AutoSamplingTheory.SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag

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 cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag :
    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.cycle171.middle_refiner.reject_opaque_testregular_hessian_wrapper
interface : String (explicit)
Text describing intended mathematical interface.
Reject the opaque wrapper shape testRegular -> hHessianOpNorm or testRegular -> hSecondFDerivOpNorm unless testRegular is expanded to a source-backed selected weak-test C2_b/bounded-Hessian field.
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.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
2. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
3. SALD.gaussianRealStdOrthonormalBasisUnit
4. hHessianOpNorm
5. testRegular
6. appendix.tex:984-995
7. appendix.tex:1026-1072
8. appendix.tex:1379-1387
9. main_body.tex:273-305
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. hSecondFDerivOpNorm
2. hDirectionalSecond
3. selected-line Taylor domination
4. scalar Ito Brownian coordinate generator leaves
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle171.lower_1_refiner.hessian_source_contract_audit
interface : String (explicit)
Text describing intended mathematical interface.
Lower_1 proof-scout audit: after rechecking the original paper anchors and searching the SALD paper source excluding sald_version_2.tex, the selected weak-test Hessian operator-norm field remains a source-contract gap. Lower_2 should implement only a source-backed C2_b/bounded-Hessian interface that supplies hHessianOpNorm, not an opaque testRegular wrapper.
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.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation
2. SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
3. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
4. SALD.gaussianRealStdOrthonormalBasisUnit
5. hHessianOpNorm
6. selected weak-test C2_b/bounded-Hessian source interface
7. appendix.tex:984-995
8. appendix.tex:1026-1072
9. appendix.tex:1379-1387
10. main_body.tex:273-305
11. paper-wide original-source search excluding sald_version_2.tex
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. lower_2 source-backed hHessianOpNorm interface
2. hSecondFDerivOpNorm
3. hDirectionalSecond
4. selected-line Taylor domination
5. scalar Ito Brownian coordinate generator leaves
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle171.lower_2_refiner.reject_unsourced_hessian_projection
interface : String (explicit)
Text describing intended mathematical interface.
Lower_2 rejection: the proposed SelectedWeakTestC2bBoundedHessian projection is not implemented because the original source audit found no source-backed selected weak-test C2_b/bounded-Hessian field. The remaining boundary is exactly hHessianOpNorm, not a Mathlib, SLT, or wrapper gap.
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.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation
2. SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation
3. SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
4. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
5. SALD.gaussianRealStdOrthonormalBasisUnit
6. hHessianOpNorm
7. SelectedWeakTestC2bBoundedHessian proposed projection rejected as unsourced
8. appendix.tex:984-995
9. appendix.tex:1026-1072
10. appendix.tex:1379-1387
11. main_body.tex:273-305
12. paper-wide original-source search excluding sald_version_2.tex
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. future source-backed selected weak-test C2_b/bounded-Hessian interface
2. hSecondFDerivOpNorm
3. hDirectionalSecond
4. selected-line Taylor domination
5. scalar Ito Brownian coordinate generator leaves
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 cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle171.middle_refiner.reject_opaque_testregular_hessian_wrapper"
      interface := "Reject the opaque wrapper shape testRegular -> hHessianOpNorm or testRegular -> hSecondFDerivOpNorm unless testRegular is expanded to a source-backed selected weak-test C2_b/bounded-Hessian field."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealStdOrthonormalBasisUnit",
        "hHessianOpNorm",
        "testRegular",
        "appendix.tex:984-995",
        "appendix.tex:1026-1072",
        "appendix.tex:1379-1387",
        "main_body.tex:273-305"
      ]
      reusedBy := [
        "hSecondFDerivOpNorm",
        "hDirectionalSecond",
        "selected-line Taylor domination",
        "scalar Ito Brownian coordinate generator leaves"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle171.lower_1_refiner.hessian_source_contract_audit"
      interface := "Lower_1 proof-scout audit: after rechecking the original paper anchors and searching the SALD paper source excluding sald_version_2.tex, the selected weak-test Hessian operator-norm field remains a source-contract gap. Lower_2 should implement only a source-backed C2_b/bounded-Hessian interface that supplies hHessianOpNorm, not an opaque testRegular wrapper."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation",
        "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealStdOrthonormalBasisUnit",
        "hHessianOpNorm",
        "selected weak-test C2_b/bounded-Hessian source interface",
        "appendix.tex:984-995",
        "appendix.tex:1026-1072",
        "appendix.tex:1379-1387",
        "main_body.tex:273-305",
        "paper-wide original-source search excluding sald_version_2.tex"
      ]
      reusedBy := [
        "lower_2 source-backed hHessianOpNorm interface",
        "hSecondFDerivOpNorm",
        "hDirectionalSecond",
        "selected-line Taylor domination",
        "scalar Ito Brownian coordinate generator leaves"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle171.lower_2_refiner.reject_unsourced_hessian_projection"
      interface := "Lower_2 rejection: the proposed SelectedWeakTestC2bBoundedHessian projection is not implemented because the original source audit found no source-backed selected weak-test C2_b/bounded-Hessian field. The remaining boundary is exactly hHessianOpNorm, not a Mathlib, SLT, or wrapper gap."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation",
        "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation",
        "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealStdOrthonormalBasisUnit",
        "hHessianOpNorm",
        "SelectedWeakTestC2bBoundedHessian proposed projection rejected as unsourced",
        "appendix.tex:984-995",
        "appendix.tex:1026-1072",
        "appendix.tex:1379-1387",
        "main_body.tex:273-305",
        "paper-wide original-source search excluding sald_version_2.tex"
      ]
      reusedBy := [
        "future source-backed selected weak-test C2_b/bounded-Hessian interface",
        "hSecondFDerivOpNorm",
        "hDirectionalSecond",
        "selected-line Taylor domination",
        "scalar Ito Brownian coordinate generator leaves"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-171 lower_1 source audit for the selected-test Hessian contract. -/

Existing module entry · Audited data-reader index · All teaching coverage