{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3ECM5TAPN33PYU2TQCPFEZT5CE","short_pith_number":"pith:3ECM5TAP","schema_version":"1.0","canonical_sha256":"d904cecc0f6ef6fc5353809e52667d11371cdefe8d1300e888815afb5f7e9307","source":{"kind":"arxiv","id":"1308.4250","version":3},"attestation_state":"computed","paper":{"title":"A finitely presented group of piecewise projective homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Justin Tatch Moore, Yash Lodha","submitted_at":"2013-08-20T08:21:46Z","abstract_excerpt":"In this article we will describe a finitely presented subgroup of Monod's group of piecewise projective homeomorphisms of R. This in particular provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian free subgroup. It is in fact the first such example which is torsion free. We will also develop a means for representing the elements of the group by labeled tree diagrams in a manner which closely parallels Richard Thompson's group F."},"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":"1308.4250","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-20T08:21:46Z","cross_cats_sorted":[],"title_canon_sha256":"01971e9f7e19cf15e2c037ea01ba0dcc849c43344ac655a8351d27e7e27e545e","abstract_canon_sha256":"d14451f1b5460caebfd4c8d653abe2009ee66a6263e4f0d76d976b9716446207"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:04.631604Z","signature_b64":"v33VVT1aYws8T6LaJJ8RF1p5Ka0rl2znqBeankSR/9cJLjIJQOyK118G1GWW3OAkCeb0Euzm0bewkNfzEtqpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d904cecc0f6ef6fc5353809e52667d11371cdefe8d1300e888815afb5f7e9307","last_reissued_at":"2026-05-18T02:46:04.630971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:04.630971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A finitely presented group of piecewise projective homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Justin Tatch Moore, Yash Lodha","submitted_at":"2013-08-20T08:21:46Z","abstract_excerpt":"In this article we will describe a finitely presented subgroup of Monod's group of piecewise projective homeomorphisms of R. This in particular provides a new example of a finitely presented group which is nonamenable and yet does not contain a nonabelian free subgroup. It is in fact the first such example which is torsion free. We will also develop a means for representing the elements of the group by labeled tree diagrams in a manner which closely parallels Richard Thompson's group F."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4250","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":"1308.4250","created_at":"2026-05-18T02:46:04.631053+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.4250v3","created_at":"2026-05-18T02:46:04.631053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4250","created_at":"2026-05-18T02:46:04.631053+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ECM5TAPN33P","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ECM5TAPN33PYU2T","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ECM5TAP","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/3ECM5TAPN33PYU2TQCPFEZT5CE","json":"https://pith.science/pith/3ECM5TAPN33PYU2TQCPFEZT5CE.json","graph_json":"https://pith.science/api/pith-number/3ECM5TAPN33PYU2TQCPFEZT5CE/graph.json","events_json":"https://pith.science/api/pith-number/3ECM5TAPN33PYU2TQCPFEZT5CE/events.json","paper":"https://pith.science/paper/3ECM5TAP"},"agent_actions":{"view_html":"https://pith.science/pith/3ECM5TAPN33PYU2TQCPFEZT5CE","download_json":"https://pith.science/pith/3ECM5TAPN33PYU2TQCPFEZT5CE.json","view_paper":"https://pith.science/paper/3ECM5TAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.4250&json=true","fetch_graph":"https://pith.science/api/pith-number/3ECM5TAPN33PYU2TQCPFEZT5CE/graph.json","fetch_events":"https://pith.science/api/pith-number/3ECM5TAPN33PYU2TQCPFEZT5CE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ECM5TAPN33PYU2TQCPFEZT5CE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ECM5TAPN33PYU2TQCPFEZT5CE/action/storage_attestation","attest_author":"https://pith.science/pith/3ECM5TAPN33PYU2TQCPFEZT5CE/action/author_attestation","sign_citation":"https://pith.science/pith/3ECM5TAPN33PYU2TQCPFEZT5CE/action/citation_signature","submit_replication":"https://pith.science/pith/3ECM5TAPN33PYU2TQCPFEZT5CE/action/replication_record"}},"created_at":"2026-05-18T02:46:04.631053+00:00","updated_at":"2026-05-18T02:46:04.631053+00:00"}