{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DLOQC7ORWTFCTV7ADLLUCIZ6YJ","short_pith_number":"pith:DLOQC7OR","canonical_record":{"source":{"id":"1405.7014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-27T19:05:57Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"db54e10ee3346b2ebaec11e92741a2b5967909519094abecc43c88ce9d8a31bb","abstract_canon_sha256":"1cf22d70586c32d569156038c706058d2dce1d22abb2bd5408db70550212c405"},"schema_version":"1.0"},"canonical_sha256":"1add017dd1b4ca29d7e01ad741233ec24278992e88ea439c230c73aafa27a05e","source":{"kind":"arxiv","id":"1405.7014","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7014","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7014v1","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7014","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"DLOQC7ORWTFC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DLOQC7ORWTFCTV7A","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DLOQC7OR","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DLOQC7ORWTFCTV7ADLLUCIZ6YJ","target":"record","payload":{"canonical_record":{"source":{"id":"1405.7014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-27T19:05:57Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"db54e10ee3346b2ebaec11e92741a2b5967909519094abecc43c88ce9d8a31bb","abstract_canon_sha256":"1cf22d70586c32d569156038c706058d2dce1d22abb2bd5408db70550212c405"},"schema_version":"1.0"},"canonical_sha256":"1add017dd1b4ca29d7e01ad741233ec24278992e88ea439c230c73aafa27a05e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:59.849496Z","signature_b64":"FZSx/Rcz2qNDMJm0MHvmwiq+sQ5QaHu4/UvCjsScle0/bYJI/BmOVZ573ne3qBfbQFnAeTiEeCGcD0qG7lvVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1add017dd1b4ca29d7e01ad741233ec24278992e88ea439c230c73aafa27a05e","last_reissued_at":"2026-05-18T02:50:59.848909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:59.848909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.7014","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kDJDjxN6COYQPgtvrJT8h+e7/yvOM1naG8LDJTAPFHUpO172s96FrevUi+LQn3ynkRYUyA5w5ruX24yJrntcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:45.857201Z"},"content_sha256":"c3238c7b6b34cd03f77e9d488a36ce071250b639fd2f10958a0aa818af913d4c","schema_version":"1.0","event_id":"sha256:c3238c7b6b34cd03f77e9d488a36ce071250b639fd2f10958a0aa818af913d4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DLOQC7ORWTFCTV7ADLLUCIZ6YJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding a closest point in a lattice of Voronoi's first kind","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alex Grant, I. Vaughan L. Clarkson, Robby G. McKilliam","submitted_at":"2014-05-27T19:05:57Z","abstract_excerpt":"We show that for those lattices of Voronoi's first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7014","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vkr0O5WIeBFAIXLjh/tupZZuFa6bD8q9B8dcdkIp3y0Z/lb2+iDkPuvZGcSzW6ZtGm6/HqbwRYA4JFTuP5rwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:45.857920Z"},"content_sha256":"f72f69f0ec491dbbf8ce9765dbf5e9ef290a042db9881acd44cb9e200a806d48","schema_version":"1.0","event_id":"sha256:f72f69f0ec491dbbf8ce9765dbf5e9ef290a042db9881acd44cb9e200a806d48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DLOQC7ORWTFCTV7ADLLUCIZ6YJ/bundle.json","state_url":"https://pith.science/pith/DLOQC7ORWTFCTV7ADLLUCIZ6YJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DLOQC7ORWTFCTV7ADLLUCIZ6YJ/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":"2026-05-31T08:38:45Z","links":{"resolver":"https://pith.science/pith/DLOQC7ORWTFCTV7ADLLUCIZ6YJ","bundle":"https://pith.science/pith/DLOQC7ORWTFCTV7ADLLUCIZ6YJ/bundle.json","state":"https://pith.science/pith/DLOQC7ORWTFCTV7ADLLUCIZ6YJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DLOQC7ORWTFCTV7ADLLUCIZ6YJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DLOQC7ORWTFCTV7ADLLUCIZ6YJ","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":"1cf22d70586c32d569156038c706058d2dce1d22abb2bd5408db70550212c405","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-27T19:05:57Z","title_canon_sha256":"db54e10ee3346b2ebaec11e92741a2b5967909519094abecc43c88ce9d8a31bb"},"schema_version":"1.0","source":{"id":"1405.7014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7014","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7014v1","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7014","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"DLOQC7ORWTFC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DLOQC7ORWTFCTV7A","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DLOQC7OR","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:f72f69f0ec491dbbf8ce9765dbf5e9ef290a042db9881acd44cb9e200a806d48","target":"graph","created_at":"2026-05-18T02:50:59Z","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":"We show that for those lattices of Voronoi's first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network.","authors_text":"Alex Grant, I. Vaughan L. Clarkson, Robby G. McKilliam","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-27T19:05:57Z","title":"Finding a closest point in a lattice of Voronoi's first kind"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7014","kind":"arxiv","version":1},"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:c3238c7b6b34cd03f77e9d488a36ce071250b639fd2f10958a0aa818af913d4c","target":"record","created_at":"2026-05-18T02:50:59Z","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":"1cf22d70586c32d569156038c706058d2dce1d22abb2bd5408db70550212c405","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-27T19:05:57Z","title_canon_sha256":"db54e10ee3346b2ebaec11e92741a2b5967909519094abecc43c88ce9d8a31bb"},"schema_version":"1.0","source":{"id":"1405.7014","kind":"arxiv","version":1}},"canonical_sha256":"1add017dd1b4ca29d7e01ad741233ec24278992e88ea439c230c73aafa27a05e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1add017dd1b4ca29d7e01ad741233ec24278992e88ea439c230c73aafa27a05e","first_computed_at":"2026-05-18T02:50:59.848909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:59.848909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FZSx/Rcz2qNDMJm0MHvmwiq+sQ5QaHu4/UvCjsScle0/bYJI/BmOVZ573ne3qBfbQFnAeTiEeCGcD0qG7lvVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:59.849496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3238c7b6b34cd03f77e9d488a36ce071250b639fd2f10958a0aa818af913d4c","sha256:f72f69f0ec491dbbf8ce9765dbf5e9ef290a042db9881acd44cb9e200a806d48"],"state_sha256":"cb848ae242986b7617d2c5c8edcd7170496ef578daac4a2016690419ec403c2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B55h/88gLjPbQw2ERcYrQSj5TE2dhB0/40DEQsiMXaEGgtSY+zP8z6qqSdV9L+NFKeR/0FXUYVhBYK1wq/djAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:38:45.861851Z","bundle_sha256":"71dc4116c43c19f8dc776ebc8a4dfb1fa7051b0a4110fd51ade42a8e5f9b553e"}}