{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3YSGIA52SBQCPELMQCW3THWSOT","short_pith_number":"pith:3YSGIA52","schema_version":"1.0","canonical_sha256":"de246403ba906027916c80adb99ed274f88417fba8275d7e0c454b3b9fd56c5c","source":{"kind":"arxiv","id":"1306.1568","version":3},"attestation_state":"computed","paper":{"title":"Equilibrium and equivariant triangulations of some small covers with minimum number of vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Biplab Basak, Soumen Sarkar","submitted_at":"2013-06-06T22:32:43Z","abstract_excerpt":"Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal $\\mathbb{Z}_2^2$-equivariant triangulations of $2$-dimensional small covers. We discuss vertex minimal equilibrium triangulations of $\\mathbb{RP}^3 \\# \\mathbb{RP}^3$, $S^1 \\times \\mathbb{RP}^2$ and a nontrivial $S^1$ bundle over $\\mathbb{RP}^2$. We construct some nice equilibrium triangulations of the real projective space $\\mathbb{RP}^n$ with $2^n +n+1$ vertices. The main tool is the theory of small covers."},"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":"1306.1568","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-06-06T22:32:43Z","cross_cats_sorted":[],"title_canon_sha256":"920c5b0dcbb668fc3c2d3c0670a3708e77d6deac690514981f8535a0cfbe6765","abstract_canon_sha256":"467084dfa68f8574c7ef7ef9902c1b7b09490fcfe78707731a99d4b3ebb7ceb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:24.594060Z","signature_b64":"fnm8UhgBRpR8M3uFP1R8vEFdQ1anKeNb7x0hODnNVZCXY1kH3hn3btWno84YJ3w8hkGY12yKqbr9wi38IgLiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de246403ba906027916c80adb99ed274f88417fba8275d7e0c454b3b9fd56c5c","last_reissued_at":"2026-05-18T01:33:24.593562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:24.593562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equilibrium and equivariant triangulations of some small covers with minimum number of vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Biplab Basak, Soumen Sarkar","submitted_at":"2013-06-06T22:32:43Z","abstract_excerpt":"Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal $\\mathbb{Z}_2^2$-equivariant triangulations of $2$-dimensional small covers. We discuss vertex minimal equilibrium triangulations of $\\mathbb{RP}^3 \\# \\mathbb{RP}^3$, $S^1 \\times \\mathbb{RP}^2$ and a nontrivial $S^1$ bundle over $\\mathbb{RP}^2$. We construct some nice equilibrium triangulations of the real projective space $\\mathbb{RP}^n$ with $2^n +n+1$ vertices. The main tool is the theory of small covers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1568","kind":"arxiv","version":3},"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":"1306.1568","created_at":"2026-05-18T01:33:24.593637+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.1568v3","created_at":"2026-05-18T01:33:24.593637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1568","created_at":"2026-05-18T01:33:24.593637+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YSGIA52SBQC","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YSGIA52SBQCPELM","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YSGIA52","created_at":"2026-05-18T12:27:32.513160+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/3YSGIA52SBQCPELMQCW3THWSOT","json":"https://pith.science/pith/3YSGIA52SBQCPELMQCW3THWSOT.json","graph_json":"https://pith.science/api/pith-number/3YSGIA52SBQCPELMQCW3THWSOT/graph.json","events_json":"https://pith.science/api/pith-number/3YSGIA52SBQCPELMQCW3THWSOT/events.json","paper":"https://pith.science/paper/3YSGIA52"},"agent_actions":{"view_html":"https://pith.science/pith/3YSGIA52SBQCPELMQCW3THWSOT","download_json":"https://pith.science/pith/3YSGIA52SBQCPELMQCW3THWSOT.json","view_paper":"https://pith.science/paper/3YSGIA52","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.1568&json=true","fetch_graph":"https://pith.science/api/pith-number/3YSGIA52SBQCPELMQCW3THWSOT/graph.json","fetch_events":"https://pith.science/api/pith-number/3YSGIA52SBQCPELMQCW3THWSOT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YSGIA52SBQCPELMQCW3THWSOT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YSGIA52SBQCPELMQCW3THWSOT/action/storage_attestation","attest_author":"https://pith.science/pith/3YSGIA52SBQCPELMQCW3THWSOT/action/author_attestation","sign_citation":"https://pith.science/pith/3YSGIA52SBQCPELMQCW3THWSOT/action/citation_signature","submit_replication":"https://pith.science/pith/3YSGIA52SBQCPELMQCW3THWSOT/action/replication_record"}},"created_at":"2026-05-18T01:33:24.593637+00:00","updated_at":"2026-05-18T01:33:24.593637+00:00"}