Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle39ForwardKlDerivativeUpperObligation

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 cycle39ForwardKlDerivativeUpperObligation : 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.forward_kl.cycle39_derivative_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.

Maintain the cycle 39 upper proof-closure packet for appendix.tex lines 168-228: prioritize the continuous forward-KL Fokker-Planck/KL derivative identity, use SALD.forwardKlPreDvDerivativeBoundScalar as the theorem-specific scalar composition from explicit analytic inputs, and then refine density/boundary and schedule-time-change interfaces before any new ledger expansion or EM interpolation work.
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDerivativeSource — 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.cycle39ForwardKlDerivativeUpperPacket
  2. SALD.cycle39ForwardKlDerivativeMiddleContract
  3. SALD.forwardKlPreDvDerivativeBoundScalar
  4. SALD.forwardKlPreDvDerivativeBoundOfProductScalar
  5. SALD.forwardKlPreDvDerivativeBoundOfVelocityScalingScalar
  6. SALD.forwardKlPreDvDerivativeBoundOfKlFiVelocityScalingScalar
  7. SALD.forwardKlInverseScheduleDerivativeScalar
  8. SALD.forwardKlTimeChangeSquareCoefficientRewriteOfProductScalar
  9. SALD.forwardKlVelocitySquareScalingScalar
  10. SALD.forwardKlTimeChangedDerivativeBoundOfProductScalar
  11. SALD.forwardKlFirstTermFisherSubstitutionScalar
  12. SALD.forwardKlTargetTransportYoungBoundScalar
  13. SALD.forwardKlPostYoungDerivativeBoundScalar
  14. SALD.forwardKlPostYoungDerivativeBoundOfCauchyScalar
  15. SALD.forwardKlLsiDerivativeBoundScalar
  16. SALD.forwardKlTimeChangedDerivativeBoundScalar
  17. SALD.forwardKlDerivativeSideConditionContract
  18. SALD.forwardKlDensityBoundaryObligation
  19. SALD.forwardKlScheduleTimeChangeObligation
  20. SALD.saldLsiKlFiDensityTestContract
  21. sald.forward_kl.density_boundary_regular
  22. sald.forward_kl.schedule_time_change
  23. probability.lsi_to_kl_fi
  24. sald.forward_kl.kl_derivative
  25. eq:FP-eq
  26. TransportVelocityContract
note : String (explicit)

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

Cycle 39 upper work records the current proof-closure priority and adds a compiled scalar pipeline. Middle synchronization adds source-shaped inverse-schedule and velocity-square scalar lemmas; lower synchronization adds the source-shaped KL/FI-to-half-Fisher scalar handoff. This does not prove mass conservation, differentiation under the integral, the SALD Fokker-Planck equation, integration by parts, target transport, LSI-to-KL/FI, inverse-schedule calculus, DV, Gronwall, EM interpolation, or thm:forward-KL.
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 cycle39ForwardKlDerivativeUpperObligation : ProofObligation where
  id := "sald.forward_kl.cycle39_derivative_upper"
  statement := "Maintain the cycle 39 upper proof-closure packet for appendix.tex lines 168-228: prioritize the continuous forward-KL Fokker-Planck/KL derivative identity, use SALD.forwardKlPreDvDerivativeBoundScalar as the theorem-specific scalar composition from explicit analytic inputs, and then refine density/boundary and schedule-time-change interfaces before any new ledger expansion or EM interpolation work."
  source := saldForwardKlDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle39ForwardKlDerivativeUpperPacket",
    "SALD.cycle39ForwardKlDerivativeMiddleContract",
    "SALD.forwardKlPreDvDerivativeBoundScalar",
    "SALD.forwardKlPreDvDerivativeBoundOfProductScalar",
    "SALD.forwardKlPreDvDerivativeBoundOfVelocityScalingScalar",
    "SALD.forwardKlPreDvDerivativeBoundOfKlFiVelocityScalingScalar",
    "SALD.forwardKlInverseScheduleDerivativeScalar",
    "SALD.forwardKlTimeChangeSquareCoefficientRewriteOfProductScalar",
    "SALD.forwardKlVelocitySquareScalingScalar",
    "SALD.forwardKlTimeChangedDerivativeBoundOfProductScalar",
    "SALD.forwardKlFirstTermFisherSubstitutionScalar",
    "SALD.forwardKlTargetTransportYoungBoundScalar",
    "SALD.forwardKlPostYoungDerivativeBoundScalar",
    "SALD.forwardKlPostYoungDerivativeBoundOfCauchyScalar",
    "SALD.forwardKlLsiDerivativeBoundScalar",
    "SALD.forwardKlTimeChangedDerivativeBoundScalar",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.forwardKlDensityBoundaryObligation",
    "SALD.forwardKlScheduleTimeChangeObligation",
    "SALD.saldLsiKlFiDensityTestContract",
    "sald.forward_kl.density_boundary_regular",
    "sald.forward_kl.schedule_time_change",
    "probability.lsi_to_kl_fi",
    "sald.forward_kl.kl_derivative",
    "eq:FP-eq",
    "TransportVelocityContract"
  ]
  note := "Cycle 39 upper work records the current proof-closure priority and adds a compiled scalar pipeline. Middle synchronization adds source-shaped inverse-schedule and velocity-square scalar lemmas; lower synchronization adds the source-shaped KL/FI-to-half-Fisher scalar handoff. This does not prove mass conservation, differentiation under the integral, the SALD Fokker-Planck equation, integration by parts, target transport, LSI-to-KL/FI, inverse-schedule calculus, DV, Gronwall, EM interpolation, or thm:forward-KL."

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