AutoSamplingTheory.SALD.cycle132GeneralMovingTargetDiscreteEmSecondGreenTestTraceZeroDag

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 cycle132GeneralMovingTargetDiscreteEmSecondGreenTestTraceZeroDag :
    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.cycle132.lower_packet.second_green_test_trace_zero
interface : String (explicit)
Text describing intended mathematical interface.
Compiled illness-area refiner: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero removes the direct hsecondGreenTraceProductZero premise by deriving it from hsecondGreenTestTraceZero via SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero. It keeps the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit.
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.cycle132GeneralMovingTargetDiscreteEmSecondGreenTestTraceZeroLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFlux
4. SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero
5. appendix.tex:1392-1427
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.discrete_forward_kl.em_interpolation_fp
3. thm:forward-KL-discrete
4. thm:general-moving-target-SALD-discrete
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.cycle132.lower_1_packet.second_green_trace_eq_test_trace_zero
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 scout continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero removes the direct hsecondGreenTestTraceZero premise by deriving it from hsecondGreenTestTraceEq plus the existing admissible-test zero boundary trace condition htestTraceZero. It keeps the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit.
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.cycle132GeneralMovingTargetDiscreteEmSecondGreenTraceEqTestTraceZeroScoutObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero
4. SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero
5. appendix.tex:1392-1427
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.discrete_forward_kl.em_interpolation_fp
3. thm:forward-KL-discrete
4. thm:general-moving-target-SALD-discrete
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.cycle132.lower_2_packet.second_green_pointwise_trace_eq
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero removes the a.e. hsecondGreenTestTraceEq premise by deriving it from hsecondGreenTestTracePointwiseEq via Filter.Eventually.of_forall, while keeping htestTraceZero, the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit.
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.cycle132GeneralMovingTargetDiscreteEmSecondGreenPointwiseTraceEqLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero
4. Filter.Eventually.of_forall
5. appendix.tex:1392-1427
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.discrete_forward_kl.em_interpolation_fp
3. thm:forward-KL-discrete
4. thm:general-moving-target-SALD-discrete
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.cycle132.remaining_laplacian_ibp_analysis
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 132: prove the density-Laplacian weak term for the EM/Brownian diffusion contribution, instantiate the first-Green residual/divergence/zero-flux facts, instantiate the second-Green residual/divergence facts, prove the box-divergence regularity/face-trace facts behind the second-Green boundary flux, prove the pointwise source trace-definition equality identifying the second-Green test trace with the admissible-test boundary trace, prove the analytic zero-test-trace theorem for source admissible tests, and prove htestLaplacian.
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. appendix.tex:1379-1387
2. appendix.tex:1392-1427
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero
6. SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox
7. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.discrete_forward_kl.em_interpolation_fp
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.cycle132.reviewer_second_green_trace_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the new theorem statement lacks a direct hsecondGreenTraceProductZero premise, hdiffusionAction, hdiffusionLaplacianTerm, first-Green subfacts, second-Green residual/divergence facts, box-divergence inputs, and htestLaplacian remain separate, and python3 tools/astis.py check passes without SLT import, non-EM fallback, wrapper churn, theorem-status promotion, fake closure, or sald_version_2 use.
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.cycle132GeneralMovingTargetDiscreteEmSecondGreenTestTraceZeroLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero
3. appendix.tex:1392-1427
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 132 reviewer
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 cycle132GeneralMovingTargetDiscreteEmSecondGreenTestTraceZeroDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle132.lower_packet.second_green_test_trace_zero"
      interface := "Compiled illness-area refiner: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero removes the direct hsecondGreenTraceProductZero premise by deriving it from hsecondGreenTestTraceZero via SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero. It keeps the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle132GeneralMovingTargetDiscreteEmSecondGreenTestTraceZeroLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFlux",
        "SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero",
        "appendix.tex:1392-1427"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle132.lower_1_packet.second_green_trace_eq_test_trace_zero"
      interface := "Compiled lower_1 scout continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero removes the direct hsecondGreenTestTraceZero premise by deriving it from hsecondGreenTestTraceEq plus the existing admissible-test zero boundary trace condition htestTraceZero. It keeps the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle132GeneralMovingTargetDiscreteEmSecondGreenTraceEqTestTraceZeroScoutObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero",
        "SALD.generalMovingTargetDiscreteTraceProductZeroOfTestTraceZero",
        "appendix.tex:1392-1427",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle132.lower_2_packet.second_green_pointwise_trace_eq"
      interface := "Compiled lower_2 continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero removes the a.e. hsecondGreenTestTraceEq premise by deriving it from hsecondGreenTestTracePointwiseEq via Filter.Eventually.of_forall, while keeping htestTraceZero, the cycle-131 box-divergence package, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle132GeneralMovingTargetDiscreteEmSecondGreenPointwiseTraceEqLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero",
        "Filter.Eventually.of_forall",
        "appendix.tex:1392-1427",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle132.remaining_laplacian_ibp_analysis"
      interface := "Remaining exact theorem boundary after cycle 132: prove the density-Laplacian weak term for the EM/Brownian diffusion contribution, instantiate the first-Green residual/divergence/zero-flux facts, instantiate the second-Green residual/divergence facts, prove the box-divergence regularity/face-trace facts behind the second-Green boundary flux, prove the pointwise source trace-definition equality identifying the second-Green test trace with the admissible-test boundary trace, prove the analytic zero-test-trace theorem for source admissible tests, and prove htestLaplacian."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "appendix.tex:1379-1387",
        "appendix.tex:1392-1427",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfPointwiseTraceEqTestTraceZero",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTraceEqTestTraceZero",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero",
        "SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox",
        "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle132.reviewer_second_green_trace_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the new theorem statement lacks a direct hsecondGreenTraceProductZero premise, hdiffusionAction, hdiffusionLaplacianTerm, first-Green subfacts, second-Green residual/divergence facts, box-divergence inputs, and htestLaplacian remain separate, and python3 tools/astis.py check passes without SLT import, non-EM fallback, wrapper churn, theorem-status promotion, fake closure, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle132GeneralMovingTargetDiscreteEmSecondGreenTestTraceZeroLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFluxOfTestTraceZero",
        "appendix.tex:1392-1427"
      ]
      reusedBy := ["cycle 132 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 133: EM second-Green pointwise test-trace zero boundary -/

/-- Cycle-133 middle packet narrowing the admissible-test zero boundary trace
input from an a.e. statement to a pointwise source theorem. -/

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