AutoSamplingTheory.SALD.cycle28GeneralVaSaldDerivativeSideLowerObligation

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 cycle28GeneralVaSaldDerivativeSideLowerObligation : 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.cycle28_derivative_side_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.

Record the cycle-28 lower compiled algebra for appendix lines 1469-1478: once eq:general_discrete_delta_def identifies delta_pi^VA as dot t(s)*c_t plus the score term minus the frozen conditional drift, tilde v_s is dot t(s)*v_t, and m_t=v_t-c_t, the cross field rewrites as delta_pi^VA+dot t(s)*m_t. The conditional drift, score, slowed-transport, pointwise vector-field identifications, Young inequalities, frozen-delta lemma, LSI, DV, time change, and theorem statement remain obligations.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteYoungSource — 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.cycle28GeneralVaSaldMiddleContract
2. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
3. SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector
4. eq:general_discrete_delta_def
5. sald.general_moving_target_discrete.em_interpolation_fp
6. sald.general_moving_target_discrete.derivative_side_conditions

note : String (explicit)

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

The compiled theorem is only module-level algebra. It does not prove the analytic equality of the paper's concrete vector fields or any Young/FI/frozen-delta side condition.

def cycle28GeneralVaSaldDerivativeSideLowerObligation : ProofObligation where
  id := "sald.general_moving_target_discrete.cycle28_derivative_side_lower"
  statement := "Record the cycle-28 lower compiled algebra for appendix lines 1469-1478: once eq:general_discrete_delta_def identifies delta_pi^VA as dot t(s)*c_t plus the score term minus the frozen conditional drift, tilde v_s is dot t(s)*v_t, and m_t=v_t-c_t, the cross field rewrites as delta_pi^VA+dot t(s)*m_t. The conditional drift, score, slowed-transport, pointwise vector-field identifications, Young inequalities, frozen-delta lemma, LSI, DV, time change, and theorem statement remain obligations."
  source := saldGeneralMovingTargetDiscreteYoungSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle28GeneralVaSaldMiddleContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector",
    "eq:general_discrete_delta_def",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.derivative_side_conditions"
  ]
  note := "The compiled theorem is only module-level algebra. It does not prove the analytic equality of the paper's concrete vector fields or any Young/FI/frozen-delta side condition."