{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LNM6RAPAJN2O5WX74Z33MFZVCT","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":"48a9477b88920b909ab1d65ee5057bcc1b6dfd28eb172a94636c1c657763436e","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-07T12:21:40Z","title_canon_sha256":"9887b8876c77030bb940abe1e2eafc094bb90287ceaa1548881420f5b57a17bf"},"schema_version":"1.0","source":{"id":"1903.02866","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.02866","created_at":"2026-07-05T04:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"1903.02866v2","created_at":"2026-07-05T04:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02866","created_at":"2026-07-05T04:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"LNM6RAPAJN2O","created_at":"2026-07-05T04:54:11Z"},{"alias_kind":"pith_short_16","alias_value":"LNM6RAPAJN2O5WX7","created_at":"2026-07-05T04:54:11Z"},{"alias_kind":"pith_short_8","alias_value":"LNM6RAPA","created_at":"2026-07-05T04:54:11Z"}],"graph_snapshots":[{"event_id":"sha256:573bc2b577ea258adaf28c7e60ef87b9a3e52f60918d5e9d9b300357d751e9fb","target":"graph","created_at":"2026-07-05T04:54:11Z","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/1903.02866/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of $d/2$ in dimension $d$, achieved by the \"standard terminal simplices\" and direct sums of them. We prove this conjecture up to dimension three and show it to be equivalent to the conjecture of Gonz\\'alez-Merino \\& Schymura (2017) that the $d$-th covering minimum of the standard terminal $n$-simplex equals $d/2$, for every $n>d$.\n  We also show that these two conjectures would follow from a discrete analog for lattice simplices of Hadwiger's formula bounding the c","authors_text":"Francisco Santos, Giulia Codenotti, Matthias Schymura","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-07T12:21:40Z","title":"The covering radius and a discrete surface area for non-hollow simplices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02866","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":"sha256:9806fa7da212cbd1aa2e67b1087c278211865c6841bfd090adb7904229e19e2b","target":"record","created_at":"2026-07-05T04:54:11Z","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":"48a9477b88920b909ab1d65ee5057bcc1b6dfd28eb172a94636c1c657763436e","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-07T12:21:40Z","title_canon_sha256":"9887b8876c77030bb940abe1e2eafc094bb90287ceaa1548881420f5b57a17bf"},"schema_version":"1.0","source":{"id":"1903.02866","kind":"arxiv","version":2}},"canonical_sha256":"5b59e881e04b74eedaffe677b6173514f134e6d1484ee4b0779a8142e4ec34da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b59e881e04b74eedaffe677b6173514f134e6d1484ee4b0779a8142e4ec34da","first_computed_at":"2026-07-05T04:54:11.109142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:54:11.109142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dW5m1ghSAIsL4UYqg5LtxOZBGxdxLado0oTNuNHedvFtqvm1rdFsnVoBjXJqr+7Qc0AzjWVJvfPmq+hhubDFAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:54:11.109603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.02866","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9806fa7da212cbd1aa2e67b1087c278211865c6841bfd090adb7904229e19e2b","sha256:573bc2b577ea258adaf28c7e60ef87b9a3e52f60918d5e9d9b300357d751e9fb"],"state_sha256":"c82fc76af90e3b92ee359b7842e7524423cc5f82cbfd16e3a3b444f05cc0f9bd"}