AutoSamplingTheory.SALD.cycle89DiscreteForwardKlClosurePressureUpperPacket

Data definition / provenance and workflow record

Meaning and type

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

def cycle89DiscreteForwardKlClosurePressureUpperPacket :
    DiscreteForwardKlUpperPacket

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.

objective : String (explicit)

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

Global phase judgment: cycle 88 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the active EM packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387. The discrete thm:forward-KL-discrete pressure test routes through the compiled cycle-85--88 EM/KL handoffs plus the existing LSI, DV, Gronwall, and accumulated-error scalar interfaces, and the next non-wrapper blocker is the derivative/integration-by-parts/FI boundary in SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative at appendix.tex:388-413, with the upstream raw KL/weak-FP inputs still at appendix.tex:1358-1387.

sourceLabels : List String (explicit)

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

Ordered data items

1. thm:forward-KL-discrete
2. proof:thm:forward-KL-discrete
3. proof:thm:forward-KL-discrete:derivative
4. proof:thm:forward-KL-discrete:conditional-fp
5. eq:KL-derivative-1-discrete
6. eq:KL-derivative-2-discrete
7. eq:KL-derivative-3-discrete
8. eq:general_KL_derivative_0_discrete
9. proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative
10. sald.discrete_forward_kl.kl_derivative
11. SALD.discreteForwardKlDerivativeObligation
12. sald.general_moving_target_discrete.em_interpolation_fp
13. sald.general_moving_target_discrete.kl_derivative

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1 only: keep main_body.tex:299-323 and appendix.tex:260-592 fixed, with sald_version_2.tex excluded.
2. Explicit active-backend check: no reviewer blocker moved the shared packet away from sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387; the pressure test only identifies the first downstream blocker for thm:forward-KL-discrete.
3. Do not add assumptions to thm:forward-KL-discrete. Any KL differentiability, weak-FP, integration-by-parts, boundary, density, or FI hypotheses remain inside named local backend obligations.
4. Use lean-stat-learning-theory only as a local style reference. Do not import it, change Lake dependencies, 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. Do not mark thm:forward-KL-discrete, sald.discrete_forward_kl.kl_derivative, sald.discrete_forward_kl.em_interpolation_fp, sald.general_moving_target_discrete.em_interpolation_fp, LSI, DV, or Gronwall formalized.
2. Do not add another supplied-hypothesis wrapper around hlog, hkl, hfp, hIBP, or hFI.
3. Do not work on display algebra, accumulated-error collection, coefficient-chain re-audit, frozen-delta estimates, or source-index rebaseline unless a reviewer finds a blocking anchor defect.
4. Do not replace the paper route through appendix.tex:388-491 with a generalized theorem statement or a weakened derivative inequality.

lowerPacket : List String (explicit)

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

Ordered data items

1. Classification: narrows-source-cited-boundary.
2. Middle should synchronize the pressure-test result in the conversion window: cycles 51/56/61/66 already supply the scalar derivative-to-DV-to-Gronwall route under explicit analytic inputs; cycles 85--88 narrow the shared EM/KL inputs; the first remaining non-wrapper blocker is appendix.tex:388-413.
3. Lower should target the integration-by-parts/Fisher-identification boundary inside SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative: from the weak-FP log-ratio action and target transport action, prove or isolate the theorem giving eq:KL-derivative-1-discrete and eq:KL-derivative-2-discrete under explicit density, boundary/no-flux, log-ratio admissibility, target-time integrability, and finite-action hypotheses.
4. If too large, lower must record exactly one smaller theorem boundary, such as divergence integration by parts for the log-ratio test, target-transport integration by parts, or Fisher-information identification of the first term. The source line and declaration must be named; wrapper-only restatement is rejected.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. Check that the packet records all three upper decisions: no cycle-88 recovery, Phase 1 stable, and the next lower packet is the discrete derivative/IBP/FI boundary reached by the pressure test.
2. Check that the active shared EM backend remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and no theorem-route work escapes into unrelated APIs.
3. Verify that the exact blocker is named as SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative at appendix.tex:388-413, with upstream raw KL/weak-FP dependencies from eq:general_KL_derivative_0_discrete at appendix.tex:1358-1387.
4. Reject any new supplied-hypothesis wrapper unless it removes an older supplied IBP/FI/log-action hypothesis or names a strictly smaller theorem boundary.
5. No source constants, signs, theorem statements, statuses, SLT imports, or Lake dependencies may change; source-index and ASTIS check must pass.

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 cycle89DiscreteForwardKlClosurePressureUpperPacket :
    DiscreteForwardKlUpperPacket where
  objective := "Global phase judgment: cycle 88 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the active EM packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.  The discrete thm:forward-KL-discrete pressure test routes through the compiled cycle-85--88 EM/KL handoffs plus the existing LSI, DV, Gronwall, and accumulated-error scalar interfaces, and the next non-wrapper blocker is the derivative/integration-by-parts/FI boundary in SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative at appendix.tex:388-413, with the upstream raw KL/weak-FP inputs still at appendix.tex:1358-1387."
  sourceLabels := [
    "thm:forward-KL-discrete",
    "proof:thm:forward-KL-discrete",
    "proof:thm:forward-KL-discrete:derivative",
    "proof:thm:forward-KL-discrete:conditional-fp",
    "eq:KL-derivative-1-discrete",
    "eq:KL-derivative-2-discrete",
    "eq:KL-derivative-3-discrete",
    "eq:general_KL_derivative_0_discrete",
    "proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative",
    "sald.discrete_forward_kl.kl_derivative",
    "SALD.discreteForwardKlDerivativeObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: keep main_body.tex:299-323 and appendix.tex:260-592 fixed, with sald_version_2.tex excluded.",
    "Explicit active-backend check: no reviewer blocker moved the shared packet away from sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387; the pressure test only identifies the first downstream blocker for thm:forward-KL-discrete.",
    "Do not add assumptions to thm:forward-KL-discrete.  Any KL differentiability, weak-FP, integration-by-parts, boundary, density, or FI hypotheses remain inside named local backend obligations.",
    "Use lean-stat-learning-theory only as a local style reference.  Do not import it, change Lake dependencies, or claim an SLT theorem is formalized."
  ]
  nonGoals := [
    "Do not mark thm:forward-KL-discrete, sald.discrete_forward_kl.kl_derivative, sald.discrete_forward_kl.em_interpolation_fp, sald.general_moving_target_discrete.em_interpolation_fp, LSI, DV, or Gronwall formalized.",
    "Do not add another supplied-hypothesis wrapper around hlog, hkl, hfp, hIBP, or hFI.",
    "Do not work on display algebra, accumulated-error collection, coefficient-chain re-audit, frozen-delta estimates, or source-index rebaseline unless a reviewer finds a blocking anchor defect.",
    "Do not replace the paper route through appendix.tex:388-491 with a generalized theorem statement or a weakened derivative inequality."
  ]
  lowerPacket := [
    "Classification: narrows-source-cited-boundary.",
    "Middle should synchronize the pressure-test result in the conversion window: cycles 51/56/61/66 already supply the scalar derivative-to-DV-to-Gronwall route under explicit analytic inputs; cycles 85--88 narrow the shared EM/KL inputs; the first remaining non-wrapper blocker is appendix.tex:388-413.",
    "Lower should target the integration-by-parts/Fisher-identification boundary inside SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative: from the weak-FP log-ratio action and target transport action, prove or isolate the theorem giving eq:KL-derivative-1-discrete and eq:KL-derivative-2-discrete under explicit density, boundary/no-flux, log-ratio admissibility, target-time integrability, and finite-action hypotheses.",
    "If too large, lower must record exactly one smaller theorem boundary, such as divergence integration by parts for the log-ratio test, target-transport integration by parts, or Fisher-information identification of the first term.  The source line and declaration must be named; wrapper-only restatement is rejected."
  ]
  reviewerChecklist := [
    "Check that the packet records all three upper decisions: no cycle-88 recovery, Phase 1 stable, and the next lower packet is the discrete derivative/IBP/FI boundary reached by the pressure test.",
    "Check that the active shared EM backend remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and no theorem-route work escapes into unrelated APIs.",
    "Verify that the exact blocker is named as SALD.discreteForwardKlDerivativeObligation / sald.discrete_forward_kl.kl_derivative at appendix.tex:388-413, with upstream raw KL/weak-FP dependencies from eq:general_KL_derivative_0_discrete at appendix.tex:1358-1387.",
    "Reject any new supplied-hypothesis wrapper unless it removes an older supplied IBP/FI/log-action hypothesis or names a strictly smaller theorem boundary.",
    "No source constants, signs, theorem statements, statuses, SLT imports, or Lake dependencies may change; source-index and ASTIS check must pass."
  ]
  status := ProofStatus.obligation

/-- Cycle-89 obligation recording the pressure-test blocker. -/