Each of the 240 nodes is an account on a small-world social graph (Watts–Strogatz style: a ring lattice with ~14% of edges rewired long-range, so a few "hub" accounts sit on many shortcuts). A node's state each tick follows an SIR-style threshold contagion:
P(share | exposed) = viralityRate × hubMultiplier(node)
belief spreads: Unaware --p--> Believes (per exposed edge, per tick)
correction spreads: Believes --q--> Corrected (once fact-check is live, same edge rule)
Corrected is terminal: immune to re-belief, and won't re-share the claim.
"Post the Claim" seeds one random hub with the false claim; it then propagates edge-by-edge exactly like a real cascade — each tick, every node currently believing rolls the virality probability against each unaware neighbour it touches, weighted up if that neighbour is a hub (hubs have far more edges and a multiplier, mirroring how a single influential account can flip a claim from niche to trending). "Publish Fact-Check" starts a second, independent contagion of the correction along the same graph, but only after the response-delay timer you set — the longer real newsrooms and platforms take to respond, the deeper the false claim has already tunnelled through the hub structure by the time the correction starts racing it.
- Virality — per-edge, per-tick probability an exposed neighbour adopts the claim.
- Response delay — seconds between the claim going live and the fact-check starting its own spread.
- Hub boost — how much more likely a hub node is to pass the claim on once it believes it, versus an ordinary node.
This is the same mechanism epidemiologists use for disease outbreaks (SIR models) applied to information instead of infection — real platform research (misinformation-cascade studies on Twitter/X and Facebook) shows false claims measurably out-race corrections specifically because of this delay and hub-amplification effect.