{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UB5GWFSUPE6DBI6YJML362NAXT","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":"fa5307edb63d328826074372ae76368fef90726fff13b4703fd2eec35af96e0c","cross_cats_sorted":["cs.CC","cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-08T14:57:05Z","title_canon_sha256":"e4445e257340e1f971f29adba440c7b598bb9ad3c1cab30426f13d76f344f784"},"schema_version":"1.0","source":{"id":"1507.02184","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02184","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02184v4","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02184","created_at":"2026-05-18T00:16:03Z"},{"alias_kind":"pith_short_12","alias_value":"UB5GWFSUPE6D","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UB5GWFSUPE6DBI6Y","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UB5GWFSU","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:8ca027f3bb49a9b9ed7fe918d491301a976ea0c6ea61a7337e7a0154a586d6a0","target":"graph","created_at":"2026-05-18T00:16:03Z","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":"Given n subspaces of a finite-dimensional vector space over a fixed finite field $\\mathbb F$, we wish to find a linear layout $V_1,V_2,\\ldots,V_n$ of the subspaces such that $\\dim((V_1+V_2+\\cdots+V_i) \\cap (V_{i+1}+\\cdots+V_n))\\le k$ for all i, such a linear layout is said to have width at most k. When restricted to 1-dimensional subspaces, this problem is equivalent to computing the trellis-width (or minimum trellis state-complexity) of a linear code in coding theory and computing the path-width of an $\\mathbb F$-represented matroid in matroid theory.\n  We present a fixed-parameter tractable ","authors_text":"Eun Jung Kim, Jisu Jeong, Sang-il Oum","cross_cats":["cs.CC","cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-08T14:57:05Z","title":"The \"art of trellis decoding\" is fixed-parameter tractable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02184","kind":"arxiv","version":4},"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:b711b6cd873176c5db550ae428ab45facc9eee318756eaad14a6db2fe2541698","target":"record","created_at":"2026-05-18T00:16:03Z","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":"fa5307edb63d328826074372ae76368fef90726fff13b4703fd2eec35af96e0c","cross_cats_sorted":["cs.CC","cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-08T14:57:05Z","title_canon_sha256":"e4445e257340e1f971f29adba440c7b598bb9ad3c1cab30426f13d76f344f784"},"schema_version":"1.0","source":{"id":"1507.02184","kind":"arxiv","version":4}},"canonical_sha256":"a07a6b1654793c30a3d84b17bf69a0bce6573ed651617d8ed348cf9c941c498b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a07a6b1654793c30a3d84b17bf69a0bce6573ed651617d8ed348cf9c941c498b","first_computed_at":"2026-05-18T00:16:03.380619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:03.380619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S7ZSut8Mxb27vqKbcoWMwbPEr6q5Or8lpwh9PMrvquFr9Ym30UMASiD2FPyiUxmz7v9TeHKouwqQR798FbL/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:03.380971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02184","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b711b6cd873176c5db550ae428ab45facc9eee318756eaad14a6db2fe2541698","sha256:8ca027f3bb49a9b9ed7fe918d491301a976ea0c6ea61a7337e7a0154a586d6a0"],"state_sha256":"b6f6387aa1d0bc145c663d57156161d08dbf79c9891e4a891b5a7a18fdcf4f7a"}