AutoSamplingTheory.SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpDag

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 cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpDag :
    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.cycle83.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 83 judgment: cycle 82 passed 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 KL-derivative handoff from the endpoint/conditional weak-FP source signs.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation
2. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
3. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
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.cycle83.middle_endpoint_source_signs_to_kl
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: connect eq:general_KL_derivative_0_discrete to the cycle-82 endpoint/conditional weak-FP source signs at the admissible log-ratio test, before integration by parts and FI identification.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
4. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.kl_derivative
2. sald.general_moving_target_discrete.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.cycle83.lower_packet.kl_derivative_endpoint_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Local proof-producing wrapper: compose endpoint/conditional weak-FP source signs with the normalized weak-FP-to-KL substitution, preserving the source signs and target-time term under explicit supplied hypotheses; the cycle83 lower companion also records the log-ratio weak-FP action paired with the dK display.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
2. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff
3. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
6. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.kl_derivative
2. thm:forward-KL-discrete
3. 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.cycle83.reviewer_kl_derivative_handoff_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: reject any sign flip, hidden analytic theorem, theorem-status promotion, SLT/Lake dependency change, or drift away from appendix.tex:1358-1387 and the active EM backend.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation
2. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation
3. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
4. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff
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 cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle83.global_phase_judgment"
      interface := "Cycle 83 judgment: cycle 82 passed 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 KL-derivative handoff from the endpoint/conditional weak-FP source signs."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
        "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.cycle83.middle_endpoint_source_signs_to_kl"
      interface := "Middle source map: connect eq:general_KL_derivative_0_discrete to the cycle-82 endpoint/conditional weak-FP source signs at the admissible log-ratio test, before integration by parts and FI identification."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle83.lower_packet.kl_derivative_endpoint_handoff"
      interface := "Local proof-producing wrapper: compose endpoint/conditional weak-FP source signs with the normalized weak-FP-to-KL substitution, preserving the source signs and target-time term under explicit supplied hypotheses; the cycle83 lower companion also records the log-ratio weak-FP action paired with the dK display."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle83.reviewer_kl_derivative_handoff_check"
      interface := "Reviewer check: reject any sign flip, hidden analytic theorem, theorem-status promotion, SLT/Lake dependency change, or drift away from appendix.tex:1358-1387 and the active EM backend."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation",
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation",
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-84 upper packet for the active EM interpolation backend after the
cycle-83 KL-derivative handoff.

The cycle focus allows a new source-cited Mathlib/measure interface only when
proof-producing work is blocked.  Cycle 83 compiled a local handoff, so this
packet keeps lower work on the active backend and records the precise fallback
boundary without opening a broad measure-theory audit.
-/

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