AutoSamplingTheory.SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsDag

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 cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsDag :
    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.cycle82.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 82 judgment: cycle 81 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest remaining proof risk is still sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, now narrowed to appendix.tex:1379-1387 weak conditional FP source signs after endpoint/conditional readiness.
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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation
2. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
3. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
5. sald.general_moving_target_discrete.em_interpolation_fp
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL-discrete
2. thm:general-moving-target-SALD-discrete
3. sald.general_moving_target_discrete.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.cycle82.middle_readiness_to_source_signs
interface : String (explicit)
Text describing intended mathematical interface.
Middle readiness-to-source-sign bridge: consume cycle-81 WeakFpPrereq readiness for hat rho_s, kernel, and bar b_{k,s}; expose common-space, conditional-kernel, and drift-regularity hypotheses to the cycle-77 generator-piece wrapper; keep density, tests, boundary behavior, generator/time derivative, and drift/diffusion source actions supplied explicitly.
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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff
3. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
4. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
6. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
7. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
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.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle82.lower_packet.weak_fp_source_signs
interface : String (explicit)
Text describing intended mathematical interface.
Selected lower packet: compose the cycle-81 endpoint/conditional readiness data with the weak-test/generator-piece source-sign interface, preserving the negative drift-divergence term and positive sigma_eta^2/2 Laplacian term under explicit hypotheses.
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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperPacket
2. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
3. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
4. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff
6. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
7. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
8. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
9. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
10. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
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.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle82.reviewer_weak_fp_source_signs_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: reject theorem-route drift, sign changes, hidden assumptions, SLT/Lake promotions, or any claim that weak FP, density/AC, generator-to-law, KL derivative, or theorem closure is formalized without a local build.
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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation
2. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
3. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
7. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff
8. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
9. sald.general_moving_target_discrete.em_interpolation_fp
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL-discrete
2. thm:general-moving-target-SALD-discrete
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 cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle82.global_phase_judgment"
      interface := "Cycle 82 judgment: cycle 81 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest remaining proof risk is still sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, now narrowed to appendix.tex:1379-1387 weak conditional FP source signs after endpoint/conditional readiness."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation",
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle82.middle_readiness_to_source_signs"
      interface := "Middle readiness-to-source-sign bridge: consume cycle-81 WeakFpPrereq readiness for hat rho_s, kernel, and bar b_{k,s}; expose common-space, conditional-kernel, and drift-regularity hypotheses to the cycle-77 generator-piece wrapper; keep density, tests, boundary behavior, generator/time derivative, and drift/diffusion source actions supplied explicitly."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
        "SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation"
      ]
      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.obligation
    },
    {
      id := "ASTIS.SALD.cycle82.lower_packet.weak_fp_source_signs"
      interface := "Selected lower packet: compose the cycle-81 endpoint/conditional readiness data with the weak-test/generator-piece source-sign interface, preserving the negative drift-divergence term and positive sigma_eta^2/2 Laplacian term under explicit hypotheses."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperPacket",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
        "SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface"
      ]
      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.obligation
    },
    {
      id := "ASTIS.SALD.cycle82.reviewer_weak_fp_source_signs_check"
      interface := "Reviewer check: reject theorem-route drift, sign changes, hidden assumptions, SLT/Lake promotions, or any claim that weak FP, density/AC, generator-to-law, KL derivative, or theorem closure is formalized without a local build."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-83 upper packet for the endpoint weak-FP to KL-derivative handoff.

Cycle 82 accepted the endpoint/conditional source-sign wrapper.  This packet
connects that accepted weak-FP source-sign output to the differentiated KL
display, still within the single EM interpolation backend.
-/

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