{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:Q6QM4EFTBVNS4FD5B5BZTBDPOY","short_pith_number":"pith:Q6QM4EFT","schema_version":"1.0","canonical_sha256":"87a0ce10b30d5b2e147d0f4399846f7606dc85d11e16b1d405649cfdbb5a074e","source":{"kind":"arxiv","id":"math/0703151","version":2},"attestation_state":"computed","paper":{"title":"On the properties of the exchange graph of a cluster algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.CO","authors_text":"Alek Vainshtein, Michael Gekhtman, Michael Shapiro","submitted_at":"2007-03-06T13:02:13Z","abstract_excerpt":"We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra $\\A$ in two cases: when $\\A$ is of geometric type and when $\\A$ is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of $\\A$. Both conjectures were formulated recently by Fomin and Zelevinsky."},"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":"math/0703151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-03-06T13:02:13Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"915763dba0177243811bd83df94130800a1c7176236d97748f104163248424a4","abstract_canon_sha256":"8e9dea350adbd5fcce0649050cb35c92aec8dd4192c216c29786d2eae2899721"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:29.901564Z","signature_b64":"W3D0hH4LLJwOq/Goto0dvZ3EeNquMylJJCxtruJyMbhEC7CywZ/8VgybMIHPvozstYZvfh4ucoId1D1tE9T9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87a0ce10b30d5b2e147d0f4399846f7606dc85d11e16b1d405649cfdbb5a074e","last_reissued_at":"2026-05-18T01:14:29.900969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:29.900969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the properties of the exchange graph of a cluster algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.CO","authors_text":"Alek Vainshtein, Michael Gekhtman, Michael Shapiro","submitted_at":"2007-03-06T13:02:13Z","abstract_excerpt":"We prove a conjecture about the vertices and edges of the exchange graph of a cluster algebra $\\A$ in two cases: when $\\A$ is of geometric type and when $\\A$ is arbitrary and its exchange matrix is nondegenerate. In the second case we also prove that the exchange graph does not depend on the coefficients of $\\A$. Both conjectures were formulated recently by Fomin and Zelevinsky."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703151","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":"math/0703151","created_at":"2026-05-18T01:14:29.901054+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0703151v2","created_at":"2026-05-18T01:14:29.901054+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703151","created_at":"2026-05-18T01:14:29.901054+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q6QM4EFTBVNS","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q6QM4EFTBVNS4FD5","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q6QM4EFT","created_at":"2026-05-18T12:25:55.427421+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/Q6QM4EFTBVNS4FD5B5BZTBDPOY","json":"https://pith.science/pith/Q6QM4EFTBVNS4FD5B5BZTBDPOY.json","graph_json":"https://pith.science/api/pith-number/Q6QM4EFTBVNS4FD5B5BZTBDPOY/graph.json","events_json":"https://pith.science/api/pith-number/Q6QM4EFTBVNS4FD5B5BZTBDPOY/events.json","paper":"https://pith.science/paper/Q6QM4EFT"},"agent_actions":{"view_html":"https://pith.science/pith/Q6QM4EFTBVNS4FD5B5BZTBDPOY","download_json":"https://pith.science/pith/Q6QM4EFTBVNS4FD5B5BZTBDPOY.json","view_paper":"https://pith.science/paper/Q6QM4EFT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0703151&json=true","fetch_graph":"https://pith.science/api/pith-number/Q6QM4EFTBVNS4FD5B5BZTBDPOY/graph.json","fetch_events":"https://pith.science/api/pith-number/Q6QM4EFTBVNS4FD5B5BZTBDPOY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q6QM4EFTBVNS4FD5B5BZTBDPOY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q6QM4EFTBVNS4FD5B5BZTBDPOY/action/storage_attestation","attest_author":"https://pith.science/pith/Q6QM4EFTBVNS4FD5B5BZTBDPOY/action/author_attestation","sign_citation":"https://pith.science/pith/Q6QM4EFTBVNS4FD5B5BZTBDPOY/action/citation_signature","submit_replication":"https://pith.science/pith/Q6QM4EFTBVNS4FD5B5BZTBDPOY/action/replication_record"}},"created_at":"2026-05-18T01:14:29.901054+00:00","updated_at":"2026-05-18T01:14:29.901054+00:00"}