AutoSamplingTheory.SALD.cycle30ForwardKlDerivativeSideMiddleObligation

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.

def cycle30ForwardKlDerivativeSideMiddleObligation : 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.cycle30_derivative_side_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.

Maintain the cycle 30 middle source-to-Lean map for appendix.tex lines 168-208, with appendix.tex:168-185 as the first lower sub-slice: mass conservation, differentiation under the KL integral, the SALD Fokker-Planck equation, boundary/integration-by-parts conditions, and the identification of the first derivative term with -FI(rho_s||tilde_pi_s).

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.cycle30ForwardKlUpperPacket
2. SALD.cycle30ForwardKlMiddleContract
3. sald.forward_kl.cycle30_derivative_side_upper
4. SALD.forwardKlDerivativeCandidateContract
5. SALD.forwardKlDerivativeSideConditionContract
6. SALD.forwardKlDensityBoundaryObligation
7. sald.forward_kl.density_boundary_regular
8. sald.forward_kl.cycle30_density_boundary_lower
9. SALD.forwardKlFirstTermFisherSubstitutionScalar
10. sald.forward_kl.kl_derivative
11. eq:SALD
12. eq:FP-eq
13. KLContract
14. FIContract
15. FokkerPlanckContract
16. TransportVelocityContract

note : String (explicit)

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

This is a middle workflow obligation, not a proof. It narrows lower work to the density/boundary backend before the target-side transport, LSI-to-KL/FI, inverse-schedule time change, DV witness, coefficient-chain audit, and Gronwall side conditions are attempted.

def cycle30ForwardKlDerivativeSideMiddleObligation : ProofObligation where
  id := "sald.forward_kl.cycle30_derivative_side_middle"
  statement := "Maintain the cycle 30 middle source-to-Lean map for appendix.tex lines 168-208, with appendix.tex:168-185 as the first lower sub-slice: mass conservation, differentiation under the KL integral, the SALD Fokker-Planck equation, boundary/integration-by-parts conditions, and the identification of the first derivative term with -FI(rho_s||tilde_pi_s)."
  source := saldForwardKlDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle30ForwardKlUpperPacket",
    "SALD.cycle30ForwardKlMiddleContract",
      "sald.forward_kl.cycle30_derivative_side_upper",
      "SALD.forwardKlDerivativeCandidateContract",
      "SALD.forwardKlDerivativeSideConditionContract",
      "SALD.forwardKlDensityBoundaryObligation",
      "sald.forward_kl.density_boundary_regular",
      "sald.forward_kl.cycle30_density_boundary_lower",
      "SALD.forwardKlFirstTermFisherSubstitutionScalar",
      "sald.forward_kl.kl_derivative",
      "eq:SALD",
      "eq:FP-eq",
    "KLContract",
    "FIContract",
    "FokkerPlanckContract",
    "TransportVelocityContract"
  ]
  note := "This is a middle workflow obligation, not a proof. It narrows lower work to the density/boundary backend before the target-side transport, LSI-to-KL/FI, inverse-schedule time change, DV witness, coefficient-chain audit, and Gronwall side conditions are attempted."