| paper | d4-conf-sagt-2021-0001 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 1, Theorem 2, Theorem 3, and Corollary 1 characterize reward-sharing schemes by axioms; none gives an algorithm, a complexity bound, or a hardness result. Bit (a) therefore fails before a continuous analogue can be anchored to a computational result. A computational task built around continuous share mass would be a new project, not a mirror of the paper’s named results.
fails bit a — no named computational result to mirror
The paper’s named results characterize absolute fair, relative fair, \(k\)-pseudo-proportional, and proportional schemes; none is a computational result for a continuous mirror to cover.
This paper contains no named computational result of the kind required for an anchor. Theorem 1 characterizes absolute fair schemes; Theorem 2 characterizes relative fair schemes; Theorem 3 characterizes their intersection; and Corollary 1 singles out the proportional scheme. These are axiomatic characterization results, not claims that a computational problem is in P, NP-hard, FPT, or otherwise computationally classified.
So I can’t honestly state a continuous problem per qualifying anchor. The paper studies which reward sharing rules satisfy specified fairness axioms, rather than a computational task whose complexity might change when the population becomes continuous. A model of a continuum of shares could be imagined, but it would require formulating a new computational problem and would not mirror one of the paper’s named results. The paper’s existing discussion of shares as the allocation units does not turn its axiomatic results into computational ones.
The proponent has no continuous computational anchor to defend. Theorem 1 characterizes absolute fair schemes, Theorem 2 characterizes relative fair schemes, Theorem 3 characterizes their intersection, and Corollary 1 singles out proportional rewards. All are axiomatic results. The paper states no complexity classification or algorithmic problem whose population version could supply a ChoCo mirror.
A large mining pool offers a plausible high-multiplicity setting: many miners may have the same relevant characteristics. But the paper’s allocation units are shares, and its awards depend on each share’s rank in an ordered round and on where the round ends. Aggregating miners by type does not preserve that history. One could instead describe a large round by a mass of shares indexed by normalized rank and define reward densities. That is a reasonable new continuum model, but it changes the paper’s “add one share” axioms into conditions on adding a positive mass. In the nonatomic limit, an individual share has zero mass; per-share awards and strict positivity need reinterpretation, and a fixed \(k\)-share cutoff in the pseudo-proportional family covers vanishing mass. Scaling those features to survive could be sensible, but the paper supplies no canonical scaling.
A computational question could be added—for example, checking whether a represented scheme satisfies the axioms, or optimizing a scheme subject to incentive constraints. Those would need a chosen encoding, input, and objective; the latter also adds constraints the paper does not analyze. Continuizing the population alone does not produce a complexity question from the stated characterizations.
So the strongest case against a ChoCo mirror is that the paper’s contribution is already axiomatic, while the natural continuous reformulation remains axiomatic too. I cannot rule out a worthwhile continuous mining-pool research project: large pools make the population regime plausible. The negative case is strong for “no computational mirror of this paper’s named results,” and weaker for the broader claim that no worthwhile continuous problem could be built from its setting.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.