AutoSamplingTheory.SALD.cycle34ForwardKlDerivativeMiddleObligation

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 cycle34ForwardKlDerivativeMiddleObligation : 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.cycle34_derivative_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 34 middle source-to-Lean map for appendix.tex lines 218-228: after the s-time post-LSI derivative inequality is available, the analytic schedule backend must supply d/dt K(s(t))=dot{s}(t)*dK/ds, ||tilde v_s||^2=dot{t}(s)^2*||v_t||^2, dot{t}(s(t))=dot{s}(t)^(-1), dot{s}(t) nonnegative and nonzero; then SALD.forwardKlTimeChangedDerivativeBoundScalar gives the t-time pre-DV inequality with coefficient (1/2)*dot{s}(t)^(-1).

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.cycle34ForwardKlDerivativeUpperPacket
2. SALD.cycle34ForwardKlDerivativeMiddleContract
3. SALD.forwardKlPostYoungDerivativeBoundScalar
4. SALD.forwardKlLsiDerivativeBoundScalar
5. SALD.forwardKlTimeChangedDerivativeBoundScalar
6. SALD.cycle34ForwardKlTargetYoungLowerObligation
7. SALD.forwardKlScheduleTimeChangeObligation
8. SALD.forwardKlDerivativeSideConditionContract
9. sald.forward_kl.cycle34_target_young_lower
10. sald.forward_kl.cycle34_derivative_scalar
11. sald.forward_kl.schedule_time_change
12. sald.forward_kl.kl_derivative

note : String (explicit)

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

This middle obligation is a synchronization and lower-packet record. The new compiled lemma is scalar real/order algebra only; the chain rule, inverse-function calculus, target velocity scaling, density/boundary backend, LSI, DV, and Gronwall remain explicit obligations.

def cycle34ForwardKlDerivativeMiddleObligation : ProofObligation where
  id := "sald.forward_kl.cycle34_derivative_middle"
  statement := "Maintain the cycle 34 middle source-to-Lean map for appendix.tex lines 218-228: after the s-time post-LSI derivative inequality is available, the analytic schedule backend must supply d/dt K(s(t))=dot{s}(t)*dK/ds, ||tilde v_s||^2=dot{t}(s)^2*||v_t||^2, dot{t}(s(t))=dot{s}(t)^(-1), dot{s}(t) nonnegative and nonzero; then SALD.forwardKlTimeChangedDerivativeBoundScalar gives the t-time pre-DV inequality with coefficient (1/2)*dot{s}(t)^(-1)."
  source := saldForwardKlDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle34ForwardKlDerivativeUpperPacket",
    "SALD.cycle34ForwardKlDerivativeMiddleContract",
    "SALD.forwardKlPostYoungDerivativeBoundScalar",
    "SALD.forwardKlLsiDerivativeBoundScalar",
    "SALD.forwardKlTimeChangedDerivativeBoundScalar",
    "SALD.cycle34ForwardKlTargetYoungLowerObligation",
    "SALD.forwardKlScheduleTimeChangeObligation",
    "SALD.forwardKlDerivativeSideConditionContract",
    "sald.forward_kl.cycle34_target_young_lower",
    "sald.forward_kl.cycle34_derivative_scalar",
    "sald.forward_kl.schedule_time_change",
    "sald.forward_kl.kl_derivative"
  ]
  note := "This middle obligation is a synchronization and lower-packet record. The new compiled lemma is scalar real/order algebra only; the chain rule, inverse-function calculus, target velocity scaling, density/boundary backend, LSI, DV, and Gronwall remain explicit obligations."