AutoSamplingTheory.SALD.cycle24GeneralVaSaldGronwallMiddleObligation

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 cycle24GeneralVaSaldGronwallMiddleObligation : 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.cycle24_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-24 middle source-to-Lean map for appendix lines 909-945 and theorem display lines 727-743: route the Gronwall output through endpoint K(T)/K(0) rewrites, coefficient regularity for the sigma-weighted a(t), b(t), exponent splitting, residual-exponent monotonicity, and zero-residual alpha-complexity without changing thm:general-moving-target-SALD or thm:unified-forward-KL.

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.cycle24GeneralVaSaldUpperPacket
2. SALD.cycle24GeneralVaSaldMiddleContract
3. SALD.generalMovingTargetGronwallInstantiationContract
4. SALD.generalMovingTargetGronwallSideConditionContract
5. sald.general_moving_target.gronwall_application
6. sald.general_moving_target.dv_m_energy
7. sald.general_moving_target.kl_derivative
8. sald.forward_kl.schedule_time_change
9. sald.gronwall.integrating_factor
10. sald.gronwall.exponent_rewrite
11. SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable
12. SALD.generalMovingTargetGronwallExpProductRewriteIntegralCongrOfPieces
13. probability.lsi_to_kl_fi

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 coefficient regularity and adjacent interval-integrability as the preferred first lower sub-slice; the compiled cycle-24 lower helpers package only the local interval-integrability closure after source hypotheses are supplied and do not prove thm:general-moving-target-SALD, Gronwall, endpoint rewrites, exponent monotonicity, or pure contraction.

def cycle24GeneralVaSaldGronwallMiddleObligation : ProofObligation where
  id := "sald.general_moving_target.cycle24_gronwall_middle"
  statement := "Maintain the cycle-24 middle source-to-Lean map for appendix lines 909-945 and theorem display lines 727-743: route the Gronwall output through endpoint K(T)/K(0) rewrites, coefficient regularity for the sigma-weighted a(t), b(t), exponent splitting, residual-exponent monotonicity, and zero-residual alpha-complexity without changing thm:general-moving-target-SALD or thm:unified-forward-KL."
  source := saldGeneralMovingTargetDvGronwallSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle24GeneralVaSaldUpperPacket",
    "SALD.cycle24GeneralVaSaldMiddleContract",
    "SALD.generalMovingTargetGronwallInstantiationContract",
    "SALD.generalMovingTargetGronwallSideConditionContract",
    "sald.general_moving_target.gronwall_application",
    "sald.general_moving_target.dv_m_energy",
    "sald.general_moving_target.kl_derivative",
    "sald.forward_kl.schedule_time_change",
    "sald.gronwall.integrating_factor",
    "sald.gronwall.exponent_rewrite",
    "SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable",
    "SALD.generalMovingTargetGronwallExpProductRewriteIntegralCongrOfPieces",
    "probability.lsi_to_kl_fi"
  ]
  note := "This is middle-role synchronization data. It selects coefficient regularity and adjacent interval-integrability as the preferred first lower sub-slice; the compiled cycle-24 lower helpers package only the local interval-integrability closure after source hypotheses are supplied and do not prove thm:general-moving-target-SALD, Gronwall, endpoint rewrites, exponent monotonicity, or pure contraction."