{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:GDHKXKOWPBDAMP3OU4WV4VYG4N","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":"5f7e22c7f477a9ca8a52eeadbd0904b12e961d8330f271d4a2d242c7c0e7f022","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2006-12-28T15:44:24Z","title_canon_sha256":"70b43d7b519db1951d44b35f9fedaf28af9df916c06c2fa0dba5d07224747815"},"schema_version":"1.0","source":{"id":"math/0612830","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612830","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612830v2","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612830","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"GDHKXKOWPBDA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GDHKXKOWPBDAMP3O","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GDHKXKOW","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:edde70601b1b910e5be6658c5555c9b7c17f5c0b5d9901255470b7b1c5c68a3f","target":"graph","created_at":"2026-05-18T04:31:30Z","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 consider closed orientable 3-dimensional hyperbolic manifolds which are cyclic branched coverings of the 3-sphere, with branching set being a two-bridge knot (or link). We establish two-sided linear bounds depending on the order of the covering for the Matveev complexity of the covering manifold. The lower estimate uses the hyperbolic volume and results of Cao-Meyerhoff and Gueritaud-Futer (who recently improved previous work of Lackenby), while the upper estimate is based on an explicit triangulation, which also allows us to give a bound on the Delzant T-invariant of the fundamental group ","authors_text":"Andrei Vesnin, Carlo Petronio","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2006-12-28T15:44:24Z","title":"Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612830","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":"sha256:2f16e8403fc7f560ca2508e6308344e6573aa79c74bcb22e38ff8a56925e3db1","target":"record","created_at":"2026-05-18T04:31:30Z","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":"5f7e22c7f477a9ca8a52eeadbd0904b12e961d8330f271d4a2d242c7c0e7f022","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2006-12-28T15:44:24Z","title_canon_sha256":"70b43d7b519db1951d44b35f9fedaf28af9df916c06c2fa0dba5d07224747815"},"schema_version":"1.0","source":{"id":"math/0612830","kind":"arxiv","version":2}},"canonical_sha256":"30ceaba9d67846063f6ea72d5e5706e354601d9c669e52f44a7802e42714816c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30ceaba9d67846063f6ea72d5e5706e354601d9c669e52f44a7802e42714816c","first_computed_at":"2026-05-18T04:31:30.122840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:30.122840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dytOchVicHWjLnYG/XBfD9nixsq9LK375aPvrLnI5hEawXIFENfYDgrASo3Z3EOlKp8dnEKDL/WL5zNmI4VsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:30.123269Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612830","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f16e8403fc7f560ca2508e6308344e6573aa79c74bcb22e38ff8a56925e3db1","sha256:edde70601b1b910e5be6658c5555c9b7c17f5c0b5d9901255470b7b1c5c68a3f"],"state_sha256":"24a4b3359b04ccf7c013ee7db70e3bb7a6ba1d9dcabadaae58cb7a65d6a2267e"}