{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5DTZQNPHKKWZIBLKYMSRX7ABF7","short_pith_number":"pith:5DTZQNPH","canonical_record":{"source":{"id":"1110.2995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-13T16:20:14Z","cross_cats_sorted":["cs.CG","cs.IT","math.IT"],"title_canon_sha256":"9109f1efed91478c150cadebd6f87b2d103422443968a9e4cda951e64584df81","abstract_canon_sha256":"73cd829c65724fabb8501ebd3d93f9f67026e60136387ae8aff5aab79c108c35"},"schema_version":"1.0"},"canonical_sha256":"e8e79835e752ad94056ac3251bfc012fd01415539823afbb2abffc0733573067","source":{"kind":"arxiv","id":"1110.2995","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5DTZQNPHKKWZIBLKYMSRX7ABF7","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-13T16:20:14Z","cross_cats_sorted":["cs.CG","cs.IT","math.IT"],"title_canon_sha256":"9109f1efed91478c150cadebd6f87b2d103422443968a9e4cda951e64584df81","abstract_canon_sha256":"73cd829c65724fabb8501ebd3d93f9f67026e60136387ae8aff5aab79c108c35"},"schema_version":"1.0"},"canonical_sha256":"e8e79835e752ad94056ac3251bfc012fd01415539823afbb2abffc0733573067","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:32.003422Z","signature_b64":"9Ons0RZ2rxDF66hXcWNUn+YH38kwlQYLlZVQDM3myUIYiymjcnIxaGN9qAn4/ty0dufltmlckAvcTkosAMfKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8e79835e752ad94056ac3251bfc012fd01415539823afbb2abffc0733573067","last_reissued_at":"2026-05-18T03:21:32.003000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:32.003000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2995","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6/T9ESEmWuRhkLIzONzzTnuvEOtJJpTlKnzS1JQGNFL0MRP7vVskeRO4C1ygKqh9EbLSx02/GEAPbo4e6RUEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:54:19.176825Z"},"content_sha256":"2f9978396db5ecb5847763bfab1cdf2d0f8d87a5c7bc7007ff84ab3081eb1e0e","schema_version":"1.0","event_id":"sha256:2f9978396db5ecb5847763bfab1cdf2d0f8d87a5c7bc7007ff84ab3081eb1e0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5DTZQNPHKKWZIBLKYMSRX7ABF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On sequences of projections of the cubic lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Antonio Campello, Jo\\~ao Strapasson","submitted_at":"2011-10-13T16:20:14Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2995","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q0h0fqgwukp18Emycnesdt9x3XPvY1hzhIj+/ftae4rhiwI7QswKCk7DW4sUgRChpogSi06uwZCXjpZ9MLtiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:54:19.177162Z"},"content_sha256":"09785251c34a721746bcdebf50ccc12158c87dd9ee96fa77eb2c98af82179f07","schema_version":"1.0","event_id":"sha256:09785251c34a721746bcdebf50ccc12158c87dd9ee96fa77eb2c98af82179f07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DTZQNPHKKWZIBLKYMSRX7ABF7/bundle.json","state_url":"https://pith.science/pith/5DTZQNPHKKWZIBLKYMSRX7ABF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DTZQNPHKKWZIBLKYMSRX7ABF7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T02:54:19Z","links":{"resolver":"https://pith.science/pith/5DTZQNPHKKWZIBLKYMSRX7ABF7","bundle":"https://pith.science/pith/5DTZQNPHKKWZIBLKYMSRX7ABF7/bundle.json","state":"https://pith.science/pith/5DTZQNPHKKWZIBLKYMSRX7ABF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DTZQNPHKKWZIBLKYMSRX7ABF7/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8LQ8gou1TX4yZGSgkgHjJWgCkhIPeQOBhupflV20XlrCcNrh0M63LXzGsarQq5rOkreWSfkDpR4kKwlgO4lAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:54:19.179128Z","bundle_sha256":"60371bf5534e827bfb090380dbbaeb2ac45a72dc84b2ee224fc4c5faca2ab449"}}