{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:LAIOI7XYL3JJC6NOS4QXCLPRPG","short_pith_number":"pith:LAIOI7XY","canonical_record":{"source":{"id":"1901.01659","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-07T04:11:47Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6a76998fe2f1445e8bd5e37714a710e3666efadcd81c81a31018cf1e13b68ac9","abstract_canon_sha256":"b3925a754cf8a158313d446422c278b126fb8e9f35e8b92cb10b3d3ab5fb846d"},"schema_version":"1.0"},"canonical_sha256":"5810e47ef85ed29179ae9721712df179a4f9d4b2cc5ee1b3506676a1f8fd98e7","source":{"kind":"arxiv","id":"1901.01659","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01659","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01659v4","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01659","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"LAIOI7XYL3JJ","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"pith_short_16","alias_value":"LAIOI7XYL3JJC6NO","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"pith_short_8","alias_value":"LAIOI7XY","created_at":"2026-07-05T02:18:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:LAIOI7XYL3JJC6NOS4QXCLPRPG","target":"record","payload":{"canonical_record":{"source":{"id":"1901.01659","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-07T04:11:47Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6a76998fe2f1445e8bd5e37714a710e3666efadcd81c81a31018cf1e13b68ac9","abstract_canon_sha256":"b3925a754cf8a158313d446422c278b126fb8e9f35e8b92cb10b3d3ab5fb846d"},"schema_version":"1.0"},"canonical_sha256":"5810e47ef85ed29179ae9721712df179a4f9d4b2cc5ee1b3506676a1f8fd98e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:18:02.428169Z","signature_b64":"3tyaGs4NRVXz/GDAumx+yuOiFu9DmJ0RH4Ee+8SRq0mZPC7rrB6NubKToBLGb5WcKL8mkfecCpN3RQrLeJnCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5810e47ef85ed29179ae9721712df179a4f9d4b2cc5ee1b3506676a1f8fd98e7","last_reissued_at":"2026-07-05T02:18:02.427708Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:18:02.427708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.01659","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TyjUJbxkwvJGVxCBhXiTWrxX9CSAU86LZAhIJIQPVhaCLdVUW7CR547Yl4JTb2VWpkyhz59pvh50he5okdpcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:37:54.773799Z"},"content_sha256":"8ff27c100203925d502d3923d9de29cef6c35e9e0f58c26d62fc5b0332c25783","schema_version":"1.0","event_id":"sha256:8ff27c100203925d502d3923d9de29cef6c35e9e0f58c26d62fc5b0332c25783"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:LAIOI7XYL3JJC6NOS4QXCLPRPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic Programming for Sequential Deterministic Quantization of Discrete Memoryless Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kui Cai, Wentu Song, Xuan He, Zhen Mei","submitted_at":"2019-01-07T04:11:47Z","abstract_excerpt":"In this paper, under a general cost function $C$, we present a dynamic programming (DP) method to obtain an optimal sequential deterministic quantizer (SDQ) for $q$-ary input discrete memoryless channel (DMC). The DP method has complexity $O(q (N-M)^2 M)$, where $N$ and $M$ are the alphabet sizes of the DMC output and quantizer output, respectively. Then, starting from the quadrangle inequality, two techniques are applied to reduce the DP method's complexity. One technique makes use of the Shor-Moran-Aggarwal-Wilber-Klawe (SMAWK) algorithm and achieves complexity $O(q (N-M) M)$. The other tech"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01659","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1901.01659/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:18:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X7MG87SXAFZcwfPW30l98jP/POkgteTvhIba6abGf0OrUEk2tIW7I+g8EvwaT3XZ33N5KXW+dJyPoOtU70z7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:37:54.774173Z"},"content_sha256":"95ebbbf2269b02e503731bbc1bb60b68a665b7fd95f21e82fcc63b2316a3656d","schema_version":"1.0","event_id":"sha256:95ebbbf2269b02e503731bbc1bb60b68a665b7fd95f21e82fcc63b2316a3656d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LAIOI7XYL3JJC6NOS4QXCLPRPG/bundle.json","state_url":"https://pith.science/pith/LAIOI7XYL3JJC6NOS4QXCLPRPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LAIOI7XYL3JJC6NOS4QXCLPRPG/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":"2026-07-07T14:37:54Z","links":{"resolver":"https://pith.science/pith/LAIOI7XYL3JJC6NOS4QXCLPRPG","bundle":"https://pith.science/pith/LAIOI7XYL3JJC6NOS4QXCLPRPG/bundle.json","state":"https://pith.science/pith/LAIOI7XYL3JJC6NOS4QXCLPRPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LAIOI7XYL3JJC6NOS4QXCLPRPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LAIOI7XYL3JJC6NOS4QXCLPRPG","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":"b3925a754cf8a158313d446422c278b126fb8e9f35e8b92cb10b3d3ab5fb846d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-07T04:11:47Z","title_canon_sha256":"6a76998fe2f1445e8bd5e37714a710e3666efadcd81c81a31018cf1e13b68ac9"},"schema_version":"1.0","source":{"id":"1901.01659","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01659","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01659v4","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01659","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"LAIOI7XYL3JJ","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"pith_short_16","alias_value":"LAIOI7XYL3JJC6NO","created_at":"2026-07-05T02:18:02Z"},{"alias_kind":"pith_short_8","alias_value":"LAIOI7XY","created_at":"2026-07-05T02:18:02Z"}],"graph_snapshots":[{"event_id":"sha256:95ebbbf2269b02e503731bbc1bb60b68a665b7fd95f21e82fcc63b2316a3656d","target":"graph","created_at":"2026-07-05T02:18:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1901.01659/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, under a general cost function $C$, we present a dynamic programming (DP) method to obtain an optimal sequential deterministic quantizer (SDQ) for $q$-ary input discrete memoryless channel (DMC). The DP method has complexity $O(q (N-M)^2 M)$, where $N$ and $M$ are the alphabet sizes of the DMC output and quantizer output, respectively. Then, starting from the quadrangle inequality, two techniques are applied to reduce the DP method's complexity. One technique makes use of the Shor-Moran-Aggarwal-Wilber-Klawe (SMAWK) algorithm and achieves complexity $O(q (N-M) M)$. The other tech","authors_text":"Kui Cai, Wentu Song, Xuan He, Zhen Mei","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-07T04:11:47Z","title":"Dynamic Programming for Sequential Deterministic Quantization of Discrete Memoryless Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01659","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":"sha256:8ff27c100203925d502d3923d9de29cef6c35e9e0f58c26d62fc5b0332c25783","target":"record","created_at":"2026-07-05T02:18:02Z","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":"b3925a754cf8a158313d446422c278b126fb8e9f35e8b92cb10b3d3ab5fb846d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-07T04:11:47Z","title_canon_sha256":"6a76998fe2f1445e8bd5e37714a710e3666efadcd81c81a31018cf1e13b68ac9"},"schema_version":"1.0","source":{"id":"1901.01659","kind":"arxiv","version":4}},"canonical_sha256":"5810e47ef85ed29179ae9721712df179a4f9d4b2cc5ee1b3506676a1f8fd98e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5810e47ef85ed29179ae9721712df179a4f9d4b2cc5ee1b3506676a1f8fd98e7","first_computed_at":"2026-07-05T02:18:02.427708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:18:02.427708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3tyaGs4NRVXz/GDAumx+yuOiFu9DmJ0RH4Ee+8SRq0mZPC7rrB6NubKToBLGb5WcKL8mkfecCpN3RQrLeJnCBg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:18:02.428169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.01659","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ff27c100203925d502d3923d9de29cef6c35e9e0f58c26d62fc5b0332c25783","sha256:95ebbbf2269b02e503731bbc1bb60b68a665b7fd95f21e82fcc63b2316a3656d"],"state_sha256":"a08a086ff6dce54773c7be813091153404b6023142d95c8d7b8206b6a85cc2fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IeI2ZVm/A6SPk8/CNMgDh75Du4TLR23a219kagCsSxgdvq7QGqRVYRpTz0Ad1davduVV9UMCf9yBQO05jIdLBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:37:54.776094Z","bundle_sha256":"228a0634654fd6d33ed98d948a64043e1b32ae59e1f1f48cf10f57414fe34b84"}}