AutoSamplingTheory.SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityUpperPacket

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.SALD.MainSkeletonAnalyticInterfaceLedger. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityUpperPacket :
    MainSkeletonAnalyticInterfaceLedger

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.

sourceBlock : AutoSamplingTheory.SourceAnchor (explicit)

Nested provenance data.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — audited data reference, not expanded and not a compiled dependency edge

objective : String (explicit)

Descriptive text even when field names say formula, theorem, inequality, derivative, source gap, or proof.

Global phase judgment: cycle 79 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet that now reduces the largest remaining proof risk is the conditional-law/measurability and named conditional drift interface inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, specifically appendix.tex:1368-1377.

sourceLabels : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. proof:thm:general-moving-target-SALD-discrete:conditional-drift
2. proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.general_moving_target_discrete.cycle74_conditional_kernel_measure_interface
5. sald.general_moving_target_discrete.cycle75_conditional_law_middle
6. thm:forward-KL-discrete
7. thm:general-moving-target-SALD-discrete

analyticInterfaces : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. Cycle 79 did not close the EM weak FP theorem; it exposed a generator-to-law boundary that still consumes the conditional kernel and measurable bar b_{k,s} field.
2. Cycles 70, 74, and 75 already identify the relevant interface: regular conditional law of X_k^eta given hat X_s=x, named hat rho_s marginal, component conditional drift integrals, and measurability/integrability of their linear combination.
3. Cycle 80 lower should sharpen that existing conditional-law interface, preferably by isolating the precise Mathlib condDistrib/condExpKernel or vector-valued conditional-integral theorem still missing.
4. Weak FP source signs, KL derivative substitution, LSI/KL/FI, DV, Gronwall, and theorem closure remain consumers of this interface and are not promoted.

theoremRoute : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. 1. Stay inside appendix.tex:1358-1387 with active slice appendix.tex:1368-1377.
2. 2. Preserve the paper definition bar b_{k,s}(x)=E[dot t_k*c_{t_k}(X_k^eta)+(sigma_eta^2/2)*nabla log pi_{t_k}(X_k^eta) | hat X_s=x].
3. 3. Reuse cycle-74 and cycle-75 source-cited Mathlib kernel/orientation interfaces rather than inventing a new broad SDE API.
4. 4. If proof-producing work is possible, compile only a supplied-hypothesis wrapper for kernel compatibility, component conditional-integral fields, and measurability/integrability of the named drift.
5. 5. If blocked, record the exact missing conditional-law theorem below formalized status with standard-Borel/probability, marginal compatibility, measurability, integrability, and vector-valued conditional expectation hypotheses explicit.

modeDiscipline : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. faithfulPaper Phase 1 only: preserve the original appendix.tex source route and keep sald_version_2.tex excluded.
2. Do not add standard-Borel, finite/probability, conditional-law, measurability, integrability, density, or admissibility hypotheses to theorem statements.
3. Use lean-stat-learning-theory only as a local Mathlib style reference; do not import it or claim an SLT theorem is formalized.

nonGoals : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. No theorem-route audit, source-index rebaseline beyond the gate, display algebra, Gronwall/DV/LSI work, frozen-delta work, broad reusable API design, or project-article export.
2. No weak conditional Fokker-Planck theorem proof, KL derivative proof, generator theorem proof, or status promotion for the EM backend.
3. No Lake dependency changes, no SLT import, and no claim that Mathlib already supplies the full SALD conditional-law theorem.

lowerPacket : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. Target exactly sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1368-1377.
2. Middle should synchronize the existing cycle-70/74/75 conditional-law rows with any lower packet: joint law, named hat rho_s marginal, condDistrib/condExpKernel orientation, component conditional drift fields, and bar b_{k,s} regularity.
3. Lower should reduce the conditional-law/measurability blocker, not move to endpoint re-audit, weak FP source signs, KL derivative handoff, display algebra, Gronwall/DV/LSI, or theorem closure.
4. The preferred lower product is either a compiled local wrapper under supplied kernel/integral hypotheses or a single narrowly cited missing Mathlib theorem.

reviewerChecklist : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. The active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, specifically appendix.tex:1368-1377.
2. Cycle 80 depends on the existing cycle-74/cycle-75 conditional-kernel interfaces and does not duplicate or promote them.
3. Both discrete theorem contracts remain contractOnly; conditional law, weak FP, generator-to-law, KL derivative, density/AC, LSI/KL/FI, DV, and Gronwall remain sourceCited or obligation unless a local declaration compiles.
4. SLT remains reference-only with no Lake dependency or import change.
5. python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass.

dependencies : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
2. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation
3. SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
4. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
5. SALD.generalMovingTargetDiscreteConditionalDriftContract
6. SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents
7. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents
8. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
9. sald.general_moving_target_discrete.em_interpolation_fp

status : AutoSamplingTheory.ProofStatus (explicit)

Stored workflow tag; honor the exact default but do not infer mathematical certification.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

def cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteDerivativeSource
  objective := "Global phase judgment: cycle 79 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet that now reduces the largest remaining proof risk is the conditional-law/measurability and named conditional drift interface inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, specifically appendix.tex:1368-1377."
  sourceLabels := [
    "proof:thm:general-moving-target-SALD-discrete:conditional-drift",
    "proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.cycle74_conditional_kernel_measure_interface",
    "sald.general_moving_target_discrete.cycle75_conditional_law_middle",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Cycle 79 did not close the EM weak FP theorem; it exposed a generator-to-law boundary that still consumes the conditional kernel and measurable bar b_{k,s} field.",
    "Cycles 70, 74, and 75 already identify the relevant interface: regular conditional law of X_k^eta given hat X_s=x, named hat rho_s marginal, component conditional drift integrals, and measurability/integrability of their linear combination.",
    "Cycle 80 lower should sharpen that existing conditional-law interface, preferably by isolating the precise Mathlib condDistrib/condExpKernel or vector-valued conditional-integral theorem still missing.",
    "Weak FP source signs, KL derivative substitution, LSI/KL/FI, DV, Gronwall, and theorem closure remain consumers of this interface and are not promoted."
  ]
  theoremRoute := [
    "1. Stay inside appendix.tex:1358-1387 with active slice appendix.tex:1368-1377.",
    "2. Preserve the paper definition bar b_{k,s}(x)=E[dot t_k*c_{t_k}(X_k^eta)+(sigma_eta^2/2)*nabla log pi_{t_k}(X_k^eta) | hat X_s=x].",
    "3. Reuse cycle-74 and cycle-75 source-cited Mathlib kernel/orientation interfaces rather than inventing a new broad SDE API.",
    "4. If proof-producing work is possible, compile only a supplied-hypothesis wrapper for kernel compatibility, component conditional-integral fields, and measurability/integrability of the named drift.",
    "5. If blocked, record the exact missing conditional-law theorem below formalized status with standard-Borel/probability, marginal compatibility, measurability, integrability, and vector-valued conditional expectation hypotheses explicit."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: preserve the original appendix.tex source route and keep sald_version_2.tex excluded.",
    "Do not add standard-Borel, finite/probability, conditional-law, measurability, integrability, density, or admissibility hypotheses to theorem statements.",
    "Use lean-stat-learning-theory only as a local Mathlib style reference; do not import it or claim an SLT theorem is formalized."
  ]
  nonGoals := [
    "No theorem-route audit, source-index rebaseline beyond the gate, display algebra, Gronwall/DV/LSI work, frozen-delta work, broad reusable API design, or project-article export.",
    "No weak conditional Fokker-Planck theorem proof, KL derivative proof, generator theorem proof, or status promotion for the EM backend.",
    "No Lake dependency changes, no SLT import, and no claim that Mathlib already supplies the full SALD conditional-law theorem."
  ]
  lowerPacket := [
    "Target exactly sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1368-1377.",
    "Middle should synchronize the existing cycle-70/74/75 conditional-law rows with any lower packet: joint law, named hat rho_s marginal, condDistrib/condExpKernel orientation, component conditional drift fields, and bar b_{k,s} regularity.",
    "Lower should reduce the conditional-law/measurability blocker, not move to endpoint re-audit, weak FP source signs, KL derivative handoff, display algebra, Gronwall/DV/LSI, or theorem closure.",
    "The preferred lower product is either a compiled local wrapper under supplied kernel/integral hypotheses or a single narrowly cited missing Mathlib theorem."
  ]
  reviewerChecklist := [
    "The active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, specifically appendix.tex:1368-1377.",
    "Cycle 80 depends on the existing cycle-74/cycle-75 conditional-kernel interfaces and does not duplicate or promote them.",
    "Both discrete theorem contracts remain contractOnly; conditional law, weak FP, generator-to-law, KL derivative, density/AC, LSI/KL/FI, DV, and Gronwall remain sourceCited or obligation unless a local declaration compiles.",
    "SLT remains reference-only with no Lake dependency or import change.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillMiddleObligation",
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents",
    "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  status := ProofStatus.obligation

/-- Cycle-80 upper obligation for the conditional-law/measurability packet. -/