{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O6JD7FCZ4TQDVLSYT55WLOQHDM","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":"a649f91898b5d30347c647c18a023cef9e8098cad4278a862fb8129958de7085","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-01T12:42:54Z","title_canon_sha256":"3b536e470a43b78f0881d5010ec8813fe3ca8410d76d49cca38160e66037e18b"},"schema_version":"1.0","source":{"id":"1409.0389","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0389","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0389v1","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0389","created_at":"2026-05-18T02:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"O6JD7FCZ4TQD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O6JD7FCZ4TQDVLSY","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O6JD7FCZ","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:f1f6b25d04a62abc2186731b3a97a6f2b92057694e23cdec11d087f2ce01ada5","target":"graph","created_at":"2026-05-18T02:43:52Z","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 the Kneser graph $K$ of a distance-regular graph $\\Gamma$ be the graph on the same vertex set as $\\Gamma$, where two vertices are adjacent when they have maximal distance in $\\Gamma$. We study the situation where the Bose-Mesner algebra of $\\Gamma$ is not generated by the adjacency matrix of $K$. In particular, we obtain strong results in the so-called `half antipodal' case.","authors_text":"A. E. Brouwer, M. A. Fiol","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-01T12:42:54Z","title":"Distance-regular graphs where the distance-$d$ graph has fewer distinct eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0389","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":"sha256:6354a68b93a3f56a278a5c831b8052ba20eb122c4c6d08f4eb83be8506b681f8","target":"record","created_at":"2026-05-18T02:43:52Z","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":"a649f91898b5d30347c647c18a023cef9e8098cad4278a862fb8129958de7085","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-01T12:42:54Z","title_canon_sha256":"3b536e470a43b78f0881d5010ec8813fe3ca8410d76d49cca38160e66037e18b"},"schema_version":"1.0","source":{"id":"1409.0389","kind":"arxiv","version":1}},"canonical_sha256":"77923f9459e4e03aae589f7b65ba071b28117695211098f7f0b5551688991ad5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77923f9459e4e03aae589f7b65ba071b28117695211098f7f0b5551688991ad5","first_computed_at":"2026-05-18T02:43:52.849751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:52.849751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AtOMb7cJ2C0qCuG8bv6tjM+PPWLg2RNQm+2XPOsSQEfNIGEMi2wNChZjoOIaKBVuHzFjt7N0m4Nz/zsnAiG9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:52.850107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0389","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6354a68b93a3f56a278a5c831b8052ba20eb122c4c6d08f4eb83be8506b681f8","sha256:f1f6b25d04a62abc2186731b3a97a6f2b92057694e23cdec11d087f2ce01ada5"],"state_sha256":"a66940a0cc6ec86e8d683f19db31d5ef5ac98cff4710fd9113fd3cd63c267e93"}