{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3U33ORHOA5CGZ7JZ4ZISVQERRT","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":"e170185860cfb3ab0519eec214fbe28ba714dbcff4f1ceb0bb747932d4f002fb","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-31T21:21:05Z","title_canon_sha256":"ba9d94aa973483594865e63638ea00ece435df789cc4ed4374f155d80d73e0eb"},"schema_version":"1.0","source":{"id":"1411.0028","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0028","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0028v1","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0028","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"3U33ORHOA5CG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3U33ORHOA5CGZ7JZ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3U33ORHO","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:fdf0dc14ac6305f8e861d541b9dac912aba6db5893c03f1ee81e9011ff424aac","target":"graph","created_at":"2026-05-18T01:38:54Z","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 discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.","authors_text":"Ivan Soprunov","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-31T21:21:05Z","title":"Lattice polytopes in coding theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0028","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:a427dfdf0b9b3b0225ddbd0c9e09e1ac7c59bcafef9c67284177c1bb7586a2e2","target":"record","created_at":"2026-05-18T01:38:54Z","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":"e170185860cfb3ab0519eec214fbe28ba714dbcff4f1ceb0bb747932d4f002fb","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-31T21:21:05Z","title_canon_sha256":"ba9d94aa973483594865e63638ea00ece435df789cc4ed4374f155d80d73e0eb"},"schema_version":"1.0","source":{"id":"1411.0028","kind":"arxiv","version":1}},"canonical_sha256":"dd37b744ee07446cfd39e6512ac0918cd4a1a69cadede4c49de8635de052db78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd37b744ee07446cfd39e6512ac0918cd4a1a69cadede4c49de8635de052db78","first_computed_at":"2026-05-18T01:38:54.057916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:54.057916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vFoyM0tDbQDnBYduzGOq8bn7zgjWWpvlMiV1OMlAFlv7WO6bqEdqh52mIYDEIl7vs1wyDtH97LIFLUvRf7P6Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:54.058537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0028","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a427dfdf0b9b3b0225ddbd0c9e09e1ac7c59bcafef9c67284177c1bb7586a2e2","sha256:fdf0dc14ac6305f8e861d541b9dac912aba6db5893c03f1ee81e9011ff424aac"],"state_sha256":"3cad9703c18fbf16e52de0653806c69ff870cda766e905bef7810478afde00d4"}