{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WJP3HA6AN22RKKDXL6IISD3XTG","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":"63001e11e4d32f3277dc3d5cdaa6e9bcc7b7f85026054e215d95618bdea4c251","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-24T17:54:21Z","title_canon_sha256":"2eb7ee9d757fe9802ca75cc8965f4be7f8ceb88c7583941e34f17dacbae13b85"},"schema_version":"1.0","source":{"id":"1512.07872","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07872","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07872v1","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07872","created_at":"2026-05-18T01:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"WJP3HA6AN22R","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJP3HA6AN22RKKDX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJP3HA6A","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:20b13fded2fb64f959632630052b07c558c2e6fadbf12d0dca01f6127bb3f509","target":"graph","created_at":"2026-05-18T01:23:45Z","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 show that the diameter of a d-dimensional lattice polytope in [0,k]^n is at most (k - 1/2) d. This result implies that the diameter of a d-dimensional half-integral polytope is at most 3/2 d. We also show that for half-integral polytopes the latter bound is tight for any d.","authors_text":"Alberto Del Pia, Carla Michini","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-24T17:54:21Z","title":"On the diameter of lattice polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07872","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":"sha256:4a5903e063149863b6b4f51a02f2f9fb2dcb84e15fc0b07795f43c59b92521f9","target":"record","created_at":"2026-05-18T01:23:45Z","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":"63001e11e4d32f3277dc3d5cdaa6e9bcc7b7f85026054e215d95618bdea4c251","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-24T17:54:21Z","title_canon_sha256":"2eb7ee9d757fe9802ca75cc8965f4be7f8ceb88c7583941e34f17dacbae13b85"},"schema_version":"1.0","source":{"id":"1512.07872","kind":"arxiv","version":1}},"canonical_sha256":"b25fb383c06eb51528775f90890f7799933a5b2134412c25f414211ae81a64fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b25fb383c06eb51528775f90890f7799933a5b2134412c25f414211ae81a64fe","first_computed_at":"2026-05-18T01:23:45.894169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:45.894169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r3r95UjnNN/DFLOE/5Agu6WIyIZt8zz2yoj3fzeHDis05Gd6V8+HPXDJX1vVtNLPSel7z0uYLbXGrnGAhJ6TCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:45.894778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07872","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a5903e063149863b6b4f51a02f2f9fb2dcb84e15fc0b07795f43c59b92521f9","sha256:20b13fded2fb64f959632630052b07c558c2e6fadbf12d0dca01f6127bb3f509"],"state_sha256":"8cc276c849263c99719f72928c7f4f5398eadabdcf783d4c332de89153c2c137"}