{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:R4Z5FBTGVTTFKNQRMFSCGDLIRT","short_pith_number":"pith:R4Z5FBTG","schema_version":"1.0","canonical_sha256":"8f33d28666ace65536116164230d688ccfe24b1077135d69403fb182ce33a041","source":{"kind":"arxiv","id":"1412.7715","version":2},"attestation_state":"computed","paper":{"title":"Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Brita E. A. Nucinkis, Simon St John-Green","submitted_at":"2014-12-24T17:16:29Z","abstract_excerpt":"We study the group $QV$, the self-maps of the infinite $2$-edge coloured binary tree which preserve the edge and colour relations at cofinitely many locations. We introduce related groups $QF$, $QT$, $\\tilde{Q}T$, and $\\tilde{Q}V$, prove that $QF$, $\\tilde{Q}T$, and $\\tilde{Q}V$ are of type $\\mathrm{F}_\\infty$, and calculate finite presentations for them. We calculate the normal subgroup structure and rational homology of all $5$ groups, the Bieri--Neumann--Strebel--Renz invariants of $QF$, and discuss the relationship of all $5$ groups with other generalisations of Thompson's groups."},"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":"1412.7715","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-24T17:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"aec2afee02a66fa0b349181a50641f6cd7e46603b839de796a9384eb488c2869","abstract_canon_sha256":"10371dd5edb0966383fadc6e2c252f141e3606cf8ef96969c8345c32935c81e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:53.207723Z","signature_b64":"ne8FYBwnGKbmJHlsuzlE00Hdmhgeru4OI2nqIKkn8wJV9wHNjM533IHvNCj8LXh5IHPYodHz5oh5TXN2saRtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f33d28666ace65536116164230d688ccfe24b1077135d69403fb182ce33a041","last_reissued_at":"2026-05-18T00:39:53.207058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:53.207058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Brita E. A. Nucinkis, Simon St John-Green","submitted_at":"2014-12-24T17:16:29Z","abstract_excerpt":"We study the group $QV$, the self-maps of the infinite $2$-edge coloured binary tree which preserve the edge and colour relations at cofinitely many locations. We introduce related groups $QF$, $QT$, $\\tilde{Q}T$, and $\\tilde{Q}V$, prove that $QF$, $\\tilde{Q}T$, and $\\tilde{Q}V$ are of type $\\mathrm{F}_\\infty$, and calculate finite presentations for them. We calculate the normal subgroup structure and rational homology of all $5$ groups, the Bieri--Neumann--Strebel--Renz invariants of $QF$, and discuss the relationship of all $5$ groups with other generalisations of Thompson's groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7715","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":"1412.7715","created_at":"2026-05-18T00:39:53.207156+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.7715v2","created_at":"2026-05-18T00:39:53.207156+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7715","created_at":"2026-05-18T00:39:53.207156+00:00"},{"alias_kind":"pith_short_12","alias_value":"R4Z5FBTGVTTF","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"R4Z5FBTGVTTFKNQR","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"R4Z5FBTG","created_at":"2026-05-18T12:28:46.137349+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/R4Z5FBTGVTTFKNQRMFSCGDLIRT","json":"https://pith.science/pith/R4Z5FBTGVTTFKNQRMFSCGDLIRT.json","graph_json":"https://pith.science/api/pith-number/R4Z5FBTGVTTFKNQRMFSCGDLIRT/graph.json","events_json":"https://pith.science/api/pith-number/R4Z5FBTGVTTFKNQRMFSCGDLIRT/events.json","paper":"https://pith.science/paper/R4Z5FBTG"},"agent_actions":{"view_html":"https://pith.science/pith/R4Z5FBTGVTTFKNQRMFSCGDLIRT","download_json":"https://pith.science/pith/R4Z5FBTGVTTFKNQRMFSCGDLIRT.json","view_paper":"https://pith.science/paper/R4Z5FBTG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.7715&json=true","fetch_graph":"https://pith.science/api/pith-number/R4Z5FBTGVTTFKNQRMFSCGDLIRT/graph.json","fetch_events":"https://pith.science/api/pith-number/R4Z5FBTGVTTFKNQRMFSCGDLIRT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R4Z5FBTGVTTFKNQRMFSCGDLIRT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R4Z5FBTGVTTFKNQRMFSCGDLIRT/action/storage_attestation","attest_author":"https://pith.science/pith/R4Z5FBTGVTTFKNQRMFSCGDLIRT/action/author_attestation","sign_citation":"https://pith.science/pith/R4Z5FBTGVTTFKNQRMFSCGDLIRT/action/citation_signature","submit_replication":"https://pith.science/pith/R4Z5FBTGVTTFKNQRMFSCGDLIRT/action/replication_record"}},"created_at":"2026-05-18T00:39:53.207156+00:00","updated_at":"2026-05-18T00:39:53.207156+00:00"}