AutoSamplingTheory.SALD.cycle129GeneralMovingTargetDiscreteEmDiffusionSourceDag

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 cycle129GeneralMovingTargetDiscreteEmDiffusionSourceDag :
    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.cycle129.lower_packet.diffusion_source_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower continuation: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated removes the direct hdiffusionSource premise from the canonical EM consumer by using SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction to compose the EM/Brownian diffusion weak action and weak Laplacian integration-by-parts identity.
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.cycle129GeneralMovingTargetDiscreteEmDiffusionSourceLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated
4. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated
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.cycle129.retired_stale_hpathDeriv_leaf
interface : String (explicit)
Text describing intended mathematical interface.
Stale-leaf retirement: do not assign lower work to hpathDeriv from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated; cycle 125 already discharged it via the concrete EM differentiability representative and Mathlib DifferentiableAt.hasDerivAt.
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.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated
2. SALD.cycle125GeneralMovingTargetDiscreteEmPathDerivDag
3. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 129 lower selection
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.cycle129.reviewer_diffusion_source_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 hdiffusionSource premise from the canonical consumer, the exact remaining theorem boundary is Brownian diffusion generator action 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.cycle129GeneralMovingTargetDiscreteEmDiffusionSourceLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction
3. SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated
4. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 129 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 cycle129GeneralMovingTargetDiscreteEmDiffusionSourceDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle129.lower_packet.diffusion_source_boundary"
      interface := "Compiled lower continuation: SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated removes the direct hdiffusionSource premise from the canonical EM consumer by using SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction to compose the EM/Brownian diffusion weak action and weak Laplacian integration-by-parts identity."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle129GeneralMovingTargetDiscreteEmDiffusionSourceLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDominated",
        "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.cycle129.retired_stale_hpathDeriv_leaf"
      interface := "Stale-leaf retirement: do not assign lower work to hpathDeriv from SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntDominated; cycle 125 already discharged it via the concrete EM differentiability representative and Mathlib DifferentiableAt.hasDerivAt."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathDominated",
        "SALD.cycle125GeneralMovingTargetDiscreteEmPathDerivDag",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 129 lower selection"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle129.reviewer_diffusion_source_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, the new theorem statement lacks the direct hdiffusionSource premise from the canonical consumer, the exact remaining theorem boundary is Brownian diffusion generator action 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.cycle129GeneralMovingTargetDiscreteEmDiffusionSourceLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpDiffusionSourceOfLaplacianAction",
        "SALD.generalMovingTargetDiscreteCanonicalBarBWeakConditionalFpNamedLawDerivativeOfEmIntervalMeasIntDerivMeasBoundIntPathValueDriftActionPairMeasNoBoundaryTraceCanonicalMeasDiffusionSourceDominated",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 129 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 130: EM weak Laplacian integration-by-parts boundary -/

/-- Cycle-130 lower-ready obligation for narrowing the remaining weak
Laplacian action input in the EM diffusion-source helper. -/

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