{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I2NPIVI25JCZC5DORDE37EW2HA","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":"d0f4f4692f08c2d14ffe88a38489443f4db9ed1546609d29754fedb3c4f481bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-01-02T16:36:24Z","title_canon_sha256":"528c4ced3aef2f8400aaca1f3ed57c7888182f0fc11622aed9a681d4dddc4e9c"},"schema_version":"1.0","source":{"id":"1401.0468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0468","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0468v1","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0468","created_at":"2026-05-18T03:03:23Z"},{"alias_kind":"pith_short_12","alias_value":"I2NPIVI25JCZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I2NPIVI25JCZC5DO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I2NPIVI2","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:cfff76f24edfcdedab584d05bd052f10676bc49d02da296568f0c749e66a428d","target":"graph","created_at":"2026-05-18T03:03:23Z","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":"The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of overlap with other balls. We study two natural choices of overlap measures and obtain the optimal lattice packings in a parameterized family of lattices which contains the FCC, BCC, and integer lattice.","authors_text":"Caroline Uhler, Mabel Iglesias-Ham, Michael Kerber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-01-02T16:36:24Z","title":"Sphere Packing with Limited Overlap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0468","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:cb1ed2b327c92bbcf7a2f77d1170692aaad6291672b71360203a166a9fc166b0","target":"record","created_at":"2026-05-18T03:03:23Z","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":"d0f4f4692f08c2d14ffe88a38489443f4db9ed1546609d29754fedb3c4f481bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-01-02T16:36:24Z","title_canon_sha256":"528c4ced3aef2f8400aaca1f3ed57c7888182f0fc11622aed9a681d4dddc4e9c"},"schema_version":"1.0","source":{"id":"1401.0468","kind":"arxiv","version":1}},"canonical_sha256":"469af4551aea4591746e88c9bf92da3810d7c54a1ae76fc73bd763f58caac151","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"469af4551aea4591746e88c9bf92da3810d7c54a1ae76fc73bd763f58caac151","first_computed_at":"2026-05-18T03:03:23.161354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:23.161354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UYmvbXQQ4JGZcjNllHeOmolpXRTBD6FShraGmFVAL02Vi8AAspYB5DEp7rqN3W+K3cYwY/TGSSUe+1oHcYLpBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:23.161972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb1ed2b327c92bbcf7a2f77d1170692aaad6291672b71360203a166a9fc166b0","sha256:cfff76f24edfcdedab584d05bd052f10676bc49d02da296568f0c749e66a428d"],"state_sha256":"61be33dd41ca8217d4c2c11eb87cc3c5b5872883d7a933cca33f4eeb222ddf3d"}