{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:M5PH5PSS4X2FJSNA4Q6EC3QUQK","short_pith_number":"pith:M5PH5PSS","schema_version":"1.0","canonical_sha256":"675e7ebe52e5f454c9a0e43c416e1482a3e7e1a77d119d7686498bcfeab7e1e0","source":{"kind":"arxiv","id":"1511.06758","version":2},"attestation_state":"computed","paper":{"title":"A note on nonabelian Freiman-Ruzsa","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Sean Eberhard","submitted_at":"2015-11-20T17:12:55Z","abstract_excerpt":"Recently Breuillard and Tointon showed that one reasonable formulation of the polynomial Freiman-Ruzsa conjecture fails for nonabelian groups. We improve and simplify their construction."},"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":"1511.06758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-11-20T17:12:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e77aca94856197ed3f9fc8f5bb6bf0a14b6af0afa832c2dc94d186612df000fc","abstract_canon_sha256":"9a1afc1c65a7a983744a0aebcd7d7d6d91d49d022bd12f209cca5dd602fc4cf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:09.095220Z","signature_b64":"wVE80s2WNPiQqFlVR2kFAOdgoKChhCvO+murJcC4qI4ibgsta6WYD/lGx3F9bsKfAy+OX9ljyXq6vjmI88UnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"675e7ebe52e5f454c9a0e43c416e1482a3e7e1a77d119d7686498bcfeab7e1e0","last_reissued_at":"2026-05-18T01:26:09.094578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:09.094578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on nonabelian Freiman-Ruzsa","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Sean Eberhard","submitted_at":"2015-11-20T17:12:55Z","abstract_excerpt":"Recently Breuillard and Tointon showed that one reasonable formulation of the polynomial Freiman-Ruzsa conjecture fails for nonabelian groups. We improve and simplify their construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06758","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":"1511.06758","created_at":"2026-05-18T01:26:09.094691+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.06758v2","created_at":"2026-05-18T01:26:09.094691+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06758","created_at":"2026-05-18T01:26:09.094691+00:00"},{"alias_kind":"pith_short_12","alias_value":"M5PH5PSS4X2F","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"M5PH5PSS4X2FJSNA","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"M5PH5PSS","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/M5PH5PSS4X2FJSNA4Q6EC3QUQK","json":"https://pith.science/pith/M5PH5PSS4X2FJSNA4Q6EC3QUQK.json","graph_json":"https://pith.science/api/pith-number/M5PH5PSS4X2FJSNA4Q6EC3QUQK/graph.json","events_json":"https://pith.science/api/pith-number/M5PH5PSS4X2FJSNA4Q6EC3QUQK/events.json","paper":"https://pith.science/paper/M5PH5PSS"},"agent_actions":{"view_html":"https://pith.science/pith/M5PH5PSS4X2FJSNA4Q6EC3QUQK","download_json":"https://pith.science/pith/M5PH5PSS4X2FJSNA4Q6EC3QUQK.json","view_paper":"https://pith.science/paper/M5PH5PSS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.06758&json=true","fetch_graph":"https://pith.science/api/pith-number/M5PH5PSS4X2FJSNA4Q6EC3QUQK/graph.json","fetch_events":"https://pith.science/api/pith-number/M5PH5PSS4X2FJSNA4Q6EC3QUQK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M5PH5PSS4X2FJSNA4Q6EC3QUQK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M5PH5PSS4X2FJSNA4Q6EC3QUQK/action/storage_attestation","attest_author":"https://pith.science/pith/M5PH5PSS4X2FJSNA4Q6EC3QUQK/action/author_attestation","sign_citation":"https://pith.science/pith/M5PH5PSS4X2FJSNA4Q6EC3QUQK/action/citation_signature","submit_replication":"https://pith.science/pith/M5PH5PSS4X2FJSNA4Q6EC3QUQK/action/replication_record"}},"created_at":"2026-05-18T01:26:09.094691+00:00","updated_at":"2026-05-18T01:26:09.094691+00:00"}