{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IKPG6BPXWWTUIQQ5NCOUFJ3D72","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":"441752213532620200a5fb9fc18cb9aad0bb81ecbac935191fa878ee332a3542","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-16T02:07:49Z","title_canon_sha256":"03338a18e33728b2659327f7dbfef9d3fdc0445c9cded1a22c0f9bc93f8fe970"},"schema_version":"1.0","source":{"id":"1401.3811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3811","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3811v1","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3811","created_at":"2026-05-18T03:02:06Z"},{"alias_kind":"pith_short_12","alias_value":"IKPG6BPXWWTU","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IKPG6BPXWWTUIQQ5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IKPG6BPX","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:6ea41dfb2eb98355b9334c058ab864b920f7c25d12970e1814380ddcfafc308b","target":"graph","created_at":"2026-05-18T03:02:06Z","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 show that we can obtain a reducible spherical curve from any non-trivial spherical curve by four or less inverse-half-twisted splices, i.e., the reductivity, which represents how reduced a spherical curve is, is four or less. We also discuss unavoidable sets of tangles for spherical curves.","authors_text":"Ayaka Shimizu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-16T02:07:49Z","title":"The reductivity of spherical curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3811","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":"sha256:5cbd1e1f8f6a58df66d324e13a2eebfd826a8b23a3ee6efe1a4c7c11612afbfd","target":"record","created_at":"2026-05-18T03:02:06Z","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":"441752213532620200a5fb9fc18cb9aad0bb81ecbac935191fa878ee332a3542","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-01-16T02:07:49Z","title_canon_sha256":"03338a18e33728b2659327f7dbfef9d3fdc0445c9cded1a22c0f9bc93f8fe970"},"schema_version":"1.0","source":{"id":"1401.3811","kind":"arxiv","version":1}},"canonical_sha256":"429e6f05f7b5a744421d689d42a763fe978777178be6328d5f6fd8d2d06229ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"429e6f05f7b5a744421d689d42a763fe978777178be6328d5f6fd8d2d06229ae","first_computed_at":"2026-05-18T03:02:06.909296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:06.909296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lFE7hxeJx7ccKaln0jL/Q0jk/i7Ux2pUvq8P9s6wa/Rbbl5mD7rRtQPeR+TeNHu42HN6fCrUn0zNz4FxgeeGBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:06.910064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.3811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cbd1e1f8f6a58df66d324e13a2eebfd826a8b23a3ee6efe1a4c7c11612afbfd","sha256:6ea41dfb2eb98355b9334c058ab864b920f7c25d12970e1814380ddcfafc308b"],"state_sha256":"4d67b28094eb16b4b306dcf40633a3b2397b4cc0178174c68145d1437e4ed9db"}