Verification of my own item-16 result, which I had flagged as resting on a
step I had not checked: "break-even" was measured as revenue SHARE >= stake
share, and share-to-pay equivalence rests on sec 6.6's issuance argument. It
does not hold as stated.
A revenue share is measured against the canonical block rate, but pay is set by
the estimator. TSI drives COUNTED density -- canonical plus recovered uncles --
to f per slot, so a run yields f/D-hat block-finding events per slot and a
deflating attack makes the lottery easier for everyone. Pay per slot is
adv_rate * f / D-hat against an honest miner's alpha * f, so the correction on
the share ratio is density/D-hat, which is below 1 whenever any uncle is
recovered. Scoring on share credits the attacker with pay it never receives.
The headline survives; one row does not. At alpha = 0.4 the true break-even
point deflates to 0.649 rather than 0.642 (against the revenue-optimal 0.811),
so 16 points of free deflation instead of 17. But at alpha = 0.36 the policy I
reported as paying 1.033x stake actually pays 0.95x, and NO policy in the sweep
both pays and deflates there -- that row is withdrawn. The exposure therefore
opens near alpha ~ 0.37-0.38, above the 1/3 selfish threshold, not at it. That
is a better result for the protocol than the one I published yesterday, which
is the direction these corrections usually do not go.
pay_vs_honest is now computed in deflation_frontier() and is the criterion
best_profitable() selects on, so the claim is reproducible rather than resting
on a hand check. The conversion neglects the multi-winner factor c(f) ~ 1.017
between events and occupied slots (sec 2.1), noted inline and small against a
16-point effect. Downstream citations in sec 1, sec 8.2 and item 16 updated.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Both eta ceilings in sec 6.6 come from adversaries optimising something else
(revenue, reorg depth), so they bound eta from above without bounding the
damage from below. Optimising the estimate directly needs no ratio transform:
each transition consumes exactly one block-finding event, so minimising
D-hat = (canonical + p_ref * countable uncles)/events is a plain average-reward
MDP over the transition table that already carries the orphan counts. One
value-iteration pass, no bisection.
Unconstrained, the answer degenerates -- and usefully. The optimum is pure
abstention: publish nothing, adopt when overtaken, D-hat = 1 - alpha exactly,
revenue zero. That is sec 6.4's withholding, which the report already shows is
CORRECT measurement rather than mis-measurement, so the unconstrained objective
asks the wrong question.
The constrained one bites. Sweeping lam * (adversary blocks) - (contribution to
D-hat) enumerates policies; the line of interest is where revenue SHARE reaches
alpha, i.e. where attacking costs nothing versus mining honestly. At alpha=0.4
such a policy drives D-hat to 0.642 where the revenue-maximiser reaches 0.811
-- 17 points of extra deflation bought with the selfish premium alone. At 0.36
and 0.45 the gaps are 0.082 and 0.103. Below the 1/3 threshold nothing
profitable deflates, so the exposure starts exactly where selfish mining does.
This revises two claims that were about revenue but read as though they were
about the adversary in general: sec 6.7's "the adversary frontier is exactly
optimal selfish mining; no compounding lever remains" and sec 8.2's echo of it.
Both now say the PROFIT frontier is bounded and the estimator frontier is not
the same policy. Note the sweep parameter is deliberately non-monotone in
revenue -- selfish mining takes a bigger share of a smaller pie, so raw block
rate is maximised by honesty and large lam returns there; it enumerates
policies rather than tracing a path.
Also closes a fairness loop these findings opened. Sec 6.7(1) credits uncle
rewards with compensating orphaned honest producers, computed on the SM1 race
where every orphan is a first-fork block. Under a private chain 20-40% of the
honest blocks destroyed are unreferenceable by construction, so those producers
are uncompensatable at ANY w_u -- not underpaid because p_ref is low, but
unreachable because no valid block may name them. The fairness guarantee
inherits the same first-fork ceiling as the density repair. Logged as item 19,
flagged as a protocol-design question rather than something a schedule fixes.
_solve_mdp is refactored into _solve_reward/_greedy_policy/_stationary/
_policy_rates so both objectives share one implementation; optimal_policy_stats
reproduces its committed figures exactly (eta 0.4413, D-hat 0.9447/0.8111 at
alpha=0.4). 251 tests pass.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
