{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5JJJGI5ORVXTZNC53E3NBCNKB7","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":"b5ef91f35c0a8b2b953b5c3289e09e6874025abf4938757c4b340699e59ffe3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-08T13:22:37Z","title_canon_sha256":"ca59e55b6a98b7c52e326e056cb5a1cd795fb3af856a1d5122f780ed5be04ef9"},"schema_version":"1.0","source":{"id":"1505.02029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02029","created_at":"2026-05-18T02:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02029v1","created_at":"2026-05-18T02:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02029","created_at":"2026-05-18T02:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"5JJJGI5ORVXT","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5JJJGI5ORVXTZNC5","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5JJJGI5O","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:924797a1f94fde6b348c6d5ae566372addd0dcc516ae924e1b2bad2cafc7a250","target":"graph","created_at":"2026-05-18T02:16:38Z","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 $X$ be a finite vertex-transitive graph of valency $d$, and let $A$ be the full automorphism group of $X$. Then the arc-type of $X$ is defined in terms of the sizes of the orbits of the action of the stabiliser $A_v$ of a given vertex $v$ on the set of arcs incident with $v$. Specifically, the arc-type is the partition of $d$ as the sum $$n_1 + n_2 + \\dots + n_t + (m_1 + m_1) + (m_2 + m_2) + \\dots + (m_s + m_s),$$ where $n_1, n_2, \\dots, n_t$ are the sizes of the self-paired orbits, and $m_1,m_1, m_2,m_2, \\dots, m_s,m_s$ are the sizes of the non-self-paired orbits, in descending order.\n  I","authors_text":"Arjana \\v{Z}itnik, Marston Conder, Toma\\v{z} Pisanski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-08T13:22:37Z","title":"Vertex-transitive graphs and their arc-types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02029","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:f5a96fa145db35fde89afead466cc789884d9b14093797768f97bb47be5b6158","target":"record","created_at":"2026-05-18T02:16:38Z","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":"b5ef91f35c0a8b2b953b5c3289e09e6874025abf4938757c4b340699e59ffe3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-08T13:22:37Z","title_canon_sha256":"ca59e55b6a98b7c52e326e056cb5a1cd795fb3af856a1d5122f780ed5be04ef9"},"schema_version":"1.0","source":{"id":"1505.02029","kind":"arxiv","version":1}},"canonical_sha256":"ea529323ae8d6f3cb45dd936d089aa0ff7e251823d804e17453816a35fef2b4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea529323ae8d6f3cb45dd936d089aa0ff7e251823d804e17453816a35fef2b4b","first_computed_at":"2026-05-18T02:16:38.130036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:38.130036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KDpZQsLV5DUfmHmcAV7ykLQJz/PyXX/Tf8uJrT4qoG61wMa6L7FjBpYLVgCeXP/JRIKummnPCB9zmP7oZ7/pBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:38.130659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5a96fa145db35fde89afead466cc789884d9b14093797768f97bb47be5b6158","sha256:924797a1f94fde6b348c6d5ae566372addd0dcc516ae924e1b2bad2cafc7a250"],"state_sha256":"d53a11a0234b56c6038a33528f3f531f27c29df908118f7eb7145abb3bf8d64a"}