mirror of
https://github.com/logos-blockchain/research.git
synced 2026-08-10 21:23:12 +00:00
3c52aeec0e
§6.9 flagged multi-coalition selfish mining as conjectural on two counts taken from the literature — that splitting a coalition can deflate D-hat FURTHER than one coalition of the same size, and that individually sub-threshold coalitions can be jointly profitable. With rival private chains in the engine, both are now measured (scripts/multi_coalition.py, fig39), and they point opposite ways. DEFLATION — REFUTED. Splitting a fixed stake into K rivals reduces estimator damage, monotonically, at every beta and K tested (t = 4.3 to 14.3): beta K=1 K=2 K=3 K=4 0.20 0.908 0.928 0.922 0.928 0.30 0.778 0.858 0.880 0.880 0.40 0.586* 0.764 0.807 0.823 The mechanism shows in the fork structure: a lone coalition holds one private chain ~2000 blocks deep, while two rivals cut each other to depth ~2. Rivals spend their advantage burying each other instead of honest work. So D-hat ~ 0.70 at alpha = 0.4 IS an upper bound on multi-coalition deflation, not the under-estimate §6.9 warned it might be. (* boundary-affected: 66% of that cell's adversarial blocks were still private at epoch end even with the lead cap. The 0.2 and 0.3 rows have <1% stranding and carry the result alone.) THRESHOLD — CONFIRMED, and 1/3 does not hold at this load: one coalition at 0.200 0.875x t = -2.5 does not pay one coalition at 0.295 1.232x t = 2.7 PAYS two rivals at 0.200 each 1.045x t = 2.5 each PAYS three rivals at 0.133 each 0.852x t = -5.1 does not pay Two results against the folklore. A single coalition already profits at alpha ~ 0.295, because the honest network forks at ~0.48 here so the public chain's HEIGHT advances at only (1-a)*f*(1-fork) while a coalition sharing one view extends privately at the full a*f — the threshold falls with the fork rate. And a 0.20 coalition that does NOT pay alone DOES pay against a second 0.20 rival: the rival displaces honest blocks too and both collect on the disruption. That is the "individually sub-threshold, jointly profitable" case, confirmed at K = 2 and not extending to K >= 3. The practical split: coalition fragmentation is good for TSI's estimator and bad for the incentive argument. "No coalition holds 1/3" is not a safety property at a load where the honest network forks appreciably, which makes rho < 1 an incentive constraint and not only an accuracy one. §8.3 item 2 narrowed accordingly; fig39 marks boundary-affected cells hollow. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>