AutoSamplingTheory.SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryDag

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 cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryDag :
    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.cycle86.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 86 judgment: cycle 85 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 the generator-to-law weak-FP theorem boundary for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to 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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation
2. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
3. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
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.cycle86.active_em_backend_check
interface : String (explicit)
Text describing intended mathematical interface.
Active packet check before assigning lower work: no reviewer blocker moved the target away from sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387; cycle 86 uses the requested generator-to-law weak-FP sub-slice appendix.tex:1379-1387, with cycle-85 conditional-field regularity as a dependency.
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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperPacket
2. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
3. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle86.middle_weak_fp_generator_to_law_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: appendix.tex:1379-1387 requires an admissible-test law derivative for hatRhoS=Law(hatX_s). The lower theorem combines sample-path generator differentiation, Bochner/parametric integral interchange, AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample, and cycle-85 conditional-field regularity before calling the existing source-sign wrappers. Classification: narrows-source-cited-boundary unless hgenerator is actually removed.
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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryMiddleObligation
2. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
4. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation
5. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
7. Mathlib.Analysis.Calculus.ParametricIntegral
8. Mathlib.MeasureTheory.Integral.Bochner.Basic
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.cycle86.lower_packet.weak_fp_generator_to_law_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Lower proof-producing handoff: SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff removes the abstract hgenerator equality by transporting the sample-space generator derivative to the law integral and using HasDerivAt uniqueness, then applies the existing generator-piece source-sign wrapper.
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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation
2. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryMiddleObligation
3. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
5. AutoSamplingTheory.lawMapIntegral
6. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
7. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
8. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
9. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
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.cycle86.reviewer_weak_fp_generator_boundary_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: reject wrapper churn, hidden weak-FP closure, source-sign or coefficient changes, theorem-status promotion, SLT/Lake dependency changes, or any packet that does not either remove a supplied generator/time-derivative/source-action hypothesis or name a strictly smaller missing theorem.
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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation
2. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
3. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation
4. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
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
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 cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle86.global_phase_judgment"
      interface := "Cycle 86 judgment: cycle 85 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 the generator-to-law weak-FP theorem boundary for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1379-1387."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
        "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
        "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.cycle86.active_em_backend_check"
      interface := "Active packet check before assigning lower work: no reviewer blocker moved the target away from sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387; cycle 86 uses the requested generator-to-law weak-FP sub-slice appendix.tex:1379-1387, with cycle-85 conditional-field regularity as a dependency."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperPacket",
        "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle86.middle_weak_fp_generator_to_law_source_map"
      interface := "Middle source map: appendix.tex:1379-1387 requires an admissible-test law derivative for hatRhoS=Law(hatX_s). The lower theorem combines sample-path generator differentiation, Bochner/parametric integral interchange, AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample, and cycle-85 conditional-field regularity before calling the existing source-sign wrappers. Classification: narrows-source-cited-boundary unless hgenerator is actually removed."
      source := saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryMiddleObligation",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation",
        "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "Mathlib.Analysis.Calculus.ParametricIntegral",
        "Mathlib.MeasureTheory.Integral.Bochner.Basic"
      ]
      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.cycle86.lower_packet.weak_fp_generator_to_law_boundary"
      interface := "Lower proof-producing handoff: SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff removes the abstract hgenerator equality by transporting the sample-space generator derivative to the law integral and using HasDerivAt uniqueness, then applies the existing generator-piece source-sign wrapper."
      source := saldGeneralMovingTargetDiscreteWeakFpGeneratorMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation",
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryMiddleObligation",
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
        "AutoSamplingTheory.lawMapIntegral",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
        "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
        "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation"
      ]
      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.cycle86.reviewer_weak_fp_generator_boundary_check"
      interface := "Reviewer check: reject wrapper churn, hidden weak-FP closure, source-sign or coefficient changes, theorem-status promotion, SLT/Lake dependency changes, or any packet that does not either remove a supplied generator/time-derivative/source-action hypothesis or name a strictly smaller missing theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperObligation",
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation",
        "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-87 upper packet for the KL/log-ratio analytic boundary.

Cycle 86 removed the abstract generator equality from the weak-FP source-sign
route by transporting a supplied sample-space derivative to the law integral.
The next lower packet should use that narrowed weak-FP boundary to reduce the
KL differentiability and log-ratio admissibility hypotheses behind
`appendix.tex` lines 1358-1366, rather than adding another wrapper around the
same `dK` display.
-/

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