AutoSamplingTheory.SALD.cycle67GuidedGeneralResidualGronwallLowerObligation

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 cycle67GuidedGeneralResidualGronwallLowerObligation :
    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.cycle67_residual_to_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 67 lower compiles SALD.generalMovingTargetResidualToGronwallBridgeScalar for appendix.tex:765-907: after the analytic backend supplies the raw KL derivative split, mass conservation, Fokker-Planck/integration-by-parts first-term identity, target-transport residual m_t=v_t-c_t, residual Young bound, LSI/KL/FI half-Fisher comparison, inverse-schedule time change, and residual DV input with Z=alpha*||m_t||^2, the wrapper derives the exact sigma-weighted Gronwall differential inequality coefficient for thm:general-moving-target-SALD.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDvGronwallSource — 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.cycle67GuidedGeneralSkeletonMiddleObligation
2. SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation
3. SALD.generalMovingTargetResidualToGronwallBridgeScalar
4. SALD.generalMovingTargetKlDerivativeResidualSplitScalar
5. SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar
6. SALD.generalMovingTargetPreDvDerivativeBoundScalar
7. SALD.generalMovingTargetPostDvGronwallCoefficientOfSigmaScheduleScalar
8. SALD.generalMovingTargetDerivativeCandidateContract
9. SALD.generalMovingTargetDerivativeObligation
10. SALD.saldLsiKlFiDensityTestContract
11. SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
12. SALD.generalMovingTargetDvPositiveAlphaScalingContract
13. SALD.generalMovingTargetDvEnergyCandidateContract
14. SALD.generalMovingTargetGronwallInstantiationContract
15. SALD.generalMovingTargetGronwallSideConditionContract
16. sald.general_moving_target.kl_derivative
17. probability.lsi_to_kl_fi
18. sald.general_moving_target.dv_m_energy
19. sald.general_moving_target.gronwall_application
20. sald.general_moving_target.gronwall_side_conditions

note : String (explicit)

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

Proof-producing scalar wrapper plus obligation only. It preserves the theorem target, source constants, and source labels. It does not prove Fokker-Planck/KL differentiation, integration by parts, target transport, residual Young, LSI/KL/FI, DV finite-log-mgf/common-space hypotheses, Gronwall, endpoint rewrites, pure contraction, or thm:general-moving-target-SALD.

def cycle67GuidedGeneralResidualGronwallLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target.cycle67_residual_to_gronwall_lower"
  statement := "Cycle 67 lower compiles SALD.generalMovingTargetResidualToGronwallBridgeScalar for appendix.tex:765-907: after the analytic backend supplies the raw KL derivative split, mass conservation, Fokker-Planck/integration-by-parts first-term identity, target-transport residual m_t=v_t-c_t, residual Young bound, LSI/KL/FI half-Fisher comparison, inverse-schedule time change, and residual DV input with Z=alpha*||m_t||^2, the wrapper derives the exact sigma-weighted Gronwall differential inequality coefficient for thm:general-moving-target-SALD."
  source := saldGeneralMovingTargetDvGronwallSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation",
    "SALD.generalMovingTargetResidualToGronwallBridgeScalar",
    "SALD.generalMovingTargetKlDerivativeResidualSplitScalar",
    "SALD.generalMovingTargetDerivativeDvGronwallCoefficientScalar",
    "SALD.generalMovingTargetPreDvDerivativeBoundScalar",
    "SALD.generalMovingTargetPostDvGronwallCoefficientOfSigmaScheduleScalar",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.generalMovingTargetDerivativeObligation",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
    "SALD.generalMovingTargetDvPositiveAlphaScalingContract",
    "SALD.generalMovingTargetDvEnergyCandidateContract",
    "SALD.generalMovingTargetGronwallInstantiationContract",
    "SALD.generalMovingTargetGronwallSideConditionContract",
    "sald.general_moving_target.kl_derivative",
    "probability.lsi_to_kl_fi",
    "sald.general_moving_target.dv_m_energy",
    "sald.general_moving_target.gronwall_application",
    "sald.general_moving_target.gronwall_side_conditions"
  ]
  note := "Proof-producing scalar wrapper plus obligation only. It preserves the theorem target, source constants, and source labels. It does not prove Fokker-Planck/KL differentiation, integration by parts, target transport, residual Young, LSI/KL/FI, DV finite-log-mgf/common-space hypotheses, Gronwall, endpoint rewrites, pure contraction, or thm:general-moving-target-SALD."

/-- Cycle-67 proof-DAG pane for the guided residual and continuous general
moving-target route. -/