{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5DTZQNPHKKWZIBLKYMSRX7ABF7","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":"73cd829c65724fabb8501ebd3d93f9f67026e60136387ae8aff5aab79c108c35","cross_cats_sorted":["cs.CG","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-13T16:20:14Z","title_canon_sha256":"9109f1efed91478c150cadebd6f87b2d103422443968a9e4cda951e64584df81"},"schema_version":"1.0","source":{"id":"1110.2995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2995","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2995v2","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2995","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"5DTZQNPHKKWZ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5DTZQNPHKKWZIBLK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5DTZQNPH","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:09785251c34a721746bcdebf50ccc12158c87dd9ee96fa77eb2c98af82179f07","target":"graph","created_at":"2026-05-18T03:21:32Z","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":"In this paper we study sequences of lattices which are, up to similarity, projections of $\\mathbb{Z}^{n+1}$ onto a hyperplane $\\bm{v}^{\\perp}$, with $\\bm{v} \\in \\mathbb{Z}^{n+1}$ and converge to a target lattice $\\Lambda$ which is equivalent to an integer lattice. We show a sufficient condition to construct sequences converging at rate $O(1/ |\\bm{v}|^{2/n})$ and exhibit explicit constructions for some important families of lattices.","authors_text":"Antonio Campello, Jo\\~ao Strapasson","cross_cats":["cs.CG","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-13T16:20:14Z","title":"On sequences of projections of the cubic lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2995","kind":"arxiv","version":2},"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":"sha256:2f9978396db5ecb5847763bfab1cdf2d0f8d87a5c7bc7007ff84ab3081eb1e0e","target":"record","created_at":"2026-05-18T03:21:32Z","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":"73cd829c65724fabb8501ebd3d93f9f67026e60136387ae8aff5aab79c108c35","cross_cats_sorted":["cs.CG","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-13T16:20:14Z","title_canon_sha256":"9109f1efed91478c150cadebd6f87b2d103422443968a9e4cda951e64584df81"},"schema_version":"1.0","source":{"id":"1110.2995","kind":"arxiv","version":2}},"canonical_sha256":"e8e79835e752ad94056ac3251bfc012fd01415539823afbb2abffc0733573067","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8e79835e752ad94056ac3251bfc012fd01415539823afbb2abffc0733573067","first_computed_at":"2026-05-18T03:21:32.003000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:32.003000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Ons0RZ2rxDF66hXcWNUn+YH38kwlQYLlZVQDM3myUIYiymjcnIxaGN9qAn4/ty0dufltmlckAvcTkosAMfKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:32.003422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f9978396db5ecb5847763bfab1cdf2d0f8d87a5c7bc7007ff84ab3081eb1e0e","sha256:09785251c34a721746bcdebf50ccc12158c87dd9ee96fa77eb2c98af82179f07"],"state_sha256":"93965a4dea5db98a0010c7c25c8e4a062e38795384b88b7a03c6ba155a3a33f6"}