{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:32KEPZGQFHCCIPKBOHRNXLHNDF","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":"d8f288c6ca1f8a561875945e480c5833949a0b996f0ae5162c9ba694d8ee918f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-31T20:37:20Z","title_canon_sha256":"e8b7ff9723b8572acd4b8528775e6009a95171bbdaedc1e9ab5d3cb2073e4905"},"schema_version":"1.0","source":{"id":"0908.0005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0005","created_at":"2026-05-18T03:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0005v1","created_at":"2026-05-18T03:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0005","created_at":"2026-05-18T03:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"32KEPZGQFHCC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"32KEPZGQFHCCIPKB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"32KEPZGQ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:20d6933a59ba4dd0b71ba78f1587544112385b178ee6d124e9914db5965c2460","target":"graph","created_at":"2026-05-18T03:12:09Z","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":"Let $M_K$ be the 2-fold branched cover of a knot $K in $S^3$. If $H_1(M_K) = {\\bf Z}_3 \\oplus {\\bf Z}_{3^{2i}} \\oplus G$ where 3 does not divide the order of $G$ then $K$ is not of order 4 in the concordance group. This obstruction detects infinite new families of knots that represent elements of order 4 in the algebraic concordance group that are not of order 4 in concordance.","authors_text":"Charles Livingston, Swatee Naik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-31T20:37:20Z","title":"Stabilizing Four-Torsion in Classical Knot Concordance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0005","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:bffea13540d0d7d404fa4ca10620ac128a4fcfc29b558daa55832e6bf800f14d","target":"record","created_at":"2026-05-18T03:12:09Z","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":"d8f288c6ca1f8a561875945e480c5833949a0b996f0ae5162c9ba694d8ee918f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-31T20:37:20Z","title_canon_sha256":"e8b7ff9723b8572acd4b8528775e6009a95171bbdaedc1e9ab5d3cb2073e4905"},"schema_version":"1.0","source":{"id":"0908.0005","kind":"arxiv","version":1}},"canonical_sha256":"de9447e4d029c4243d4171e2dbaced1970d6005b0109a9f3585bfd349e7c1f41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de9447e4d029c4243d4171e2dbaced1970d6005b0109a9f3585bfd349e7c1f41","first_computed_at":"2026-05-18T03:12:09.345198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:09.345198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LQ9QDMgyOt5PPPi1as5JF30E1SnIATJ3VfR6F2XMQHmwzW2GgWP8EIqZrXlpzgkSfBJSkXEXvR1WExJKCDpLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:09.346015Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.0005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bffea13540d0d7d404fa4ca10620ac128a4fcfc29b558daa55832e6bf800f14d","sha256:20d6933a59ba4dd0b71ba78f1587544112385b178ee6d124e9914db5965c2460"],"state_sha256":"968ff0b03507d6da5828696bed5d3490daf1e1f24f3992b90d9acc6468c07b17"}