AutoSamplingTheory.SALD.forwardKlGronwallApplicationObligation

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 forwardKlGronwallApplicationObligation : 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.gronwall_application

statement : String (explicit)

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

Instantiate lem:gronwall on appendix lines 242-252 with a(t)=dot{s}(t)*C_LSI(t)-(1/2)*dot{s}(t)^(-1)*alpha^(-1) and b(t)=(1/2)*dot{s}(t)^(-1)*E_alpha(pi_t,v_t), preserving the two exponential factors in main_body.tex lines 243-246.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlGronwallSource — 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.gronwall.integrating_factor
2. sald.forward_kl.kl_derivative
3. sald.forward_kl.dv_energy_bound

note : String (explicit)

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

Do not replace this with a different Gronwall normalization; forwardKlGronwallInstantiationContract records the source's a(t), b(t), exponent split, and regularity gaps.

def forwardKlGronwallApplicationObligation : ProofObligation where
  id := "sald.forward_kl.gronwall_application"
  statement := "Instantiate lem:gronwall on appendix lines 242-252 with a(t)=dot{s}(t)*C_LSI(t)-(1/2)*dot{s}(t)^(-1)*alpha^(-1) and b(t)=(1/2)*dot{s}(t)^(-1)*E_alpha(pi_t,v_t), preserving the two exponential factors in main_body.tex lines 243-246."
  source := saldForwardKlGronwallSource
  status := ProofStatus.obligation
  dependsOn := ["sald.gronwall.integrating_factor", "sald.forward_kl.kl_derivative", "sald.forward_kl.dv_energy_bound"]
  note := "Do not replace this with a different Gronwall normalization; forwardKlGronwallInstantiationContract records the source's a(t), b(t), exponent split, and regularity gaps."