{"paper":{"title":"Coloring Chains for Compression with Uncertain Priors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Noah Golowich","submitted_at":"2017-07-11T05:12:08Z","abstract_excerpt":"Haramaty and Sudan considered the problem of transmitting a message between two people, Alice and Bob, when Alice's and Bob's priors on the message are allowed to differ by at most a given factor. To find a deterministic compression scheme for this problem, they showed that it is sufficient to obtain an upper bound on the chromatic number of a graph, denoted $U(N,s,k)$ for parameters $N,s,k$, whose vertices are nested sequences of subsets and whose edges are between vertices that have similar sequences of sets. In turn, there is a close relationship between the problem of determining the chrom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03132","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}