{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5LWPHV6IEWYK3WJRSSQBDPKZ6I","short_pith_number":"pith:5LWPHV6I","schema_version":"1.0","canonical_sha256":"eaecf3d7c825b0add93194a011bd59f237b329b8ed14c6431826f60eb141b5b9","source":{"kind":"arxiv","id":"1206.2260","version":1},"attestation_state":"computed","paper":{"title":"Flows on Simplicial Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Matthias Beck, Yvonne Kemper","submitted_at":"2012-06-11T15:39:04Z","abstract_excerpt":"Given a graph $G$, the number of nowhere-zero $\\ZZ_q$-flows $\\phi_G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero $\\ZZ_q$-flows to simplicial complexes $\\Delta$ of dimension greater than one, and prove the polynomiality of the corresponding function $\\phi_{\\Delta}(q)$ for certain $q$ and certain subclasses of simplicial complexes."},"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":"1206.2260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-06-11T15:39:04Z","cross_cats_sorted":[],"title_canon_sha256":"9ed2bbe9ba4262f9062803c4a45367542cb3b26f80f1efbc609a5c7cdfaff5d3","abstract_canon_sha256":"25cbfde360da65bde1f7b9024c402476ca02b64cd08cb605e30ce6f178fc3d4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.153212Z","signature_b64":"rW/D+8ymLC1yqddyMycCGMmIvud5cn/G/KJ1n8H+r6CtsLDtvq3IdtBYy5oyVXlRK+t/FONX6CVC4OMgRr6WCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eaecf3d7c825b0add93194a011bd59f237b329b8ed14c6431826f60eb141b5b9","last_reissued_at":"2026-05-18T03:11:24.152504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.152504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flows on Simplicial Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Matthias Beck, Yvonne Kemper","submitted_at":"2012-06-11T15:39:04Z","abstract_excerpt":"Given a graph $G$, the number of nowhere-zero $\\ZZ_q$-flows $\\phi_G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero $\\ZZ_q$-flows to simplicial complexes $\\Delta$ of dimension greater than one, and prove the polynomiality of the corresponding function $\\phi_{\\Delta}(q)$ for certain $q$ and certain subclasses of simplicial complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2260","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":"1206.2260","created_at":"2026-05-18T03:11:24.152618+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.2260v1","created_at":"2026-05-18T03:11:24.152618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2260","created_at":"2026-05-18T03:11:24.152618+00:00"},{"alias_kind":"pith_short_12","alias_value":"5LWPHV6IEWYK","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"5LWPHV6IEWYK3WJR","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"5LWPHV6I","created_at":"2026-05-18T12:26:56.085431+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/5LWPHV6IEWYK3WJRSSQBDPKZ6I","json":"https://pith.science/pith/5LWPHV6IEWYK3WJRSSQBDPKZ6I.json","graph_json":"https://pith.science/api/pith-number/5LWPHV6IEWYK3WJRSSQBDPKZ6I/graph.json","events_json":"https://pith.science/api/pith-number/5LWPHV6IEWYK3WJRSSQBDPKZ6I/events.json","paper":"https://pith.science/paper/5LWPHV6I"},"agent_actions":{"view_html":"https://pith.science/pith/5LWPHV6IEWYK3WJRSSQBDPKZ6I","download_json":"https://pith.science/pith/5LWPHV6IEWYK3WJRSSQBDPKZ6I.json","view_paper":"https://pith.science/paper/5LWPHV6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.2260&json=true","fetch_graph":"https://pith.science/api/pith-number/5LWPHV6IEWYK3WJRSSQBDPKZ6I/graph.json","fetch_events":"https://pith.science/api/pith-number/5LWPHV6IEWYK3WJRSSQBDPKZ6I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5LWPHV6IEWYK3WJRSSQBDPKZ6I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5LWPHV6IEWYK3WJRSSQBDPKZ6I/action/storage_attestation","attest_author":"https://pith.science/pith/5LWPHV6IEWYK3WJRSSQBDPKZ6I/action/author_attestation","sign_citation":"https://pith.science/pith/5LWPHV6IEWYK3WJRSSQBDPKZ6I/action/citation_signature","submit_replication":"https://pith.science/pith/5LWPHV6IEWYK3WJRSSQBDPKZ6I/action/replication_record"}},"created_at":"2026-05-18T03:11:24.152618+00:00","updated_at":"2026-05-18T03:11:24.152618+00:00"}