foculus

consensus by convergence. a particle is final when $\phi^*_i > \tau$

specs

implementable, normative — what a builder implements against:

protocol.md — the protocol spec: network model, state, conflicts, fork choice, seven-step protocol, safety/liveness, performance. amended to fold in domain-local certification, the support-switching rule, and the conditional spectral-gap theorem — see security-at-scale.md for the derivations

parameters.md — every protocol constant in one place: tri-kernel weights, VDF delays, precision floor, reorg depth, epoch windows — derived, measured, or explicitly chosen

gossip.md — the propagation layer VEC P4 assumes: no message envelope, a signal is the gossip message; push for new signals, pull for VEC P2 completeness proofs. topology starts with explicit domain subscription (proven, gossipsub-style, via radio); graph-inferred peer affinity is named as a future direction, not the starting design — see the document's own opening for why

provable-consensus.md — circuit spec: proving φ* in a zheng circuit, cost analysis, recursive composition

vec.md — verified eventual consistency: six properties (P1-P6), CRDT safety, NMT completeness, DAS availability

beacon.md — epoch randomness beacon $b_E$: VDF over finalized signals; unpredictable, unbiasable, verifiable, live

fold-mining.md — second lottery: HyperNova fold tree aggregates settlement tickets into one O(1) accumulator per cluster; closes settlement liveness

security-at-scale.md — the derivation record for protocol.md's amendments: safety and liveness at $N \to 10^{15}$, localized to reward specification's ε-support domains (L1, L2), the support-switching rule and its proof (T1), the spectral gap as a conditional theorem (T2), corrected domain/shard composition (S4) and liveness (S5)

docs/explanation

narrative, not normative:

overview.md — what is foculus, consensus as equilibrium, finality as point of no return

convergence.md — convergence theory: fixed points, contraction, spectral gap, five worked examples

life-of-a-signal.md — a signal's full lifecycle walked in real time: gossip and tri-kernel convergence to finality (~4s), then the epoch pipeline — beacon, settlement lottery, fold, mint — to a spendable Shapley share (~1-3min); includes who computes the beacon, a tuned-vs-conservative timing table, and three open scheduling tensions

roadmap

open problems, one file each — not phased milestones, specific unsolved questions with enough context to pick up. see roadmap/README.md for the index.