AutoSamplingTheory.SALD.cycle61DiscreteForwardKlSkeletonDag

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 cycle61DiscreteForwardKlSkeletonDag : 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.forward_KL_discrete.cycle61_global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Upper judgment for cycle 61: cycle 60 passed and needs no recovery; Phase 1 is stable only for theorem-level discrete route recovery, not broad backfill; the largest remaining risk is the Gronwall-to-accumulated-error bridge for thm:forward-KL-discrete.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — 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.cycle61DiscreteForwardKlSkeletonUpperPacket
2. SALD.cycle60ForwardKlSkeletonMiddleObligation
3. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
4. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL-discrete
2. ASTIS-SALD-001 cycle 61
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.forward_KL_discrete.cycle61_five_backend_check
interface : String (explicit)
Text describing intended mathematical interface.
Explicit cycle-61 check before assigning lower work: endpoint-safe Gronwall, common-space DV with finite log-mgf, LSI/KL/FI density-test bridge, continuous FP/KL derivative reuse, and EM endpoint/conditional-law Fokker-Planck are all named source-cited or obligation interfaces.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — 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.saldGronwallEndpointCalculusContract
2. SALD.discreteForwardKlGronwallInstantiationContract
3. dvVariationalFormulaInterface saldDvVariationSource
4. SALD.saldDvFiniteLogMgfContract
5. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
6. SALD.saldLsiKlFiDensityTestContract
7. SALD.forwardKlDerivativeSideConditionContract
8. SALD.cycle60ForwardKlDerivativeRawLowerObligation
9. SALD.discreteForwardKlEmInterpolationSideConditionContract
10. sald.discrete_forward_kl.em_interpolation_fp
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL
2. thm:forward-KL-discrete
3. prop:guided_path_residual
4. thm:general-moving-target-SALD
5. thm:unified-forward-KL
6. 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.forward_KL_discrete.cycle61_recovered_theorem_route
interface : String (explicit)
Text describing intended mathematical interface.
Recovered discrete theorem route: consume EM endpoint/conditional-FP, frozen defect, LSI, DV velocity, cycle-56 time-changed Gronwall input, and accumulated-error bridge in the source order of appendix.tex:260-592 and main_body.tex:299-323.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — 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.cycle61DiscreteForwardKlSkeletonObligation
2. SALD.cycle56DiscreteForwardKlSkeletonObligation
3. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
4. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
5. SALD.discreteForwardKlStatementContract
6. SALD.discreteForwardKlEmInterpolationSideConditionContract
7. sald.discrete_forward_kl.em_interpolation_fp
8. SALD.discreteForwardKlDerivativeCandidateContract
9. sald.discrete_forward_kl.kl_derivative
10. SALD.frozenDeltaCrossLipSaldContract
11. SALD.saldLsiKlFiDensityTestContract
12. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
13. sald.discrete_forward_kl.dv_velocity_bound
14. SALD.discreteForwardKlGronwallInstantiationContract
15. sald.discrete_forward_kl.gronwall_accumulation
16. SALD.discreteForwardKlAccumulatedErrorBridgeContract
17. sald.discrete_forward_kl.accumulated_error_bridge
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL-discrete
2. cycle61 middle route audit
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.forward_KL_discrete.cycle61_middle_route_audit
interface : String (explicit)
Text describing intended mathematical interface.
Middle audit for the recovered discrete route: verify source order from EM interpolation through derivative, LSI, DV, cycle-56 pointwise Gronwall, and select the accumulated-error bridge to the main-body linear-slowdown display as the lower packet.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — 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.cycle61DiscreteForwardKlSkeletonMiddleContract
2. SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation
3. SALD.cycle61DiscreteForwardKlSkeletonObligation
4. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
5. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
6. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
7. SALD.discreteForwardKlStatementContract
8. SALD.discreteForwardKlEmInterpolationSideConditionContract
9. sald.discrete_forward_kl.em_interpolation_fp
10. SALD.discreteForwardKlDerivativeCandidateContract
11. sald.discrete_forward_kl.kl_derivative
12. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
13. sald.discrete_forward_kl.dv_velocity_bound
14. SALD.discreteForwardKlGronwallInstantiationContract
15. SALD.discreteForwardKlAccumulatedErrorBridgeContract
16. sald.discrete_forward_kl.accumulated_error_bridge
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL-discrete
2. cycle61 lower accumulated-error 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.forward_KL_discrete.cycle61_lower_packet.gronwall_accumulated
interface : String (explicit)
Text describing intended mathematical interface.
Selected lower packet for cycle 61: refine sald.discrete_forward_kl.accumulated_error_bridge over appendix.tex:557-590 and main_body.tex:309-323, using the supplied cycle-56 pointwise Gronwall input and preserving the linear-slowdown constants.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — 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.cycle61DiscreteForwardKlSkeletonMiddleObligation
2. SALD.cycle61DiscreteForwardKlSkeletonObligation
3. SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation
4. SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar
5. SALD.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged
6. SALD.discreteForwardKlGronwallInstantiationContract
7. SALD.discreteForwardKlAccumulatedErrorBridgeContract
8. SALD.discreteForwardKlAccumulatedErrorBridgeObligation
9. SALD.discreteForwardKlGronwallCoeffIntervalIntegrable
10. SALD.discreteForwardKlGronwallCoeffIntegralSubSub
11. SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces
12. SALD.discreteForwardKlResidualExponentBoundScalar
13. SALD.discreteForwardKlResidualExpBoundScalar
14. SALD.discreteForwardKlAlphaComplexityCollectionScalar
15. SALD.discreteForwardKlDeltaAccumulationScalar
16. SALD.discreteForwardKlAccumulatedErrorCollectionScalar
17. SALD.discreteForwardKlResidualIntegralDisplayBoundScalar
18. sald.discrete_forward_kl.gronwall_accumulation
19. sald.discrete_forward_kl.linear_slowdown_specialization
20. sald.discrete_forward_kl.residual_exponent_bound
21. sald.discrete_forward_kl.accumulated_error_bridge
22. sald.gronwall.integrating_factor
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.discrete_forward_kl.accumulated_error_bridge
2. thm:forward-KL-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 cycle61DiscreteForwardKlSkeletonDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle61_global_phase_judgment"
      interface := "Upper judgment for cycle 61: cycle 60 passed and needs no recovery; Phase 1 is stable only for theorem-level discrete route recovery, not broad backfill; the largest remaining risk is the Gronwall-to-accumulated-error bridge for thm:forward-KL-discrete."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle61DiscreteForwardKlSkeletonUpperPacket",
        "SALD.cycle60ForwardKlSkeletonMiddleObligation",
        "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle56DiscreteForwardKlGronwallLowerObligation"
      ]
      reusedBy := ["thm:forward-KL-discrete", "ASTIS-SALD-001 cycle 61"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle61_five_backend_check"
      interface := "Explicit cycle-61 check before assigning lower work: endpoint-safe Gronwall, common-space DV with finite log-mgf, LSI/KL/FI density-test bridge, continuous FP/KL derivative reuse, and EM endpoint/conditional-law Fokker-Planck are all named source-cited or obligation interfaces."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.saldGronwallEndpointCalculusContract",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "dvVariationalFormulaInterface saldDvVariationSource",
        "SALD.saldDvFiniteLogMgfContract",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.forwardKlDerivativeSideConditionContract",
        "SALD.cycle60ForwardKlDerivativeRawLowerObligation",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      reusedBy := [
        "thm:forward-KL",
        "thm:forward-KL-discrete",
        "prop:guided_path_residual",
        "thm:general-moving-target-SALD",
        "thm:unified-forward-KL",
        "thm:general-moving-target-SALD-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle61_recovered_theorem_route"
      interface := "Recovered discrete theorem route: consume EM endpoint/conditional-FP, frozen defect, LSI, DV velocity, cycle-56 time-changed Gronwall input, and accumulated-error bridge in the source order of appendix.tex:260-592 and main_body.tex:299-323."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle61DiscreteForwardKlSkeletonObligation",
        "SALD.cycle56DiscreteForwardKlSkeletonObligation",
        "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
        "SALD.discreteForwardKlStatementContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.frozenDeltaCrossLipSaldContract",
        "SALD.saldLsiKlFiDensityTestContract",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle61 middle route audit"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle61_middle_route_audit"
      interface := "Middle audit for the recovered discrete route: verify source order from EM interpolation through derivative, LSI, DV, cycle-56 pointwise Gronwall, and select the accumulated-error bridge to the main-body linear-slowdown display as the lower packet."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle61DiscreteForwardKlSkeletonMiddleContract",
        "SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle61DiscreteForwardKlSkeletonObligation",
        "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "SALD.discreteForwardKlStatementContract",
        "SALD.discreteForwardKlEmInterpolationSideConditionContract",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "SALD.discreteForwardKlDerivativeCandidateContract",
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete", "cycle61 lower accumulated-error packet"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle61_lower_packet.gronwall_accumulated"
      interface := "Selected lower packet for cycle 61: refine sald.discrete_forward_kl.accumulated_error_bridge over appendix.tex:557-590 and main_body.tex:309-323, using the supplied cycle-56 pointwise Gronwall input and preserving the linear-slowdown constants."
      source := saldForwardKlDiscreteAccumulatedErrorSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle61DiscreteForwardKlSkeletonObligation",
        "SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation",
        "SALD.discreteForwardKlPostDvTimeChangedDerivativeScalar",
        "SALD.discreteForwardKlPointwiseGronwallInputOfPostDvTimeChanged",
        "SALD.discreteForwardKlGronwallInstantiationContract",
        "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
        "SALD.discreteForwardKlAccumulatedErrorBridgeObligation",
        "SALD.discreteForwardKlGronwallCoeffIntervalIntegrable",
        "SALD.discreteForwardKlGronwallCoeffIntegralSubSub",
        "SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces",
        "SALD.discreteForwardKlResidualExponentBoundScalar",
        "SALD.discreteForwardKlResidualExpBoundScalar",
        "SALD.discreteForwardKlAlphaComplexityCollectionScalar",
        "SALD.discreteForwardKlDeltaAccumulationScalar",
        "SALD.discreteForwardKlAccumulatedErrorCollectionScalar",
        "SALD.discreteForwardKlResidualIntegralDisplayBoundScalar",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.linear_slowdown_specialization",
        "sald.discrete_forward_kl.residual_exponent_bound",
        "sald.discrete_forward_kl.accumulated_error_bridge",
        "sald.gronwall.integrating_factor"
      ]
      reusedBy := ["sald.discrete_forward_kl.accumulated_error_bridge", "thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-62 upper packet for the guided residual and continuous general
moving-target theorem route after the accepted cycle-61 discrete recovery.

This is workflow data only.  It records the upper phase judgment, checks the
five slow analytic interfaces before assigning follow-up work, and keeps the
source route `appendix.tex:619-951` fixed while selecting one lower packet.
-/

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