{"paper":{"title":"Valued Mosaics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Alessandro Linzi","submitted_at":"2026-08-11T07:58:38Z","abstract_excerpt":"Nakamura--Reyes showed that the category of commutative mosaics---unital reversible hypermagmas, without associativity---is complete, cocomplete, and has free objects, in contrast to commutative polygroups. Krasner's multivalued addition is designed around ultrametric balls; we take that valuation-theoretic motivation as primary and equip mosaics with valuations, as unit-reflecting unitary morphisms into the tropical polygroup $T(\\Gamma)$. Value-preserving morphisms form the slice over $T(\\Gamma)$, which is complete and cocomplete. The larger lax category of valued mosaics over a fixed ordered"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10616","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/2608.10616/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"}