{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HL6UKIT5W542R7IJWIPDMLIGUH","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":"ed37ebc42aae33f53c84378caa99a0cac1ad364b8f911458c01074f0398e05cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-01T14:38:55Z","title_canon_sha256":"3c1a03737157a8036978171b7e9bf6d4b250b1c2a5b15a7c4273397c44605b49"},"schema_version":"1.0","source":{"id":"1304.0367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0367","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0367v1","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0367","created_at":"2026-05-18T03:29:17Z"},{"alias_kind":"pith_short_12","alias_value":"HL6UKIT5W542","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HL6UKIT5W542R7IJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HL6UKIT5","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:c18e5de708f89ea9a5c575db62dc7a4b813f40987da5ea424cfb4d3bc5ffda8b","target":"graph","created_at":"2026-05-18T03:29:17Z","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 examine certain symmetries in the deficiencies of a rational surgery on a knot in $S^3$ by comparing the $\\text{Spin}^c$-structures on the rational surgery with those on a related integral surgery. We then provide an application of these symmetries in the form of a theorem that obstructs Dehn surgeries in $S^3$. This last part unifies and generalises theorems by Greene underlying his work on the cabling conjecture, the lens space realisation problem, and the unknotting number of alternating 3-braids.","authors_text":"Julian Gibbons","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-01T14:38:55Z","title":"Deficiency Symmetries of Surgeries in $S^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0367","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":"sha256:7bd233b930c2b6d4634e2f668c51537c61fc7329caa2a56c4f216ea50e7220c5","target":"record","created_at":"2026-05-18T03:29:17Z","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":"ed37ebc42aae33f53c84378caa99a0cac1ad364b8f911458c01074f0398e05cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-04-01T14:38:55Z","title_canon_sha256":"3c1a03737157a8036978171b7e9bf6d4b250b1c2a5b15a7c4273397c44605b49"},"schema_version":"1.0","source":{"id":"1304.0367","kind":"arxiv","version":1}},"canonical_sha256":"3afd45227db779a8fd09b21e362d06a1d234f7203b95ba83ef9b4d0ca78cdb0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3afd45227db779a8fd09b21e362d06a1d234f7203b95ba83ef9b4d0ca78cdb0d","first_computed_at":"2026-05-18T03:29:17.145305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:17.145305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fHn+euZ8o9K+SE4Wx+iu4bBwdMzgeOvu/vjLSboxd2aLZ80x8AT8x/7GJjzRll2ube6k8fA1KmogMSEi+L5dAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:17.146008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bd233b930c2b6d4634e2f668c51537c61fc7329caa2a56c4f216ea50e7220c5","sha256:c18e5de708f89ea9a5c575db62dc7a4b813f40987da5ea424cfb4d3bc5ffda8b"],"state_sha256":"e2f403c856e00d842180b1afbd9aa55702d12d1eed410b3c0d7b4d73a23a48ea"}