AutoSamplingTheory.SALD.cycle131GeneralMovingTargetDiscreteEmSecondGreenNoBoundaryFluxDag

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 cycle131GeneralMovingTargetDiscreteEmSecondGreenNoBoundaryFluxDag :
    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.cycle131.middle_packet.second_green_no_boundary_flux
interface : String (explicit)
Text describing intended mathematical interface.
Compiled illness-area refiner: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux removes the direct hsecondGreen premise left by SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux. It derives the second Green identity from hsecondGreenResidual, hsecondGreenDivergence, and hsecondGreenZeroBoundary, while keeping hdiffusionAction, hdiffusionLaplacianTerm, the first-Green subfacts, 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.cycle131GeneralMovingTargetDiscreteEmSecondGreenNoBoundaryFluxLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux
4. SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox
5. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
6. appendix.tex:1379-1427
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.cycle131.lower_1_packet.second_green_trace_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 handoff: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary removes the direct hsecondGreenZeroBoundary premise by deriving it from a boundary-flux integral representation and a.e. zero second-Green trace product. It keeps hsecondGreenResidual, hsecondGreenDivergence, 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.cycle131GeneralMovingTargetDiscreteEmSecondGreenTraceBoundaryLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux
4. MeasureTheory.integral_congr_ae
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.cycle131.lower_2_packet.second_green_box_boundary_flux
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFlux removes the direct hsecondGreenBoundaryFluxIntegral premise from the lower_1 trace-boundary theorem by deriving it from SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox. It keeps hsecondGreenTraceProductZero, 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.cycle131GeneralMovingTargetDiscreteEmSecondGreenBoxBoundaryFluxLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFlux
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary
4. SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox
5. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
6. 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.cycle131.remaining_laplacian_ibp_analysis
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 131: 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 trace-product-zero for source admissible tests, and prove the test-Laplacian normalization.
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.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFlux
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux
6. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux
7. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
8. SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox
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.cycle131.reviewer_second_green_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 hsecondGreen premise, hdiffusionAction, hdiffusionLaplacianTerm, first-Green subfacts, 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.cycle131GeneralMovingTargetDiscreteEmSecondGreenNoBoundaryFluxLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux
3. appendix.tex:1379-1427
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 131 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 cycle131GeneralMovingTargetDiscreteEmSecondGreenNoBoundaryFluxDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle131.middle_packet.second_green_no_boundary_flux"
      interface := "Compiled illness-area refiner: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux removes the direct hsecondGreen premise left by SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux. It derives the second Green identity from hsecondGreenResidual, hsecondGreenDivergence, and hsecondGreenZeroBoundary, while keeping hdiffusionAction, hdiffusionLaplacianTerm, the first-Green subfacts, and htestLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle131GeneralMovingTargetDiscreteEmSecondGreenNoBoundaryFluxLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux",
        "SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox",
        "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable",
        "appendix.tex:1379-1427"
      ]
      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.cycle131.lower_1_packet.second_green_trace_boundary"
      interface := "Compiled lower_1 handoff: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary removes the direct hsecondGreenZeroBoundary premise by deriving it from a boundary-flux integral representation and a.e. zero second-Green trace product. It keeps hsecondGreenResidual, hsecondGreenDivergence, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle131GeneralMovingTargetDiscreteEmSecondGreenTraceBoundaryLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux",
        "MeasureTheory.integral_congr_ae",
        "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.cycle131.lower_2_packet.second_green_box_boundary_flux"
      interface := "Compiled lower_2 continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFlux removes the direct hsecondGreenBoundaryFluxIntegral premise from the lower_1 trace-boundary theorem by deriving it from SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox. It keeps hsecondGreenTraceProductZero, second-Green residual/divergence facts, first-Green subfacts, hdiffusionAction, hdiffusionLaplacianTerm, and htestLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle131GeneralMovingTargetDiscreteEmSecondGreenBoxBoundaryFluxLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFlux",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary",
        "SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox",
        "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable",
        "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.cycle131.remaining_laplacian_ibp_analysis"
      interface := "Remaining exact theorem boundary after cycle 131: 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 trace-product-zero for source admissible tests, and prove the test-Laplacian normalization."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "appendix.tex:1379-1387",
        "appendix.tex:1392-1427",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenBoxBoundaryFlux",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenTraceBoundary",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux",
        "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable",
        "SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle131.reviewer_second_green_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the new theorem statement lacks a direct hsecondGreen premise, hdiffusionAction, hdiffusionLaplacianTerm, first-Green subfacts, 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.cycle131GeneralMovingTargetDiscreteEmSecondGreenNoBoundaryFluxLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfSecondGreenNoBoundaryFlux",
        "appendix.tex:1379-1427"
      ]
      reusedBy := ["cycle 131 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-132 lower packet narrowing the remaining second-Green trace-product
zero input to the source-facing zero-test-trace condition for admissible weak
tests. -/

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