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

=== Assistant: Proceeding. ===
Proceeding. Below is METHODS BLOCK 16 — CERTIFICATION STOP RULE (ARTIFACT #7), expanded to maximum algorithmic depth using machine-learning–style formalism (asymptotic guarantees, dataset accumulation semantics, monotone acceptance, and machine-verifiable certification). This block defines when “STAND” becomes certified—not merely provisional—without weakening falsifiability.

METHODS BLOCK 16 — CERTIFICATION STOP RULE (ARTIFACT #7)

OBJECTIVE
Define a deterministic stopping rule that upgrades a provisional STAND verdict into a CERTIFIED STAND under accumulating independent evidence and increasing precision. Certification is asymptotic, monotone, and revocable only by future falsification under expanded data. No probabilistic confidence statements are used.

SCOPE AND AUTHORITY
• Executed only if Global Verdict = STAND (Block 12)
• Consumes only immutable artifacts from prior blocks
• Cannot override any collapse
• Produces a certification flag and horizon metadata

ML analogy: PAC-style acceptance without probabilistic bounds; monotone accept-only rule under increasing sample complexity.

DATASET SEQUENCE
Define a sequence of datasets {D₁, D₂, …, D_H} such that:

• Each D_i individually satisfies Data Validity (Block 9)
• D_i are mutually independent per declared independence structure
• Independence encoded in covariances and provenance
• D_{i+1} ⊃ D_i or is disjoint but from the same domain class
• No dataset influences model structure (A2)

Let H be the certification horizon, a finite integer declared pre-run.

ACCUMULATION OPERATOR
Define cumulative dataset:

𝒟_k = ⋃_{i=1}^k D_i

Union respects covariance structure; block covariance expanded accordingly. No reweighting or pruning.

CERTIFICATION PRECONDITIONS
For each k = 1…H, the following must hold under 𝒟_k:
# DataValidity(𝒟_k)=VALID
# StructuralViolationFlag(𝒟_k)=0
# FeasibleFlag(𝒟_k)=1
# EvidenceFailure(𝒟_k)=0
# PrecisionFailure(𝒟_k)=0

Any violation at any k aborts certification permanently and forces collapse per Block 12.

MONOTONIC SURVIVAL
Define survival indicator:

S_k = 1 iff all five conditions above hold at k; else 0.

Certification requires:
∀ k ∈ {1,…,H}: S_k = 1.

This enforces monotonic survivability across increasing data.

PRECISION COUPLING
At each k, precision scaling (Block 14) must be evaluated up to declared p_max.

Certification requires stability under precision escalation at each k.

ML analogy: acceptance only if classifier output is invariant under shrinking perturbation radius at all training set sizes up to H.

NO STATISTICAL ACCUMULATION
Forbidden:
• Averaging evidence across k
• Summing Bayes factors
• Relaxing Λ with k
• Using law-of-large-numbers arguments

Each k is a fresh, full evaluation.

CERTIFIED STAND DEFINITION
Define certification flag:

CERTIFIED_STAND = 1 iff
(Global Verdict = STAND) AND (∀ k ≤ H: S_k = 1)

Else CERTIFIED_STAND = 0.

CERTIFIED_STAND is a meta-verdict layered atop STAND.

REVOCABILITY
Certification is conditionally stable:

• New datasets D_{H+1}, D_{H+2}, … may revoke certification
• Revocation occurs only via standard collapse logic
• Past certification artifacts remain immutable but superseded

No grandfathering.

FAILURE MODES
• Any dependence between D_i not encoded ⇒ INVALID
• Adaptive choice of H ⇒ INVALID
• Conditioning inclusion of D_i on prior outcomes ⇒ INVALID
• Skipping precision scaling at any k ⇒ INVALID

ARTIFACT EMISSION
Emit immutable CertificationRecord:

⟨
H,
k_max_tested,
CERTIFIED_STAND,
FirstFailure_k (if any),
DatasetHashes,
PrecisionBounds
⟩

Hashed and audit-logged.

PIPELINE ROLE
CertificationRecord feeds exclusively into:
• Audit Log (Block 19)
• External certification/reporting interfaces

No computational block may consume certification to alter evaluation.

ML INTERPRETATION
This block implements algorithmic certification under data growth:

• No training
• No generalization bounds
• No confidence intervals
• Pure survival across expanding, independent test sets

Comparable to verifying a fixed program against an increasing suite of adversarial test cases.

END METHODS BLOCK 16.

If you confirm, the next block will be METHODS BLOCK 17 — PIPELINE DAG, expanded into execution ordering, dependency enforcement, static scheduling, and CI-style orchestration semantics.

© Robert R. Frost
2026-01-03