{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:FQDVZS4BDVV7QSYFHPPG3X4V4K","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":"2e436b8d98dd75827fe63022388d0f6f730acf79bc1f864b8fa283dc6a0d1bae","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2006-09-05T15:57:42Z","title_canon_sha256":"a0edd40540d61dd32982b1a0ce0d314754c254f87a2ecea228af892629eae8a7"},"schema_version":"1.0","source":{"id":"math/0609147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609147","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609147v1","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609147","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"pith_short_12","alias_value":"FQDVZS4BDVV7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"FQDVZS4BDVV7QSYF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"FQDVZS4B","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:ea580ae3915df0e6d8cf364774c478d6d80aeca90eb0f4e1021e4ce4252e8f19","target":"graph","created_at":"2026-05-18T04:33:27Z","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":"A Magnus subgroup of a one-relator group is the free subgroup freely generated by a proper subset of the generators. Two such subgroups can intersect in the obvious way or in a larger, exceptional way. The condition of non-exceptional intersection of Magnus subgroups of a one-relator group is applied to give criteria for the resulting cyclically presented groups to contain nonabelian free subgroups.","authors_text":"James Howie, Martin Edjvet","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2006-09-05T15:57:42Z","title":"Intersections of Magnus subgroups and embedding theorems for cyclically presented groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609147","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":"sha256:95d91a240eb4acf51130c722df84fc303ce6b9fe3391d655064e0a99c41dff6a","target":"record","created_at":"2026-05-18T04:33:27Z","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":"2e436b8d98dd75827fe63022388d0f6f730acf79bc1f864b8fa283dc6a0d1bae","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2006-09-05T15:57:42Z","title_canon_sha256":"a0edd40540d61dd32982b1a0ce0d314754c254f87a2ecea228af892629eae8a7"},"schema_version":"1.0","source":{"id":"math/0609147","kind":"arxiv","version":1}},"canonical_sha256":"2c075ccb811d6bf84b053bde6ddf95e28016b2b8a5d4eb781ec4ccc49c711e80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c075ccb811d6bf84b053bde6ddf95e28016b2b8a5d4eb781ec4ccc49c711e80","first_computed_at":"2026-05-18T04:33:27.505131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:27.505131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GD3UoD0YWDICZHMaZTC/dgBxkhSFIQI7D0utbiGpQgrXguE6Xp0kMo0Nz4mHuWuj8m9HrxKzZ4O/1oWj3t1iAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:27.505606Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95d91a240eb4acf51130c722df84fc303ce6b9fe3391d655064e0a99c41dff6a","sha256:ea580ae3915df0e6d8cf364774c478d6d80aeca90eb0f4e1021e4ce4252e8f19"],"state_sha256":"d0088e1d38c84b62c2850d3049c8f2a09294ab37789839d5f5b5fa28a85df810"}