AutoSamplingTheory.SALD.discreteForwardKlGronwallAccumulationObligation

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 discreteForwardKlGronwallAccumulationObligation : 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.discrete_forward_kl.gronwall_accumulation

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 appendix lines 526-592: apply lem:gronwall with a(t)=dot{s}(t)*C_LSI(t)-dot{s}(t)^(-1)*alpha^(-1)-2*dot{s}(t)*eta^2*alpha'^(-1)*Gamma(t) to obtain the source general-schedule bound for KL(rho_K^eta||pi_T).

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteGronwallSource — 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.discrete_forward_kl.kl_derivative
3. sald.discrete_forward_kl.dv_velocity_bound
4. sald.discrete_forward_kl.stitched_interval_regularity
5. SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
6. SALD.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged

note : String (explicit)

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

This obligation stops at the appendix Gronwall display. The cycle-56 pointwise wrapper now gives the exact source derivative input for Gronwall after the post-DV s-time inequality and inverse-schedule identities are supplied. The passage to the main-body linear-slowdown constants is tracked separately by sald.discrete_forward_kl.linear_slowdown_specialization.

def discreteForwardKlGronwallAccumulationObligation : ProofObligation where
  id := "sald.discrete_forward_kl.gronwall_accumulation"
  statement := "Formalize appendix lines 526-592: apply lem:gronwall with a(t)=dot{s}(t)*C_LSI(t)-dot{s}(t)^(-1)*alpha^(-1)-2*dot{s}(t)*eta^2*alpha'^(-1)*Gamma(t) to obtain the source general-schedule bound for KL(rho_K^eta||pi_T)."
  source := saldForwardKlDiscreteGronwallSource
  status := ProofStatus.obligation
  dependsOn := ["sald.gronwall.integrating_factor", "sald.discrete_forward_kl.kl_derivative", "sald.discrete_forward_kl.dv_velocity_bound", "sald.discrete_forward_kl.stitched_interval_regularity", "SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar", "SALD.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged"]
  note := "This obligation stops at the appendix Gronwall display. The cycle-56 pointwise wrapper now gives the exact source derivative input for Gronwall after the post-DV s-time inequality and inverse-schedule identities are supplied. The passage to the main-body linear-slowdown constants is tracked separately by sald.discrete_forward_kl.linear_slowdown_specialization."