{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:T2U3I4F6KMHAVFDIBXC66DTYTA","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":"d4e3a8ed473d2b7ceb36608a74b3c098f58d5dd2c998f1cc002c54974a6c52bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-05-12T09:11:00Z","title_canon_sha256":"f6a347c566686cf6802f398f460a2898b3547e5bcbabe3d484acfbd490f65a88"},"schema_version":"1.0","source":{"id":"2505.07369","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.07369","created_at":"2026-07-05T11:14:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.07369v2","created_at":"2026-07-05T11:14:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07369","created_at":"2026-07-05T11:14:28Z"},{"alias_kind":"pith_short_12","alias_value":"T2U3I4F6KMHA","created_at":"2026-07-05T11:14:28Z"},{"alias_kind":"pith_short_16","alias_value":"T2U3I4F6KMHAVFDI","created_at":"2026-07-05T11:14:28Z"},{"alias_kind":"pith_short_8","alias_value":"T2U3I4F6","created_at":"2026-07-05T11:14:28Z"}],"graph_snapshots":[{"event_id":"sha256:c4637fb793590db89ae4a5ea45fb5a52667f7686537d2d3123e7f7c22cec8f62","target":"graph","created_at":"2026-07-05T11:14:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.07369/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 2021, Ordentlich, Regev and Weiss made a breakthrough that the lattice covering density of any $n$-dimensional convex body is upper bounded by $cn^{2}$, improving on the best previous bound established by Rogers in 1959. However, for the Euclidean ball, Rogers obtained the better upper bound $n(\\log_{e}n)^{c}$, and this result was extended to certain symmetric convex bodies by Gritzmann. The constant $c$ above is independent on $n$. In this paper, we show that such a bound can be achieved for more general classes of convex bodies without symmetry, including anti-blocking bodies, locally ant","authors_text":"Fei Xue, Jun Wang, Matthias Schymura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-05-12T09:11:00Z","title":"On lattice coverings by locally anti-blocking bodies and polytopes with few vertices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07369","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":"sha256:125c9ca7b12c826399cccbb9ac34d77a17431c007627c7936f00372e254310eb","target":"record","created_at":"2026-07-05T11:14:28Z","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":"d4e3a8ed473d2b7ceb36608a74b3c098f58d5dd2c998f1cc002c54974a6c52bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-05-12T09:11:00Z","title_canon_sha256":"f6a347c566686cf6802f398f460a2898b3547e5bcbabe3d484acfbd490f65a88"},"schema_version":"1.0","source":{"id":"2505.07369","kind":"arxiv","version":2}},"canonical_sha256":"9ea9b470be530e0a94680dc5ef0e78983bd278c0698b2ccdbd013013029b1a3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ea9b470be530e0a94680dc5ef0e78983bd278c0698b2ccdbd013013029b1a3c","first_computed_at":"2026-07-05T11:14:28.941617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:14:28.941617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tNZUOjSc2h9m8Itrc6TeRQHBCB159EKPwJNL56q0XZWRk3H+M7AyhSSfTPoZddumtzx6iABBw8rSjXxSfaVSCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:14:28.942092Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.07369","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:125c9ca7b12c826399cccbb9ac34d77a17431c007627c7936f00372e254310eb","sha256:c4637fb793590db89ae4a5ea45fb5a52667f7686537d2d3123e7f7c22cec8f62"],"state_sha256":"eb9c854c2006ebf9dc89633bacf51748e4ec7dde6b8995b24b53ffc4fb8dacb6"}