Editing Openai/69596681-3f7c-8006-b9fd-01d9d8191763 (section)

=== User: Below is a maximally dense, machine-executable METHODS SPECIFICATION that incorporates and closes all seven missing art… ===
Below is a maximally dense, machine-executable METHODS SPECIFICATION that incorporates and closes all seven missing artifacts, fully integrated into the prior formalism. This is written for direct machine ingestion (static analysis, CI enforcement, theorem checking). No narrative. No spacing between blocks. Heavy algebra. All operators frozen.

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METHODS BLOCK 0 — GLOBAL SPEC HASH (DEPLOYMENT LOCK)
Define canonical serialization .Define method hash .All executions must report .Any mismatch ⇒ INVALID.

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METHODS BLOCK 1 — AXIOMS (HARD)
A0:Epistemic authority iff realized empirical .A1:No synthetic data instantiate operators.A2:All structure frozen pre-run.A3:Decisions binary, irreversible.A4:MC monotone to falsification.A5:No optimization objectives.A6:No hidden state.A7:Reproducibility required.

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METHODS BLOCK 2 — TYPES
 scalar. observables. dataset. parameters. baseline dimension. SPD covariance. verdict..

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METHODS BLOCK 3 — MODEL MAP
Prediction operator .Baseline .IR manifold .IR envelope .

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METHODS BLOCK 4 — RESIDUAL OPERATOR
..Residual field .

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METHODS BLOCK 5 — STRUCTURAL VIOLATION
Tolerance ..

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METHODS BLOCK 6 — FEASIBILITY / PARAMETER FORCING
Feasibility .Minimal dimension .Decision:  OK; forced; COLLAPSE.

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METHODS BLOCK 7 — PARAMETER IDENTIFIABILITY (ARTIFACT #2)
Equivalence .Identifiable basis  s.t. Fisher  full-rank on .Redundant params projected out before .

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METHODS BLOCK 8 — LIKELIHOOD KERNEL (ARTIFACT #1)
Per-observation likelihood  with optional heavy-tail mixture fixed a priori: .Heteroskedastic  allowed.Block covariance  allowed.Normalization explicit.

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METHODS BLOCK 9 — DATA VALIDITY OPERATOR (ARTIFACT #4)
\mathcal{Q}(D)=VALID iff metadata complete, epochs consistent, calibration hashes match, independence assumptions satisfied, no domain leakage;else INVALID.Execution abort if INVALID.

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METHODS BLOCK 10 — BAYESIAN EVIDENCE
Evidence .Statistic .Threshold .

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METHODS BLOCK 11 — INTEGRATION CONTRACT (ARTIFACT #3)
Integrator \texttt{Integrator}=NestedSampling with fixed live points , tolerance , seed .Convergence required;else INVALID.Output reproducible.

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METHODS BLOCK 12 — GLOBAL COLLAPSE
.Verdict:1⇒COLLAPSE;0⇒STAND.

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METHODS BLOCK 13 — MONTE CARLO (ROBUSTNESS)
Empirical likelihood .Draws .Indicators .Frequency .Threshold .Early stop at .Range .

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METHODS BLOCK 14 — PRECISION SCALING
..If  COLLAPSE.

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METHODS BLOCK 15 — FAILURE ATTRIBUTION GRAPH (ARTIFACT #5)
If  emit tuple  where operator∈{STRUCT,FEAS, BAYES,PREC}.Queryable DAG.

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METHODS BLOCK 16 — CERTIFICATION STOP RULE (ARTIFACT #7)
Define certification horizon  s.t.  under increasing precision and independent datasets ⇒ CERTIFIED STAND.

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METHODS BLOCK 17 — PIPELINE DAG
Validate →Residuals→→→Integrator→→→MC→Attribution→Artifact.Emit hash .

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METHODS BLOCK 18 — ML INTERPRETATION
Hard-boundary classifier .No loss.No training.MC estimates robustness neighborhood.Bayes = complexity penalty.

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METHODS BLOCK 19 — AUDIT
Inputs, outputs, code, thresholds hashed.SHA-256 logs.Immutable JSON.

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END OF MAXIMAL METHODS.
This section closes all seven artifacts and yields a deployable, auditable, machine-complete specification.

© Robert R. Frost
2026-01-03