Marcin Pawlowski feafe8ec92
Close the sec 6.5 scope variants; static withholding can reach the fold
Whale coalitions, jitter > 0 and very slow beta were the residual "untested
adversary variants" of open item 11. None moves a conclusion:

- Concentration does not change the deflation (suppression D-hat within noise
  at every stake), and a whale coalition reproduces the sec 6.4 withholding law
  D-hat -> (1-beta_adv) more cleanly than a random one: 0.9005/0.6997/0.5010
  against a predicted 0.9/0.7/0.5. The "lumpier share statistic" worry points
  the other way, and for a reason that is about coalition CONSTRUCTION rather
  than concentration: a random coalition grows until its stake first reaches
  the target, so the last node added overshoots by its own size -- a whale,
  under a Pareto tail. Realised block share at a nominal beta_adv = 0.1 is
  0.137 +- 0.108. Logged as item 17: the beta_adv axis is a nominal target.
- jitter up to 1 slot changes nothing under attack (notch 0.390 -> 0.410,
  attacker share flat, range_ratio identically 0), as sec 6.1 found honestly.
- Slow beta shrinks the notch (0.415 -> 0.080 for beta 1 -> 0.1) at flat
  attacker take, but sinks the MEAN estimate to 0.765 at beta = 0.05: the
  estimator can no longer track back up during the honest half of the cycle.
  Slowing beta buys the defender nothing on either axis.

Unplanned: study A blew past the memory guard, which turned out to be the
sec 6.2 fold being reached. The mechanism is sec 6.2's own -- rho_eff = rho/r,
and withholding deflates r by design, so a 50 % coalition doubles the load onto
rho_eff ~ 1.1 at the design point. Swept directly, the estimate collapses once
in 144 runs at delta_max = 8 (a concentrated 50 % coalition) and never at
delta_max = 4. That retires "not an observed dynamical trap" but is one event,
so the claim is stated as a rare tail and the rate is logged unmeasured as
item 18.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
2026-08-05 16:53:56 +02:00
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