AutoSamplingTheory.SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperPacket

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 cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperPacket :
    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.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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 74 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 proof risk is still sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to the conditional-law/measurability and named conditional drift construction interface for 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. thm:forward-KL-discrete
6. 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 74 supplied the exact source-cited condDistrib/condExpKernel blocker; cycle 75 should not create a second broad interface.
2. The conditional-law layer must connect the joint law of (X_k^eta,hat X_s), the named marginal hat rho_s, the conditional kernel of X_k^eta given hat X_s=x, and the two component conditional drift integrals.
3. Cycles 70 and 71 already provide local named-drift and endpoint-to-conditional wrappers; cycle 75 lower should try to feed those wrappers with a concrete conditional-kernel construction or record the exact missing Mathlib theorem.
4. Weak conditional Fokker-Planck, log-ratio admissibility, density/AC, KL differentiation, integration by parts, LSI/KL/FI, DV, Gronwall, and theorem closure remain obligations.

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 the active lower slice appendix.tex:1368-1377.
2. 2. Start from the cycle-74 source-cited interface rather than a new theorem route: regular conditional law/condExpKernel for X_k^eta conditioned on hat X_s=x.
3. 3. Preserve the named hat rho_s marginal from the endpoint-to-conditional compatibility wrappers and the paper's bar b_{k,s} component fields.
4. 4. If local proof-producing work is possible, prove only a tiny supplied-hypothesis wrapper around kernel construction/compatibility/measurability; otherwise leave a narrowly cited missing Mathlib theorem.

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1: keep appendix.tex and main_body.tex as the only SALD sources and keep sald_version_2.tex out of scope.
2. Do not add standard-Borel, finite-measure, measurability, integrability, density, admissibility, or endpoint assumptions to theorem statements.
3. Use lean-stat-learning-theory only as a local Mathlib style reference; do not add it as a dependency and do not claim any SLT theorem as formalized.

nonGoals : List String (explicit)

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

Ordered data items

1. No weak conditional Fokker-Planck theorem proof, no KL derivative proof, no theorem-route audit, no display algebra, and no broad reusable API design.
2. No status promotion for sald.general_moving_target_discrete.em_interpolation_fp, sald.general_moving_target_discrete.kl_derivative, thm:forward-KL-discrete, or thm:general-moving-target-SALD-discrete.
3. No Lake dependency changes, no SLT import, and no project-article export.

lowerPacket : List String (explicit)

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

Ordered data items

1. Target exactly the conditional-law/measurability layer feeding SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface and SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents.
2. Preferred lower sub-slice: instantiate or wrap Mathlib condDistrib/condExpKernel facts for the joint law of (X_k^eta,hat X_s), its second marginal hat rho_s, and vector-valued component integrals for dot t_k*c_{t_k} and (sigma_eta^2/2)*nabla log pi_{t_k}.
3. If blocked, record one missing theorem with standard-Borel/probability, marginal compatibility, measurability, integrability, and vector-valued conditional expectation hypotheses explicit.
4. Do not switch to endpoint-law re-audit, weak FP, KL derivative, Gronwall/DV/LSI, frozen-delta, or theorem display work.

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 75 depends on the cycle-74 conditional-kernel source-cited interface and does not duplicate or promote it.
3. Any lower proof is only a local wrapper under explicit kernel/measurability/integrability hypotheses; the actual conditional law, weak FP, and KL differentiation remain below formalized unless compiled locally.
4. The conversion window, proof-obligation ledger, source index, and SLT audit agree that SLT is reference-only and not imported.
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.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation
3. SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceLowerObligation
4. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents
5. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
6. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
7. SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents
8. sald.general_moving_target_discrete.em_interpolation_fp
9. Mathlib.Probability.Kernel.Condexp
10. Mathlib.Probability.Kernel.CondDistrib

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 cycle75GeneralMovingTargetDiscreteConditionalLawBackfillUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Global phase judgment: cycle 74 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 proof risk is still sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to the conditional-law/measurability and named conditional drift construction interface for 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",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Cycle 74 supplied the exact source-cited condDistrib/condExpKernel blocker; cycle 75 should not create a second broad interface.",
    "The conditional-law layer must connect the joint law of (X_k^eta,hat X_s), the named marginal hat rho_s, the conditional kernel of X_k^eta given hat X_s=x, and the two component conditional drift integrals.",
    "Cycles 70 and 71 already provide local named-drift and endpoint-to-conditional wrappers; cycle 75 lower should try to feed those wrappers with a concrete conditional-kernel construction or record the exact missing Mathlib theorem.",
    "Weak conditional Fokker-Planck, log-ratio admissibility, density/AC, KL differentiation, integration by parts, LSI/KL/FI, DV, Gronwall, and theorem closure remain obligations."
  ]
  theoremRoute := [
    "1. Stay inside appendix.tex:1358-1387, with the active lower slice appendix.tex:1368-1377.",
    "2. Start from the cycle-74 source-cited interface rather than a new theorem route: regular conditional law/condExpKernel for X_k^eta conditioned on hat X_s=x.",
    "3. Preserve the named hat rho_s marginal from the endpoint-to-conditional compatibility wrappers and the paper's bar b_{k,s} component fields.",
    "4. If local proof-producing work is possible, prove only a tiny supplied-hypothesis wrapper around kernel construction/compatibility/measurability; otherwise leave a narrowly cited missing Mathlib theorem."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: keep appendix.tex and main_body.tex as the only SALD sources and keep sald_version_2.tex out of scope.",
    "Do not add standard-Borel, finite-measure, measurability, integrability, density, admissibility, or endpoint assumptions to theorem statements.",
    "Use lean-stat-learning-theory only as a local Mathlib style reference; do not add it as a dependency and do not claim any SLT theorem as formalized."
  ]
  nonGoals := [
    "No weak conditional Fokker-Planck theorem proof, no KL derivative proof, no theorem-route audit, no display algebra, and no broad reusable API design.",
    "No status promotion for sald.general_moving_target_discrete.em_interpolation_fp, sald.general_moving_target_discrete.kl_derivative, thm:forward-KL-discrete, or thm:general-moving-target-SALD-discrete.",
    "No Lake dependency changes, no SLT import, and no project-article export."
  ]
  lowerPacket := [
    "Target exactly the conditional-law/measurability layer feeding SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface and SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents.",
    "Preferred lower sub-slice: instantiate or wrap Mathlib condDistrib/condExpKernel facts for the joint law of (X_k^eta,hat X_s), its second marginal hat rho_s, and vector-valued component integrals for dot t_k*c_{t_k} and (sigma_eta^2/2)*nabla log pi_{t_k}.",
    "If blocked, record one missing theorem with standard-Borel/probability, marginal compatibility, measurability, integrability, and vector-valued conditional expectation hypotheses explicit.",
    "Do not switch to endpoint-law re-audit, weak FP, KL derivative, Gronwall/DV/LSI, frozen-delta, or theorem display work."
  ]
  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 75 depends on the cycle-74 conditional-kernel source-cited interface and does not duplicate or promote it.",
    "Any lower proof is only a local wrapper under explicit kernel/measurability/integrability hypotheses; the actual conditional law, weak FP, and KL differentiation remain below formalized unless compiled locally.",
    "The conversion window, proof-obligation ledger, source index, and SLT audit agree that SLT is reference-only and not imported.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceMiddleObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceLowerObligation",
    "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfComponents",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.generalMovingTargetDiscreteNamedConditionalDriftComponents",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "Mathlib.Probability.Kernel.Condexp",
    "Mathlib.Probability.Kernel.CondDistrib"
  ]
  status := ProofStatus.obligation

/-- Cycle-75 upper obligation for the focused conditional-law backfill. -/