{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NZRHQWNCWFIMDJ6IFXV6MDGJCZ","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":"1ee53c8ffe26ad358c958348717908c19bd14b930d698dc13a6ea98eacdfe88d","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-02-26T04:07:47Z","title_canon_sha256":"6da9515f7405ecf10b756df8d04ba78a99d8e691b995b035925fbff8828af857"},"schema_version":"1.0","source":{"id":"1402.6404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6404","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6404v1","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6404","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"NZRHQWNCWFIM","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NZRHQWNCWFIMDJ6I","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NZRHQWNC","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:082a5af63af134c80bf3ab3df8c775b9f54298b28518b2162e1d250994bba1f3","target":"graph","created_at":"2026-05-18T02:57:44Z","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":"Trellises are crucial graphical representations of codes. While conventional trellises are well understood, the general theory of (tail-biting) trellises is still under development. Iterative decoding concretely motivates such theory. In this paper we first develop a new algebraic framework for a systematic analysis of linear trellises which enables us to address open foundational questions. In particular, we present a useful and powerful characterization of linear trellis isomorphy. We also obtain a new proof of the Factorization Theorem of Koetter/Vardy and point out unnoticed problems for t","authors_text":"David Conti, Nigel Boston","cross_cats":["cs.DM","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-02-26T04:07:47Z","title":"On the Algebraic Structure of Linear Trellises"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6404","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:b6e0fc2e3147c619cebbfa0cee32063b5a0b6bb0bb56a5dac5386718538e0b48","target":"record","created_at":"2026-05-18T02:57:44Z","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":"1ee53c8ffe26ad358c958348717908c19bd14b930d698dc13a6ea98eacdfe88d","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-02-26T04:07:47Z","title_canon_sha256":"6da9515f7405ecf10b756df8d04ba78a99d8e691b995b035925fbff8828af857"},"schema_version":"1.0","source":{"id":"1402.6404","kind":"arxiv","version":1}},"canonical_sha256":"6e627859a2b150c1a7c82debe60cc9164be4a5acb5f3af8552a3df5f7230ae31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e627859a2b150c1a7c82debe60cc9164be4a5acb5f3af8552a3df5f7230ae31","first_computed_at":"2026-05-18T02:57:44.596858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:44.596858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L5vxKgc3oQKiL+HiXLsLaONYHmkRuvDtdADx+FzBctMtnSORNhwobCv7YTqc622K07RyipGgKqgGGULOqmYaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:44.597290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6e0fc2e3147c619cebbfa0cee32063b5a0b6bb0bb56a5dac5386718538e0b48","sha256:082a5af63af134c80bf3ab3df8c775b9f54298b28518b2162e1d250994bba1f3"],"state_sha256":"1c2f67d2edeb3a5756cbe191f1457815adf907ab0e36702f4fdf743ac3436108"}