{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZZPR3R5FSYF5LMRPSAV6A7KI3M","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":"f5a273817bb6bd73e90c2293bb2ac2984d18d67a5edf0d6efd3e9a010b64b3d3","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-04T11:06:54Z","title_canon_sha256":"54536074d50cf9cb00bbe3239f2725155a05deaef85239bf9777a3b7fe9de9d9"},"schema_version":"1.0","source":{"id":"1203.0728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0728","created_at":"2026-05-18T04:00:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0728v1","created_at":"2026-05-18T04:00:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0728","created_at":"2026-05-18T04:00:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZZPR3R5FSYF5","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZZPR3R5FSYF5LMRP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZZPR3R5F","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:55c2c12eede76e9ba25eaa6f74bf48db6f627ac683f8dc6f50ff1a9070e625c0","target":"graph","created_at":"2026-05-18T04:00:50Z","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":"Upper and lower bounds are derived for the quantity in the title, which is tabulated for modest values of $n$ and $k.$ An application to graphs with many cycles is given.","authors_text":"A. Alahmadi, C. Thomassen, P. Sol\\'e, R. dela Cruz, R. E. L. Aldred","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-04T11:06:54Z","title":"The maximum number of minimal codewords in an $[n,k]-$code"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0728","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":"sha256:08174f4feaf13f7c7731120c399a1893e056c352294088e2fa760bb4ba9d6841","target":"record","created_at":"2026-05-18T04:00:50Z","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":"f5a273817bb6bd73e90c2293bb2ac2984d18d67a5edf0d6efd3e9a010b64b3d3","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-04T11:06:54Z","title_canon_sha256":"54536074d50cf9cb00bbe3239f2725155a05deaef85239bf9777a3b7fe9de9d9"},"schema_version":"1.0","source":{"id":"1203.0728","kind":"arxiv","version":1}},"canonical_sha256":"ce5f1dc7a5960bd5b22f902be07d48db0f188e8baf1abe36bc8c524d1cafd6f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce5f1dc7a5960bd5b22f902be07d48db0f188e8baf1abe36bc8c524d1cafd6f4","first_computed_at":"2026-05-18T04:00:50.705354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:50.705354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AvI9HJcxDyskP70FFl6rVynW24Q0VjWIm9WaIlLsTPMZg83LK3RPHvOf4srgSwUQdGS3Hp+4HezDFSuKwVjdAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:50.705912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08174f4feaf13f7c7731120c399a1893e056c352294088e2fa760bb4ba9d6841","sha256:55c2c12eede76e9ba25eaa6f74bf48db6f627ac683f8dc6f50ff1a9070e625c0"],"state_sha256":"e84c612d93106f2311d78cb02f690bc4b64404d56d22721c9f26db669371f01d"}