{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:KOODY2GYFBVS5RJ7SAJ77C23VA","short_pith_number":"pith:KOODY2GY","schema_version":"1.0","canonical_sha256":"539c3c68d8286b2ec53f9013ff8b5ba814f343c946ef84261aa0d153009ce262","source":{"kind":"arxiv","id":"1201.0660","version":3},"attestation_state":"computed","paper":{"title":"Stable complexity and simplicial volume of manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Bruno Martelli, Roberto Frigerio, Stefano Francaviglia","submitted_at":"2012-01-03T15:16:59Z","abstract_excerpt":"Let the complexity of a closed manifold M be the minimal number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with respect to finite coverings, and by taking the infimum on all finite coverings of M normalized by the covering degree we can promote it to a multiplicative invariant, a characteristic number already considered by Milnor and Thurston, which call the \"stable complexity\" of M.\n  We study here the relation between the stable complexity of M and Gromov's simplicial volume ||M||. It is immediate to show that ||M|| is smaller or equal than the stable "},"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":"1201.0660","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-03T15:16:59Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"e43914e1470675dd89225c7abdea0f8f6487023d09037bb275df1278ade05d4b","abstract_canon_sha256":"df2e6d9b9cb1666f90a982a1619fb9dfb7e977ea3714feb1911b16c6ede22922"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:53.911371Z","signature_b64":"Lc8WrlP+H3bm/fh7gQNw5Zcnczs7QUu53XN1umDOWptuUREpdSnEiHXSyfGchqFHnsZw8bjmvpZFqkf+gBuUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"539c3c68d8286b2ec53f9013ff8b5ba814f343c946ef84261aa0d153009ce262","last_reissued_at":"2026-05-18T02:57:53.910668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:53.910668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable complexity and simplicial volume of manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Bruno Martelli, Roberto Frigerio, Stefano Francaviglia","submitted_at":"2012-01-03T15:16:59Z","abstract_excerpt":"Let the complexity of a closed manifold M be the minimal number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with respect to finite coverings, and by taking the infimum on all finite coverings of M normalized by the covering degree we can promote it to a multiplicative invariant, a characteristic number already considered by Milnor and Thurston, which call the \"stable complexity\" of M.\n  We study here the relation between the stable complexity of M and Gromov's simplicial volume ||M||. It is immediate to show that ||M|| is smaller or equal than the stable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0660","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":"1201.0660","created_at":"2026-05-18T02:57:53.910787+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.0660v3","created_at":"2026-05-18T02:57:53.910787+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0660","created_at":"2026-05-18T02:57:53.910787+00:00"},{"alias_kind":"pith_short_12","alias_value":"KOODY2GYFBVS","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KOODY2GYFBVS5RJ7","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KOODY2GY","created_at":"2026-05-18T12:27:11.947152+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/KOODY2GYFBVS5RJ7SAJ77C23VA","json":"https://pith.science/pith/KOODY2GYFBVS5RJ7SAJ77C23VA.json","graph_json":"https://pith.science/api/pith-number/KOODY2GYFBVS5RJ7SAJ77C23VA/graph.json","events_json":"https://pith.science/api/pith-number/KOODY2GYFBVS5RJ7SAJ77C23VA/events.json","paper":"https://pith.science/paper/KOODY2GY"},"agent_actions":{"view_html":"https://pith.science/pith/KOODY2GYFBVS5RJ7SAJ77C23VA","download_json":"https://pith.science/pith/KOODY2GYFBVS5RJ7SAJ77C23VA.json","view_paper":"https://pith.science/paper/KOODY2GY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.0660&json=true","fetch_graph":"https://pith.science/api/pith-number/KOODY2GYFBVS5RJ7SAJ77C23VA/graph.json","fetch_events":"https://pith.science/api/pith-number/KOODY2GYFBVS5RJ7SAJ77C23VA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KOODY2GYFBVS5RJ7SAJ77C23VA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KOODY2GYFBVS5RJ7SAJ77C23VA/action/storage_attestation","attest_author":"https://pith.science/pith/KOODY2GYFBVS5RJ7SAJ77C23VA/action/author_attestation","sign_citation":"https://pith.science/pith/KOODY2GYFBVS5RJ7SAJ77C23VA/action/citation_signature","submit_replication":"https://pith.science/pith/KOODY2GYFBVS5RJ7SAJ77C23VA/action/replication_record"}},"created_at":"2026-05-18T02:57:53.910787+00:00","updated_at":"2026-05-18T02:57:53.910787+00:00"}