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

=== Assistant: Proceeding. ===
Proceeding. Below is METHODS BLOCK 13 — MONTE CARLO (ROBUSTNESS), expanded to maximum algorithmic depth using machine-learning–style language (stress testing, adversarial perturbations, frequency guarantees, early stopping). This block never rescues a theory; it quantifies robustness of an already-determined verdict neighborhood.

METHODS BLOCK 13 — MONTE CARLO (ROBUSTNESS)

OBJECTIVE
Quantify robustness of the frozen verdict under admissible perturbations of inputs, noise realizations, and precision limits. This block estimates a failure frequency over a certified perturbation neighborhood. It is evaluative only and cannot change upstream decisions except to trigger additional collapse via precision scaling.

SCOPE AND AUTHORITY
• Executed after Global Collapse logic inputs are available
• Cannot override Structural, Feasibility, or Evidence decisions
• May only introduce PrecisionFailure (Block 14)
• Synthetic draws permitted here ONLY (A1 exception)

ML analogy: adversarial stress testing, not training or validation.

PERTURBATION SPACE
Define admissible perturbation operator Π acting on datasets and covariances:

Π : (D, Σ, seed_j) → (D_j, Σ_j)

Constraints:
• Π preserves schema, metadata, and provenance tags
• Π does NOT alter Model Map, parameters, priors, thresholds
• Π draws from declared noise models only
• Π does not condition on model performance

Examples (must be pre-declared):
• Noise resampling consistent with Σ
• Calibration jitter within certified bounds
• Finite-precision rounding perturbations

No adversarial crafting based on gradients or residuals.

DRAW DEFINITION
Define number of Monte Carlo draws N_MC ∈ ℕ⁺, fixed pre-run.

For j = 1…N_MC:
• Generate perturbed dataset D_j = Π(D, Σ, seed_j)
• Enforce Data Validity on D_j (schema-only; provenance inherited)
• Recompute residuals, likelihood, evidence inputs as required
• Evaluate collapse indicators without modifying structure

Seeds {seed_j} fixed and emitted.

INDICATOR FUNCTION
Define binary indicator for each draw:

I_j = 1 iff any of the following occur under D_j:
• StructuralViolationFlag_j = 1
• FeasibleFlag_j = 0
• EvidenceFailure_j = 1

Else I_j = 0.

Note: ValidityFail cannot occur here by construction; if it does, execution INVALID.

EMPIRICAL FAILURE FREQUENCY
Compute empirical frequency:

f = (1 / N_MC) ∑_{j=1}^{N_MC} I_j

This estimates the measure of the collapse region within the perturbation neighborhood.

THRESHOLD AND EARLY STOP
Define robustness threshold f_c ∈ (0,1], fixed pre-run.

Decision rule:
If f ≥ f_c ⇒ RobustnessFailure = 1
Else RobustnessFailure = 0

Early stopping permitted:
If at any iteration t, (1/t) ∑_{j=1}^t I_j ≥ f_c ⇒ stop and set RobustnessFailure=1.

Early stop cannot trigger RobustnessFailure=0.

ML analogy: one-sided sequential test with no false-negative control.

NO CONFIDENCE INTERVALS
Forbidden:
• Confidence bounds on f
• p-values
• Hypothesis tests
• Variance reduction tricks

The empirical frequency itself is the artifact.

PRECISION LINKAGE
RobustnessFailure feeds into Block 14 (Precision Scaling) as an indicator that increasing precision may induce collapse.

If RobustnessFailure=1, downstream precision escalation is mandatory.

FAILURE MODES
• Adaptive perturbation design ⇒ INVALID
• Conditioning Π on I_j outcomes ⇒ INVALID
• Changing N_MC mid-run ⇒ INVALID
• Attempting to average away rare collapses ⇒ INVALID

ARTIFACT EMISSION
Emit immutable MonteCarloRecord:

⟨
N_MC,
SeedsHash,
f,
f_c,
RobustnessFailure,
EarlyStopIteration (if any)
⟩

Hashed and audit-logged.

PIPELINE ROLE
Outputs feed exclusively into:
• Precision Scaling (Block 14)
• Failure Attribution (Block 15)
• Audit (Block 19)

ML INTERPRETATION
This block implements robustness certification via empirical stress testing:

• No learning
• No model update
• No tuning
• Binary failure detection

Equivalent to verifying that a fixed classifier’s decision is stable under admissible perturbations.

END METHODS BLOCK 13.

If you confirm, the next block will be METHODS BLOCK 14 — PRECISION SCALING, expanded into asymptotic precision logic, monotone limits, and collapse triggering at infinite-resolution limits.

© Robert R. Frost
2026-01-03