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

=== Assistant: Proceeding. ===
Proceeding. Below is METHODS BLOCK 12 — GLOBAL COLLAPSE, expanded to maximum algorithmic depth with machine-learning–style rigor (short-circuit logic, irreversible state transitions, lattice ordering, and certification interaction). This block is the sole authority that maps upstream signals to a terminal decision.

METHODS BLOCK 12 — GLOBAL COLLAPSE

OBJECTIVE
Define a deterministic, irreversible decision operator that aggregates upstream hard gates and evaluative signals into a single terminal verdict. This block enforces short-circuit semantics and monotone falsification. No probabilistic smoothing, no rescoring, no recovery.

DECISION DOMAIN
Inputs are Boolean or scalar flags emitted by prior blocks. No raw data, parameters, or likelihoods are consumed directly.

Let the decision input vector be:

S = ⟨
V_struct,           // Block 5 structural violation flag ∈{0,1}
FeasibleFlag,       // Block 6 feasibility flag ∈{0,1}
EvidenceFailure,    // Block 10 evidence failure flag ∈{0,1}
PrecisionFailure,   // Block 14 precision scaling flag ∈{0,1}
ValidityFlag        // Block 9 data validity flag ∈{VALID,INVALID}
⟩

ValidityFlag is mapped to boolean: ValidityFail = 1 iff INVALID.

VERDICT TYPE
Verdict ∈ {0,1}.
0 ≡ STAND (theory survives current data).
1 ≡ COLLAPSE (theory falsified at IR level).

PARTIAL ORDER (DECISION LATTICE)
Define a total preorder over failure causes by decisiveness:

ValidityFail ≻ V_struct ≻ FeasibleFail ≻ EvidenceFailure ≻ PrecisionFailure

Higher-precedence failures dominate and short-circuit lower ones.

GLOBAL COLLAPSE RULE
Define collapse operator C(S):

Verdict = 1 iff
(ValidityFail = 1) OR
(V_struct = 1) OR
(FeasibleFlag = 0) OR
(EvidenceFailure = 1) OR
(PrecisionFailure = 1)

Else Verdict = 0.

This is a strict OR over failure conditions, with precedence used only for attribution.

SHORT-CIRCUIT SEMANTICS
Evaluation proceeds in precedence order:
# If ValidityFail=1 ⇒ Verdict=1, stop.
# Else if V_struct=1 ⇒ Verdict=1, stop.
# Else if FeasibleFlag=0 ⇒ Verdict=1, stop.
# Else if EvidenceFailure=1 ⇒ Verdict=1, stop.
# Else if PrecisionFailure=1 ⇒ Verdict=1, stop.
# Else Verdict=0.

No downstream computation may override an earlier stop.

IRREVERSIBILITY
Once Verdict=1 under MethodHash H and dataset D:

• Verdict(H,D)=1 is cached immutably.
• For any D′ ⊃ D with same MethodHash: Verdict(H,D′)=1 necessarily.
• Re-execution with identical inputs cannot revert Verdict.

This enforces A3 and A4.

STATE MODEL
Verdict defines a two-state automaton:

State 0 (STAND) → may transition to 1 (COLLAPSE).
State 1 (COLLAPSE) → absorbing; no outgoing transitions.

No hysteresis. No cooldown. No grace periods.

NO CONFIDENCE OR GRADATION
Forbidden outputs:
• Confidence scores
• Probabilities
• Margins
• “Weak” or “strong” collapse labels

Only the Boolean verdict is authoritative.

ML ANALOGY
This block implements a hard classifier with zero tolerance:

• Decision boundary fixed
• No loss function
• No calibration
• No ROC tradeoff
• No threshold tuning

Equivalent to a safety-critical reject/accept gate in certified ML.

FAILURE MODES
• Missing any input flag ⇒ INVALID
• Attempt to weight or combine flags numerically ⇒ INVALID
• Attempt to override precedence ⇒ INVALID
• Attempt to soften decision based on diagnostics ⇒ INVALID

ARTIFACT EMISSION
Emit immutable DecisionRecord:

⟨
MethodHash,
DataHash,
Verdict,
Trigger = first-failing condition in precedence order,
Timestamp
⟩

Hashed and audit-logged.

PIPELINE ROLE
Verdict feeds into:
• Failure Attribution Graph (Block 15)
• Certification Stop Rule (Block 16)
• Audit Log (Block 19)

No other block may emit or modify Verdict.

END METHODS BLOCK 12.

If you confirm, the next block will be METHODS BLOCK 13 — MONTE CARLO (ROBUSTNESS), expanded into adversarial perturbation logic, robustness neighborhoods, and frequency-based stress testing—again at maximum algorithmic depth.

© Robert R. Frost
2026-01-03