AutoSamplingTheory.SALD.cycle53UnifiedDiscreteGeneralDag

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 cycle53UnifiedDiscreteGeneralDag : 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.unified_discrete_general.cycle53_upper_route
interface : String (explicit)
Text describing intended mathematical interface.
Final upper route check for skeleton sprint 5: consume the cycle-52 continuous general route for thm:unified-forward-KL and the cycle-48 discrete general route for thm:general-moving-target-SALD-discrete, with all five slow analytic interfaces explicit.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteSource — 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.cycle53UnifiedDiscreteGeneralUpperPacket
2. SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation
3. SALD.cycle52GuidedGeneralSkeletonObligation
4. SALD.cycle48UnifiedDiscreteSkeletonObligation
5. sald.unified_forward_kl.specialization
6. sald.general_moving_target_discrete.kl_derivative
7. sald.general_moving_target_discrete.dv_m_energy
8. sald.general_moving_target_discrete.gronwall_side_conditions
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:unified-forward-KL
2. thm:general-moving-target-SALD-discrete
3. cycle53 lower packet
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.unified_discrete_general.cycle53_middle_route_audit
interface : String (explicit)
Text describing intended mathematical interface.
Middle route audit for cycle 53: check the unified specialization and discrete general EM/Fokker-Planck/frozen-delta/LSI/DV/Gronwall chain against the source order, keep the Measure.map endpoint backfill scoped to endpoint laws, and hand off the discrete KL derivative backend.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteSource — 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.cycle53UnifiedDiscreteGeneralMiddleContract
2. SALD.cycle53UnifiedDiscreteGeneralMiddleObligation
3. SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation
4. SALD.cycle52GuidedGeneralSkeletonMiddleObligation
5. SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation
6. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
7. sald.unified_forward_kl.specialization
8. sald.general_moving_target_discrete.em_interpolation_fp
9. sald.general_moving_target_discrete.kl_derivative
10. sald.general_moving_target_discrete.dv_m_energy
11. sald.general_moving_target_discrete.gronwall_side_conditions
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:unified-forward-KL
2. thm:general-moving-target-SALD-discrete
3. cycle53 lower packet
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.general_moving_target_discrete.cycle53_measure_map_endpoint_backfill
interface : String (explicit)
Text describing intended mathematical interface.
Narrow measure-theory backfill: a.e. equality of endpoint process representatives implies equality of their Measure.map pushforward laws, giving a concrete endpoint-law handoff below the abstract law interface.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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. AutoSamplingTheory.lawMapEqOfAEEq
2. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
3. SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation
4. sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.general_moving_target_discrete.em_interpolation_fp
2. sald.general_moving_target_discrete.kl_derivative
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 cycle53UnifiedDiscreteGeneralDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle53_upper_route"
      interface := "Final upper route check for skeleton sprint 5: consume the cycle-52 continuous general route for thm:unified-forward-KL and the cycle-48 discrete general route for thm:general-moving-target-SALD-discrete, with all five slow analytic interfaces explicit."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle53UnifiedDiscreteGeneralUpperPacket",
        "SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.cycle52GuidedGeneralSkeletonObligation",
        "SALD.cycle48UnifiedDiscreteSkeletonObligation",
        "sald.unified_forward_kl.specialization",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.dv_m_energy",
        "sald.general_moving_target_discrete.gronwall_side_conditions"
      ]
      reusedBy := ["thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete", "cycle53 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.unified_discrete_general.cycle53_middle_route_audit"
      interface := "Middle route audit for cycle 53: check the unified specialization and discrete general EM/Fokker-Planck/frozen-delta/LSI/DV/Gronwall chain against the source order, keep the Measure.map endpoint backfill scoped to endpoint laws, and hand off the discrete KL derivative backend."
      source := saldGeneralMovingTargetDiscreteSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle53UnifiedDiscreteGeneralMiddleContract",
        "SALD.cycle53UnifiedDiscreteGeneralMiddleObligation",
        "SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation",
        "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
        "SALD.cycle48UnifiedDiscreteSkeletonMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
        "sald.unified_forward_kl.specialization",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative",
        "sald.general_moving_target_discrete.dv_m_energy",
        "sald.general_moving_target_discrete.gronwall_side_conditions"
      ]
      reusedBy := ["thm:unified-forward-KL", "thm:general-moving-target-SALD-discrete", "cycle53 lower packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.general_moving_target_discrete.cycle53_measure_map_endpoint_backfill"
      interface := "Narrow measure-theory backfill: a.e. equality of endpoint process representatives implies equality of their Measure.map pushforward laws, giving a concrete endpoint-law handoff below the abstract law interface."
      source := saldGeneralMovingTargetDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "AutoSamplingTheory.lawMapEqOfAEEq",
        "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
        "SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation",
        "sald.general_moving_target_discrete.cycle48_em_endpoint_conditional_fp_audit"
      ]
      reusedBy := ["sald.general_moving_target_discrete.em_interpolation_fp", "sald.general_moving_target_discrete.kl_derivative"]
      status := ProofStatus.formalized
    }
  ]

/-- Cycle-54 upper packet for the repeated analytic-interface sprint.

Cycle 54 returns to the sprint-1 focus after the full theorem route has been
threaded once.  The objective is to check that the five slow analytic backends
are still precise source-cited or obligation-level interfaces, and to hand the
next lower work to a theorem-useful backend rather than to another isolated
scalar lemma.
-/

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