{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KKQZCQYHVTHEOZJPOCMVEKWVVJ","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":"8956bb9641ab6d30b69e4ddc9f8bbb530b0c8c36cfc7d22f3697f84bd19d2a26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-12-20T13:15:18Z","title_canon_sha256":"bedfcfaee1fe4df1921701fc97d8b2b5d1dc6ce69d066c18a036f7ccca4f2270"},"schema_version":"1.0","source":{"id":"1912.09804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.09804","created_at":"2026-07-05T05:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1912.09804v1","created_at":"2026-07-05T05:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.09804","created_at":"2026-07-05T05:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"KKQZCQYHVTHE","created_at":"2026-07-05T05:33:57Z"},{"alias_kind":"pith_short_16","alias_value":"KKQZCQYHVTHEOZJP","created_at":"2026-07-05T05:33:57Z"},{"alias_kind":"pith_short_8","alias_value":"KKQZCQYH","created_at":"2026-07-05T05:33:57Z"}],"graph_snapshots":[{"event_id":"sha256:40e87f28ed3b14b3a946cbd618239747d1868bd248706a9ecc4216f0431ac365","target":"graph","created_at":"2026-07-05T05:33:57Z","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/1912.09804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the minimum number of minimal codewords in linear codes from the point of view of projective geometry. We derive bounds and in some cases determine the exact values. We also present an extension to minimal subcode supports.","authors_text":"Alfred Wassermann, Michael Kiermaier, Romar dela Cruz, Sascha Kurz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-12-20T13:15:18Z","title":"On the minimum number of minimal codewords"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.09804","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:bed0e8d03a0db00c41e9bcad717446c58dfa817f60acdd41bef71daf3b987dbe","target":"record","created_at":"2026-07-05T05:33:57Z","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":"8956bb9641ab6d30b69e4ddc9f8bbb530b0c8c36cfc7d22f3697f84bd19d2a26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-12-20T13:15:18Z","title_canon_sha256":"bedfcfaee1fe4df1921701fc97d8b2b5d1dc6ce69d066c18a036f7ccca4f2270"},"schema_version":"1.0","source":{"id":"1912.09804","kind":"arxiv","version":1}},"canonical_sha256":"52a1914307acce47652f7099522ad5aa54d212ea92e0a451575a397969adeaf3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52a1914307acce47652f7099522ad5aa54d212ea92e0a451575a397969adeaf3","first_computed_at":"2026-07-05T05:33:57.487002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:33:57.487002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fAlQjl0mn3OcLTe/XmRiXZ94JjoN6wYRKX4c0rLEFGk0zZMLYy2TVQrpTxZe1C8I+U4iVVFW/plP2bthnDWuCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:33:57.487570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.09804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bed0e8d03a0db00c41e9bcad717446c58dfa817f60acdd41bef71daf3b987dbe","sha256:40e87f28ed3b14b3a946cbd618239747d1868bd248706a9ecc4216f0431ac365"],"state_sha256":"34cd602c050ed4591a664d039d917755fd19156a59023781c1392517039fbfd0"}