3 Commits

Author	SHA1	Message	Date
Marcin Pawlowski	3c52aeec0e	Settle §6.9's multi-coalition conjecture: refuted for deflation, confirmed for the threshold ... §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>	2026-08-10 12:42:54 +02:00
Marcin Pawlowski	097543a5f9	Re-measure the W pairing paired, and correct my own severity numbers ... The W = 12 pairing is now measured the way a ~0.001 claim has to be: every integer W from 8 to 15, 32 replicates, and paired_streams so the whole grid runs on common random numbers (_base_key excludes both uncle_window_anchor and window_absorption, so a replicate draws one stake vector, one graph and one lottery for every cell). The earlier unpaired sweep reported +0.0008 against a standard error of 0.0009 — it could not resolve its own headline. Paired against today's recipe (uncle-anchored, W = 10): parent W=10 -0.0056 +- 0.0005 t = -10.4 parent W=11 -0.0024 +- 0.0005 t = -4.5 parent W=12 +0.00004 +- 0.00050 t = 0.1 <- parity parent W=14 +0.0016 +- 0.0004 t = 3.5 W = 12 is the smallest window reaching parity, and the parity is exact rather than marginal: W = 11, one interval short, is still resolvably worse. p_ref agrees at the same window (0.938 vs 0.939) instead of lagging to W = 15 as the unpaired edition had it. Also states what the sweep makes visible: widening today's uncle-anchored rule buys +0.0018 on its own, so W = 12 makes the swap cost-neutral against the CURRENT recipe rather than optimal in absolute terms. CORRECTIONS to the previous commit, which measured contamination on the wrong RNG stream. The engine draws stake from seedseq_for(config).spawn(...)[0]; I used rng_for(config), the root. Both are valid stake draws, neither is the same vector. Redone properly: - The capstone draw was NOT contaminated: 0 of 8 replicates over 1.25x its label, worst 0.369 against 0.30, no majority. My "2 of 8, one a 61% majority" was wrong and is withdrawn from §8.4 and §9. - The finding that survives is sharper: on that same mild overshoot the spec's rule moved 0.001 and the parent-anchored variant moved 0.016. A rule leaning harder on the reference window is far more sensitive to an oversized suppressing coalition. - Genuinely contaminated: §6.12's 12-replicate W sweep (2 majorities, worst 0.720) and §6.8's selfish margin at a=0.3 and a=0.4 (2 and 1 majorities). §6.5's variants and §6.8's a=0.2 arm are clean; §8.3 item 20 narrowed to the one sweep that still needs re-running. - The general severity is worse than first stated, not better: at the report's geometry a nominal 0.3 realised a majority in 12% of replicates. Two more defects found on the way: - stake_for(config) added, because scripts used rng_for and the engine uses the spawned child — so every script that rebuilt a tree was analysing a different network than the trajectory it was compared against. All scripts and tests now use it. - A coalition member could receive a private block BEFORE its parent: the arrival was clamped against the PRODUCER's view of the parent and applied to the whole coalition, so a member still awaiting a public parent got the child first. Now clamped per member. Caught by the existing arrival-order test once the stake derivation was corrected. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>	2026-08-10 12:37:21 +02:00
Marcin Pawlowski	516783146d	Fix adversary coalition sizing; add rival coalitions and a lead cap ... Three engine defects, found while building the multi-coalition study §6.9 flags as open. The first is the serious one. 1. COALITION SIZING (engine._adversary_mask, `random` selection — the default). The coalition was the smallest random prefix whose stake reached the target. Under a Pareto tail a whale straddling the cut carries it far past its label: over 60 replicates, a nominal adversary_frac of 0.4 realised a MAJORITY in ~10% of them and reached 0.97, and 0.2 reached 0.90. The median was always on-label, which is why it hid — it distorts the tail, not the centre. Both other places in the code that size a set by stake had already rejected this rule: the `whale` arm uses fit-then-close, and _churn_inactive_mask documents the identical failure ("a 30% label realising up to ~53%"). The `random` arm kept it. Now fit-then-close in random order, and a draw where the tail leaves no subset near the label warns instead of silently running a different attacker. Realised stake is now within 0.1% of its label. Re-ran the load-bearing studies. §8.4 capstone (2 of 8 replicates contaminated, one a 61% majority): spec rule 0.994 -> 0.995, p_ref 0.936 -> 0.937. The parent-anchored variant is far more sensitive — 0.974 -> 0.990, p_ref 0.875 -> 0.923 — because a tighter window and a larger suppressing coalition compound, so §8.4's argument for the W = 12 pairing rested on 0.021 of cost that is really 0.006. The pairing itself survives re-measurement and is now better supported: p_ref reaches parity at W = 12 too, not at 15. §6.8's uncle-margin sweep and §6.5's random-arm variants are flagged as needing re-measurement (§8.3 item 20), not silently carried. 2. SM1 NEVER TERMINATED under a forking honest network. Textbook SM1 waits while it leads, assuming the lead returns to zero. But honest blocks fork against each other, so the public chain's HEIGHT grows at ~(1-a)*f*(1-fork) while a coalition sharing one view extends privately at the full a*f; past a fork rate of ~1 - a/(1-a) the private chain outruns the public one and `wait` never fires. The lead ran to thousands and every block was stranded at the epoch boundary — 98% of adversarial blocks at alpha=0.4, delta_max=8 — scoring an attacker that WON the race as having earned nothing. selfish_lead_cap (default: the finality depth k) publishes a lead that can no longer be caught. Inert unless `wait` stops terminating; pinned paired. 3. RIVAL COALITIONS (adversary_coalitions = K) for the §6.9 study: K private chains, each invisible to the others by the same arrival sentinel that hides them from honest nodes, so they orphan each other as well as the honest chain. Stake-balanced partition (LPT), K=1 bit-identical to the single-coalition path. Also corrects §8.4's closing paragraph, which still quoted a pre-countable D-hat/D of 1.001 and fork rates that contradicted its own table. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>	2026-08-10 12:21:00 +02:00