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Fix a vertex $x \\in X$, and define $\\mathcal{R}_f = \\mathcal{R} \\setminus \\{yz \\mid \\partial(x,y) = \\partial(x,z)\\}$, where $\\partial$ denotes the path-length distance in $\\Gamma$. Observe that the graph $\\Gamma_f=(X,\\mathcal{R}_f)$ is bipartite. We say that $\\Gamma$ supports a uniform structure with respect to $x$ whenever $\\Gamma_f$ has a uniform structure with respect to $x$.\n  Assume that $\\Gamma$ is a distance-regular graph with classical para"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2305.08937","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-05-15T18:18:48Z","cross_cats_sorted":[],"title_canon_sha256":"58a1e53ac952b214c7cad4a9f7ed3d72f16cb68bff06c115f3ec94775d855303","abstract_canon_sha256":"03d13eb98088bcb0c7cd12156fe6d902f99651d22c25ad004de25ba7f6fba19e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:10:41.596076Z","signature_b64":"hojLbhZUy9yT9d/miJxuy8ly7i3oEIUZNFaXJof8zG3hB5XshGewWtOwcGbqtZnlDtVQ6tzhD4DT+eqv7v5HCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40b11547e18fbed822a09a1d1c81d2cee99fc2ff95d1d09e53305e5cc314e842","last_reissued_at":"2026-07-05T06:10:41.595519Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:10:41.595519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distance-regular graphs with classical parameters that support a uniform structure: case $q \\le 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Blas Fern\\'andez, Giusy Monzillo, Roghayeh Maleki, \\v{S}tefko Miklavi\\v{c}","submitted_at":"2023-05-15T18:18:48Z","abstract_excerpt":"Let $\\Gamma=(X,\\mathcal{R})$ denote a finite, simple, connected, and undirected non-bipartite graph with vertex set $X$ and edge set $\\mathcal{R}$. 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We say that $\\Gamma$ supports a uniform structure with respect to $x$ whenever $\\Gamma_f$ has a uniform structure with respect to $x$.\n  Assume that $\\Gamma$ is a distance-regular graph with classical para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08937","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.08937/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2305.08937","created_at":"2026-07-05T06:10:41.595587+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.08937v1","created_at":"2026-07-05T06:10:41.595587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.08937","created_at":"2026-07-05T06:10:41.595587+00:00"},{"alias_kind":"pith_short_12","alias_value":"ICYRKR7BR67N","created_at":"2026-07-05T06:10:41.595587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ICYRKR7BR67NQIVA","created_at":"2026-07-05T06:10:41.595587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ICYRKR7B","created_at":"2026-07-05T06:10:41.595587+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.19400","citing_title":"Raising and lowering maps for tridiagonal pairs","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3","json":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3.json","graph_json":"https://pith.science/api/pith-number/ICYRKR7BR67NQIVATIORZAOSZ3/graph.json","events_json":"https://pith.science/api/pith-number/ICYRKR7BR67NQIVATIORZAOSZ3/events.json","paper":"https://pith.science/paper/ICYRKR7B"},"agent_actions":{"view_html":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3","download_json":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3.json","view_paper":"https://pith.science/paper/ICYRKR7B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.08937&json=true","fetch_graph":"https://pith.science/api/pith-number/ICYRKR7BR67NQIVATIORZAOSZ3/graph.json","fetch_events":"https://pith.science/api/pith-number/ICYRKR7BR67NQIVATIORZAOSZ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3/action/storage_attestation","attest_author":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3/action/author_attestation","sign_citation":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3/action/citation_signature","submit_replication":"https://pith.science/pith/ICYRKR7BR67NQIVATIORZAOSZ3/action/replication_record"}},"created_at":"2026-07-05T06:10:41.595587+00:00","updated_at":"2026-07-05T06:10:41.595587+00:00"}