{"paper":{"title":"Mathematical Foundations for Peer-to-Peer Lattice Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO","math.PR"],"primary_cat":"cs.DC","authors_text":"Danil Gorinevski (cybiont GmbH, Sch\\\"ubelbach, Switzerland)","submitted_at":"2026-04-24T16:28:16Z","abstract_excerpt":"Five propositions on synchronous peer-to-peer computation on a grid graph in $\\mathbb{Z}^2$.\n  \\textbf{Proposition~1} gives three lower bounds: a transport-work bound $\\sum_i a_i \\ell_i \\ge W_1(\\mu,\\nu)$, a completion-depth bound $D_{\\min} \\ge r_\\mu$ on the support radius, and a compressive-reduction edge bound $|E'| \\ge \\operatorname{St}_G(\\operatorname{supp}(\\mu)\\cup\\{x_\\star\\})$. A negative result: for corner-sink dimension-order routing, the sink-trunk route-load functional has variance $\\Theta(f(1-f)P^2)$ under i.i.d.\\ Bernoulli activation, refuting $O(fP^{3/2})$ concentration.\n  \\textbf{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22832","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22832/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}