AutoSamplingTheory.SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureDag

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 cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureDag :
    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.cycle79.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 79 judgment: cycle 78 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 the weak generator-to-law time-derivative theorem behind appendix.tex:1379-1387.
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.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperObligation
2. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
3. SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation
4. 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.cycle79.middle_weak_fp_generator_measure_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle conversion map for appendix.tex:1379-1387: align the paper's associated Fokker-Planck invocation with the source-cited theorem boundary for differentiating the frozen EM Measure.map law/test integral and identifying the generator action before cycle-77 source signs and cycle-78 KL substitution.
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.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureMiddleObligation
2. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
3. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperObligation
4. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
5. SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation
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.cycle79.lower_packet.weak_fp_generator_measure_interface
interface : String (explicit)
Text describing intended mathematical interface.
Minimal cited measure/calculus interface: audit Mathlib Measure.map, Bochner integral, and parametric-integral tools as prerequisites for differentiating the frozen EM interpolation law/test integral and identifying the weak generator action before the cycle-77 and cycle-78 wrappers consume it.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource — 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.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
4. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
5. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
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.sourceCited — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle79.lower_measure_map_integral_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Local proof-producing Measure.map handoff: rewrite weak-test integrals against the frozen EM mapped law to sample-space integrals, and transport a supplied sample-space HasDerivAt statement back to the mapped-law weak-test integral.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource — audited data reference, not expanded and not a compiled dependency edge
targetLean : String (explicit)
Textual planned implementation destination.
AutoSamplingTheory/Probability.lean
dependsOn : List String (explicit)
Declared input names as strings, default empty.
Ordered data items
1. AutoSamplingTheory.lawMapIntegral
2. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
3. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation
4. 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.formalized — 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 cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle79.global_phase_judgment"
      interface := "Cycle 79 judgment: cycle 78 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 the weak generator-to-law time-derivative theorem behind appendix.tex:1379-1387."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperObligation",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
        "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation",
        "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.cycle79.middle_weak_fp_generator_measure_source_map"
      interface := "Middle conversion map for appendix.tex:1379-1387: align the paper's associated Fokker-Planck invocation with the source-cited theorem boundary for differentiating the frozen EM Measure.map law/test integral and identifying the generator action before cycle-77 source signs and cycle-78 KL substitution."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureMiddleObligation",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperObligation",
        "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
        "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation"
      ]
      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.cycle79.lower_packet.weak_fp_generator_measure_interface"
      interface := "Minimal cited measure/calculus interface: audit Mathlib Measure.map, Bochner integral, and parametric-integral tools as prerequisites for differentiating the frozen EM interpolation law/test integral and identifying the weak generator action before the cycle-77 and cycle-78 wrappers consume it."
      source := saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract"
      ]
      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.sourceCited
    },
    {
      id := "ASTIS.SALD.cycle79.lower_measure_map_integral_handoff"
      interface := "Local proof-producing Measure.map handoff: rewrite weak-test integrals against the frozen EM mapped law to sample-space integrals, and transport a supplied sample-space HasDerivAt statement back to the mapped-law weak-test integral."
      source := saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource
      targetLean := "AutoSamplingTheory/Probability.lean"
      dependsOn := [
        "AutoSamplingTheory.lawMapIntegral",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation",
        "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.formalized
    }
  ]

/-- Cycle-80 upper packet returning to the conditional-law/measurability layer.

Cycle 79 exposed the weak generator-to-law theorem boundary, but that theorem
still depends on the conditional law and named drift field from
`appendix.tex:1368-1377`.  Cycle 80 therefore selects the first preferred
lower packet again, not another theorem-route audit or weak-FP algebra slice.
-/

Existing module entry · Audited data-reader index · All teaching coverage