{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QKFCNYPQS6GKR45L66YTOKT5RT","short_pith_number":"pith:QKFCNYPQ","schema_version":"1.0","canonical_sha256":"828a26e1f0978ca8f3abf7b1372a7d8cd198ca45592d4f3cd897220960c70a56","source":{"kind":"arxiv","id":"1305.3906","version":1},"attestation_state":"computed","paper":{"title":"Algebraic structures of tropical mathematics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Louis Rowen, Manfred Knebusch, Zur Izhakian","submitted_at":"2013-05-16T19:57:03Z","abstract_excerpt":"Tropical mathematics often is defined over an ordered cancellative monoid $\\tM$, usually taken to be $(\\RR, +)$ or $(\\QQ, +)$. Although a rich theory has arisen from this viewpoint, cf. [L1], idempotent semirings possess a restricted algebraic structure theory, and also do not reflect certain valuation-theoretic properties, thereby forcing researchers to rely often on combinatoric techniques.\n  In this paper we describe an alternative structure, more compatible with valuation theory, studied by the authors over the past few years, that permits fuller use of algebraic theory especially in under"},"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":"1305.3906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-16T19:57:03Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"887ef1a0868ba916d4188a61ca5ab415c8322ab3399e432c409f1a82a3c3dc37","abstract_canon_sha256":"a74512aa6a0792e4ed0c00786412e3624ade3807447db8a92bf4c60ba22eb9fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:33.707147Z","signature_b64":"ZZkaTo7540imZb1FpNzSVnYiea+LbmIMwHFzhDfk8QBh1nJ0d8g0F33H+uBjyBwOH5CMCjkX8bZOAMJjSO5IAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"828a26e1f0978ca8f3abf7b1372a7d8cd198ca45592d4f3cd897220960c70a56","last_reissued_at":"2026-05-18T03:25:33.706642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:33.706642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic structures of tropical mathematics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Louis Rowen, Manfred Knebusch, Zur Izhakian","submitted_at":"2013-05-16T19:57:03Z","abstract_excerpt":"Tropical mathematics often is defined over an ordered cancellative monoid $\\tM$, usually taken to be $(\\RR, +)$ or $(\\QQ, +)$. Although a rich theory has arisen from this viewpoint, cf. [L1], idempotent semirings possess a restricted algebraic structure theory, and also do not reflect certain valuation-theoretic properties, thereby forcing researchers to rely often on combinatoric techniques.\n  In this paper we describe an alternative structure, more compatible with valuation theory, studied by the authors over the past few years, that permits fuller use of algebraic theory especially in under"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3906","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":"1305.3906","created_at":"2026-05-18T03:25:33.706708+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.3906v1","created_at":"2026-05-18T03:25:33.706708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3906","created_at":"2026-05-18T03:25:33.706708+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKFCNYPQS6GK","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKFCNYPQS6GKR45L","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKFCNYPQ","created_at":"2026-05-18T12:27:57.521954+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/QKFCNYPQS6GKR45L66YTOKT5RT","json":"https://pith.science/pith/QKFCNYPQS6GKR45L66YTOKT5RT.json","graph_json":"https://pith.science/api/pith-number/QKFCNYPQS6GKR45L66YTOKT5RT/graph.json","events_json":"https://pith.science/api/pith-number/QKFCNYPQS6GKR45L66YTOKT5RT/events.json","paper":"https://pith.science/paper/QKFCNYPQ"},"agent_actions":{"view_html":"https://pith.science/pith/QKFCNYPQS6GKR45L66YTOKT5RT","download_json":"https://pith.science/pith/QKFCNYPQS6GKR45L66YTOKT5RT.json","view_paper":"https://pith.science/paper/QKFCNYPQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.3906&json=true","fetch_graph":"https://pith.science/api/pith-number/QKFCNYPQS6GKR45L66YTOKT5RT/graph.json","fetch_events":"https://pith.science/api/pith-number/QKFCNYPQS6GKR45L66YTOKT5RT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKFCNYPQS6GKR45L66YTOKT5RT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKFCNYPQS6GKR45L66YTOKT5RT/action/storage_attestation","attest_author":"https://pith.science/pith/QKFCNYPQS6GKR45L66YTOKT5RT/action/author_attestation","sign_citation":"https://pith.science/pith/QKFCNYPQS6GKR45L66YTOKT5RT/action/citation_signature","submit_replication":"https://pith.science/pith/QKFCNYPQS6GKR45L66YTOKT5RT/action/replication_record"}},"created_at":"2026-05-18T03:25:33.706708+00:00","updated_at":"2026-05-18T03:25:33.706708+00:00"}