> run verify or tamper attack…
Scripted Merkle attacks only — illustrates post-PoP fusion binding, not a full red team.
Attacks the fused beacon after leaves exist — not the PoP door. Adversary tampers a leaf locally; honest Merkle recompute diverges. Publishing a forged root requires breaking SHA-256 (not API access).
A single Statistical Mimicry attack has a measured per-node false-accept rate α = 0.826 (May 2026). That is not P(genuine) — P(genuine) on that frame was ≈ 0.174. Under independence, joint false-accept is bounded by αⁿ:
| Honest Nodes Required | Joint false-accept bound | Security Interpretation |
|---|---|---|
| 1 | 0.826 | One room — may still look plausible |
| 10 | 0.826^10 ≈ 0.148 | About 15% joint false-accept if rooms are independent |
| 50 | 0.826^50 ≈ 7.1 × 10−5 | Much smaller under independence |
| 100 | 0.826^100 ≈ 5.0 × 10−9 | Arithmetic under independence — not a measured fleet |
| 1000 | 0.826^1000 ≈ 9.6 × 10−84 | Arithmetic under independence — not a measured fleet |
α = 0.826 is the per-node false-accept rate on the Statistical Mimicry frame (1 − P(genuine) ≈ 1 − 0.174), measured on the production path in May 2026. The fused beacon requires every independently certified node to clear the gate in the same window. The probability compounds as αⁿ under independence.
Cost math — single leaf vs fused epoch (model)
One PoP leaf (Q≈0.72): $12,000 vs $0.0008 genuine → ~15,000,000×
Merkle root forgery (no leaf injection): classical preimage ~2256 hash operations
Fused epoch (n × per-leaf): $1.20M vs $0.0008 → ~1,500,000,000×
The five-class conjunction is the second part of our PoP certified epoch process. It adds together - physical, cryptographic, logistical, statistical and temporal - within the same space and time of a certified epoch and is beyond what we can compute today.