{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EV5IZFKY3VHGE4KJB5VZ6O7QKG","short_pith_number":"pith:EV5IZFKY","schema_version":"1.0","canonical_sha256":"257a8c9558dd4e6271490f6b9f3bf051bb17a1bda3d9e743777324211ae22d70","source":{"kind":"arxiv","id":"1604.05989","version":1},"attestation_state":"computed","paper":{"title":"Finding well approximating lattices for a finite set of points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A. Hajdu, L. Hajdu, R. Tijdeman","submitted_at":"2016-04-20T14:59:50Z","abstract_excerpt":"In this paper we address the problem of finding well approximating lattices for a given finite set $A$ of points in ${\\mathbb R}^n$. More precisely, we search for $\\v{o},\\v{d_1}, \\dots,\\v{d_n}\\in \\mathbb{R}^n$ such that $\\v{a}-\\v{o}$ is close to $\\Lambda=\\v{d_1}\\mathbb{Z}+\\dots+\\v{d_n}\\mathbb{Z}$ for every $\\v{a}\\in A$. First we deal with the one-dimensional case, where we show that in a sense the results are almost the best possible. These results easily extend to the multi-dimensional case where the directions of the axes are given, too. Thereafter we treat the general multi-dimensional case"},"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":"1604.05989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-20T14:59:50Z","cross_cats_sorted":[],"title_canon_sha256":"c6d0c497521a7dcb52fad90106eb0e211b139d64f9c023bc4cdd8cd0c4fa6204","abstract_canon_sha256":"33a71a0ad134286983e5703e6203eadad75d18c7e7beb686fc57103941598d2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:34.009909Z","signature_b64":"EKWJ5rgUolkXS8qdJYFKroWeqBqFjNJjdkf/e4r0ij/3cgPLFkANxRr4gLfytG+O9zzMSgcH6EKkwnksgGZtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"257a8c9558dd4e6271490f6b9f3bf051bb17a1bda3d9e743777324211ae22d70","last_reissued_at":"2026-05-18T01:16:34.009432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:34.009432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding well approximating lattices for a finite set of points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A. Hajdu, L. Hajdu, R. Tijdeman","submitted_at":"2016-04-20T14:59:50Z","abstract_excerpt":"In this paper we address the problem of finding well approximating lattices for a given finite set $A$ of points in ${\\mathbb R}^n$. More precisely, we search for $\\v{o},\\v{d_1}, \\dots,\\v{d_n}\\in \\mathbb{R}^n$ such that $\\v{a}-\\v{o}$ is close to $\\Lambda=\\v{d_1}\\mathbb{Z}+\\dots+\\v{d_n}\\mathbb{Z}$ for every $\\v{a}\\in A$. First we deal with the one-dimensional case, where we show that in a sense the results are almost the best possible. These results easily extend to the multi-dimensional case where the directions of the axes are given, too. Thereafter we treat the general multi-dimensional case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05989","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":""},"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":"1604.05989","created_at":"2026-05-18T01:16:34.009507+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.05989v1","created_at":"2026-05-18T01:16:34.009507+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05989","created_at":"2026-05-18T01:16:34.009507+00:00"},{"alias_kind":"pith_short_12","alias_value":"EV5IZFKY3VHG","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"EV5IZFKY3VHGE4KJ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"EV5IZFKY","created_at":"2026-05-18T12:30:15.759754+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/EV5IZFKY3VHGE4KJB5VZ6O7QKG","json":"https://pith.science/pith/EV5IZFKY3VHGE4KJB5VZ6O7QKG.json","graph_json":"https://pith.science/api/pith-number/EV5IZFKY3VHGE4KJB5VZ6O7QKG/graph.json","events_json":"https://pith.science/api/pith-number/EV5IZFKY3VHGE4KJB5VZ6O7QKG/events.json","paper":"https://pith.science/paper/EV5IZFKY"},"agent_actions":{"view_html":"https://pith.science/pith/EV5IZFKY3VHGE4KJB5VZ6O7QKG","download_json":"https://pith.science/pith/EV5IZFKY3VHGE4KJB5VZ6O7QKG.json","view_paper":"https://pith.science/paper/EV5IZFKY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.05989&json=true","fetch_graph":"https://pith.science/api/pith-number/EV5IZFKY3VHGE4KJB5VZ6O7QKG/graph.json","fetch_events":"https://pith.science/api/pith-number/EV5IZFKY3VHGE4KJB5VZ6O7QKG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EV5IZFKY3VHGE4KJB5VZ6O7QKG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EV5IZFKY3VHGE4KJB5VZ6O7QKG/action/storage_attestation","attest_author":"https://pith.science/pith/EV5IZFKY3VHGE4KJB5VZ6O7QKG/action/author_attestation","sign_citation":"https://pith.science/pith/EV5IZFKY3VHGE4KJB5VZ6O7QKG/action/citation_signature","submit_replication":"https://pith.science/pith/EV5IZFKY3VHGE4KJB5VZ6O7QKG/action/replication_record"}},"created_at":"2026-05-18T01:16:34.009507+00:00","updated_at":"2026-05-18T01:16:34.009507+00:00"}