{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:I3OJREJJ7CVZAEO55L2TGXNSR4","short_pith_number":"pith:I3OJREJJ","canonical_record":{"source":{"id":"1401.2496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-11T02:52:59Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c6543151c0006c7a3177cf00b82cbde430e55be54be0d4b89675c2827c3e6750","abstract_canon_sha256":"2aca13099da2e45c30d0aef05e18e9ba84f54ef54914aba54d5e1a176671fbc0"},"schema_version":"1.0"},"canonical_sha256":"46dc989129f8ab9011ddeaf5335db28f1e83eff3ff31df20cf145940c434bc97","source":{"kind":"arxiv","id":"1401.2496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2496","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2496v1","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2496","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"pith_short_12","alias_value":"I3OJREJJ7CVZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I3OJREJJ7CVZAEO5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I3OJREJJ","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:I3OJREJJ7CVZAEO55L2TGXNSR4","target":"record","payload":{"canonical_record":{"source":{"id":"1401.2496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-11T02:52:59Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c6543151c0006c7a3177cf00b82cbde430e55be54be0d4b89675c2827c3e6750","abstract_canon_sha256":"2aca13099da2e45c30d0aef05e18e9ba84f54ef54914aba54d5e1a176671fbc0"},"schema_version":"1.0"},"canonical_sha256":"46dc989129f8ab9011ddeaf5335db28f1e83eff3ff31df20cf145940c434bc97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:33.380132Z","signature_b64":"RQwHJF5YOX/7x1EUcXzenEsxsZISCr8kzt/bhAktpIgo3aZSeYUTVp+MAOH7VtsuxM0yKmplpuDCZ84Wv+PFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46dc989129f8ab9011ddeaf5335db28f1e83eff3ff31df20cf145940c434bc97","last_reissued_at":"2026-05-18T03:02:33.379280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:33.379280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.2496","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:02:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpFYp67hTLNvwOFrpkfi/HAerJbUzLiHHU3QGmnZYSttEoDBFqXt8WefoZvo+NCjGKlP6EQiIeZJCm8ZMv56Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:56:26.957310Z"},"content_sha256":"056fa3eba5c97767e5de26e67ce570c81ed403f66447f860a492dbafcb4b8a32","schema_version":"1.0","event_id":"sha256:056fa3eba5c97767e5de26e67ce570c81ed403f66447f860a492dbafcb4b8a32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:I3OJREJJ7CVZAEO55L2TGXNSR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reduction of Error-Trellises for Tail-Biting Convolutional Codes Using Shifted Error-Subsequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Koji Okino, Masato Tajima, Tatsuto Murayama","submitted_at":"2014-01-11T02:52:59Z","abstract_excerpt":"In this paper, we discuss the reduction of error-trellises for tail-biting convolutional codes. In the case where some column of a parity-check matrix has a monomial factor (with indeterminate D), we show that the associated tail-biting error-trellis can be reduced by cyclically shifting the corresponding error-subsequence by l (the power of D) time units. We see that the resulting reduced error-trellis is again tail-biting. Moreover, we show that reduction is also possible using backward-shifted error-subsequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2496","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:02:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EwkekIjvBVGrkaguA/gQWWKjRFbQ5xckzW2kqizrAVvhdsxS/4pDMGyjOeLoZ/AgcLNkvIWKHXydcSKQ3UwFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T22:56:26.957678Z"},"content_sha256":"c6aa6874825290ccea285edcaf5d05de1221a44be40255a30ad96972eee4b270","schema_version":"1.0","event_id":"sha256:c6aa6874825290ccea285edcaf5d05de1221a44be40255a30ad96972eee4b270"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3OJREJJ7CVZAEO55L2TGXNSR4/bundle.json","state_url":"https://pith.science/pith/I3OJREJJ7CVZAEO55L2TGXNSR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3OJREJJ7CVZAEO55L2TGXNSR4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-02T22:56:26Z","links":{"resolver":"https://pith.science/pith/I3OJREJJ7CVZAEO55L2TGXNSR4","bundle":"https://pith.science/pith/I3OJREJJ7CVZAEO55L2TGXNSR4/bundle.json","state":"https://pith.science/pith/I3OJREJJ7CVZAEO55L2TGXNSR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3OJREJJ7CVZAEO55L2TGXNSR4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I3OJREJJ7CVZAEO55L2TGXNSR4","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":"2aca13099da2e45c30d0aef05e18e9ba84f54ef54914aba54d5e1a176671fbc0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-11T02:52:59Z","title_canon_sha256":"c6543151c0006c7a3177cf00b82cbde430e55be54be0d4b89675c2827c3e6750"},"schema_version":"1.0","source":{"id":"1401.2496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2496","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2496v1","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2496","created_at":"2026-05-18T03:02:33Z"},{"alias_kind":"pith_short_12","alias_value":"I3OJREJJ7CVZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I3OJREJJ7CVZAEO5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I3OJREJJ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:c6aa6874825290ccea285edcaf5d05de1221a44be40255a30ad96972eee4b270","target":"graph","created_at":"2026-05-18T03:02:33Z","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":"In this paper, we discuss the reduction of error-trellises for tail-biting convolutional codes. In the case where some column of a parity-check matrix has a monomial factor (with indeterminate D), we show that the associated tail-biting error-trellis can be reduced by cyclically shifting the corresponding error-subsequence by l (the power of D) time units. We see that the resulting reduced error-trellis is again tail-biting. Moreover, we show that reduction is also possible using backward-shifted error-subsequences.","authors_text":"Koji Okino, Masato Tajima, Tatsuto Murayama","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-11T02:52:59Z","title":"Reduction of Error-Trellises for Tail-Biting Convolutional Codes Using Shifted Error-Subsequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2496","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":"sha256:056fa3eba5c97767e5de26e67ce570c81ed403f66447f860a492dbafcb4b8a32","target":"record","created_at":"2026-05-18T03:02:33Z","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":"2aca13099da2e45c30d0aef05e18e9ba84f54ef54914aba54d5e1a176671fbc0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-11T02:52:59Z","title_canon_sha256":"c6543151c0006c7a3177cf00b82cbde430e55be54be0d4b89675c2827c3e6750"},"schema_version":"1.0","source":{"id":"1401.2496","kind":"arxiv","version":1}},"canonical_sha256":"46dc989129f8ab9011ddeaf5335db28f1e83eff3ff31df20cf145940c434bc97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46dc989129f8ab9011ddeaf5335db28f1e83eff3ff31df20cf145940c434bc97","first_computed_at":"2026-05-18T03:02:33.379280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:33.379280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RQwHJF5YOX/7x1EUcXzenEsxsZISCr8kzt/bhAktpIgo3aZSeYUTVp+MAOH7VtsuxM0yKmplpuDCZ84Wv+PFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:33.380132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:056fa3eba5c97767e5de26e67ce570c81ed403f66447f860a492dbafcb4b8a32","sha256:c6aa6874825290ccea285edcaf5d05de1221a44be40255a30ad96972eee4b270"],"state_sha256":"6ba0c872a5c396509d91fe8774b6c8c9d6912dd228b37f08d93f39f985e78d50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"60CKL4XYuKtrQxRkzpUS9jQEtdKEgMPz50+plOKZGsFJTXMzlHSSK5n3HImaHU1dNXstiTIIJ6l/XzNmXke2AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T22:56:26.959595Z","bundle_sha256":"b98fe2463f20e1997dc9c5b9af5a8e9afbca44563916bfa0ead9a3cae5ecf26d"}}