{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:G5MMTORCOWPSSS7IACUBTQK5NI","short_pith_number":"pith:G5MMTORC","canonical_record":{"source":{"id":"0911.1072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-11-05T16:15:29Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"87242bb9d4188f883e88b2f8d86e73691ff4d1db5e6761050eb80b70db7699f2","abstract_canon_sha256":"340c3b02dd6b856d5599ae90a92a28b8900a991909b44095296b32020f33aa1e"},"schema_version":"1.0"},"canonical_sha256":"3758c9ba22759f294be800a819c15d6a04b603328ebea085de29c6d7ca20c5c5","source":{"kind":"arxiv","id":"0911.1072","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1072","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1072v1","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1072","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"G5MMTORCOWPS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G5MMTORCOWPSSS7I","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G5MMTORC","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:G5MMTORCOWPSSS7IACUBTQK5NI","target":"record","payload":{"canonical_record":{"source":{"id":"0911.1072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-11-05T16:15:29Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"87242bb9d4188f883e88b2f8d86e73691ff4d1db5e6761050eb80b70db7699f2","abstract_canon_sha256":"340c3b02dd6b856d5599ae90a92a28b8900a991909b44095296b32020f33aa1e"},"schema_version":"1.0"},"canonical_sha256":"3758c9ba22759f294be800a819c15d6a04b603328ebea085de29c6d7ca20c5c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:10.981944Z","signature_b64":"n/idWtQD+4Yp/Z1IlEdhqpMYLyfmdwY492SxCx1x3d9Vsp2TJ38Jv+jC1vuCnxFI2wEwBeYJlhFzwEVSbR4/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3758c9ba22759f294be800a819c15d6a04b603328ebea085de29c6d7ca20c5c5","last_reissued_at":"2026-05-18T04:21:10.981330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:10.981330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.1072","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":"2026-05-18T04:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vaDUeOp4ZRwBmV0zIHbF+Dow/udNeggcvLCDQ5klxdQw7mL6uOcaruq0U5bbXYBXnsBGaSqlvEDHLG7rNHXzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:19:38.618669Z"},"content_sha256":"4d722f862da4d6bf164b334e0bca6e0056bd4f6b659c7692e25714d3065d8ebf","schema_version":"1.0","event_id":"sha256:4d722f862da4d6bf164b334e0bca6e0056bd4f6b659c7692e25714d3065d8ebf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:G5MMTORCOWPSSS7IACUBTQK5NI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error Correcting Coding for a Non-symmetric Ternary Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexandre Graell i Amat, Eirik Rosnes, Nicolas Bitouze","submitted_at":"2009-11-05T16:15:29Z","abstract_excerpt":"Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not allowed, is considered. The resulting channel is non-symmetric, therefore classical linear codes are not optimal for this channel. We define the maximum-likelihood (ML) decoding rule for ternary codes over this channel and show that it is complex to compute, since it depends on the channel error probability. A simpler alternative decoding rule which depends only "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1072","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":"2026-05-18T04:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ma+25ILyuWcvebGuFhh7KOAN9j4b4bTVnXEJaYqcDxPWs68QqR/EZ8+DKfbRxNRc8CXBZhZ7YK5w+r4sQ7SCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:19:38.619016Z"},"content_sha256":"3ad2f79c243ca33fd7b9e13178cac9cdcca9b2d4413d98b66f851d117998a188","schema_version":"1.0","event_id":"sha256:3ad2f79c243ca33fd7b9e13178cac9cdcca9b2d4413d98b66f851d117998a188"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5MMTORCOWPSSS7IACUBTQK5NI/bundle.json","state_url":"https://pith.science/pith/G5MMTORCOWPSSS7IACUBTQK5NI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5MMTORCOWPSSS7IACUBTQK5NI/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":"2026-05-28T05:19:38Z","links":{"resolver":"https://pith.science/pith/G5MMTORCOWPSSS7IACUBTQK5NI","bundle":"https://pith.science/pith/G5MMTORCOWPSSS7IACUBTQK5NI/bundle.json","state":"https://pith.science/pith/G5MMTORCOWPSSS7IACUBTQK5NI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5MMTORCOWPSSS7IACUBTQK5NI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:G5MMTORCOWPSSS7IACUBTQK5NI","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":"340c3b02dd6b856d5599ae90a92a28b8900a991909b44095296b32020f33aa1e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-11-05T16:15:29Z","title_canon_sha256":"87242bb9d4188f883e88b2f8d86e73691ff4d1db5e6761050eb80b70db7699f2"},"schema_version":"1.0","source":{"id":"0911.1072","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1072","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1072v1","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1072","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"G5MMTORCOWPS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G5MMTORCOWPSSS7I","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G5MMTORC","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:3ad2f79c243ca33fd7b9e13178cac9cdcca9b2d4413d98b66f851d117998a188","target":"graph","created_at":"2026-05-18T04:21:10Z","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":"Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not allowed, is considered. The resulting channel is non-symmetric, therefore classical linear codes are not optimal for this channel. We define the maximum-likelihood (ML) decoding rule for ternary codes over this channel and show that it is complex to compute, since it depends on the channel error probability. A simpler alternative decoding rule which depends only ","authors_text":"Alexandre Graell i Amat, Eirik Rosnes, Nicolas Bitouze","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-11-05T16:15:29Z","title":"Error Correcting Coding for a Non-symmetric Ternary Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1072","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":"sha256:4d722f862da4d6bf164b334e0bca6e0056bd4f6b659c7692e25714d3065d8ebf","target":"record","created_at":"2026-05-18T04:21:10Z","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":"340c3b02dd6b856d5599ae90a92a28b8900a991909b44095296b32020f33aa1e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-11-05T16:15:29Z","title_canon_sha256":"87242bb9d4188f883e88b2f8d86e73691ff4d1db5e6761050eb80b70db7699f2"},"schema_version":"1.0","source":{"id":"0911.1072","kind":"arxiv","version":1}},"canonical_sha256":"3758c9ba22759f294be800a819c15d6a04b603328ebea085de29c6d7ca20c5c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3758c9ba22759f294be800a819c15d6a04b603328ebea085de29c6d7ca20c5c5","first_computed_at":"2026-05-18T04:21:10.981330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:10.981330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n/idWtQD+4Yp/Z1IlEdhqpMYLyfmdwY492SxCx1x3d9Vsp2TJ38Jv+jC1vuCnxFI2wEwBeYJlhFzwEVSbR4/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:10.981944Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1072","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d722f862da4d6bf164b334e0bca6e0056bd4f6b659c7692e25714d3065d8ebf","sha256:3ad2f79c243ca33fd7b9e13178cac9cdcca9b2d4413d98b66f851d117998a188"],"state_sha256":"86a786f69046df0dbde8c38b87c257307ae022862679a9ea7b360fdb3a6ba7f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcWa3t56xjgDVKJoesvq/Aa1EoiicxAnNd7inHbiPFcdj2JwW1dB85+Vw7OjTrwhPNw2W4k9PjRBUfFEgjWGDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:19:38.620956Z","bundle_sha256":"f139b9d5496625d7cecd161f25b90030235381e7990a937fc53ca8c58fad3654"}}