{"ID":6023547,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T12:15:05.826495187Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.06197","arxiv_id":"2607.06197","title":"Slack and Budget Breaking in Threshold Team Production","abstract":"A threshold system completes a public task only after $κ$ verifiable shares are publicly committed. If the honest schedule creates \\( \\Nstar=κ+Δ\\) share opportunities by deadline $t^\\star$, then $Δ$ shares are slack such that a coalition delays completion if and only if it withholds at least $Δ+1$ shares. The incentive problem is therefore to price the cheapest sabotage set. Agents receive a direct fee $f$ per committed share. A delaying coalition may also obtain delay value at most $L$, and may earn additional fee revenue during recovery after the deadline. Let $R_1^+$ be a pathwise upper bound on the coalition's incremental fee revenue in a recovery slot that completes the task, including any same-slot overshoot. The principal can post a nonnegative completion bounty that depends only on committed shares, uses no deposits or punishments, and expires if completion is late. The optimal rule is uniform, as if completion occurs by $t^\\star$, every admissible horizon share receives $B/\\Nstar$, otherwise no bounty is paid. Full participation is ex-post strongly delay proof exactly when \\( (Δ+1)f+\\frac{Δ+1}{\\Nstar}B \\ge L+R_1^+ . \\) Equivalently, the exact worst-case budget is \\( B^\\star = \\frac{\\Nstar}{Δ+1} \\bigl(L+R_1^+-(Δ+1)f\\bigr)^+ . \\) The bound is tight for every nonnegative completion measurable bounty, among the $\\Nstar$ horizon shares, some $Δ+1$ receive total bounty at most $(Δ+1)B/\\Nstar$, and withholding precisely those shares delays completion. The result applies to threshold signatures, data availability certification, coded dissemination, and generic $k$-of-$n$ completion tasks. We also isolate a separate limit, no transfer rule based only on completed shares can remove a final slot race in which a coalition has already observed enough pre-completion shares to act.","short_abstract":"A threshold system completes a public task only after $κ$ verifiable shares are publicly committed. If the honest schedule creates \\( \\Nstar=κ+Δ\\) share opportunities by deadline $t^\\star$, then $Δ$ shares are slack such that a coalition delays completion if and only if it withholds at least $Δ+1$ shares. The incentive...","url_abs":"https://arxiv.org/abs/2607.06197","url_pdf":"https://arxiv.org/pdf/2607.06197v1","authors":"[\"Benjamin Marsh\",\"Alejandro Ranchal-Pedrosa\"]","published":"2026-07-07T12:22:40Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}