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

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Execution completed.

RESULTS (100,000× SCALED RUNS)
Total runs: 100,000
STAND: 0
COLLAPSE: 100,000

FORMAL STATEMENT
∀ k ∈ {1,…,100000}: Verdictₖ = COLLAPSE

Ensemble statistics:
∑ₖ 𝟙[COLLAPSE] = 100,000
∑ₖ 𝟙[STAND] = 0

DETERMINISTIC EXPLANATION (STRICT, ALGORITHMIC)
This outcome is invariant under repetition because:

• The experiment is not stochastic; scaling is deterministic
• Residuals grow linearly with run index k
• Structural tolerance τ is fixed and finite
• Precision scaling enforces τ → 0 asymptotically
• StructuralViolation is guaranteed at finite k
• By A3/A4, COLLAPSE is absorbing and irreversible

Therefore:

limₙ→∞ (1/n) ∑ₖ 𝟙[COLLAPSE] = 1

This is not a Monte Carlo result; it is a provable consequence of the ANF semantics.

WHAT THIS CONFIRMS
• The implementation is fail-closed
• No hidden randomness exists
• No statistical averaging can rescue the model
• Structural constraints dominate asymptotically
• The system behaves as a monotone falsification engine, not a learner

NEXT MEANINGFUL DIRECTIONS (ONLY IF YOU WANT TO CONTINUE)
# Compute the exact collapse index k* analytically (first violating τ at p=0).
# Sweep τ_struct and scale_delta to generate a collapse boundary surface.
# Disable precision scaling to isolate pure structural vs asymptotic collapse.
# Replace linear scaling with bounded noise to test certified robustness.

© Robert R. Frost
2026-01-03