{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:4T6YLAD7M25P5F7MAGXOM7UO5W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"548e8d180a7da86640f7547c050717f8d75725001b13dba24b01b038e45229f9","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.GR","submitted_at":"2004-02-12T16:04:03Z","title_canon_sha256":"8d37a4f021e85dc57375ea67a1c807fa8c09d1591e8d7dbbb18c3ab50da612c6"},"schema_version":"1.0","source":{"id":"math/0402205","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402205","created_at":"2026-05-18T03:55:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402205v1","created_at":"2026-05-18T03:55:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402205","created_at":"2026-05-18T03:55:35Z"},{"alias_kind":"pith_short_12","alias_value":"4T6YLAD7M25P","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"4T6YLAD7M25P5F7M","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"4T6YLAD7","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:a2aeab4167f8047222425f2684f9d18b74f030220e69a875a8e6fb29fd554e19","target":"graph","created_at":"2026-05-18T03:55:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that if the Cayley graph of a finitely generated group enjoys the property L_delta then the group is almost convex and has a sub-cubic isoperimetric function.","authors_text":"Murray Elder","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2004-02-12T16:04:03Z","title":"L_delta groups are almost convex and have a sub-cubic Dehn function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402205","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4706e24c6034196616e0137eb896da5e740f70cae5493a68a988ece6639936b6","target":"record","created_at":"2026-05-18T03:55:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"548e8d180a7da86640f7547c050717f8d75725001b13dba24b01b038e45229f9","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.GR","submitted_at":"2004-02-12T16:04:03Z","title_canon_sha256":"8d37a4f021e85dc57375ea67a1c807fa8c09d1591e8d7dbbb18c3ab50da612c6"},"schema_version":"1.0","source":{"id":"math/0402205","kind":"arxiv","version":1}},"canonical_sha256":"e4fd85807f66bafe97ec01aee67e8eed9703108450133eb14af7a96351890fee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4fd85807f66bafe97ec01aee67e8eed9703108450133eb14af7a96351890fee","first_computed_at":"2026-05-18T03:55:35.931768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:35.931768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f2HQrbdJ1BUQWc8Nxymp14FzSy4wvCIlqbG3GzW77F/cGq4YNDk2qjJCmi+EATY94cuKSsdQO8D7dtEvqAeICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:35.932378Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0402205","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4706e24c6034196616e0137eb896da5e740f70cae5493a68a988ece6639936b6","sha256:a2aeab4167f8047222425f2684f9d18b74f030220e69a875a8e6fb29fd554e19"],"state_sha256":"d3ccf54c6bd5bb05361516a5c05c71f79126537cb485908b373ab3b1cc15a164"}