AutoSamplingTheory.SALD.forwardKlScheduleTimeChangeObligation

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 forwardKlScheduleTimeChangeObligation : 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.schedule_time_change

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Formalize the inverse-schedule calculus in appendix lines 191-228: tilde_v_s=dot{t}(s)*v_{t(s)}, d/dt K(s(t))=dot{s}(t)*dK/ds, dot{s}(t)*dot{t}(s(t))=1, dot{t}(s(t))=dot{s}(t)^(-1), and dot{s}(t)*dot{t}(s(t))^2=dot{s}(t)^(-1). Once these analytic inputs are supplied, SALD.forwardKlTimeChangedDerivativeBoundScalar and the cycle 39 source-shaped scalar lemmas perform the handoff to the t-time pre-DV inequality.

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.cycle34ForwardKlDerivativeMiddleContract
4. SALD.cycle34ForwardKlDerivativeMiddleObligation
5. sald.forward_kl.cycle30_derivative_side_upper
6. sald.forward_kl.cycle30_derivative_side_middle
7. sald.forward_kl.cycle34_derivative_middle
8. sald.forward_kl.cycle39_derivative_middle
9. SALD.forwardKlDerivativeSideConditionContract
10. SALD.forwardKlTimeChangedDerivativeBoundScalar
11. SALD.forwardKlInverseScheduleDerivativeScalar
12. SALD.forwardKlTimeChangeSquareCoefficientRewriteOfProductScalar
13. SALD.forwardKlVelocitySquareScalingScalar
14. SALD.forwardKlTimeChangedDerivativeBoundOfProductScalar
15. SALD.forwardKlPreDvDerivativeBoundOfProductScalar
16. SALD.forwardKlPreDvDerivativeBoundOfVelocityScalingScalar
17. SALD.forwardKlPreDvDerivativeBoundOfKlFiVelocityScalingScalar
18. TransportVelocityContract
19. sald.forward_kl.density_boundary_regular

note : String (explicit)

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

This preserves the source time-change from the s-inequality to the t-inequality without adding an unstated theorem assumption. Cycle 34 formalizes the downstream real-order coefficient rewrite from a pre-rewritten inverse derivative, and cycle 39 adds source-shaped scalar algebra from dotS*dotT=1 and velocity norm-square scaling; the analytic schedule facts remain here.

def forwardKlScheduleTimeChangeObligation : ProofObligation where
  id := "sald.forward_kl.schedule_time_change"
  statement := "Formalize the inverse-schedule calculus in appendix lines 191-228: tilde_v_s=dot{t}(s)*v_{t(s)}, d/dt K(s(t))=dot{s}(t)*dK/ds, dot{s}(t)*dot{t}(s(t))=1, dot{t}(s(t))=dot{s}(t)^(-1), and dot{s}(t)*dot{t}(s(t))^2=dot{s}(t)^(-1). Once these analytic inputs are supplied, SALD.forwardKlTimeChangedDerivativeBoundScalar and the cycle 39 source-shaped scalar lemmas perform the handoff to the t-time pre-DV inequality."
  source := saldForwardKlDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle30ForwardKlUpperPacket",
    "SALD.cycle30ForwardKlMiddleContract",
    "SALD.cycle34ForwardKlDerivativeMiddleContract",
    "SALD.cycle34ForwardKlDerivativeMiddleObligation",
    "sald.forward_kl.cycle30_derivative_side_upper",
    "sald.forward_kl.cycle30_derivative_side_middle",
    "sald.forward_kl.cycle34_derivative_middle",
    "sald.forward_kl.cycle39_derivative_middle",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.forwardKlTimeChangedDerivativeBoundScalar",
    "SALD.forwardKlInverseScheduleDerivativeScalar",
    "SALD.forwardKlTimeChangeSquareCoefficientRewriteOfProductScalar",
    "SALD.forwardKlVelocitySquareScalingScalar",
    "SALD.forwardKlTimeChangedDerivativeBoundOfProductScalar",
    "SALD.forwardKlPreDvDerivativeBoundOfProductScalar",
    "SALD.forwardKlPreDvDerivativeBoundOfVelocityScalingScalar",
    "SALD.forwardKlPreDvDerivativeBoundOfKlFiVelocityScalingScalar",
    "TransportVelocityContract",
    "sald.forward_kl.density_boundary_regular"
  ]
  note := "This preserves the source time-change from the s-inequality to the t-inequality without adding an unstated theorem assumption. Cycle 34 formalizes the downstream real-order coefficient rewrite from a pre-rewritten inverse derivative, and cycle 39 adds source-shaped scalar algebra from dotS*dotT=1 and velocity norm-square scaling; the analytic schedule facts remain here."