{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:35URGC3B74YPCELRYBBCV6QL6Y","short_pith_number":"pith:35URGC3B","canonical_record":{"source":{"id":"1202.3939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-17T15:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"15735d0447278e0deb0870f8190f44468e41c03b176f17d45d5f85bc62887284","abstract_canon_sha256":"2f14c431162ef6b064f3fe6197c6ff3a2a839456582abdeff67e0aa4411b7d58"},"schema_version":"1.0"},"canonical_sha256":"df69130b61ff30f11171c0422afa0bf61477bc5ebbb0f1b1cee7053dc32bd44b","source":{"kind":"arxiv","id":"1202.3939","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3939","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3939v2","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3939","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"35URGC3B74YP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"35URGC3B74YPCELR","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"35URGC3B","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:35URGC3B74YPCELRYBBCV6QL6Y","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-17T15:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"15735d0447278e0deb0870f8190f44468e41c03b176f17d45d5f85bc62887284","abstract_canon_sha256":"2f14c431162ef6b064f3fe6197c6ff3a2a839456582abdeff67e0aa4411b7d58"},"schema_version":"1.0"},"canonical_sha256":"df69130b61ff30f11171c0422afa0bf61477bc5ebbb0f1b1cee7053dc32bd44b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:11.760570Z","signature_b64":"ndNYZ5fnZkjRxiraNROqMXFYaQVfUOkRzUy5y2eLBeVyff+kRb6abb2Ez06i8WigF8vyGS/hU/C2NuBzgnJbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df69130b61ff30f11171c0422afa0bf61477bc5ebbb0f1b1cee7053dc32bd44b","last_reissued_at":"2026-05-18T03:49:11.759868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:11.759868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3939","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nlWabjg/lGQDZP5/m7mCl5X/nZ4rxavXR8ZY+QEK7ojevrClcrZDCOjNBazb7qYseM7KKnTgd7xwXYbHtt9sAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:35:47.816745Z"},"content_sha256":"a77e91ea922481769059a9fb1211d8fd3e938bbf10c4a3b50f8c0f028ff2d7e7","schema_version":"1.0","event_id":"sha256:a77e91ea922481769059a9fb1211d8fd3e938bbf10c4a3b50f8c0f028ff2d7e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:35URGC3B74YPCELRYBBCV6QL6Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Test elements in torsion-free hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Daniel Groves","submitted_at":"2012-02-17T15:44:20Z","abstract_excerpt":"We prove that in a torsion-free hyperbolic group, an element is a test element if and only if it is not contained in a proper retract."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3939","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3VZ9TscYT+AO5SqkFMTEpXuqs/ElW3RESo3usiBqPYK6NIyas0N/KXJXhr82s2iYnpsRLXCWDUWpIjUK14hXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:35:47.817297Z"},"content_sha256":"659fee2294ead7d806ce7d77b7d640ceaab0d18299afbb12c0ce940462d3422c","schema_version":"1.0","event_id":"sha256:659fee2294ead7d806ce7d77b7d640ceaab0d18299afbb12c0ce940462d3422c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/35URGC3B74YPCELRYBBCV6QL6Y/bundle.json","state_url":"https://pith.science/pith/35URGC3B74YPCELRYBBCV6QL6Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/35URGC3B74YPCELRYBBCV6QL6Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T02:35:47Z","links":{"resolver":"https://pith.science/pith/35URGC3B74YPCELRYBBCV6QL6Y","bundle":"https://pith.science/pith/35URGC3B74YPCELRYBBCV6QL6Y/bundle.json","state":"https://pith.science/pith/35URGC3B74YPCELRYBBCV6QL6Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/35URGC3B74YPCELRYBBCV6QL6Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:35URGC3B74YPCELRYBBCV6QL6Y","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":"2f14c431162ef6b064f3fe6197c6ff3a2a839456582abdeff67e0aa4411b7d58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-17T15:44:20Z","title_canon_sha256":"15735d0447278e0deb0870f8190f44468e41c03b176f17d45d5f85bc62887284"},"schema_version":"1.0","source":{"id":"1202.3939","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3939","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3939v2","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3939","created_at":"2026-05-18T03:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"35URGC3B74YP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"35URGC3B74YPCELR","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"35URGC3B","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:659fee2294ead7d806ce7d77b7d640ceaab0d18299afbb12c0ce940462d3422c","target":"graph","created_at":"2026-05-18T03:49:11Z","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 in a torsion-free hyperbolic group, an element is a test element if and only if it is not contained in a proper retract.","authors_text":"Daniel Groves","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-17T15:44:20Z","title":"Test elements in torsion-free hyperbolic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3939","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:a77e91ea922481769059a9fb1211d8fd3e938bbf10c4a3b50f8c0f028ff2d7e7","target":"record","created_at":"2026-05-18T03:49:11Z","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":"2f14c431162ef6b064f3fe6197c6ff3a2a839456582abdeff67e0aa4411b7d58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-17T15:44:20Z","title_canon_sha256":"15735d0447278e0deb0870f8190f44468e41c03b176f17d45d5f85bc62887284"},"schema_version":"1.0","source":{"id":"1202.3939","kind":"arxiv","version":2}},"canonical_sha256":"df69130b61ff30f11171c0422afa0bf61477bc5ebbb0f1b1cee7053dc32bd44b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df69130b61ff30f11171c0422afa0bf61477bc5ebbb0f1b1cee7053dc32bd44b","first_computed_at":"2026-05-18T03:49:11.759868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:11.759868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ndNYZ5fnZkjRxiraNROqMXFYaQVfUOkRzUy5y2eLBeVyff+kRb6abb2Ez06i8WigF8vyGS/hU/C2NuBzgnJbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:11.760570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3939","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a77e91ea922481769059a9fb1211d8fd3e938bbf10c4a3b50f8c0f028ff2d7e7","sha256:659fee2294ead7d806ce7d77b7d640ceaab0d18299afbb12c0ce940462d3422c"],"state_sha256":"d003911b371a4154b550b02c2dff756ca66e5ce12d32db2b88a1eb614aed3083"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8SLQ4joMBRwMQ3vOOPC6+vmKbHZ2XLnL8tJ0ynl7iIqfL49ict1PiU4PKp0GmDE/ojLHHNm/29zE8bGRGHyMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:35:47.820218Z","bundle_sha256":"74d6f7a51984e3642eda8af0ae9abf456f3b5e5098e3cf4b7954a38d2191c63e"}}