{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JJ3C7BF6NLLUB7H2JL3MMGPKUH","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":"06583c59391d8404c1c712b5d6aaf574319ccab9dc0cd94dae71b7a953e95160","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-17T17:43:27Z","title_canon_sha256":"48fee7d22420e94831a03aa87b868980a448e1f05942b9cc6b753138c6325297"},"schema_version":"1.0","source":{"id":"1707.05294","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05294","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05294v2","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05294","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"JJ3C7BF6NLLU","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JJ3C7BF6NLLUB7H2","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JJ3C7BF6","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:a52a4e02829bbd7992b1403d4ccb82e5e19a84b5dc3d60089a0a298dd7bec48a","target":"graph","created_at":"2026-05-17T23:48:53Z","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":"In 1976, Loupekine introduced (via Isaacs) a very general way of constructing new snarks from old snarks by cyclically connecting multipoles constructed from smaller snarks. In this paper, we generalize Loupekine's construction to produce a variety of snarks which can be drawn with $m$-fold rotational symmetry for $m\\geq 3$ (and often, $m$ odd), constructed as $\\mathbb{Z}_{m}$ lifts of \\emph{voltage graphs} with certain properties; we call these snarks \\emph{cyclic pseudo-Loupekine snarks}. In particular, we discuss three infinite families of snarks which can be drawn with $\\mathbb{Z}_{m}$ rot","authors_text":"D\\'eborah Oliveros, Gordon I. Williams, Leah Wrenn Berman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-17T17:43:27Z","title":"Cyclic pseudo-{L}oupekine snarks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05294","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:ed68ad577d68be2b0723b26cc49300141cbfe3feebc3e393485a2f12b8935c77","target":"record","created_at":"2026-05-17T23:48:53Z","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":"06583c59391d8404c1c712b5d6aaf574319ccab9dc0cd94dae71b7a953e95160","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-17T17:43:27Z","title_canon_sha256":"48fee7d22420e94831a03aa87b868980a448e1f05942b9cc6b753138c6325297"},"schema_version":"1.0","source":{"id":"1707.05294","kind":"arxiv","version":2}},"canonical_sha256":"4a762f84be6ad740fcfa4af6c619eaa1c6e242c6076e7a749fa10848d268543a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a762f84be6ad740fcfa4af6c619eaa1c6e242c6076e7a749fa10848d268543a","first_computed_at":"2026-05-17T23:48:53.124381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:53.124381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iBElv2qiY/sW9JLKYQKNh4slJSwGl4wU6IDBGDUxfTV17F3Tg20mzJp0uIKJD316ToNdMjsbp5jslY7w7I4IAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:53.124811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05294","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed68ad577d68be2b0723b26cc49300141cbfe3feebc3e393485a2f12b8935c77","sha256:a52a4e02829bbd7992b1403d4ccb82e5e19a84b5dc3d60089a0a298dd7bec48a"],"state_sha256":"2280d1d9c32881007bb0d72d0b49cce2fbb0890ceba6db24261cb49faf96e504"}