{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:M4KIKQ4VQRKHZFFL6N6HOBOQF7","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":"6804ce491ccf9772b934cc1dcfd21449a294ac99367829ebbbfbccc7c2dd7e45","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-04-13T22:37:37Z","title_canon_sha256":"5b77c6eec368326ff455b40d45b38c8f35a4ab025612d1cea1aae78f72889092"},"schema_version":"1.0","source":{"id":"0904.2022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2022","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2022v1","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2022","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"M4KIKQ4VQRKH","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"M4KIKQ4VQRKHZFFL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"M4KIKQ4V","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:484ef9b4bdc26a8c85abb5be4b3d68a64648a9bb32b77b7977af72e1a2461e65","target":"graph","created_at":"2026-05-18T00:59:11Z","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":"The linear-programming decoding performance of a binary linear code crucially depends on the structure of the fundamental cone of the parity-check matrix that describes the code. Towards a better understanding of fundamental cones and the vectors therein, we introduce the notion of absdet-pseudo-codewords and perm-pseudo-codewords: we give the definitions, we discuss some simple examples, and we list some of their properties.","authors_text":"Pascal O. Vontobel, Roxana Smarandache","cross_cats":["cs.DM","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-04-13T22:37:37Z","title":"Absdet-Pseudo-Codewords and Perm-Pseudo-Codewords: Definitions and Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2022","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":"sha256:31b3a8844f7d60080bd6d41e0a4e66b8582470c4343abe46b2ba9f67a3a90cf1","target":"record","created_at":"2026-05-18T00:59:11Z","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":"6804ce491ccf9772b934cc1dcfd21449a294ac99367829ebbbfbccc7c2dd7e45","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-04-13T22:37:37Z","title_canon_sha256":"5b77c6eec368326ff455b40d45b38c8f35a4ab025612d1cea1aae78f72889092"},"schema_version":"1.0","source":{"id":"0904.2022","kind":"arxiv","version":1}},"canonical_sha256":"671485439584547c94abf37c7705d02ffa84c761b62cb621d0e96aa95bd10b3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"671485439584547c94abf37c7705d02ffa84c761b62cb621d0e96aa95bd10b3e","first_computed_at":"2026-05-18T00:59:11.414901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:11.414901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7oNTvs+bvkIRmbvX1Wv9wDFP7im5F8a/c8kO7Anz4HuaVn2G2lie+FNIBydo6RCjHll2XnxcJ/LhdnJqHjZ4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:11.415602Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31b3a8844f7d60080bd6d41e0a4e66b8582470c4343abe46b2ba9f67a3a90cf1","sha256:484ef9b4bdc26a8c85abb5be4b3d68a64648a9bb32b77b7977af72e1a2461e65"],"state_sha256":"04d075b3a67760fc908a7009039aad0d5839c1a694b64a27b4b44f605aee0a64"}