AutoSamplingTheory.SALD.cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorReflectDag

Data definition / provenance and workflow record

Meaning and type

The result has data type List AutoSamplingTheory.ProofDagBlock. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorReflectDag :
    List ProofDagBlock

Construction and field-by-field explanation

Construct an ordered list of the following data items. It is not a logical conjunction or proof DAG.

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.

Ordered data items

id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle167.middle_packet.reflected_set_univ_taylor_compat
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv proves the reflected Set.univ first-order Taylor-polynomial compatibility for the selected scalar line from the algebraic reflection q |-> -q and Mathlib deriv_comp_neg.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv
2. deriv_comp_neg
3. taylorWithinEval_succ
4. Set.univ
5. appendix.tex:984-995
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect
2. hFirstQuadraticRemainder
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle167.middle_packet.signed_interval_without_reflect_hypothesis
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect removes hNegTaylorReflect from the signed interval first-order quadratic remainder theorem by supplying it internally from the reflection lemma.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorReflectMiddleObligation
2. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect
3. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylor
4. SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv
5. hNonnegCont
6. hNonnegSecond
7. hNonnegTaylorCompat
8. hNegCont
9. hNegSecond
10. hNegTaylorCompat
11. appendix.tex:984-995
12. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.gaussianRealSelectedTestLineFirstOrderTaylorQuotientBoundOfQuadraticRemainder
2. SALD.gaussianRealSelectedTestLineSecondOrderTaylorQuotientBoundOfFirstOrderAndSecondCoeff
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle167.remaining_signed_interval_regularity_data
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after discharging hNegTaylorReflect: prove signed interval ContDiffOn, signed interval second-derivative domination, and interval-to-Set.univ Taylor compatibility for the selected and reflected lines from the paper's selected-test bounded-Hessian/regularity hypotheses; hSecondCoeff remains separate.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/SALD.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect
2. hNonnegCont
3. hNonnegSecond
4. hNonnegTaylorCompat
5. hNegCont
6. hNegSecond
7. hNegTaylorCompat
8. selected-test second-derivative or bounded-Hessian source hypothesis
9. interval-to-Set.univ taylorWithinEval compatibility
10. appendix.tex:984-995
11. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hFirst
2. SALD.gaussianRealSelectedTestLineSecondOrderTaylorQuotientBoundOfFirstOrderAndSecondCoeff
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorReflectDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle167.middle_packet.reflected_set_univ_taylor_compat"
      interface := "Compiled theorem: SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv proves the reflected Set.univ first-order Taylor-polynomial compatibility for the selected scalar line from the algebraic reflection q |-> -q and Mathlib deriv_comp_neg."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv",
        "deriv_comp_neg",
        "taylorWithinEval_succ",
        "Set.univ",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect",
        "hFirstQuadraticRemainder"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle167.middle_packet.signed_interval_without_reflect_hypothesis"
      interface := "Compiled theorem: SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect removes hNegTaylorReflect from the signed interval first-order quadratic remainder theorem by supplying it internally from the reflection lemma."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle167GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoTaylorReflectMiddleObligation",
        "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect",
        "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylor",
        "SALD.gaussianRealSelectedTestLineFirstOrderTaylorReflectSetUniv",
        "hNonnegCont",
        "hNonnegSecond",
        "hNonnegTaylorCompat",
        "hNegCont",
        "hNegSecond",
        "hNegTaylorCompat",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.gaussianRealSelectedTestLineFirstOrderTaylorQuotientBoundOfQuadraticRemainder",
        "SALD.gaussianRealSelectedTestLineSecondOrderTaylorQuotientBoundOfFirstOrderAndSecondCoeff"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle167.remaining_signed_interval_regularity_data"
      interface := "Remaining exact theorem boundary after discharging hNegTaylorReflect: prove signed interval ContDiffOn, signed interval second-derivative domination, and interval-to-Set.univ Taylor compatibility for the selected and reflected lines from the paper's selected-test bounded-Hessian/regularity hypotheses; hSecondCoeff remains separate."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.gaussianRealSelectedTestLineFirstOrderQuadraticRemainderBoundOfSignedIntervalTaylorNoReflect",
        "hNonnegCont",
        "hNonnegSecond",
        "hNonnegTaylorCompat",
        "hNegCont",
        "hNegSecond",
        "hNegTaylorCompat",
        "selected-test second-derivative or bounded-Hessian source hypothesis",
        "interval-to-Set.univ taylorWithinEval compatibility",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "hFirst",
        "SALD.gaussianRealSelectedTestLineSecondOrderTaylorQuotientBoundOfFirstOrderAndSecondCoeff"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-167 lower_1 Taylor-compatibility narrowing packet. -/

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