AutoSamplingTheory.SALD.cycle20GeneralVaSaldDiscreteGronwallMiddleObligation

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 cycle20GeneralVaSaldDiscreteGronwallMiddleObligation : 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.cycle20_gronwall_middle

statement : String (explicit)

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

Maintain the cycle-20 middle source-to-Lean map for appendix lines 1573-1600 and theorem display lines 1316-1347: define K(t) from the stitched EM interpolation, apply the constant inverse-schedule rewrite to the residual and frozen-delta coefficients, expose the a(t), b(t) regularity required by lem:gronwall, and route exact display matching to sald.general_moving_target_discrete.gronwall_side_conditions without changing coefficients.

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.cycle20GeneralVaSaldUpperPacket
2. SALD.cycle20GeneralVaSaldMiddleContract
3. SALD.generalMovingTargetDiscreteGronwallInstantiationContract
4. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
5. SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar
6. SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar
7. SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar
8. SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar
9. SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged
10. sald.general_moving_target_discrete.gronwall_application
11. sald.general_moving_target_discrete.constant_schedule_stitching
12. sald.general_moving_target_discrete.kl_derivative
13. sald.general_moving_target_discrete.dv_m_energy
14. sald.gronwall.integrating_factor

note : String (explicit)

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

This is middle-role synchronization data. It selects the constant-schedule coefficient rewrite as the preferred first lower sub-slice, but does not prove thm:general-moving-target-SALD-discrete, Gronwall, endpoint stitching, or coefficient regularity.

def cycle20GeneralVaSaldDiscreteGronwallMiddleObligation : ProofObligation where
  id := "sald.general_moving_target_discrete.cycle20_gronwall_middle"
  statement := "Maintain the cycle-20 middle source-to-Lean map for appendix lines 1573-1600 and theorem display lines 1316-1347: define K(t) from the stitched EM interpolation, apply the constant inverse-schedule rewrite to the residual and frozen-delta coefficients, expose the a(t), b(t) regularity required by lem:gronwall, and route exact display matching to sald.general_moving_target_discrete.gronwall_side_conditions without changing coefficients."
  source := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle20GeneralVaSaldUpperPacket",
    "SALD.cycle20GeneralVaSaldMiddleContract",
    "SALD.generalMovingTargetDiscreteGronwallInstantiationContract",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "SALD.generalMovingTargetDiscreteConstantScheduleSquareScalar",
    "SALD.generalMovingTargetDiscreteResidualCoefficientRewriteScalar",
    "SALD.generalMovingTargetDiscreteGammaCoefficientRewriteScalar",
    "SALD.generalMovingTargetDiscreteDeltaCoefficientRewriteScalar",
    "SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged",
    "sald.general_moving_target_discrete.gronwall_application",
    "sald.general_moving_target_discrete.constant_schedule_stitching",
    "sald.general_moving_target_discrete.kl_derivative",
    "sald.general_moving_target_discrete.dv_m_energy",
    "sald.gronwall.integrating_factor"
  ]
  note := "This is middle-role synchronization data. It selects the constant-schedule coefficient rewrite as the preferred first lower sub-slice, but does not prove thm:general-moving-target-SALD-discrete, Gronwall, endpoint stitching, or coefficient regularity."