identifies the next analytic blocker and lower packet; it does not prove KL differentiability, weak FP, integration by parts, FI identification, 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 cycle89DiscreteForwardKlClosurePressureUpperObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle89_closure_pressure_upper"
  statement := "Cycle 89 upper pressure-tests thm:forward-KL-discrete through the current compiled EM/KL handoffs and existing LSI, DV, Gronwall, and accumulated-error interfaces. The route reaches SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative, where the first non-wrapper blocker is appendix.tex lines 388-413: turn the weak-FP log-ratio action and target transport action into eq:KL-derivative-1-discrete and eq:KL-derivative-2-discrete by integration by parts and Fisher-information identification. Upstream raw KL differentiation, mass conservation, log-ratio admissibility, target-time integrability, and weak conditional FP remain source-cited under appendix.tex lines 1358-1387. Classification: narrows-source-cited-boundary."
  source := saldForwardKlDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle89DiscreteForwardKlClosurePressureUpperPacket",
    "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",
    "probability.lsi_to_kl_fi",
    "lem:dv_variation",
    "lem:gronwall",
    "eq:LSI-KL-FI"
  ]
  note := "Upper pressure-test record only. It identifies the next analytic blocker and lower packet; it does not prove KL differentiability, weak FP, integration by parts, FI identification, LSI, DV, Gronwall, or theorem closure."

/-- Cycle-89 middle source map for the discrete forward-KL pressure test. -/

Existing module entry · Audited data-reader index · All teaching coverage