{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MYPGJMK6624CZNCFCTBQDAMB4Z","short_pith_number":"pith:MYPGJMK6","schema_version":"1.0","canonical_sha256":"661e64b15ef6b82cb44514c3018181e679dde07706983284909e58727013c46e","source":{"kind":"arxiv","id":"1504.04187","version":1},"attestation_state":"computed","paper":{"title":"The complexity of balanced presentations and the Andrews-Curtis conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Martin R. Bridson","submitted_at":"2015-04-16T11:32:45Z","abstract_excerpt":"Motivated by problems in topology, we explore the complexity of balanced group presentations. We obtain large lower bounds on the complexity of Andrews-Curtis trivialisations, beginning in rank 4. Our results are based on a new understanding of how Dehn functions of groups behave under certain kinds of push-outs.\n  We consider groups $S$ with presentations of deficiency 1 satisfying certain technical conditions and construct balanced group presentations $\\P_w$ indexed by words $w$ in the generators of $S$. If $w=1$ in $S$ then $\\P_w$ is Andrews-Curtis trivialisable and the number of Andrews-Cu"},"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":"1504.04187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-16T11:32:45Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"e214a37bfa04ae739fb3633d9dafb21561da44b403c966e774e812cfa75f8bf0","abstract_canon_sha256":"6bf4a3565fa061a87ece5a0c2cd2c5b99db4cef4ec464f0e1a1cf6ab66aee9d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:39.533072Z","signature_b64":"4C/sW4UYwP+SAacgmEu8+tv0Fx7QLMmnL8rwtNT7Ik/Q6JuMVN8j0hrXK48GUBraL11kfHymw0Q8WohCXsjWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"661e64b15ef6b82cb44514c3018181e679dde07706983284909e58727013c46e","last_reissued_at":"2026-05-18T02:18:39.532382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:39.532382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The complexity of balanced presentations and the Andrews-Curtis conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Martin R. Bridson","submitted_at":"2015-04-16T11:32:45Z","abstract_excerpt":"Motivated by problems in topology, we explore the complexity of balanced group presentations. We obtain large lower bounds on the complexity of Andrews-Curtis trivialisations, beginning in rank 4. Our results are based on a new understanding of how Dehn functions of groups behave under certain kinds of push-outs.\n  We consider groups $S$ with presentations of deficiency 1 satisfying certain technical conditions and construct balanced group presentations $\\P_w$ indexed by words $w$ in the generators of $S$. If $w=1$ in $S$ then $\\P_w$ is Andrews-Curtis trivialisable and the number of Andrews-Cu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04187","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":"1504.04187","created_at":"2026-05-18T02:18:39.532515+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04187v1","created_at":"2026-05-18T02:18:39.532515+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04187","created_at":"2026-05-18T02:18:39.532515+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYPGJMK6624C","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYPGJMK6624CZNCF","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYPGJMK6","created_at":"2026-05-18T12:29:32.376354+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/MYPGJMK6624CZNCFCTBQDAMB4Z","json":"https://pith.science/pith/MYPGJMK6624CZNCFCTBQDAMB4Z.json","graph_json":"https://pith.science/api/pith-number/MYPGJMK6624CZNCFCTBQDAMB4Z/graph.json","events_json":"https://pith.science/api/pith-number/MYPGJMK6624CZNCFCTBQDAMB4Z/events.json","paper":"https://pith.science/paper/MYPGJMK6"},"agent_actions":{"view_html":"https://pith.science/pith/MYPGJMK6624CZNCFCTBQDAMB4Z","download_json":"https://pith.science/pith/MYPGJMK6624CZNCFCTBQDAMB4Z.json","view_paper":"https://pith.science/paper/MYPGJMK6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04187&json=true","fetch_graph":"https://pith.science/api/pith-number/MYPGJMK6624CZNCFCTBQDAMB4Z/graph.json","fetch_events":"https://pith.science/api/pith-number/MYPGJMK6624CZNCFCTBQDAMB4Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYPGJMK6624CZNCFCTBQDAMB4Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYPGJMK6624CZNCFCTBQDAMB4Z/action/storage_attestation","attest_author":"https://pith.science/pith/MYPGJMK6624CZNCFCTBQDAMB4Z/action/author_attestation","sign_citation":"https://pith.science/pith/MYPGJMK6624CZNCFCTBQDAMB4Z/action/citation_signature","submit_replication":"https://pith.science/pith/MYPGJMK6624CZNCFCTBQDAMB4Z/action/replication_record"}},"created_at":"2026-05-18T02:18:39.532515+00:00","updated_at":"2026-05-18T02:18:39.532515+00:00"}