{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EU5U23PYBD3RPNOIYF6DGR2Q2L","short_pith_number":"pith:EU5U23PY","schema_version":"1.0","canonical_sha256":"253b4d6df808f717b5c8c17c334750d2ea3e03b73584132ac1c047c1a9cdedbb","source":{"kind":"arxiv","id":"1403.3516","version":2},"attestation_state":"computed","paper":{"title":"A sharp threshold for collapse of the random triangular group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Ehud Friedgut, Sylwia Antoniuk, Tomasz {\\L}uczak","submitted_at":"2014-03-14T09:47:56Z","abstract_excerpt":"The random triangular group $\\Gamma(n,p)$ is the group given by a random group presentation with $n$ generators in which every relator of length three is present independently with probability $p$. We show that in the evolution of $\\Gamma(n,p)$ the property of collapsing to the trivial group admits a very sharp threshold."},"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":"1403.3516","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-14T09:47:56Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"63edbb49dcb7728c73db95190b617f854bd01d64ed144bae950905549e44404b","abstract_canon_sha256":"cf066623efe964092ecc361ccf074bfa653f8cf5dc3b08d7fcd6c24c023ba439"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:44.547067Z","signature_b64":"V8n3JU3c6TIP9mMoX3We4Ci/msGOmP6W+8lVMBYitzv82U8mlEs+ukcR1wUZmsMqi1l6rwQlSbMHmtXqajeACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"253b4d6df808f717b5c8c17c334750d2ea3e03b73584132ac1c047c1a9cdedbb","last_reissued_at":"2026-05-18T00:57:44.546412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:44.546412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp threshold for collapse of the random triangular group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Ehud Friedgut, Sylwia Antoniuk, Tomasz {\\L}uczak","submitted_at":"2014-03-14T09:47:56Z","abstract_excerpt":"The random triangular group $\\Gamma(n,p)$ is the group given by a random group presentation with $n$ generators in which every relator of length three is present independently with probability $p$. We show that in the evolution of $\\Gamma(n,p)$ the property of collapsing to the trivial group admits a very sharp threshold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3516","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":"1403.3516","created_at":"2026-05-18T00:57:44.546524+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.3516v2","created_at":"2026-05-18T00:57:44.546524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3516","created_at":"2026-05-18T00:57:44.546524+00:00"},{"alias_kind":"pith_short_12","alias_value":"EU5U23PYBD3R","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"EU5U23PYBD3RPNOI","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"EU5U23PY","created_at":"2026-05-18T12:28:28.263976+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/EU5U23PYBD3RPNOIYF6DGR2Q2L","json":"https://pith.science/pith/EU5U23PYBD3RPNOIYF6DGR2Q2L.json","graph_json":"https://pith.science/api/pith-number/EU5U23PYBD3RPNOIYF6DGR2Q2L/graph.json","events_json":"https://pith.science/api/pith-number/EU5U23PYBD3RPNOIYF6DGR2Q2L/events.json","paper":"https://pith.science/paper/EU5U23PY"},"agent_actions":{"view_html":"https://pith.science/pith/EU5U23PYBD3RPNOIYF6DGR2Q2L","download_json":"https://pith.science/pith/EU5U23PYBD3RPNOIYF6DGR2Q2L.json","view_paper":"https://pith.science/paper/EU5U23PY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.3516&json=true","fetch_graph":"https://pith.science/api/pith-number/EU5U23PYBD3RPNOIYF6DGR2Q2L/graph.json","fetch_events":"https://pith.science/api/pith-number/EU5U23PYBD3RPNOIYF6DGR2Q2L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EU5U23PYBD3RPNOIYF6DGR2Q2L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EU5U23PYBD3RPNOIYF6DGR2Q2L/action/storage_attestation","attest_author":"https://pith.science/pith/EU5U23PYBD3RPNOIYF6DGR2Q2L/action/author_attestation","sign_citation":"https://pith.science/pith/EU5U23PYBD3RPNOIYF6DGR2Q2L/action/citation_signature","submit_replication":"https://pith.science/pith/EU5U23PYBD3RPNOIYF6DGR2Q2L/action/replication_record"}},"created_at":"2026-05-18T00:57:44.546524+00:00","updated_at":"2026-05-18T00:57:44.546524+00:00"}