The final test: Erdős-Rényi G(n, 1/n) at criticality — the exact
moment where disconnected clusters become a giant hairball component.
Why this problem:
- Mathematically SOLVED (Erdős-Rényi 1960 phase transition)
- Extreme density at p=1/n (maximum entropy, minimum structure)
- Known answer: largest component Θ(n^{2/3}), spectral gap ≈ 1
- Can VERIFY: does Φ-corkscrew find the critical point?
- Tensor network representation (quimb) for efficient computation
- Multi-mode: ESP32 / photonic / quantum / GPU / CPU all valid
Multi-mode execution:
ESP32: n≤50, Q16.16 fixed-point, BLE broadcast
Photonic: eigenvalues from transmission spectrum (O(1) measurement)
Quantum: graph state + phase estimation (exponential for eigvals)
Tensor network (quimb): n≤10000, production mode
Verification:
Expected: largest component ~n^{2/3}, gap ≈ 1
System finds: spiral index → Σ basin, moderate FAMM pressure
5 watchdogs should agree (problem is well-posed)
Refs: arXiv (Erdős-Rényi model),
https://github.com/jcmgray/quimb (tensor network library),
SILVERSIGHT_LATTICE.md (5 watchdog consensus)
