{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T6WAR6BKTQC4ELCSOZMLULT7U6","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":"10a20a1072d9cbc8a3d109d0050b631c415f362b7f0e5c3ea959aebb33aba743","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-27T11:31:23Z","title_canon_sha256":"3a3b7505d909b6affb06433215d8a21b154742be5c7cc3a4baf24cc5f843046a"},"schema_version":"1.0","source":{"id":"1607.08044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08044","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08044v2","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08044","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"T6WAR6BKTQC4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T6WAR6BKTQC4ELCS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T6WAR6BK","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:9ed15b5235848f46d5f9db828e795a09fc76167f6f661e027da3d64de7dd4ba6","target":"graph","created_at":"2026-05-18T00:41:46Z","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 extend some part of the unpublished paper written by Mednykh and Rasskazov. Using the approach indicated in this paper we derive the Riley-Mednykh polynomial for some family of the $2$-bridge knot orbifolds. As a result we obtain explicit formulae for the volume of cone-manifolds and the Chern-Simons invariant of orbifolds of the knot with Conway's notation $C(2n,4)$.","authors_text":"Aleksey Rasskazov, Alexander Mednykh, Ji-Young Ham, Joongul Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-27T11:31:23Z","title":"On the volume and the Chern-Simons invariant for the $2$-bridge knot orbifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08044","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":"sha256:472d718684dbc2d0f2a369d7c2df2e0437e2a3ba8ecbe93d7772b5b9fd959b83","target":"record","created_at":"2026-05-18T00:41:46Z","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":"10a20a1072d9cbc8a3d109d0050b631c415f362b7f0e5c3ea959aebb33aba743","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-27T11:31:23Z","title_canon_sha256":"3a3b7505d909b6affb06433215d8a21b154742be5c7cc3a4baf24cc5f843046a"},"schema_version":"1.0","source":{"id":"1607.08044","kind":"arxiv","version":2}},"canonical_sha256":"9fac08f82a9c05c22c527658ba2e7fa7b87db59165496ebb270ab4b7ea0032aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fac08f82a9c05c22c527658ba2e7fa7b87db59165496ebb270ab4b7ea0032aa","first_computed_at":"2026-05-18T00:41:46.378504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:46.378504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9EC7jbHTvTtF3W9JlCaccPP7cZpsidi7A2p2PQbIosqWtPnTWWzOkFSelaEEpm24jNrfeiavyAb6I569Q+1ZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:46.379231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:472d718684dbc2d0f2a369d7c2df2e0437e2a3ba8ecbe93d7772b5b9fd959b83","sha256:9ed15b5235848f46d5f9db828e795a09fc76167f6f661e027da3d64de7dd4ba6"],"state_sha256":"5ed1136a8d314f1050ed99d746f950b314b413a78e052b9a9a825c70b7657a62"}