Five bugs prevented the full consensus pipeline from producing results:
1. k-reachability with k=0 required weight > 0, but some vertices had
weight 0. Fixed: k <= 0 degenerates to simple past-containment check.
2. SVP incorrectly included the current round (v.round). The paper's
Algorithm 6 only includes rounds strictly < v.round. With the current
round in SVP, the voting set contained only the vertex itself (peers
are spacelike), making agreement impossible.
3. Stage delta (δ) was computed as the SVP index, but the paper defines
δ = d_{svp}(s, t) as distance from s=max(svp). Fixed: δ=0 at the
newest round (initial proposal), increasing toward older rounds.
4. The voting set was recomputed per-round, but Algorithm 7 line 6
computes it ONCE for s=max(svp). Fixed: single voting set S shared
across all stages.
5. Demo parameters (difficulty=2, pow_zeros=0) made thresholds
unreachable. Calibrated: difficulty=1, pow_zeros=2 gives weights
that cross both the is_last (3*d) and SVP (6*d) thresholds.
Result: 3 honest nodes now converge on identical total order. Leaders
are elected via the full BA* pipeline (initial proposal → presorting →
gradecast → BBA binary agreement). Byzantine nodes cannot prevent
convergence.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
Complete Python PoC of "Probabilistically Self Organizing Total Order
in Unstructured P2P Networks". Implements all 10 algorithms from the paper:
message generation, integrity checks, Lamport graphs, virtual synchronous
rounds, safe voting patterns, virtual leader election (BA*), longest chain
rule, total order via Kahn's algorithm, and push/pull gossip.
Includes simulation harness, full node binary, and 72 passing tests.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
