{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PRPK2V6CCGAVHG5A6K5HEH6H6K","short_pith_number":"pith:PRPK2V6C","schema_version":"1.0","canonical_sha256":"7c5ead57c21181539ba0f2ba721fc7f29a5096dd7bf1d9f014d287a3e4a58b9e","source":{"kind":"arxiv","id":"1303.7451","version":2},"attestation_state":"computed","paper":{"title":"Tropical convexity over max-min semiring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Sergei Sergeev, Viorel Nitica","submitted_at":"2013-03-29T18:11:33Z","abstract_excerpt":"This is a survey on an analogue of tropical convexity developed over the max-min semiring, starting with the descriptions of max-min segments, semispaces, hyperplanes and an account of separation and non-separation results based on semispaces. There are some new results. In particular, we give new \"colorful\" extensions of the max-min Caratheodory theorem. In the end of the paper, we list some consequences of the topological Radon and Tverberg theorems (like Helly and Centerpoint theorems), valid over a more general class of max-T semirings, where multiplication is a triangular norm."},"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":"1303.7451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-03-29T18:11:33Z","cross_cats_sorted":[],"title_canon_sha256":"a85438a9ac21df06a62e47f96ac7fbb7e5ceb1e502a498e14784cc71773772eb","abstract_canon_sha256":"b591ff8c76768d06205023c8e1e25e851aef04c7fa5502be888fdac4de34148f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:39.111999Z","signature_b64":"clhQACyOEhw/4EUL5raz9ld9h8oGROfVzAlQYaZRTGEigzqv3TcB3bRvbG81IkczCJKVbnVaXiXmiOTqrDKCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c5ead57c21181539ba0f2ba721fc7f29a5096dd7bf1d9f014d287a3e4a58b9e","last_reissued_at":"2026-05-17T23:50:39.111589Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:39.111589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tropical convexity over max-min semiring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Sergei Sergeev, Viorel Nitica","submitted_at":"2013-03-29T18:11:33Z","abstract_excerpt":"This is a survey on an analogue of tropical convexity developed over the max-min semiring, starting with the descriptions of max-min segments, semispaces, hyperplanes and an account of separation and non-separation results based on semispaces. There are some new results. In particular, we give new \"colorful\" extensions of the max-min Caratheodory theorem. In the end of the paper, we list some consequences of the topological Radon and Tverberg theorems (like Helly and Centerpoint theorems), valid over a more general class of max-T semirings, where multiplication is a triangular norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7451","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.7451","created_at":"2026-05-17T23:50:39.111645+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.7451v2","created_at":"2026-05-17T23:50:39.111645+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7451","created_at":"2026-05-17T23:50:39.111645+00:00"},{"alias_kind":"pith_short_12","alias_value":"PRPK2V6CCGAV","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PRPK2V6CCGAVHG5A","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PRPK2V6C","created_at":"2026-05-18T12:27:54.935989+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/PRPK2V6CCGAVHG5A6K5HEH6H6K","json":"https://pith.science/pith/PRPK2V6CCGAVHG5A6K5HEH6H6K.json","graph_json":"https://pith.science/api/pith-number/PRPK2V6CCGAVHG5A6K5HEH6H6K/graph.json","events_json":"https://pith.science/api/pith-number/PRPK2V6CCGAVHG5A6K5HEH6H6K/events.json","paper":"https://pith.science/paper/PRPK2V6C"},"agent_actions":{"view_html":"https://pith.science/pith/PRPK2V6CCGAVHG5A6K5HEH6H6K","download_json":"https://pith.science/pith/PRPK2V6CCGAVHG5A6K5HEH6H6K.json","view_paper":"https://pith.science/paper/PRPK2V6C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.7451&json=true","fetch_graph":"https://pith.science/api/pith-number/PRPK2V6CCGAVHG5A6K5HEH6H6K/graph.json","fetch_events":"https://pith.science/api/pith-number/PRPK2V6CCGAVHG5A6K5HEH6H6K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PRPK2V6CCGAVHG5A6K5HEH6H6K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PRPK2V6CCGAVHG5A6K5HEH6H6K/action/storage_attestation","attest_author":"https://pith.science/pith/PRPK2V6CCGAVHG5A6K5HEH6H6K/action/author_attestation","sign_citation":"https://pith.science/pith/PRPK2V6CCGAVHG5A6K5HEH6H6K/action/citation_signature","submit_replication":"https://pith.science/pith/PRPK2V6CCGAVHG5A6K5HEH6H6K/action/replication_record"}},"created_at":"2026-05-17T23:50:39.111645+00:00","updated_at":"2026-05-17T23:50:39.111645+00:00"}