{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:E3RNKHONBKJGH3ARRRGDBT7SAW","short_pith_number":"pith:E3RNKHON","schema_version":"1.0","canonical_sha256":"26e2d51dcd0a9263ec118c4c30cff205ad7befb765bf560a523bef736f976f2a","source":{"kind":"arxiv","id":"2608.04542","version":1},"attestation_state":"computed","paper":{"title":"A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan Kristian Haugland","submitted_at":"2026-08-05T07:20:58Z","abstract_excerpt":"With regard to the Hadwiger-Nelson problem, several 5-chromatic unit distance graphs in the Euclidean plane have been discovered in recent years. While most constructions rely heavily on the Moser spindle, Voronov \\textit{et al.} found examples on 64513 vertices that completely avoid it. In this note, we improve upon this result by presenting a 5-chromatic unit distance graph on 2131 vertices that similarly does not contain the Moser spindle. It is constructed utilizing the arcs of a 7-fold symmetric unit distance graph on 21 vertices."},"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":"2608.04542","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-08-05T07:20:58Z","cross_cats_sorted":[],"title_canon_sha256":"271c17b6ca4564fdeb086763336b6499837a380ca93c06ac8246dd3c91b0fe75","abstract_canon_sha256":"57eda1fe65e1700e1f60f6ca017e8116775bcaeb8f71c38d09afba126d025c64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:35:48.317035Z","signature_b64":"4Wuw/3dKXjrdr2iFWKnJ4qjyAY9MptXxlTfM+KHS7lxd0EaISZhJRS8zvJUN6BTr18BQNSqddbaYHQ1gH/utCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26e2d51dcd0a9263ec118c4c30cff205ad7befb765bf560a523bef736f976f2a","last_reissued_at":"2026-08-06T01:35:48.315278Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:35:48.315278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan Kristian Haugland","submitted_at":"2026-08-05T07:20:58Z","abstract_excerpt":"With regard to the Hadwiger-Nelson problem, several 5-chromatic unit distance graphs in the Euclidean plane have been discovered in recent years. While most constructions rely heavily on the Moser spindle, Voronov \\textit{et al.} found examples on 64513 vertices that completely avoid it. In this note, we improve upon this result by presenting a 5-chromatic unit distance graph on 2131 vertices that similarly does not contain the Moser spindle. It is constructed utilizing the arcs of a 7-fold symmetric unit distance graph on 21 vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04542","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/2608.04542/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":"2608.04542","created_at":"2026-08-06T01:35:48.317354+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04542v1","created_at":"2026-08-06T01:35:48.317354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04542","created_at":"2026-08-06T01:35:48.317354+00:00"},{"alias_kind":"pith_short_12","alias_value":"E3RNKHONBKJG","created_at":"2026-08-06T01:35:48.317354+00:00"},{"alias_kind":"pith_short_16","alias_value":"E3RNKHONBKJGH3AR","created_at":"2026-08-06T01:35:48.317354+00:00"},{"alias_kind":"pith_short_8","alias_value":"E3RNKHON","created_at":"2026-08-06T01:35:48.317354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW","json":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW.json","graph_json":"https://pith.science/api/pith-number/E3RNKHONBKJGH3ARRRGDBT7SAW/graph.json","events_json":"https://pith.science/api/pith-number/E3RNKHONBKJGH3ARRRGDBT7SAW/events.json","paper":"https://pith.science/paper/E3RNKHON"},"agent_actions":{"view_html":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW","download_json":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW.json","view_paper":"https://pith.science/paper/E3RNKHON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04542&json=true","fetch_graph":"https://pith.science/api/pith-number/E3RNKHONBKJGH3ARRRGDBT7SAW/graph.json","fetch_events":"https://pith.science/api/pith-number/E3RNKHONBKJGH3ARRRGDBT7SAW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW/action/storage_attestation","attest_author":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW/action/author_attestation","sign_citation":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW/action/citation_signature","submit_replication":"https://pith.science/pith/E3RNKHONBKJGH3ARRRGDBT7SAW/action/replication_record"}},"created_at":"2026-08-06T01:35:48.317354+00:00","updated_at":"2026-08-06T01:35:48.317354+00:00"}