{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WOQ6NT5IBEN74KQ6I3NP7ORO4I","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":"c5d0402641883e3d00720c3c6896241d0dba243775f3801240f66e34e52a6308","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-16T15:38:00Z","title_canon_sha256":"5e3c19f6c241131799fa5ecf34b2e834978f28141eaac2d584ec3ae01098568a"},"schema_version":"1.0","source":{"id":"1202.3625","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3625","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3625v2","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3625","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"WOQ6NT5IBEN7","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WOQ6NT5IBEN74KQ6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WOQ6NT5I","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:6e7518ca253269ac5a683c05d93d4d122f5fe05e6847a4bf4803f213d20cd203","target":"graph","created_at":"2026-05-18T02:54:22Z","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":"We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial. This yields both a generalization and a refinement of the weight enumerator of a linear code. In particular, one can deal with infinitely many finite fields simultaneously by defining a weight enumerator for codes over infinite fields.","authors_text":"Thomas B\\\"achler, Wilhelm Plesken","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-16T15:38:00Z","title":"From Linear Codes to Hyperplane Arrangements via Thomas Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3625","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:e980b53c07c06bf75cd88d11248f4c57783b198bfdafc04031a60dc2e2db208f","target":"record","created_at":"2026-05-18T02:54:22Z","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":"c5d0402641883e3d00720c3c6896241d0dba243775f3801240f66e34e52a6308","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-02-16T15:38:00Z","title_canon_sha256":"5e3c19f6c241131799fa5ecf34b2e834978f28141eaac2d584ec3ae01098568a"},"schema_version":"1.0","source":{"id":"1202.3625","kind":"arxiv","version":2}},"canonical_sha256":"b3a1e6cfa8091bfe2a1e46daffba2ee23640670e1937c5a48924ad807fb2f2f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3a1e6cfa8091bfe2a1e46daffba2ee23640670e1937c5a48924ad807fb2f2f9","first_computed_at":"2026-05-18T02:54:22.478282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:22.478282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dS2vewc+I7kof2K3K28+EytPZeL2VNA2t+GmpLu7JEZOAnvY8AIX4vK0vfgF1LSiQ1EVVi1TK/mhiWGLOEqqBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:22.478680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e980b53c07c06bf75cd88d11248f4c57783b198bfdafc04031a60dc2e2db208f","sha256:6e7518ca253269ac5a683c05d93d4d122f5fe05e6847a4bf4803f213d20cd203"],"state_sha256":"9fc7de124fe3e89f38343eb30ba441897d2a4761bf4b2c3f00b68cc411a41002"}