{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YOLRXKIYUX32W7LYTG5UZ4JSSZ","short_pith_number":"pith:YOLRXKIY","schema_version":"1.0","canonical_sha256":"c3971ba918a5f7ab7d7899bb4cf1329651466c1dbfe0a4e136848116b4d74077","source":{"kind":"arxiv","id":"2608.10616","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.10616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-08-11T07:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"1d713ca909fa1b09e30b71c9320b53d1544381e151256851f9cbe49e08295ef4","abstract_canon_sha256":"8fa64d340c6dc9137eac57e20d54026e8e1b412b3abc15e72190756cb2610191"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:22:52.264088Z","signature_b64":"dcLnNB/QkXH7J+MCNSDrp5v/BHjtfJPQA9MRRBKrHJC54pRQ9E+K4ucEzdBnkh7jBGcSFhMyoZjyWpaq+RSfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3971ba918a5f7ab7d7899bb4cf1329651466c1dbfe0a4e136848116b4d74077","last_reissued_at":"2026-08-12T01:22:52.262329Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:22:52.262329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.10616","created_at":"2026-08-12T01:22:52.266137+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.10616v1","created_at":"2026-08-12T01:22:52.266137+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10616","created_at":"2026-08-12T01:22:52.266137+00:00"},{"alias_kind":"pith_short_12","alias_value":"YOLRXKIYUX32","created_at":"2026-08-12T01:22:52.266137+00:00"},{"alias_kind":"pith_short_16","alias_value":"YOLRXKIYUX32W7LY","created_at":"2026-08-12T01:22:52.266137+00:00"},{"alias_kind":"pith_short_8","alias_value":"YOLRXKIY","created_at":"2026-08-12T01:22:52.266137+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ","json":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ.json","graph_json":"https://pith.science/api/pith-number/YOLRXKIYUX32W7LYTG5UZ4JSSZ/graph.json","events_json":"https://pith.science/api/pith-number/YOLRXKIYUX32W7LYTG5UZ4JSSZ/events.json","paper":"https://pith.science/paper/YOLRXKIY"},"agent_actions":{"view_html":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ","download_json":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ.json","view_paper":"https://pith.science/paper/YOLRXKIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.10616&json=true","fetch_graph":"https://pith.science/api/pith-number/YOLRXKIYUX32W7LYTG5UZ4JSSZ/graph.json","fetch_events":"https://pith.science/api/pith-number/YOLRXKIYUX32W7LYTG5UZ4JSSZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ/action/storage_attestation","attest_author":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ/action/author_attestation","sign_citation":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ/action/citation_signature","submit_replication":"https://pith.science/pith/YOLRXKIYUX32W7LYTG5UZ4JSSZ/action/replication_record"}},"created_at":"2026-08-12T01:22:52.266137+00:00","updated_at":"2026-08-12T01:22:52.266137+00:00"}