AutoSamplingTheory.SALD.cycle89DiscreteForwardKlClosurePressureDag

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 cycle89DiscreteForwardKlClosurePressureDag : 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.cycle89.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 89 judgment: cycle 88 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single packet that reduces the largest proof risk after the pressure test is the discrete derivative/IBP/FI boundary reached by 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.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation
2. SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.discrete_forward_kl.kl_derivative
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. thm:forward-KL-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.cycle89.active_em_backend_check
interface : String (explicit)
Text describing intended mathematical interface.
Before assigning lower work, confirm that the active shared backend still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The pressure test does not move the backend; it identifies the downstream discrete derivative blocker reached after the current EM/KL handoffs.
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.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation
2. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
3. sald.general_moving_target_discrete.em_interpolation_fp
4. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.forward_KL_discrete.cycle89_pressure_route
interface : String (explicit)
Text describing intended mathematical interface.
Pressure-test route: thm:forward-KL-discrete consumes current EM/KL wrappers, SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar, discrete DV velocity, cycle-56 Gronwall input, and cycle-61/cycle-66 accumulated-error displays; the first non-wrapper blocker is the analytic derivative action before those scalar handoffs.
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.cycle89DiscreteForwardKlClosurePressureUpperObligation
2. SALD.discreteForwardKlStatementContract
3. SALD.discreteForwardKlDerivativeObligation
4. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
5. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
6. SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation
7. SALD.cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation
8. SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation
9. probability.lsi_to_kl_fi
10. sald.discrete_forward_kl.dv_velocity_bound
11. sald.discrete_forward_kl.gronwall_accumulation
12. 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
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.cycle89_middle_route_audit
interface : String (explicit)
Text describing intended mathematical interface.
Middle route audit: synchronize the pressure-test result with the source-to-Lean DAG. Cycles 85--88 supply the current EM/KL handoffs, cycles 51/56/61/66 supply theorem-specific scalar route interfaces, and the first remaining non-wrapper blocker is the derivative/IBP/FI action at appendix.tex:388-413 plus target transport at appendix.tex:414-436.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — 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.cycle89DiscreteForwardKlClosurePressureMiddleObligation
2. SALD.cycle89DiscreteForwardKlClosurePressureUpperObligation
3. SALD.discreteForwardKlDerivativeObligation
4. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
5. SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation
6. SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation
7. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
8. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
9. sald.discrete_forward_kl.kl_derivative
10. sald.general_moving_target_discrete.em_interpolation_fp
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.discrete_forward_kl.kl_derivative
2. thm:forward-KL-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.cycle89_next_blocker
interface : String (explicit)
Text describing intended mathematical interface.
Next blocker: appendix.tex:388-413, eq:KL-derivative-1-discrete, plus appendix.tex:414-436 for the target transport action. Exact Lean declaration: SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative. Lower should prove or isolate the integration-by-parts and Fisher-information theorem boundary, not add a supplied-hypothesis wrapper.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — 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.discreteForwardKlDerivativeObligation
2. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
3. sald.discrete_forward_kl.em_interpolation_fp
4. sald.discrete_forward_kl.em_conditional_fokker_planck
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
6. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
7. eq:general_KL_derivative_0_discrete
8. eq:LSI-KL-FI
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.discrete_forward_kl.kl_derivative
2. thm:forward-KL-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.cycle89_lower_derivative_ibp_split
interface : String (explicit)
Text describing intended mathematical interface.
Lower proof-producing split: replace the opaque post-IBP derivative display by raw KL differentiation plus three named analytic facts: mass conservation, first-term divergence IBP/FI identification for eq:KL-derivative-1-discrete, and target-transport IBP for eq:KL-derivative-2-discrete. The scalar route to eq:KL-derivative-5-discrete now compiles through SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar.
source : AutoSamplingTheory.SourceAnchor (explicit)
Source pointer.
AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — 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.cycle89DiscreteForwardKlClosurePressureLowerObligation
2. SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar
3. SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar
4. SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar
5. SALD.discreteForwardKlDerivativeObligation
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
7. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
8. eq:KL-derivative-0-discrete
9. eq:KL-derivative-1-discrete
10. eq:KL-derivative-2-discrete
11. eq:LSI-KL-FI
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. sald.discrete_forward_kl.kl_derivative
2. SALD.cycle51DiscreteForwardKlDerivativeLowerObligation
3. thm:forward-KL-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.cycle89.reviewer_pressure_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the pressure test keeps theorem constants and source labels fixed, names SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative as the exact next blocker, and prevents wrapper churn or status promotion.
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.cycle89DiscreteForwardKlClosurePressureUpperObligation
2. SALD.discreteForwardKlStatementContract
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.discrete_forward_kl.kl_derivative
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. 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 cycle89DiscreteForwardKlClosurePressureDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle89.global_phase_judgment"
      interface := "Cycle 89 judgment: cycle 88 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single packet that reduces the largest proof risk after the pressure test is the discrete derivative/IBP/FI boundary reached by thm:forward-KL-discrete."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation",
        "SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.kl_derivative"
      ]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle89.active_em_backend_check"
      interface := "Before assigning lower work, confirm that the active shared backend still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The pressure test does not move the backend; it identifies the downstream discrete derivative blocker reached after the current EM/KL handoffs."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation",
        "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
        "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
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle89_pressure_route"
      interface := "Pressure-test route: thm:forward-KL-discrete consumes current EM/KL wrappers, SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar, discrete DV velocity, cycle-56 Gronwall input, and cycle-61/cycle-66 accumulated-error displays; the first non-wrapper blocker is the analytic derivative action before those scalar handoffs."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle89DiscreteForwardKlClosurePressureUpperObligation",
        "SALD.discreteForwardKlStatementContract",
        "SALD.discreteForwardKlDerivativeObligation",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
        "SALD.cycle61DiscreteForwardKlAccumulatedErrorLowerObligation",
        "SALD.cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation",
        "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation",
        "probability.lsi_to_kl_fi",
        "sald.discrete_forward_kl.dv_velocity_bound",
        "sald.discrete_forward_kl.gronwall_accumulation",
        "sald.discrete_forward_kl.accumulated_error_bridge"
      ]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle89_middle_route_audit"
      interface := "Middle route audit: synchronize the pressure-test result with the source-to-Lean DAG. Cycles 85--88 supply the current EM/KL handoffs, cycles 51/56/61/66 supply theorem-specific scalar route interfaces, and the first remaining non-wrapper blocker is the derivative/IBP/FI action at appendix.tex:388-413 plus target transport at appendix.tex:414-436."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle89DiscreteForwardKlClosurePressureMiddleObligation",
        "SALD.cycle89DiscreteForwardKlClosurePressureUpperObligation",
        "SALD.discreteForwardKlDerivativeObligation",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation",
        "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation",
        "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
        "sald.discrete_forward_kl.kl_derivative",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := [
        "sald.discrete_forward_kl.kl_derivative",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle89_next_blocker"
      interface := "Next blocker: appendix.tex:388-413, eq:KL-derivative-1-discrete, plus appendix.tex:414-436 for the target transport action. Exact Lean declaration: SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative. Lower should prove or isolate the integration-by-parts and Fisher-information theorem boundary, not add a supplied-hypothesis wrapper."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.discreteForwardKlDerivativeObligation",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "sald.discrete_forward_kl.em_interpolation_fp",
        "sald.discrete_forward_kl.em_conditional_fokker_planck",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
        "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
        "eq:general_KL_derivative_0_discrete",
        "eq:LSI-KL-FI"
      ]
      reusedBy := [
        "sald.discrete_forward_kl.kl_derivative",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle89_lower_derivative_ibp_split"
      interface := "Lower proof-producing split: replace the opaque post-IBP derivative display by raw KL differentiation plus three named analytic facts: mass conservation, first-term divergence IBP/FI identification for eq:KL-derivative-1-discrete, and target-transport IBP for eq:KL-derivative-2-discrete. The scalar route to eq:KL-derivative-5-discrete now compiles through SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle89DiscreteForwardKlClosurePressureLowerObligation",
        "SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfKlFiScalar",
        "SALD.discreteForwardKlDerivativeObligation",
        "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
        "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
        "eq:KL-derivative-0-discrete",
        "eq:KL-derivative-1-discrete",
        "eq:KL-derivative-2-discrete",
        "eq:LSI-KL-FI"
      ]
      reusedBy := [
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle89.reviewer_pressure_check"
      interface := "Reviewer check: accept only if the pressure test keeps theorem constants and source labels fixed, names SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative as the exact next blocker, and prevents wrapper churn or status promotion."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle89DiscreteForwardKlClosurePressureUpperObligation",
        "SALD.discreteForwardKlStatementContract",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.kl_derivative"
      ]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-90 upper packet for the reviewed discrete KL mass-conservation blocker.

The active EM backend remains the shared `appendix.tex:1358-1387` route, but
cycle 89's reviewer accepted a theorem-route blocker for
`thm:forward-KL-discrete`: the raw discrete KL derivative still has an explicit
mass term.  This upper packet selects the smallest reviewed sub-boundary,
`hmass : massTerm = 0`, before the larger first-term IBP/FI and target-transport
IBP identities.
-/

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