{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YOX5GFB4DLUMAAG5WD6V5A2F7Z","short_pith_number":"pith:YOX5GFB4","schema_version":"1.0","canonical_sha256":"c3afd3143c1ae8c000ddb0fd5e8345fe533d222206e18da9067f19c134bfd96d","source":{"kind":"arxiv","id":"1305.3903","version":1},"attestation_state":"computed","paper":{"title":"Semigroup identities in the monoid of triangular tropical matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Zur Izhakian","submitted_at":"2013-05-16T19:48:17Z","abstract_excerpt":"We show that the submonoid of all nxn triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities."},"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":"1305.3903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-16T19:48:17Z","cross_cats_sorted":[],"title_canon_sha256":"3d840a37055768129613b641554f3298a6c6af4881b099debd2a6d740b4befd6","abstract_canon_sha256":"8adfe59c14d9464828abdfc92a0b96352ca04ac0f877bcb4454f162249be3054"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:33.713432Z","signature_b64":"5hlyplRGFIs+5vJPsJfW1EMsUI1egwYSvhMElC6EGrk6evAGcLUhTPU3IsNDdOYm/5z7IlgKK/+NvJ9H81l1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3afd3143c1ae8c000ddb0fd5e8345fe533d222206e18da9067f19c134bfd96d","last_reissued_at":"2026-05-18T03:25:33.712971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:33.712971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semigroup identities in the monoid of triangular tropical matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Zur Izhakian","submitted_at":"2013-05-16T19:48:17Z","abstract_excerpt":"We show that the submonoid of all nxn triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3903","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":""},"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":"1305.3903","created_at":"2026-05-18T03:25:33.713038+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.3903v1","created_at":"2026-05-18T03:25:33.713038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3903","created_at":"2026-05-18T03:25:33.713038+00:00"},{"alias_kind":"pith_short_12","alias_value":"YOX5GFB4DLUM","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YOX5GFB4DLUMAAG5","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YOX5GFB4","created_at":"2026-05-18T12:28:09.283467+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/YOX5GFB4DLUMAAG5WD6V5A2F7Z","json":"https://pith.science/pith/YOX5GFB4DLUMAAG5WD6V5A2F7Z.json","graph_json":"https://pith.science/api/pith-number/YOX5GFB4DLUMAAG5WD6V5A2F7Z/graph.json","events_json":"https://pith.science/api/pith-number/YOX5GFB4DLUMAAG5WD6V5A2F7Z/events.json","paper":"https://pith.science/paper/YOX5GFB4"},"agent_actions":{"view_html":"https://pith.science/pith/YOX5GFB4DLUMAAG5WD6V5A2F7Z","download_json":"https://pith.science/pith/YOX5GFB4DLUMAAG5WD6V5A2F7Z.json","view_paper":"https://pith.science/paper/YOX5GFB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.3903&json=true","fetch_graph":"https://pith.science/api/pith-number/YOX5GFB4DLUMAAG5WD6V5A2F7Z/graph.json","fetch_events":"https://pith.science/api/pith-number/YOX5GFB4DLUMAAG5WD6V5A2F7Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YOX5GFB4DLUMAAG5WD6V5A2F7Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YOX5GFB4DLUMAAG5WD6V5A2F7Z/action/storage_attestation","attest_author":"https://pith.science/pith/YOX5GFB4DLUMAAG5WD6V5A2F7Z/action/author_attestation","sign_citation":"https://pith.science/pith/YOX5GFB4DLUMAAG5WD6V5A2F7Z/action/citation_signature","submit_replication":"https://pith.science/pith/YOX5GFB4DLUMAAG5WD6V5A2F7Z/action/replication_record"}},"created_at":"2026-05-18T03:25:33.713038+00:00","updated_at":"2026-05-18T03:25:33.713038+00:00"}