AutoSamplingTheory.SALD.generalMovingTargetGronwallSideConditionObligation

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 generalMovingTargetGronwallSideConditionObligation : 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.gronwall_side_conditions

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 908-945: after applying lem:gronwall, identify K(T)=KL(rho_S||pi_T) and K(0)=KL(rho_0||pi_0), prove the sigma-weighted a(t), b(t) regularity needed by Gronwall, split exp(-int a), justify dropping the nonpositive LSI contribution from the residual exponent, and show c_t=v_t makes E_alpha(pi_t,m_t)=0.

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.general_moving_target.cycle24_gronwall_middle
4. sald.forward_kl.schedule_time_change
5. sald.general_moving_target.kl_derivative
6. sald.general_moving_target.dv_m_energy
7. sald.general_moving_target.gronwall_application
8. sald.gronwall.integrating_factor
9. SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable
10. SALD.generalMovingTargetGronwallExpProductRewriteIntegralCongrOfPieces
11. def:alpha-complexity

note : String (explicit)

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

generalMovingTargetGronwallSideConditionContract records endpoint rewrites, coefficient regularity, exponent splitting, residual-exponent sign facts, and zero-residual alpha-complexity without changing thm:general-moving-target-SALD. SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable only assembles a(t) and carries b(t) interval-integrability after the theorem-specific regularity hypotheses are provided.

def generalMovingTargetGronwallSideConditionObligation : ProofObligation where
  id := "sald.general_moving_target.gronwall_side_conditions"
  statement := "Formalize appendix lines 908-945: after applying lem:gronwall, identify K(T)=KL(rho_S||pi_T) and K(0)=KL(rho_0||pi_0), prove the sigma-weighted a(t), b(t) regularity needed by Gronwall, split exp(-int a), justify dropping the nonpositive LSI contribution from the residual exponent, and show c_t=v_t makes E_alpha(pi_t,m_t)=0."
  source := saldGeneralMovingTargetDvGronwallSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle24GeneralVaSaldUpperPacket",
    "SALD.cycle24GeneralVaSaldMiddleContract",
    "sald.general_moving_target.cycle24_gronwall_middle",
    "sald.forward_kl.schedule_time_change",
    "sald.general_moving_target.kl_derivative",
    "sald.general_moving_target.dv_m_energy",
    "sald.general_moving_target.gronwall_application",
    "sald.gronwall.integrating_factor",
    "SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable",
    "SALD.generalMovingTargetGronwallExpProductRewriteIntegralCongrOfPieces",
    "def:alpha-complexity"
  ]
  note := "generalMovingTargetGronwallSideConditionContract records endpoint rewrites, coefficient regularity, exponent splitting, residual-exponent sign facts, and zero-residual alpha-complexity without changing thm:general-moving-target-SALD. SALD.generalMovingTargetGronwallCoeffAdjacentIntervalIntegrable only assembles a(t) and carries b(t) interval-integrability after the theorem-specific regularity hypotheses are provided."