{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7VRMP6QN7MWQA5VR2XXAA7LYJM","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":"eff14f6f7fcf46db65537c13d3e7e1263e75598a20993902d750b5880c210f10","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-06T15:18:15Z","title_canon_sha256":"6d7648b7efad192c22883669082bdaeba8f982e5226c87ddfd9ec446458fab14"},"schema_version":"1.0","source":{"id":"1506.02163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02163","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02163v2","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02163","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"7VRMP6QN7MWQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7VRMP6QN7MWQA5VR","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7VRMP6QN","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:20722beaecede7bce460b42d69ec0c861b7cbcd7a7878081604cfc8b7d797796","target":"graph","created_at":"2026-05-18T00:47:29Z","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 propose a new method to bound the capacity of checkerboard codes on the hexagonal lattice. This produces rigorous bounds that are tighter than those commonly known.","authors_text":"Jie Ding, Mohammad Noshad, Vahid Tarokh, Zhun Deng","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-06T15:18:15Z","title":"Capacity of Hexagonal Checkerboard Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02163","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":"sha256:8d0c5af4c038091b30af55ac0c65d3a890e0f69e7db2117e84dc9ab1bb1e7fe5","target":"record","created_at":"2026-05-18T00:47:29Z","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":"eff14f6f7fcf46db65537c13d3e7e1263e75598a20993902d750b5880c210f10","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-06T15:18:15Z","title_canon_sha256":"6d7648b7efad192c22883669082bdaeba8f982e5226c87ddfd9ec446458fab14"},"schema_version":"1.0","source":{"id":"1506.02163","kind":"arxiv","version":2}},"canonical_sha256":"fd62c7fa0dfb2d0076b1d5ee007d784b193b0f16368886bf29b8ccf458bace70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd62c7fa0dfb2d0076b1d5ee007d784b193b0f16368886bf29b8ccf458bace70","first_computed_at":"2026-05-18T00:47:29.583014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:29.583014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j92M+SYuL4NrXfOw1KAdJTMLOC6OQfsSokbzTqxn1aVvih+OjCzg6fQDL/RMF8DCroU5ujyYg/N9GYbi72KjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:29.583508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d0c5af4c038091b30af55ac0c65d3a890e0f69e7db2117e84dc9ab1bb1e7fe5","sha256:20722beaecede7bce460b42d69ec0c861b7cbcd7a7878081604cfc8b7d797796"],"state_sha256":"d74dcdc7888bf9c88a71ff1aab7241eb0035b058fe7105cf9adc9b884b964df2"}