AutoSamplingTheory.SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag

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 cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag :
    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.cycle172.middle_refiner.blueprint_refreshed_hessian_source_contract
interface : String (explicit)
Text describing intended mathematical interface.
Blueprint refresh preserved the same illness area: the exact live boundary is hHessianOpNorm, not Brownian unit direction or hSecondFDerivOpNorm, because those Lean bridges are already compiled.
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.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
2. SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation
3. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
4. SALD.gaussianRealStdOrthonormalBasisUnit
5. hHessianOpNorm
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. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle172.middle_refiner.reject_same_field_projection
interface : String (explicit)
Text describing intended mathematical interface.
Reject testRegular -> hHessianOpNorm, testRegular -> hSecondFDerivOpNorm, and SelectedWeakTestC2bBoundedHessian projection work unless the source correspondence first defines the bounded-Hessian field independently of the missing bound.
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.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
2. ASTIS.SALD.cycle171.lower_2_refiner.reject_unsourced_hessian_projection
3. hHessianOpNorm
4. testRegular
5. SelectedWeakTestC2bBoundedHessian projection rejected without source backing
6. paper-wide original-source search excluding sald_version_2.tex
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. next lower source-contract recovery packet
2. reviewer wrapper-churn check
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.cycle172.lower_1_refiner.hessian_source_contract_proof_route
interface : String (explicit)
Text describing intended mathematical interface.
Lower_1 proof-scout route: the only implementable next theorem is a source-backed projection from an independently defined selected weak-test C2_b/bounded-Hessian field to hHessianOpNorm. Since the original source anchors and search still do not supply that field, this packet rejects testRegular and SelectedWeakTestC2bBoundedHessian wrapper churn and keeps hHessianOpNorm as a source-contract 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.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation
2. SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
3. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
4. SALD.gaussianRealStdOrthonormalBasisUnit
5. hHessianOpNorm
6. source-backed selected weak-test C2_b/bounded-Hessian field
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 theorem shape
2. reviewer wrapper-churn check
3. hSecondFDerivOpNorm
4. hDirectionalSecond
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.cycle172.lower_2_refiner.reject_score_or_unsourced_test_hessian_projection
interface : String (explicit)
Text describing intended mathematical interface.
Lower_2 implementation attempt: the source-backed projection theorem named by lower_1 is not implementable because the original paper does not define the needed selected weak-test bounded-Hessian field. The VP score Hessian result in iteration_complexity.tex is also rejected for this boundary because it bounds the score, not the selected weak test sourceTest. The remaining boundary is exactly hHessianOpNorm.
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.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation
2. SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation
3. SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation
4. SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm
5. SALD.gaussianRealStdOrthonormalBasisUnit
6. hHessianOpNorm
7. iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest
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. reviewer wrapper-churn check
3. hSecondFDerivOpNorm
4. hDirectionalSecond
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 cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle172.middle_refiner.blueprint_refreshed_hessian_source_contract"
      interface := "Blueprint refresh preserved the same illness area: the exact live boundary is hHessianOpNorm, not Brownian unit direction or hSecondFDerivOpNorm, because those Lean bridges are already compiled."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "SALD.cycle171GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealStdOrthonormalBasisUnit",
        "hHessianOpNorm",
        "appendix.tex:984-995",
        "appendix.tex:1026-1072",
        "appendix.tex:1379-1387",
        "main_body.tex:273-305"
      ]
      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
    },
    {
      id := "ASTIS.SALD.cycle172.middle_refiner.reject_same_field_projection"
      interface := "Reject testRegular -> hHessianOpNorm, testRegular -> hSecondFDerivOpNorm, and SelectedWeakTestC2bBoundedHessian projection work unless the source correspondence first defines the bounded-Hessian field independently of the missing bound."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "ASTIS.SALD.cycle171.lower_2_refiner.reject_unsourced_hessian_projection",
        "hHessianOpNorm",
        "testRegular",
        "SelectedWeakTestC2bBoundedHessian projection rejected without source backing",
        "paper-wide original-source search excluding sald_version_2.tex"
      ]
      reusedBy := [
        "next lower source-contract recovery packet",
        "reviewer wrapper-churn check"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle172.lower_1_refiner.hessian_source_contract_proof_route"
      interface := "Lower_1 proof-scout route: the only implementable next theorem is a source-backed projection from an independently defined selected weak-test C2_b/bounded-Hessian field to hHessianOpNorm. Since the original source anchors and search still do not supply that field, this packet rejects testRegular and SelectedWeakTestC2bBoundedHessian wrapper churn and keeps hHessianOpNorm as a source-contract gap."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation",
        "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealStdOrthonormalBasisUnit",
        "hHessianOpNorm",
        "source-backed selected weak-test C2_b/bounded-Hessian field",
        "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 theorem shape",
        "reviewer wrapper-churn check",
        "hSecondFDerivOpNorm",
        "hDirectionalSecond"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle172.lower_2_refiner.reject_score_or_unsourced_test_hessian_projection"
      interface := "Lower_2 implementation attempt: the source-backed projection theorem named by lower_1 is not implementable because the original paper does not define the needed selected weak-test bounded-Hessian field. The VP score Hessian result in iteration_complexity.tex is also rejected for this boundary because it bounds the score, not the selected weak test sourceTest. The remaining boundary is exactly hHessianOpNorm."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower2Obligation",
        "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceLower1Obligation",
        "SALD.cycle172GeneralMovingTargetDiscreteEmGeneratorLaplacianEventFieldFrozenScalarBrownianItoHessianSourceMiddleObligation",
        "SALD.gaussianRealSelectedTestSecondFDerivOpNormOfFDerivFDerivOpNorm",
        "SALD.gaussianRealStdOrthonormalBasisUnit",
        "hHessianOpNorm",
        "iteration_complexity.tex:309-321 score Hessian bound rejected for sourceTest",
        "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",
        "reviewer wrapper-churn check",
        "hSecondFDerivOpNorm",
        "hDirectionalSecond"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 172 lower_1: Hessian source-contract proof scout -/

/-- Cycle-172 lower_1 proof-scout audit for the selected-test Hessian source
contract. -/

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