AutoSamplingTheory.SALD.cycle95DiscreteForwardKlClosurePressureUpperObligation

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 cycle95DiscreteForwardKlClosurePressureUpperObligation :
    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.cycle95_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 95 upper pressure-tests thm:forward-KL-discrete after the cycle-94 barB weak-action handoff. The existing theorem route already has compiled scalar wrappers for the KL/log-ratio mass handoff, LSI, DV, Gronwall, and accumulated-error display under named analytic inputs. The first non-wrapper blocker is not a new display wrapper: it is ASTIS.SALD.cycle94.remaining_barB_divergence_boundary, namely the conditional-expectation generator identity producing the weak pairing against barB and the divergence/no-boundary theorem identifying that pairing with -driftDiv at appendix.tex lines 1368-1387. Classification: narrows-source-cited-boundary.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource — 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.cycle95DiscreteForwardKlClosurePressureUpperPacket
SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation
SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff
SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction
SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
SALD.discreteForwardKlPostLsiDerivativeBoundOfLawConstantTestMassScalar
SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
SALD.discreteForwardKlMainDisplayBoundScalar
sald.general_moving_target_discrete.em_interpolation_fp
sald.discrete_forward_kl.em_interpolation_fp
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
ASTIS.SALD.cycle94.remaining_barB_divergence_boundary
appendix.tex:1368-1377
appendix.tex:1379-1387
main_body.tex:299-323

note : String (explicit)

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

Upper routing record only. It selects the next lower packet and does not prove conditional expectation, divergence integration by parts, weak FP, KL differentiability, LSI, DV, Gronwall, accumulated-error closure, or either discrete theorem.

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 cycle95DiscreteForwardKlClosurePressureUpperObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle95_closure_pressure_upper"
  statement := "Cycle 95 upper pressure-tests thm:forward-KL-discrete after the cycle-94 barB weak-action handoff. The existing theorem route already has compiled scalar wrappers for the KL/log-ratio mass handoff, LSI, DV, Gronwall, and accumulated-error display under named analytic inputs. The first non-wrapper blocker is not a new display wrapper: it is ASTIS.SALD.cycle94.remaining_barB_divergence_boundary, namely the conditional-expectation generator identity producing the weak pairing against barB and the divergence/no-boundary theorem identifying that pairing with -driftDiv at appendix.tex lines 1368-1387. Classification: narrows-source-cited-boundary."
  source := saldGeneralMovingTargetDiscreteWeakFpDriftActionMathlibSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle95DiscreteForwardKlClosurePressureUpperPacket",
    "SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfFiniteKlLlrLawConstantTestMassWithLogAction",
    "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
    "SALD.discreteForwardKlPostLsiDerivativeBoundOfLawConstantTestMassScalar",
    "SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar",
    "SALD.discreteForwardKlMainDisplayBoundScalar",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "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",
    "ASTIS.SALD.cycle94.remaining_barB_divergence_boundary",
    "appendix.tex:1368-1377",
    "appendix.tex:1379-1387",
    "main_body.tex:299-323"
  ]
  note := "Upper routing record only. It selects the next lower packet and does not prove conditional expectation, divergence integration by parts, weak FP, KL differentiability, LSI, DV, Gronwall, accumulated-error closure, or either discrete theorem."

/-- Cycle-95 middle source map for the discrete forward-KL pressure test. -/

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