How Rare Is a Flip? — Kenneth Cheng

Technical figure from How Rare Is a Flip? — A reviewed research figure synchronized from the private technical workspace. The original aspect ratio and labels are preserved.

Editorial overview

The literature gate returned REFRAME: efficient rare-event sampling for genetic switches is already established, so a generic “enhanced sampling beats direct simulation” claim would not be new. The defensible project is a reliability-boundary benchmark, but only its smallest Phase-1 foundation has been executed so far.

Read How Rare Is a Flip? for the declared exclusive-toggle CTMC, the fixed first-hit event, the finite-state probability bracket, the seeded SSA comparison, the retained failed truncation, and the exact limits on interpretation.

Key findings

At cap 20, the FSP bracket was 0.2575946379–0.2575946395 with overflow probability 1.62e-9.
Seeded naive SSA recorded 1580 hits in 6000 trajectories, or 0.26333, with a 95% Wilson interval of 0.25234–0.27463.
Thirty of 32 independently seeded batch intervals intersected the FSP bracket; this is a smoke diagnostic, not a definitive coverage study.

Limitations

This is only the synthetic low-copy Phase-1 smoke regime, not the final preregistered rarity ladder.
The retained cap-18 failure and the passing cap-20 truncation audit validate reference handling, not a biological model.
AMS and FFPilot were not implemented or evaluated, so the study makes no rare-event speedup or method-ranking claim.

Technical record

Detailed source, calculations, generated figures, and reproduction instructions are maintained in a private technical workspace. Public articles contain only manually reviewed interpretation and approved figures.

Version history

2026-08-29 — Curated overview reviewed against repository evidence.