AutoSamplingTheory.SALD.cycle59GeneralMovingTargetDiscreteGronwallLowerObligation

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 cycle59GeneralMovingTargetDiscreteGronwallLowerObligation :
    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.general_moving_target_discrete.cycle59_gronwall_lower

statement : String (explicit)

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

Cycle 59 lower compiles two local theorem-display wrappers for appendix.tex lines 1573-1600. SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput turns the cycle-58 pointwise t-time derivative inequality into named Gronwall coefficient functions a(t) and b(t) matching eq:general_KL_derivative_8_discrete. SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar rewrites a supplied Gronwall bound from K(T) and K(0) to KL(rho_K^eta||pi_T) and KL(rho_0||pi_0). Stitched endpoint laws, coefficient regularity, endpoint-safe Gronwall, and exact theorem-display instantiation remain in sald.general_moving_target_discrete.gronwall_side_conditions.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteGronwallSideConditionSource — 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.cycle59MainSkeletonAnalyticMiddleObligation
2. SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged
3. SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput
4. SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar
5. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
6. SALD.generalMovingTargetDiscreteGronwallSideConditionObligation
7. sald.general_moving_target_discrete.gronwall_application
8. sald.general_moving_target_discrete.constant_schedule_stitching
9. sald.gronwall.integrating_factor

note : String (explicit)

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

Proof-producing local Real/logical wrappers only. This does not prove EM endpoint stitching, coefficient continuity/integrability, the closed-interval Gronwall theorem, or any DV, LSI/KL/FI, KL derivative, conditional-Fokker-Planck, or theorem-level statement.

def cycle59GeneralMovingTargetDiscreteGronwallLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle59_gronwall_lower"
  statement := "Cycle 59 lower compiles two local theorem-display wrappers for appendix.tex lines 1573-1600. SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput turns the cycle-58 pointwise t-time derivative inequality into named Gronwall coefficient functions a(t) and b(t) matching eq:general_KL_derivative_8_discrete. SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar rewrites a supplied Gronwall bound from K(T) and K(0) to KL(rho_K^eta||pi_T) and KL(rho_0||pi_0). Stitched endpoint laws, coefficient regularity, endpoint-safe Gronwall, and exact theorem-display instantiation remain in sald.general_moving_target_discrete.gronwall_side_conditions."
  source := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle59MainSkeletonAnalyticMiddleObligation",
    "SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged",
    "SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput",
    "SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionObligation",
    "sald.general_moving_target_discrete.gronwall_application",
    "sald.general_moving_target_discrete.constant_schedule_stitching",
    "sald.gronwall.integrating_factor"
  ]
  note := "Proof-producing local Real/logical wrappers only. This does not prove EM endpoint stitching, coefficient continuity/integrability, the closed-interval Gronwall theorem, or any DV, LSI/KL/FI, KL derivative, conditional-Fokker-Planck, or theorem-level statement."

/-- Cycle-59 proof-DAG pane for the post-cycle-58 analytic-interface check. -/