AutoSamplingTheory.SALD.cycle28GeneralVaSaldDerivativeSideMiddleObligation

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 cycle28GeneralVaSaldDerivativeSideMiddleObligation : 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_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-28 middle source-to-Lean map for appendix lines 1469-1511: rewrite the derivative cross field as delta_pi^VA+dot t(s)*m_{t(s)}, split the derivative cross term into frozen and residual parts, preserve the two sigma_eta^2/8 Young shares, and route the remaining analytic work to sald.general_moving_target_discrete.derivative_side_conditions without changing theorem coefficients.

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.cycle28GeneralVaSaldUpperPacket
2. SALD.cycle28GeneralVaSaldMiddleContract
3. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
4. SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector
5. SALD.generalMovingTargetDiscreteYoungFisherShareScalar
6. SALD.generalMovingTargetDiscreteTwoYoungFisherBudgetScalar
7. SALD.generalMovingTargetDiscreteResidualYoungCoefficientScalar
8. sald.general_moving_target_discrete.em_interpolation_fp
9. sald.general_moving_target_discrete.frozen_delta_cross_lip
10. sald.general_moving_target_discrete.derivative_side_conditions
11. 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. The compiled module helper closes only algebra after the concrete field identifications are supplied, and the three scalar helpers close only real coefficient bookkeeping for the Young shares. Inner-product Young, frozen-delta, LSI, DV, time change, and the full derivative theorem remain obligations.

def cycle28GeneralVaSaldDerivativeSideMiddleObligation : ProofObligation where
  id := "sald.general_moving_target_discrete.cycle28_derivative_side_middle"
  statement := "Maintain the cycle-28 middle source-to-Lean map for appendix lines 1469-1511: rewrite the derivative cross field as delta_pi^VA+dot t(s)*m_{t(s)}, split the derivative cross term into frozen and residual parts, preserve the two sigma_eta^2/8 Young shares, and route the remaining analytic work to sald.general_moving_target_discrete.derivative_side_conditions without changing theorem coefficients."
  source := saldGeneralMovingTargetDiscreteYoungSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle28GeneralVaSaldUpperPacket",
    "SALD.cycle28GeneralVaSaldMiddleContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector",
    "SALD.generalMovingTargetDiscreteYoungFisherShareScalar",
    "SALD.generalMovingTargetDiscreteTwoYoungFisherBudgetScalar",
    "SALD.generalMovingTargetDiscreteResidualYoungCoefficientScalar",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.frozen_delta_cross_lip",
    "sald.general_moving_target_discrete.derivative_side_conditions",
    "probability.lsi_to_kl_fi"
  ]
  note := "This is middle-role synchronization data. The compiled module helper closes only algebra after the concrete field identifications are supplied, and the three scalar helpers close only real coefficient bookkeeping for the Young shares. Inner-product Young, frozen-delta, LSI, DV, time change, and the full derivative theorem remain obligations."