{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QABCDSGFSIWDNBXA7OWTOFIKLA","short_pith_number":"pith:QABCDSGF","schema_version":"1.0","canonical_sha256":"800221c8c5922c3686e0fbad37150a583b0ac76a248db8cc90b04cc50e17b089","source":{"kind":"arxiv","id":"1307.2853","version":2},"attestation_state":"computed","paper":{"title":"On the dimension of max-min convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Sergei Sergeev, Viorel Nitica","submitted_at":"2013-07-10T16:54:14Z","abstract_excerpt":"We introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity. We introduce a max-min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope. We describe the relation between this rank and the notion of strong regularity in max-min algebra, which is traditionally defined in terms of unique solvability of linear systems and trapezoidal property."},"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":"1307.2853","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-07-10T16:54:14Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fecb49d273a3337c4de65545dd84677c474162dab7ac3d068f15671bb3be8a84","abstract_canon_sha256":"50fbd78f5df099ba58c8d9d944f32b9fe28f65b330a03a37150dcaff63066c11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:39.100012Z","signature_b64":"QB/t/HeFT4ZJMxsr8r+oB9Z7CXV/ZoNW3Pl9dsfl+OGEcWjD10daFHK6f3FwlBh7ZL1UbejpWRiegAn4u20BAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"800221c8c5922c3686e0fbad37150a583b0ac76a248db8cc90b04cc50e17b089","last_reissued_at":"2026-05-17T23:50:39.099542Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:39.099542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the dimension of max-min convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Sergei Sergeev, Viorel Nitica","submitted_at":"2013-07-10T16:54:14Z","abstract_excerpt":"We introduce a notion of dimension of max-min convex sets, following the approach of tropical convexity. We introduce a max-min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope. We describe the relation between this rank and the notion of strong regularity in max-min algebra, which is traditionally defined in terms of unique solvability of linear systems and trapezoidal property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2853","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":"1307.2853","created_at":"2026-05-17T23:50:39.099605+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.2853v2","created_at":"2026-05-17T23:50:39.099605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2853","created_at":"2026-05-17T23:50:39.099605+00:00"},{"alias_kind":"pith_short_12","alias_value":"QABCDSGFSIWD","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QABCDSGFSIWDNBXA","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QABCDSGF","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/QABCDSGFSIWDNBXA7OWTOFIKLA","json":"https://pith.science/pith/QABCDSGFSIWDNBXA7OWTOFIKLA.json","graph_json":"https://pith.science/api/pith-number/QABCDSGFSIWDNBXA7OWTOFIKLA/graph.json","events_json":"https://pith.science/api/pith-number/QABCDSGFSIWDNBXA7OWTOFIKLA/events.json","paper":"https://pith.science/paper/QABCDSGF"},"agent_actions":{"view_html":"https://pith.science/pith/QABCDSGFSIWDNBXA7OWTOFIKLA","download_json":"https://pith.science/pith/QABCDSGFSIWDNBXA7OWTOFIKLA.json","view_paper":"https://pith.science/paper/QABCDSGF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.2853&json=true","fetch_graph":"https://pith.science/api/pith-number/QABCDSGFSIWDNBXA7OWTOFIKLA/graph.json","fetch_events":"https://pith.science/api/pith-number/QABCDSGFSIWDNBXA7OWTOFIKLA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QABCDSGFSIWDNBXA7OWTOFIKLA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QABCDSGFSIWDNBXA7OWTOFIKLA/action/storage_attestation","attest_author":"https://pith.science/pith/QABCDSGFSIWDNBXA7OWTOFIKLA/action/author_attestation","sign_citation":"https://pith.science/pith/QABCDSGFSIWDNBXA7OWTOFIKLA/action/citation_signature","submit_replication":"https://pith.science/pith/QABCDSGFSIWDNBXA7OWTOFIKLA/action/replication_record"}},"created_at":"2026-05-17T23:50:39.099605+00:00","updated_at":"2026-05-17T23:50:39.099605+00:00"}