{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:TRCHXQDOJBOKDNAWLB3IR2SUTE","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":"0318e7ff402f8d7e25cf12529324c52e147d9c1f91b19ddcb685c963488ec205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2004-04-02T21:00:14Z","title_canon_sha256":"2db8e19391740157addf1ab9c2018b9d85b31e7c05b74b700d21dd47c0e8d078"},"schema_version":"1.0","source":{"id":"math/0404040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404040","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404040v2","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404040","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"pith_short_12","alias_value":"TRCHXQDOJBOK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"TRCHXQDOJBOKDNAW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"TRCHXQDO","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:b71c4e9b8b659d130b90b57649c90e04f547061c38a75d1cbd2b56a95b484d83","target":"graph","created_at":"2026-05-18T02:28:29Z","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 suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.","authors_text":"D.V. Osin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2004-04-02T21:00:14Z","title":"Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404040","kind":"arxiv","version":2},"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":"sha256:0b903dd6ca27a3c114bdedc83ac96d56656a30374cea3b32765d1af543b0e90e","target":"record","created_at":"2026-05-18T02:28:29Z","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":"0318e7ff402f8d7e25cf12529324c52e147d9c1f91b19ddcb685c963488ec205","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2004-04-02T21:00:14Z","title_canon_sha256":"2db8e19391740157addf1ab9c2018b9d85b31e7c05b74b700d21dd47c0e8d078"},"schema_version":"1.0","source":{"id":"math/0404040","kind":"arxiv","version":2}},"canonical_sha256":"9c447bc06e485ca1b416587688ea549933a229d2582cce63f20ca020c683e985","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c447bc06e485ca1b416587688ea549933a229d2582cce63f20ca020c683e985","first_computed_at":"2026-05-18T02:28:29.744285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:29.744285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ThC2Ic3yqUuv2BuQEqmSm8O23UCyC36meAEFyBEq4QDf42aqq4y85uLpOVVyhmGmsRLDeMWSTJdRjuItxVCkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:29.744793Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0404040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b903dd6ca27a3c114bdedc83ac96d56656a30374cea3b32765d1af543b0e90e","sha256:b71c4e9b8b659d130b90b57649c90e04f547061c38a75d1cbd2b56a95b484d83"],"state_sha256":"637bc1e248c9123c406ad02a3ac9d408b968e99c9429eed8be61cf8f888a6e29"}