AutoSamplingTheory.SALD.cycle30ForwardKlDerivativeSideUpperObligation

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 cycle30ForwardKlDerivativeSideUpperObligation : 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_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 30 upper-role target for appendix.tex lines 168-228: lower work should first refine SALD.forwardKlDerivativeSideConditionContract, SALD.forwardKlDensityBoundaryObligation, and sald.forward_kl.density_boundary_regular for mass conservation, differentiation under the KL integral, SALD/target integration by parts, slowed-target transport, and the exact Young 1/2 coefficients, while leaving the inverse-schedule time-change, LSI, DV, and Gronwall backends as separate obligations.

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.forwardKlDerivativeCandidateContract
3. SALD.forwardKlDerivativeSideConditionContract
4. SALD.forwardKlMovingTargetDependencyContract
5. SALD.forwardKlEndpointScheduleContract
6. SALD.saldLsiKlFiDensityTestContract
7. SALD.lsiKlFiDensityTestObligation
8. sald.forward_kl.density_boundary_regular
9. sald.forward_kl.schedule_time_change
10. sald.forward_kl.kl_derivative
11. sald.forward_kl.moving_target_dependency_chain
12. eq:SALD
13. eq:FP-eq
14. eq:LSI-KL-FI
15. TransportVelocityContract

note : String (explicit)

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

This is an upper workflow obligation, not a proof. It keeps the source theorem and constants fixed, directs lower work to the derivative side-condition interface, and prevents density, boundary, inverse-schedule, LSI, DV, or Gronwall assumptions from being silently added to thm:forward-KL.

def cycle30ForwardKlDerivativeSideUpperObligation : ProofObligation where
  id := "sald.forward_kl.cycle30_derivative_side_upper"
  statement := "Maintain the cycle 30 upper-role target for appendix.tex lines 168-228: lower work should first refine SALD.forwardKlDerivativeSideConditionContract, SALD.forwardKlDensityBoundaryObligation, and sald.forward_kl.density_boundary_regular for mass conservation, differentiation under the KL integral, SALD/target integration by parts, slowed-target transport, and the exact Young 1/2 coefficients, while leaving the inverse-schedule time-change, LSI, DV, and Gronwall backends as separate obligations."
  source := saldForwardKlDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle30ForwardKlUpperPacket",
    "SALD.forwardKlDerivativeCandidateContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.forwardKlMovingTargetDependencyContract",
    "SALD.forwardKlEndpointScheduleContract",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.lsiKlFiDensityTestObligation",
    "sald.forward_kl.density_boundary_regular",
    "sald.forward_kl.schedule_time_change",
    "sald.forward_kl.kl_derivative",
    "sald.forward_kl.moving_target_dependency_chain",
    "eq:SALD",
    "eq:FP-eq",
    "eq:LSI-KL-FI",
    "TransportVelocityContract"
  ]
  note := "This is an upper workflow obligation, not a proof. It keeps the source theorem and constants fixed, directs lower work to the derivative side-condition interface, and prevents density, boundary, inverse-schedule, LSI, DV, or Gronwall assumptions from being silently added to thm:forward-KL."