{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QW5O3JW5QHZDZUQOSUIDGYNLXQ","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":"5213f5d92878751b830e61f1b4265bf6d5fca912da11051fa39d1f40b948b73c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-09-15T14:03:22Z","title_canon_sha256":"4a1f046af5570fa5029edc04628e39885148902337dfa9e0a047e9fd9e974683"},"schema_version":"1.0","source":{"id":"1509.04565","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04565","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04565v2","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04565","created_at":"2026-05-18T01:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"QW5O3JW5QHZD","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QW5O3JW5QHZDZUQO","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QW5O3JW5","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:eafa2fa050c22eeacf79dc659c1df8efe3c9a3fae19536746fdafe632d4aa5cb","target":"graph","created_at":"2026-05-18T01:10:42Z","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":"Partial cubes are graphs isometrically embeddable into hypercubes. In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: $K_2 \\, \\square \\, C_{2n}$, for some $n\\geq 2$, the generalized Petersen graph $G(10,3)$, the cubic permutahedron, the truncated cuboctahedron, or the truncated icosidodecahedron. This classification is a generalization of results of Bre\\v{s}ar et al.~from 2004 on cubic mirror graphs, it includes all cubic, distance-regular partial cubes (Weichsel, 1992), and presents a contribution to the classification of ","authors_text":"Tilen Marc","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-09-15T14:03:22Z","title":"Classification of vertex-transitive cubic partial cubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04565","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:a08ff0fde73b39d9e32553b3181719a97cbc2427b78a137dcff3869a5c70a3ee","target":"record","created_at":"2026-05-18T01:10:42Z","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":"5213f5d92878751b830e61f1b4265bf6d5fca912da11051fa39d1f40b948b73c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-09-15T14:03:22Z","title_canon_sha256":"4a1f046af5570fa5029edc04628e39885148902337dfa9e0a047e9fd9e974683"},"schema_version":"1.0","source":{"id":"1509.04565","kind":"arxiv","version":2}},"canonical_sha256":"85baeda6dd81f23cd20e95103361abbc06536531f37975ea4e29d237d239c78a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85baeda6dd81f23cd20e95103361abbc06536531f37975ea4e29d237d239c78a","first_computed_at":"2026-05-18T01:10:42.991602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:42.991602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oWFl3+X8N62uVHQTO1iVQiq7M7+swgPs2+x2vkZ02YyXW3m2BE/YvbZQsPEJKQgqQ/CT42+9joPvm4/qHZM1DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:42.992045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04565","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a08ff0fde73b39d9e32553b3181719a97cbc2427b78a137dcff3869a5c70a3ee","sha256:eafa2fa050c22eeacf79dc659c1df8efe3c9a3fae19536746fdafe632d4aa5cb"],"state_sha256":"d4eb7dec0fb78816b7a68a832abfcd5f776b365a62b0f2b7aa18c2cad3bf3b21"}