Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. 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 cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation :
    ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

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.

id : String (explicit)

Stable obligation identifier.

sald.unified_discrete_general.cycle68_discrete_general_bridge
statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Source-cited theorem bridge for cycle 68: after the unified theorem is identified as the appendix specialization c_t <- u_t of thm:general-moving-target-SALD, route the discrete general theorem from appendix.tex:1313-1603 through the general EM interpolation endpoint and conditional-law/Fokker-Planck interface, frozen-delta cross bound, discrete KL derivative with LSI, residual DV for Z=alpha*||m_t||^2, constant inverse-schedule time change, and the final Gronwall/display side-condition interface. This bridge remains below formalized until all analytic dependencies build locally.
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteSource — audited data reference, not expanded and not a compiled dependency edge
status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification
dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

  1. SALD.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket
  2. SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation
  3. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
  4. SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation
  5. SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
  6. SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation
  7. SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation
  8. SALD.unifiedForwardKlSpecializationContract
  9. sald.unified_forward_kl.transport_velocity_bridge
  10. sald.unified_forward_kl.specialization
  11. SALD.generalMovingTargetDiscreteStatementContract
  12. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
  13. SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation
  14. SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation
  15. SALD.generalMovingTargetDiscreteConditionalDriftContract
  16. sald.general_moving_target_discrete.em_interpolation_fp
  17. SALD.generalMovingTargetDiscreteDerivativeCandidateContract
  18. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
  19. sald.general_moving_target_discrete.frozen_delta_cross_lip
  20. SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector
  21. SALD.generalMovingTargetDiscreteYoungFisherShareScalar
  22. SALD.generalMovingTargetDiscreteTwoYoungFisherBudgetScalar
  23. SALD.generalMovingTargetDiscreteResidualYoungCoefficientScalar
  24. sald.general_moving_target_discrete.kl_derivative
  25. SALD.saldLsiKlFiDensityTestContract
  26. probability.lsi_to_kl_fi
  27. dvVariationalFormulaInterface saldDvVariationSource
  28. SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract
  29. sald.general_moving_target_discrete.dv_m_energy
  30. SALD.generalMovingTargetDiscreteDerivativeDvTimeChangedScalar
  31. SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged
  32. SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput
  33. SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar
  34. SALD.generalMovingTargetDiscreteGronwallDisplayBridgeScalar
  35. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation
  36. SALD.generalMovingTargetDiscreteGronwallInstantiationContract
  37. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
  38. sald.general_moving_target_discrete.gronwall_application
  39. sald.general_moving_target_discrete.gronwall_side_conditions
  40. lem:gronwall
  41. lem:dv_variation
  42. eq:LSI-KL-FI
  43. def:alpha-complexity
note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Selected lower packet for cycle 68. It is not a proof of EM conditional laws, density/AC, weak Fokker-Planck, KL differentiation, frozen-delta analysis, LSI/KL/FI, DV, Gronwall, or theorem closure.
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 cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation :
    ProofObligation where
  id := "sald.unified_discrete_general.cycle68_discrete_general_bridge"
  statement := "Source-cited theorem bridge for cycle 68: after the unified theorem is identified as the appendix specialization c_t <- u_t of thm:general-moving-target-SALD, route the discrete general theorem from appendix.tex:1313-1603 through the general EM interpolation endpoint and conditional-law/Fokker-Planck interface, frozen-delta cross bound, discrete KL derivative with LSI, residual DV for Z=alpha*||m_t||^2, constant inverse-schedule time change, and the final Gronwall/display side-condition interface. This bridge remains below formalized until all analytic dependencies build locally."
  source := saldGeneralMovingTargetDiscreteSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket",
    "SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation",
    "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation",
    "SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation",
    "SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation",
    "SALD.unifiedForwardKlSpecializationContract",
    "sald.unified_forward_kl.transport_velocity_bridge",
    "sald.unified_forward_kl.specialization",
    "SALD.generalMovingTargetDiscreteStatementContract",
    "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "SALD.generalMovingTargetDiscreteDerivativeCandidateContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.frozen_delta_cross_lip",
    "SALD.generalMovingTargetDiscreteFrozenResidualAlgebraVector",
    "SALD.generalMovingTargetDiscreteYoungFisherShareScalar",
    "SALD.generalMovingTargetDiscreteTwoYoungFisherBudgetScalar",
    "SALD.generalMovingTargetDiscreteResidualYoungCoefficientScalar",
    "sald.general_moving_target_discrete.kl_derivative",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract",
    "sald.general_moving_target_discrete.dv_m_energy",
    "SALD.generalMovingTargetDiscreteDerivativeDvTimeChangedScalar",
    "SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged",
    "SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput",
    "SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar",
    "SALD.generalMovingTargetDiscreteGronwallDisplayBridgeScalar",
    "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation",
    "SALD.generalMovingTargetDiscreteGronwallInstantiationContract",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "sald.general_moving_target_discrete.gronwall_application",
    "sald.general_moving_target_discrete.gronwall_side_conditions",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "Selected lower packet for cycle 68. It is not a proof of EM conditional laws, density/AC, weak Fokker-Planck, KL differentiation, frozen-delta analysis, LSI/KL/FI, DV, Gronwall, or theorem closure."

/-- Cycle-68 middle audit for the unified and discrete general theorem route.

This source-to-Lean synchronization layer verifies the upper packet in the
paper order and keeps lower work on the source-cited discrete general bridge.
-/

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