AutoSamplingTheory.SALD.cycle41GronwallMiddleObligation

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 cycle41GronwallMiddleObligation : 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.gronwall.cycle41_deriv_wrapper

statement : String (explicit)

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

Record the cycle 41 proof-producing Gronwall wrapper for appendix.tex lines 47-71: SALD.gronwallIntegratingFactorBoundOfDifferentiable rewrites the paper's dK/dt as deriv K and proves the displayed bound from continuous a,b, differentiable K, the source inequality with deriv K, and one explicit interval-integrability hypothesis for the product-derivative integrand; SALD.gronwallIntegratingFactorBoundOfC1 discharges that remaining integrability condition when deriv K is continuous.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGronwallSource — 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.cycle36GronwallMiddleObligation
2. SALD.gronwallIntegratingFactorBoundOfDifferentiable
3. SALD.gronwallIntegratingFactorBoundOfC1
4. SALD.gronwallIntegratingFactorBoundOfIntegral
5. SALD.gronwallCoefficientSideConditionsOfContinuous
6. SALD.gronwallEndpointIntegralRewrite
7. sald.gronwall.endpoint_calculus
8. sald.gronwall.integrating_factor

note : String (explicit)

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

This narrows the remaining source bridge from an arbitrary K' witness to the actual Lean derivative deriv K. It does not mark lem:gronwall formalized, because the paper's bare phrase differentiable on [0,t1] still needs an endpoint-safe or absolute-continuity interpretation strong enough to justify the FTC/integrability side condition without silently assuming C1 regularity.

def cycle41GronwallMiddleObligation : ProofObligation where
  id := "sald.gronwall.cycle41_deriv_wrapper"
  statement := "Record the cycle 41 proof-producing Gronwall wrapper for appendix.tex lines 47-71: SALD.gronwallIntegratingFactorBoundOfDifferentiable rewrites the paper's dK/dt as deriv K and proves the displayed bound from continuous a,b, differentiable K, the source inequality with deriv K, and one explicit interval-integrability hypothesis for the product-derivative integrand; SALD.gronwallIntegratingFactorBoundOfC1 discharges that remaining integrability condition when deriv K is continuous."
  source := saldGronwallSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle36GronwallMiddleObligation",
    "SALD.gronwallIntegratingFactorBoundOfDifferentiable",
    "SALD.gronwallIntegratingFactorBoundOfC1",
    "SALD.gronwallIntegratingFactorBoundOfIntegral",
    "SALD.gronwallCoefficientSideConditionsOfContinuous",
    "SALD.gronwallEndpointIntegralRewrite",
    "sald.gronwall.endpoint_calculus",
    "sald.gronwall.integrating_factor"
  ]
  note := "This narrows the remaining source bridge from an arbitrary K' witness to the actual Lean derivative deriv K. It does not mark lem:gronwall formalized, because the paper's bare phrase differentiable on [0,t1] still needs an endpoint-safe or absolute-continuity interpretation strong enough to justify the FTC/integrability side condition without silently assuming C1 regularity."

/-- Cycle-41 lower endpoint-safe Gronwall interior-derivative assembly record. -/