AutoSamplingTheory.SALD.cycle90DiscreteForwardKlMassConservationDag

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 cycle90DiscreteForwardKlMassConservationDag : 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.cycle90.global_phase_judgment
interface : String (explicit)
Text describing intended mathematical interface.
Cycle 90 judgment: cycle 89 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest remaining proof risk after reviewer pressure is the discrete KL derivative mass-conservation hypothesis hmass before hfirst/htarget.
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.cycle89DiscreteForwardKlClosurePressureLowerObligation
2. SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar
3. SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar
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.cycle90.active_em_backend_exception_check
interface : String (explicit)
Text describing intended mathematical interface.
Confirm that the active shared backend remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. Cycle 90 leaves direct EM work only because the cycle-89 reviewer identified the theorem-route blocker hmass/hfirst/htarget.
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.cycle89DiscreteForwardKlClosurePressureLowerObligation
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
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.cycle90_middle_mass_derivative_route
interface : String (explicit)
Text describing intended mathematical interface.
Middle source map: replace the primitive hmass scalar input by the smaller theorem boundary totalMass'(s0)=massTerm plus totalMass=1 near s0, then use the compiled HasDerivAt local-constant lemma to feed the cycle-89 raw KL route.
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.cycle90DiscreteForwardKlMassConservationMiddleObligation
2. SALD.discreteForwardKlMassTermZeroOfTotalMassDerivative
3. SALD.discreteForwardKlDerivativeSplitOfMassDerivativeScalar
4. SALD.discreteForwardKlPostLsiDerivativeBoundOfMassDerivativeScalar
5. SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar
6. SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar
7. eq:KL-derivative-0-discrete
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.forward_KL_discrete.cycle90_lower_law_constant_test_mass
interface : String (explicit)
Text describing intended mathematical interface.
Lower compiled route: specialize totalMass to the concrete mapped-law constant weak-test pairing for hat rho_s=Law(hat X_s), prove its law integral is one and its derivative is zero using Measure.map probability normalization and AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample, then feed the cycle-89 raw KL scalar route. Remaining boundary: identify the paper massTerm with this concrete derivative.
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.cycle90DiscreteForwardKlMassConservationLowerObligation
2. SALD.discreteForwardKlLawConstantTestTotalMassOne
3. SALD.discreteForwardKlLawConstantTestHasDerivAtZero
4. SALD.discreteForwardKlMassTermZeroOfLawConstantTestDerivative
5. SALD.discreteForwardKlDerivativeSplitOfLawConstantTestMassScalar
6. SALD.discreteForwardKlPostLsiDerivativeBoundOfLawConstantTestMassScalar
7. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
8. SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar
9. SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar
10. eq:KL-derivative-0-discrete
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.forward_KL_discrete.cycle90_mass_conservation_lower_packet
interface : String (explicit)
Text describing intended mathematical interface.
Selected lower packet: prove or isolate massTerm = 0 from the source claim int partial_s hat rho_s dx = 0 in eq:KL-derivative-0-discrete, using the probability-law normalization of hat rho_s and derivative-under-integral/constant-test semantics. Cycle 90 lower has discharged the local constant-test derivative part for a concrete Measure.map law; the remaining boundary is the raw KL massTerm-to-constant-test-derivative identification.
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.cycle90DiscreteForwardKlMassConservationUpperObligation
2. SALD.cycle90DiscreteForwardKlMassConservationMiddleObligation
3. SALD.cycle90DiscreteForwardKlMassConservationLowerObligation
4. SALD.discreteForwardKlMassTermZeroOfTotalMassDerivative
5. SALD.discreteForwardKlMassTermZeroOfLawConstantTestDerivative
6. SALD.discreteForwardKlPostLsiDerivativeBoundOfMassDerivativeScalar
7. SALD.discreteForwardKlPostLsiDerivativeBoundOfLawConstantTestMassScalar
8. SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar
9. SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar
10. SALD.discreteForwardKlDerivativeObligation
11. eq:KL-derivative-0-discrete
12. eq:general_KL_derivative_0_discrete
13. Mathlib.MeasureTheory.Integral.Bochner.Basic
14. Mathlib.Analysis.Calculus.ParametricIntegral
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.cycle90.reviewer_mass_conservation_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if cycle 90 either removes the supplied hmass hypothesis or names a strictly smaller mass-conservation theorem boundary; reject LSI/DV/Gronwall drift, wrapper churn, and status promotion.
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.cycle90DiscreteForwardKlMassConservationUpperObligation
2. SALD.cycle90DiscreteForwardKlMassConservationMiddleObligation
3. SALD.discreteForwardKlDerivativeObligation
4. sald.discrete_forward_kl.kl_derivative
5. 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
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 cycle90DiscreteForwardKlMassConservationDag : List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle90.global_phase_judgment"
      interface := "Cycle 90 judgment: cycle 89 passed and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the largest remaining proof risk after reviewer pressure is the discrete KL derivative mass-conservation hypothesis hmass before hfirst/htarget."
      source := saldForwardKlDiscreteProofSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle89DiscreteForwardKlClosurePressureLowerObligation",
        "SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar",
        "sald.discrete_forward_kl.kl_derivative"
      ]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle90.active_em_backend_exception_check"
      interface := "Confirm that the active shared backend remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. Cycle 90 leaves direct EM work only because the cycle-89 reviewer identified the theorem-route blocker hmass/hfirst/htarget."
      source := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityLowerObligation",
        "SALD.cycle89DiscreteForwardKlClosurePressureLowerObligation",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.kl_derivative"
      ]
      reusedBy := ["thm:forward-KL-discrete", "thm:general-moving-target-SALD-discrete"]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle90_middle_mass_derivative_route"
      interface := "Middle source map: replace the primitive hmass scalar input by the smaller theorem boundary totalMass'(s0)=massTerm plus totalMass=1 near s0, then use the compiled HasDerivAt local-constant lemma to feed the cycle-89 raw KL route."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle90DiscreteForwardKlMassConservationMiddleObligation",
        "SALD.discreteForwardKlMassTermZeroOfTotalMassDerivative",
        "SALD.discreteForwardKlDerivativeSplitOfMassDerivativeScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfMassDerivativeScalar",
        "SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar",
        "eq:KL-derivative-0-discrete"
      ]
      reusedBy := [
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle90_lower_law_constant_test_mass"
      interface := "Lower compiled route: specialize totalMass to the concrete mapped-law constant weak-test pairing for hat rho_s=Law(hat X_s), prove its law integral is one and its derivative is zero using Measure.map probability normalization and AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample, then feed the cycle-89 raw KL scalar route. Remaining boundary: identify the paper massTerm with this concrete derivative."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle90DiscreteForwardKlMassConservationLowerObligation",
        "SALD.discreteForwardKlLawConstantTestTotalMassOne",
        "SALD.discreteForwardKlLawConstantTestHasDerivAtZero",
        "SALD.discreteForwardKlMassTermZeroOfLawConstantTestDerivative",
        "SALD.discreteForwardKlDerivativeSplitOfLawConstantTestMassScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfLawConstantTestMassScalar",
        "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
        "SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar",
        "eq:KL-derivative-0-discrete"
      ]
      reusedBy := [
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.forward_KL_discrete.cycle90_mass_conservation_lower_packet"
      interface := "Selected lower packet: prove or isolate massTerm = 0 from the source claim int partial_s hat rho_s dx = 0 in eq:KL-derivative-0-discrete, using the probability-law normalization of hat rho_s and derivative-under-integral/constant-test semantics. Cycle 90 lower has discharged the local constant-test derivative part for a concrete Measure.map law; the remaining boundary is the raw KL massTerm-to-constant-test-derivative identification."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle90DiscreteForwardKlMassConservationUpperObligation",
        "SALD.cycle90DiscreteForwardKlMassConservationMiddleObligation",
        "SALD.cycle90DiscreteForwardKlMassConservationLowerObligation",
        "SALD.discreteForwardKlMassTermZeroOfTotalMassDerivative",
        "SALD.discreteForwardKlMassTermZeroOfLawConstantTestDerivative",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfMassDerivativeScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfLawConstantTestMassScalar",
        "SALD.discreteForwardKlDerivativeSplitOfRawIbpsScalar",
        "SALD.discreteForwardKlPostLsiDerivativeBoundOfRawIbpsScalar",
        "SALD.discreteForwardKlDerivativeObligation",
        "eq:KL-derivative-0-discrete",
        "eq:general_KL_derivative_0_discrete",
        "Mathlib.MeasureTheory.Integral.Bochner.Basic",
        "Mathlib.Analysis.Calculus.ParametricIntegral"
      ]
      reusedBy := [
        "sald.discrete_forward_kl.kl_derivative",
        "SALD.cycle51DiscreteForwardKlDerivativeLowerObligation",
        "thm:forward-KL-discrete"
      ]
      status := ProofStatus.obligation
    },
    {
      id := "ASTIS.SALD.cycle90.reviewer_mass_conservation_check"
      interface := "Reviewer check: accept only if cycle 90 either removes the supplied hmass hypothesis or names a strictly smaller mass-conservation theorem boundary; reject LSI/DV/Gronwall drift, wrapper churn, and status promotion."
      source := saldForwardKlDiscreteDerivativeSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle90DiscreteForwardKlMassConservationUpperObligation",
        "SALD.cycle90DiscreteForwardKlMassConservationMiddleObligation",
        "SALD.discreteForwardKlDerivativeObligation",
        "sald.discrete_forward_kl.kl_derivative",
        "sald.general_moving_target_discrete.em_interpolation_fp"
      ]
      reusedBy := ["thm:forward-KL-discrete"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 91: conditional-kernel component-field backfill -/

/-- Cycle-91 middle obligation for the conditional-kernel theorem boundary.

This records the post-cycle-90 return to the active EM backend:
`appendix.tex:1368-1377`, where `bar b_{k,s}` is defined by conditioning on
`\hat X_s=x`.  The cycle keeps the lower packet on the Mathlib
`condDistrib`/named-law component-field boundary instead of adding another
abstract supplied-hypothesis wrapper.
-/

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