{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LI6MEJWGR4SC73EZLZOR7PSEHE","short_pith_number":"pith:LI6MEJWG","schema_version":"1.0","canonical_sha256":"5a3cc226c68f242fec995e5d1fbe4439035b1ba418a343fad8e8f218208d58af","source":{"kind":"arxiv","id":"2606.29415","version":1},"attestation_state":"computed","paper":{"title":"Algorithmic exploration of the unit distance problem in the rational plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Panteleimon Rodis","submitted_at":"2026-06-28T14:25:17Z","abstract_excerpt":"This paper presents reproducible experimental evidence on unit-distance graph density that surpasses recent theoretical lower bounds. Our approach is based on a novel algorithmic exploration of the rational plane for the generation of unit-distance graphs. An efficient algorithm for this utility must perform a local-breadth search on a bounded and finite set of elements and generate a graph that potentially encompasses the general properties of a unit-distance graph, not affected by restrictions on its generation. To this end, we show that our approach accomplishes this purpose by overcoming t"},"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":"2606.29415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-06-28T14:25:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"11e5860af99d85a5096b858e91f6d779f4f93af11aa0638782ad359e3ff8597a","abstract_canon_sha256":"54e911707d2959279909e2cd92461c5cf103ff7812efd9bb464c54735e1e30ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:18:05.343967Z","signature_b64":"5Geuc5mjwYeEg8Q8h2vIL0+erb7PLHEwIuzIRvjjAfOdcKAktvL4ir5BMCf1jRoBke8AGiYP535F7BN0EscTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a3cc226c68f242fec995e5d1fbe4439035b1ba418a343fad8e8f218208d58af","last_reissued_at":"2026-06-30T01:18:05.343042Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:18:05.343042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithmic exploration of the unit distance problem in the rational plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Panteleimon Rodis","submitted_at":"2026-06-28T14:25:17Z","abstract_excerpt":"This paper presents reproducible experimental evidence on unit-distance graph density that surpasses recent theoretical lower bounds. Our approach is based on a novel algorithmic exploration of the rational plane for the generation of unit-distance graphs. An efficient algorithm for this utility must perform a local-breadth search on a bounded and finite set of elements and generate a graph that potentially encompasses the general properties of a unit-distance graph, not affected by restrictions on its generation. To this end, we show that our approach accomplishes this purpose by overcoming t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29415","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/2606.29415/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":"2606.29415","created_at":"2026-06-30T01:18:05.343333+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29415v1","created_at":"2026-06-30T01:18:05.343333+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29415","created_at":"2026-06-30T01:18:05.343333+00:00"},{"alias_kind":"pith_short_12","alias_value":"LI6MEJWGR4SC","created_at":"2026-06-30T01:18:05.343333+00:00"},{"alias_kind":"pith_short_16","alias_value":"LI6MEJWGR4SC73EZ","created_at":"2026-06-30T01:18:05.343333+00:00"},{"alias_kind":"pith_short_8","alias_value":"LI6MEJWG","created_at":"2026-06-30T01:18:05.343333+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/LI6MEJWGR4SC73EZLZOR7PSEHE","json":"https://pith.science/pith/LI6MEJWGR4SC73EZLZOR7PSEHE.json","graph_json":"https://pith.science/api/pith-number/LI6MEJWGR4SC73EZLZOR7PSEHE/graph.json","events_json":"https://pith.science/api/pith-number/LI6MEJWGR4SC73EZLZOR7PSEHE/events.json","paper":"https://pith.science/paper/LI6MEJWG"},"agent_actions":{"view_html":"https://pith.science/pith/LI6MEJWGR4SC73EZLZOR7PSEHE","download_json":"https://pith.science/pith/LI6MEJWGR4SC73EZLZOR7PSEHE.json","view_paper":"https://pith.science/paper/LI6MEJWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29415&json=true","fetch_graph":"https://pith.science/api/pith-number/LI6MEJWGR4SC73EZLZOR7PSEHE/graph.json","fetch_events":"https://pith.science/api/pith-number/LI6MEJWGR4SC73EZLZOR7PSEHE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LI6MEJWGR4SC73EZLZOR7PSEHE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LI6MEJWGR4SC73EZLZOR7PSEHE/action/storage_attestation","attest_author":"https://pith.science/pith/LI6MEJWGR4SC73EZLZOR7PSEHE/action/author_attestation","sign_citation":"https://pith.science/pith/LI6MEJWGR4SC73EZLZOR7PSEHE/action/citation_signature","submit_replication":"https://pith.science/pith/LI6MEJWGR4SC73EZLZOR7PSEHE/action/replication_record"}},"created_at":"2026-06-30T01:18:05.343333+00:00","updated_at":"2026-06-30T01:18:05.343333+00:00"}