{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NMEA2TYQY27SNHNOTUEINTPIBG","short_pith_number":"pith:NMEA2TYQ","schema_version":"1.0","canonical_sha256":"6b080d4f10c6bf269dae9d0886cde809a8d570fa4f24e144e03613c2b9263a8d","source":{"kind":"arxiv","id":"1703.04555","version":2},"attestation_state":"computed","paper":{"title":"Computing Kazhdan constants by semidefinite programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Koji Fujiwara, Yuichi Kabaya","submitted_at":"2017-03-13T21:30:44Z","abstract_excerpt":"Kazhdan constants of discrete groups are hard to compute and the actual constants are known only for several classes of groups. By solving a semidefinite programming problem by a computer, we obtain a lower bound of the Kazhdan constant of a discrete group. Positive lower bounds imply that the group has property (T). We study lattices on $\\tilde{A}_2$-buildings in detail. For $\\tilde{A}_2$-groups, our numerical bounds look identical to the known actual constants. That suggests that our approach is effective. For a family of groups, $G_1, \\cdots, G_4$, that are studied by Ronan, Tits and others"},"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":"1703.04555","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-13T21:30:44Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"898dc7ea5df241d573953280eba0539ca972722702725e9af75caa80e513f344","abstract_canon_sha256":"9665630e84df0379b548e8d483257ce7ebedfeb6dcdae06a9c6da3e252193a01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:09.132397Z","signature_b64":"JsPHKK5XABmnBlAO1Xijljb1EPqOMeuyoveYWM9ZkEiEz9U97zDkWaIhin5jrkhd1+4pEAAqa4B0/GXrZ+uJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b080d4f10c6bf269dae9d0886cde809a8d570fa4f24e144e03613c2b9263a8d","last_reissued_at":"2026-05-18T00:48:09.131835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:09.131835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Kazhdan constants by semidefinite programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Koji Fujiwara, Yuichi Kabaya","submitted_at":"2017-03-13T21:30:44Z","abstract_excerpt":"Kazhdan constants of discrete groups are hard to compute and the actual constants are known only for several classes of groups. By solving a semidefinite programming problem by a computer, we obtain a lower bound of the Kazhdan constant of a discrete group. Positive lower bounds imply that the group has property (T). We study lattices on $\\tilde{A}_2$-buildings in detail. For $\\tilde{A}_2$-groups, our numerical bounds look identical to the known actual constants. That suggests that our approach is effective. For a family of groups, $G_1, \\cdots, G_4$, that are studied by Ronan, Tits and others"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04555","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":"1703.04555","created_at":"2026-05-18T00:48:09.131924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.04555v2","created_at":"2026-05-18T00:48:09.131924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04555","created_at":"2026-05-18T00:48:09.131924+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMEA2TYQY27S","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMEA2TYQY27SNHNO","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMEA2TYQ","created_at":"2026-05-18T12:31:34.259226+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/NMEA2TYQY27SNHNOTUEINTPIBG","json":"https://pith.science/pith/NMEA2TYQY27SNHNOTUEINTPIBG.json","graph_json":"https://pith.science/api/pith-number/NMEA2TYQY27SNHNOTUEINTPIBG/graph.json","events_json":"https://pith.science/api/pith-number/NMEA2TYQY27SNHNOTUEINTPIBG/events.json","paper":"https://pith.science/paper/NMEA2TYQ"},"agent_actions":{"view_html":"https://pith.science/pith/NMEA2TYQY27SNHNOTUEINTPIBG","download_json":"https://pith.science/pith/NMEA2TYQY27SNHNOTUEINTPIBG.json","view_paper":"https://pith.science/paper/NMEA2TYQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.04555&json=true","fetch_graph":"https://pith.science/api/pith-number/NMEA2TYQY27SNHNOTUEINTPIBG/graph.json","fetch_events":"https://pith.science/api/pith-number/NMEA2TYQY27SNHNOTUEINTPIBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMEA2TYQY27SNHNOTUEINTPIBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMEA2TYQY27SNHNOTUEINTPIBG/action/storage_attestation","attest_author":"https://pith.science/pith/NMEA2TYQY27SNHNOTUEINTPIBG/action/author_attestation","sign_citation":"https://pith.science/pith/NMEA2TYQY27SNHNOTUEINTPIBG/action/citation_signature","submit_replication":"https://pith.science/pith/NMEA2TYQY27SNHNOTUEINTPIBG/action/replication_record"}},"created_at":"2026-05-18T00:48:09.131924+00:00","updated_at":"2026-05-18T00:48:09.131924+00:00"}