AutoSamplingTheory.SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryDag

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 cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryDag :
    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.cycle87.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 87 judgment: cycle 86 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 KL/log-ratio analytic boundary for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1358-1366.
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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation
2. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
3. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation
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.cycle87.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 87 uses the requested KL/log-ratio sub-slice appendix.tex:1358-1366.
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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperPacket
2. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
3. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation
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
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.cycle87.lower_packet.kl_log_ratio_boundary
interface : String (explicit)
Text describing intended mathematical interface.
Selected lower packet: prove or sharply narrow KL differentiability at the admissible log-ratio weak test for eq:general_KL_derivative_0_discrete, including log-ratio measurability/integrability, mass conservation, target-time derivative integrability, and the handoff from weak-FP action to dK. Classification: discharges-supplied-hypothesis if an older hkl, hlog, log-action, measurability, or integrability supplied hypothesis is removed; otherwise narrows-source-cited-boundary only if a smaller missing theorem is named.
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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation
2. SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
4. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
5. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
6. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation
7. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
8. eq:general_KL_derivative_0_discrete
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. sald.discrete_forward_kl.em_interpolation_fp
4. thm:forward-KL-discrete
5. 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.cycle87.middle_kl_log_ratio_source_map
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: split the old hkl display into raw KL differentiation with an explicit mass term, mass conservation integral partial_s hat rho_s dx=0, target-time derivative integrability, and log-ratio measurability/integrability/admissibility before applying 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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation
2. eq:general_KL_derivative_0_discrete
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
4. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
5. sald.general_moving_target_discrete.kl_derivative
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.cycle87.lower_kl_mass_conservation_handoff
interface : String (explicit)
Text describing intended mathematical interface.
Lower scalar handoff: SALD.generalMovingTargetDiscreteKlDerivativeMassConservationDropScalar and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction formalize the mass-term drop and route the raw KL display through the existing log-ratio weak-FP source-sign handoff.
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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation
2. SALD.generalMovingTargetDiscreteKlDerivativeMassConservationDropScalar
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
5. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
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. sald.discrete_forward_kl.em_interpolation_fp
4. thm:forward-KL-discrete
5. 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.cycle87.lower_kl_log_ratio_regularity
interface : String (explicit)
Text describing intended mathematical interface.
Lower log-ratio regularity: represent the paper test log(hat rho_s / tilde pi_s) by Mathlib llr, expose its RN-derivative zero-set convention, and derive absolute continuity plus AEStronglyMeasurable/Integrable llr from finite KL via InformationTheory.klDiv_ne_top_iff.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteKlLogRatioMathlibSource — 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.generalMovingTargetDiscreteKlLogRatioLlrDef
2. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
3. Mathlib.InformationTheory.KullbackLeibler.Basic
4. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
5. eq:general_KL_derivative_0_discrete
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. sald.discrete_forward_kl.em_interpolation_fp
4. thm:forward-KL-discrete
5. 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.cycle87.reviewer_kl_log_ratio_boundary_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: reject wrapper churn, hidden KL differentiability closure, missing log-ratio admissibility regularity, target-time sign changes, theorem-status promotion, SLT/Lake dependency changes, or any packet that does not remove a KL/log-ratio supplied hypothesis or name a strictly smaller missing theorem.
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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation
2. SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation
3. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
4. SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
5. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation
6. sald.general_moving_target_discrete.em_interpolation_fp
7. sald.general_moving_target_discrete.kl_derivative
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 cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle87.global_phase_judgment"
      interface := "Cycle 87 judgment: cycle 86 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 KL/log-ratio analytic boundary for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1358-1366."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation",
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation",
        "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.cycle87.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 87 uses the requested KL/log-ratio sub-slice appendix.tex:1358-1366."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperPacket",
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation",
        "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.cycle87.lower_packet.kl_log_ratio_boundary"
      interface := "Selected lower packet: prove or sharply narrow KL differentiability at the admissible log-ratio weak test for eq:general_KL_derivative_0_discrete, including log-ratio measurability/integrability, mass conservation, target-time derivative integrability, and the handoff from weak-FP action to dK. Classification: discharges-supplied-hypothesis if an older hkl, hlog, log-action, measurability, or integrability supplied hypothesis is removed; otherwise narrows-source-cited-boundary only if a smaller missing theorem is named."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation",
        "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
        "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation",
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
        "eq:general_KL_derivative_0_discrete"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "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.cycle87.middle_kl_log_ratio_source_map"
      interface := "Middle source map: split the old hkl display into raw KL differentiation with an explicit mass term, mass conservation integral partial_s hat rho_s dx=0, target-time derivative integrability, and log-ratio measurability/integrability/admissibility before applying weak-FP source signs."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryMiddleObligation",
        "eq:general_KL_derivative_0_discrete",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
        "sald.general_moving_target_discrete.kl_derivative"
      ]
      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.cycle87.lower_kl_mass_conservation_handoff"
      interface := "Lower scalar handoff: SALD.generalMovingTargetDiscreteKlDerivativeMassConservationDropScalar and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction formalize the mass-term drop and route the raw KL display through the existing log-ratio weak-FP source-sign handoff."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation",
        "SALD.generalMovingTargetDiscreteKlDerivativeMassConservationDropScalar",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
        "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "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.cycle87.lower_kl_log_ratio_regularity"
      interface := "Lower log-ratio regularity: represent the paper test log(hat rho_s / tilde pi_s) by Mathlib llr, expose its RN-derivative zero-set convention, and derive absolute continuity plus AEStronglyMeasurable/Integrable llr from finite KL via InformationTheory.klDiv_ne_top_iff."
      source := saldGeneralMovingTargetDiscreteKlLogRatioMathlibSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteKlLogRatioLlrDef",
        "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
        "Mathlib.InformationTheory.KullbackLeibler.Basic",
        "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
        "eq:general_KL_derivative_0_discrete"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.kl_derivative",
        "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.cycle87.reviewer_kl_log_ratio_boundary_check"
      interface := "Reviewer check: reject wrapper churn, hidden KL differentiability closure, missing log-ratio admissibility regularity, target-time sign changes, theorem-status promotion, SLT/Lake dependency changes, or any packet that does not remove a KL/log-ratio supplied hypothesis or name a strictly smaller missing theorem."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperObligation",
        "SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation",
        "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
        "SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
        "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.general_moving_target_discrete.kl_derivative"
      ]
      reusedBy := [
        "thm:forward-KL-discrete",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-88 middle packet for the log-ratio weak-test admissibility boundary.

Cycle 87 discharged the generic finite-KL log-ratio regularity side
conditions.  The next non-wrapper boundary is the supplied
`hlog : Admissible logRatioTest` hypothesis consumed by the weak-FP-to-KL
handoffs.  This packet records the smaller theorem that lower should target:
turn the Mathlib `llr hatRhoS tildePiS` representative into an admissible
weak Fokker--Planck test by a smoothing/Sobolev approximation and boundary
closure theorem, without claiming KL differentiability or weak FP closure.
-/

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