{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:O5TKVVUDRWSWC2OGPIK6VYA5KJ","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":"ccf55b46eff350bd1a0ccd6d6d46bbf4cfd9226a66c21d5d714dfa0993ec2b88","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-11-29T06:36:33Z","title_canon_sha256":"9a8e7ca6ece39d68b71377c91962e7afb806fb65a9915bbc1499f8885bfd1260"},"schema_version":"1.0","source":{"id":"2512.00347","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.00347","created_at":"2026-06-23T03:13:52Z"},{"alias_kind":"arxiv_version","alias_value":"2512.00347v5","created_at":"2026-06-23T03:13:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.00347","created_at":"2026-06-23T03:13:52Z"},{"alias_kind":"pith_short_12","alias_value":"O5TKVVUDRWSW","created_at":"2026-06-23T03:13:52Z"},{"alias_kind":"pith_short_16","alias_value":"O5TKVVUDRWSWC2OG","created_at":"2026-06-23T03:13:52Z"},{"alias_kind":"pith_short_8","alias_value":"O5TKVVUD","created_at":"2026-06-23T03:13:52Z"}],"graph_snapshots":[{"event_id":"sha256:65adeac29c133ef2b715bb560338d33dd0223f1edda11f3c0ea9835646dca2dc","target":"graph","created_at":"2026-06-23T03:13:52Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"via suitably companding the ranks in ORBGRAND according to the inverse cumulative distribution function (CDF) of channel reliability, the resulting CDF-ORBGRAND algorithm exactly achieves the mutual information, i.e., the symmetric capacity."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The result holds for general binary-input memoryless channels under symmetric input distribution; if the input distribution deviates from symmetry or the channel has memory, the exact capacity achievement may not hold."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"CDF-ORBGRAND exactly achieves the symmetric capacity for binary-input memoryless channels under symmetric inputs and the BICM capacity in bit-interleaved coded modulation."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"By companding ranks in ORBGRAND with the inverse CDF of channel reliability, CDF-ORBGRAND exactly achieves the symmetric capacity for binary-input memoryless channels under symmetric inputs."}],"snapshot_sha256":"5558b3f66e7433bcfa71d6d6028e418b6cdb99588d9e0dead4016cf265937c93"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e0c963dc94fdcfc2bdbd0ce4378f2eefa7603558b703e71a9a0cb00866647296"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.00347/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Within the family of guessing-based decoding algorithms, ordered reliability bits GRAND (ORBGRAND) has attracted considerable attention due to its efficient use of soft information and suitability for hardware implementation. It has also been shown that ORBGRAND achieves a rate very close to the capacity of an additive white Gaussian noise channel under antipodal signaling. In this work, it is further established that, for general binary-input memoryless channels under symmetric input distribution, via suitably companding the ranks in ORBGRAND according to the inverse cumulative distribution f","authors_text":"Wenyi Zhang, Zhuang Li","cross_cats":["math.IT"],"headline":"By companding ranks in ORBGRAND with the inverse CDF of channel reliability, CDF-ORBGRAND exactly achieves the symmetric capacity for binary-input memoryless channels under symmetric inputs.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-11-29T06:36:33Z","title":"ORBGRAND Is Exactly Capacity-achieving via Rank Companding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.00347","kind":"arxiv","version":5},"verdict":{"created_at":"2026-05-17T03:53:30.601518Z","id":"ad83b2c9-6d16-4d48-87ad-a85e182bffe0","model_set":{"reader":"grok-4.3"},"one_line_summary":"CDF-ORBGRAND exactly achieves the symmetric capacity for binary-input memoryless channels under symmetric inputs and the BICM capacity in bit-interleaved coded modulation.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"By companding ranks in ORBGRAND with the inverse CDF of channel reliability, CDF-ORBGRAND exactly achieves the symmetric capacity for binary-input memoryless channels under symmetric inputs.","strongest_claim":"via suitably companding the ranks in ORBGRAND according to the inverse cumulative distribution function (CDF) of channel reliability, the resulting CDF-ORBGRAND algorithm exactly achieves the mutual information, i.e., the symmetric capacity.","weakest_assumption":"The result holds for general binary-input memoryless channels under symmetric input distribution; if the input distribution deviates from symmetry or the channel has memory, the exact capacity achievement may not hold."}},"verdict_id":"ad83b2c9-6d16-4d48-87ad-a85e182bffe0"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1dfeb8016f0a518cb46295229e7fdd3fb035aafd951f5de8878c352e46f73953","target":"record","created_at":"2026-06-23T03:13:52Z","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":"ccf55b46eff350bd1a0ccd6d6d46bbf4cfd9226a66c21d5d714dfa0993ec2b88","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-11-29T06:36:33Z","title_canon_sha256":"9a8e7ca6ece39d68b71377c91962e7afb806fb65a9915bbc1499f8885bfd1260"},"schema_version":"1.0","source":{"id":"2512.00347","kind":"arxiv","version":5}},"canonical_sha256":"7766aad6838da56169c67a15eae01d52679027b966af4d4450549fafb4e0af69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7766aad6838da56169c67a15eae01d52679027b966af4d4450549fafb4e0af69","first_computed_at":"2026-06-23T03:13:52.030403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:52.030403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ol64aYzLfbpAM5b3q2ikRSvz8WaQ+4tMOKlFePyXOtIxAq0e1RITDu1FbHm+p4QSlZV3pjHktT+iAWj//enADw==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:52.030830Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.00347","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dfeb8016f0a518cb46295229e7fdd3fb035aafd951f5de8878c352e46f73953","sha256:65adeac29c133ef2b715bb560338d33dd0223f1edda11f3c0ea9835646dca2dc"],"state_sha256":"7a6db7eb13729f7d10f9a54d8aa8cb19eb6ce42f66037158874dffbba27af21d"}