AutoSamplingTheory.SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendDag

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 cycle84GeneralMovingTargetDiscreteActiveEmBackendDag :
    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.cycle84.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 84 judgment: cycle 83 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, and the lower packet should continue proof-producing EM-backend consolidation before any new cited measure interface.
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.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation
2. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
3. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff
4. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
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.cycle84.middle_active_em_backend_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: keep eq:general_KL_derivative_0_discrete, the conditional drift bar b_{k,s}, the weak FP source signs, and the log-ratio KL handoff aligned through the existing cycle-80 to cycle-83 wrappers before any measure-interface fallback.
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.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation
2. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation
3. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
4. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
5. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
6. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
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.cycle84.lower_packet.active_em_backend
interface : String (explicit)
Text describing intended mathematical interface.
Selected lower packet: consume the cycle-81 endpoint/conditional readiness, cycle-82 endpoint weak-FP source signs, and cycle-83 log-ratio KL handoff to tighten the active EM interpolation FP backend; keep all analytic hypotheses explicit.
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.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperPacket
2. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation
3. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
4. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
5. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
6. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
7. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
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.cycle84.blocked_measure_interface_escape_hatch
interface : String (explicit)
Text describing intended mathematical interface.
Fallback only if blocked: add one narrow source-cited conditional-law or generator-to-law weak-FP theorem boundary, with common-space, density/AC, admissible-test, finite-integral, boundary, and coefficient hypotheses explicit and status below formalized.
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.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation
2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
3. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
4. sald.general_moving_target_discrete.em_interpolation_fp
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.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle84.reviewer_active_em_backend_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: reject a fallback interface without a concrete block, any source sign or coefficient change, hidden analytic theorem claim, theorem-status promotion, SLT/Lake dependency change, or drift outside appendix.tex:1358-1387.
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.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation
2. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation
3. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation
4. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
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 cycle84GeneralMovingTargetDiscreteActiveEmBackendDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle84.global_phase_judgment"
      interface := "Cycle 84 judgment: cycle 83 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, and the lower packet should continue proof-producing EM-backend consolidation before any new cited measure interface."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation",
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff",
        "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
        "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.cycle84.middle_active_em_backend_source_map"
      interface := "Middle source map: keep eq:general_KL_derivative_0_discrete, the conditional drift bar b_{k,s}, the weak FP source signs, and the log-ratio KL handoff aligned through the existing cycle-80 to cycle-83 wrappers before any measure-interface fallback."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation",
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation",
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction"
      ]
      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.cycle84.lower_packet.active_em_backend"
      interface := "Selected lower packet: consume the cycle-81 endpoint/conditional readiness, cycle-82 endpoint weak-FP source signs, and cycle-83 log-ratio KL handoff to tighten the active EM interpolation FP backend; keep all analytic hypotheses explicit."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperPacket",
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation",
        "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
        "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
        "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
        "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction"
      ]
      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.cycle84.blocked_measure_interface_escape_hatch"
      interface := "Fallback only if blocked: add one narrow source-cited conditional-law or generator-to-law weak-FP theorem boundary, with common-space, density/AC, admissible-test, finite-integral, boundary, and coefficient hypotheses explicit and status below formalized."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation",
        "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
        "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle84.reviewer_active_em_backend_check"
      interface := "Reviewer check: reject a fallback interface without a concrete block, any source sign or coefficient change, hidden analytic theorem claim, theorem-status promotion, SLT/Lake dependency change, or drift outside appendix.tex:1358-1387."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperObligation",
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendMiddleObligation",
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation",
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-85 upper packet for the post-cycle-84 conditional-kernel theorem
boundary.

Cycle 84 compiled another endpoint-level handoff under supplied hypotheses.  In
cycle 85 the lower work must stop adding wrappers of the same shape and instead
reduce the conditional-law theorem boundary behind appendix.tex lines
1368-1377, or record one exact missing Mathlib theorem with hypotheses.
-/

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