AutoSamplingTheory.SALD.cycle130GeneralMovingTargetDiscreteEmLaplacianIbPDag

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 cycle130GeneralMovingTargetDiscreteEmLaplacianIbPDag :
    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.cycle130.lower_packet.weak_laplacian_ibp_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower-ready continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts derives the old hlaplacianAction from the positive sigmaCoeff-scaled density-Laplacian weak term and the weak Laplacian integration-by-parts identity; SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts then reuses the cycle-129 diffusion-source helper while keeping hdiffusionAction 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.cycle130GeneralMovingTargetDiscreteEmLaplacianIbPLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction
5. 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. thm:forward-KL-discrete
3. 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.cycle130.lower_1_packet.green_laplacian_ibp_route
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 scout route: SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity derives the old hweakLaplacianIbP shape from first-Green density-Laplacian-to-negative-gradient-pairing, second-Green negative-gradient-pairing-to-test-Laplacian, and test-Laplacian normalization facts. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP feeds that route into the existing cycle-130 diffusion-source helper without reintroducing direct hweakLaplacianIbP.
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.cycle130GeneralMovingTargetDiscreteEmGreenLaplacianIbPScoutObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP
4. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts
5. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
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.cycle130.lower_2_packet.first_green_no_boundary_flux
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux removes the direct hfirstGreen premise from the lower_1 Green route by deriving the first Green identity from a density-Laplacian residual identity, a divergence-theorem boundary-flux identity, and zero boundary flux. The second Green identity, test-Laplacian normalization, hdiffusionAction, and hdiffusionLaplacianTerm remain 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.cycle130GeneralMovingTargetDiscreteEmFirstGreenNoBoundaryFluxLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP
4. SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox
5. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
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.cycle130.remaining_laplacian_ibp_analysis
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 130 lower_2: prove the density-Laplacian weak term for the EM/Brownian diffusion contribution, instantiate the first-Green residual/divergence/zero-flux facts for the source density and admissible tests, then prove the second Green identity and 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:1368-1377
3. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux
4. SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity
5. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP
6. MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable
7. 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.cycle130.reviewer_laplacian_ibp_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 the direct hlaplacianAction premise, hdiffusionAction remains separate, the remaining boundary is the density-Laplacian weak term plus weak Laplacian integration by parts, 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.cycle130GeneralMovingTargetDiscreteEmLaplacianIbPLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts
3. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 130 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 cycle130GeneralMovingTargetDiscreteEmLaplacianIbPDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle130.lower_packet.weak_laplacian_ibp_boundary"
      interface := "Compiled lower-ready continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts derives the old hlaplacianAction from the positive sigmaCoeff-scaled density-Laplacian weak term and the weak Laplacian integration-by-parts identity; SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts then reuses the cycle-129 diffusion-source helper while keeping hdiffusionAction separate."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle130GeneralMovingTargetDiscreteEmLaplacianIbPLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianActionOfIntegrationByParts",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle130.lower_1_packet.green_laplacian_ibp_route"
      interface := "Compiled lower_1 scout route: SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity derives the old hweakLaplacianIbP shape from first-Green density-Laplacian-to-negative-gradient-pairing, second-Green negative-gradient-pairing-to-test-Laplacian, and test-Laplacian normalization facts. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP feeds that route into the existing cycle-130 diffusion-source helper without reintroducing direct hweakLaplacianIbP."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle130GeneralMovingTargetDiscreteEmGreenLaplacianIbPScoutObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts",
        "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable",
        "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.cycle130.lower_2_packet.first_green_no_boundary_flux"
      interface := "Compiled lower_2 continuation: SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux removes the direct hfirstGreen premise from the lower_1 Green route by deriving the first Green identity from a density-Laplacian residual identity, a divergence-theorem boundary-flux identity, and zero boundary flux. The second Green identity, test-Laplacian normalization, hdiffusionAction, and hdiffusionLaplacianTerm remain explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle130GeneralMovingTargetDiscreteEmFirstGreenNoBoundaryFluxLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP",
        "SALD.generalMovingTargetDiscreteBoundaryFluxIntegralOfDivergenceTheoremBox",
        "MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable",
        "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.cycle130.remaining_laplacian_ibp_analysis"
      interface := "Remaining exact theorem boundary after cycle 130 lower_2: prove the density-Laplacian weak term for the EM/Brownian diffusion contribution, instantiate the first-Green residual/divergence/zero-flux facts for the source density and admissible tests, then prove the second Green identity and test-Laplacian normalization."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "appendix.tex:1379-1387",
        "appendix.tex:1368-1377",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfFirstGreenNoBoundaryFlux",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpLaplacianIbPOfGreenIdentity",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfGreenLaplacianIbP",
        "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.cycle130.reviewer_laplacian_ibp_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the new theorem statement lacks the direct hlaplacianAction premise, hdiffusionAction remains separate, the remaining boundary is the density-Laplacian weak term plus weak Laplacian integration by parts, 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.cycle130GeneralMovingTargetDiscreteEmLaplacianIbPLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianIntegrationByParts",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 130 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-70 proof-DAG pane for the EM conditional-law/measurability backfill. -/

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