{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XA6TSV5VOJ4SIB5CKYRQSVMQTW","short_pith_number":"pith:XA6TSV5V","canonical_record":{"source":{"id":"1301.6111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T18:13:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cc65cfe3e16f490814524db62a8a1fd10798eba7973110f438603bfccea9f4d5","abstract_canon_sha256":"ebe433d558aa4199d5d5343e3061e573b5772b54d2155a4b9042c2669d35e203"},"schema_version":"1.0"},"canonical_sha256":"b83d3957b572792407a256230955909dafd138bd4cfa1d581881fd9de8e2bf8f","source":{"kind":"arxiv","id":"1301.6111","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6111","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6111v2","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6111","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"XA6TSV5VOJ4S","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XA6TSV5VOJ4SIB5C","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XA6TSV5V","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XA6TSV5VOJ4SIB5CKYRQSVMQTW","target":"record","payload":{"canonical_record":{"source":{"id":"1301.6111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T18:13:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cc65cfe3e16f490814524db62a8a1fd10798eba7973110f438603bfccea9f4d5","abstract_canon_sha256":"ebe433d558aa4199d5d5343e3061e573b5772b54d2155a4b9042c2669d35e203"},"schema_version":"1.0"},"canonical_sha256":"b83d3957b572792407a256230955909dafd138bd4cfa1d581881fd9de8e2bf8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:55.037848Z","signature_b64":"cKNKgZM/oMMH47KE7/uJAYrJvU78nFtWaZrMgCygZ5OyoOoZHweFfz3pBtC+E4VEQd6YYufTYCdbSytpBpEfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b83d3957b572792407a256230955909dafd138bd4cfa1d581881fd9de8e2bf8f","last_reissued_at":"2026-05-18T03:03:55.037142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:55.037142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.6111","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VmrbjgzQ/xZMfce+Tb6Z7yBJLFVtee5Yn2kt57QKJoHBOIaiABFYvM8mNpz8WVkS77GUZma98BXlPGYW6TLdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:35:18.523888Z"},"content_sha256":"e30f6dd35eaee577d4ed4363f66869f5cadd6d87154d4c20caf180bfe4dbcc5b","schema_version":"1.0","event_id":"sha256:e30f6dd35eaee577d4ed4363f66869f5cadd6d87154d4c20caf180bfe4dbcc5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XA6TSV5VOJ4SIB5CKYRQSVMQTW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Proof of Threshold Saturation for Spatially-Coupled LDPC Codes on BMS Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrew J. Young, Henry D. Pfister, Nicolas Macris, Santhosh Kumar","submitted_at":"2013-01-25T18:13:53Z","abstract_excerpt":"Low-density parity-check (LDPC) convolutional codes have been shown to exhibit excellent performance under low-complexity belief-propagation decoding [1], [2]. This phenomenon is now termed threshold saturation via spatial coupling. The underlying principle behind this appears to be very general and spatially-coupled (SC) codes have been successfully applied in numerous areas. Recently, SC regular LDPC codes have been proven to achieve capacity universally, over the class of binary memoryless symmetric (BMS) channels, under belief-propagation decoding [3], [4].\n  In [5], [6], potential functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6111","kind":"arxiv","version":2},"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":"2026-05-18T03:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpTM2BLbOKoWd7nLfBOWO4HFdlRhutOwm0WOYrNzOcawtsr0pAoyS+U8Kds8aSxji03fJBDcGFDJv3YBP26uCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:35:18.524259Z"},"content_sha256":"155c99d60bf45d7b524e0116f251b2f45755c688bec087450e5eb70f8ebe9ea5","schema_version":"1.0","event_id":"sha256:155c99d60bf45d7b524e0116f251b2f45755c688bec087450e5eb70f8ebe9ea5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XA6TSV5VOJ4SIB5CKYRQSVMQTW/bundle.json","state_url":"https://pith.science/pith/XA6TSV5VOJ4SIB5CKYRQSVMQTW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XA6TSV5VOJ4SIB5CKYRQSVMQTW/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":"2026-05-28T00:35:18Z","links":{"resolver":"https://pith.science/pith/XA6TSV5VOJ4SIB5CKYRQSVMQTW","bundle":"https://pith.science/pith/XA6TSV5VOJ4SIB5CKYRQSVMQTW/bundle.json","state":"https://pith.science/pith/XA6TSV5VOJ4SIB5CKYRQSVMQTW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XA6TSV5VOJ4SIB5CKYRQSVMQTW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XA6TSV5VOJ4SIB5CKYRQSVMQTW","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":"ebe433d558aa4199d5d5343e3061e573b5772b54d2155a4b9042c2669d35e203","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T18:13:53Z","title_canon_sha256":"cc65cfe3e16f490814524db62a8a1fd10798eba7973110f438603bfccea9f4d5"},"schema_version":"1.0","source":{"id":"1301.6111","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6111","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6111v2","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6111","created_at":"2026-05-18T03:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"XA6TSV5VOJ4S","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XA6TSV5VOJ4SIB5C","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XA6TSV5V","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:155c99d60bf45d7b524e0116f251b2f45755c688bec087450e5eb70f8ebe9ea5","target":"graph","created_at":"2026-05-18T03:03:55Z","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":"Low-density parity-check (LDPC) convolutional codes have been shown to exhibit excellent performance under low-complexity belief-propagation decoding [1], [2]. This phenomenon is now termed threshold saturation via spatial coupling. The underlying principle behind this appears to be very general and spatially-coupled (SC) codes have been successfully applied in numerous areas. Recently, SC regular LDPC codes have been proven to achieve capacity universally, over the class of binary memoryless symmetric (BMS) channels, under belief-propagation decoding [3], [4].\n  In [5], [6], potential functio","authors_text":"Andrew J. Young, Henry D. Pfister, Nicolas Macris, Santhosh Kumar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T18:13:53Z","title":"A Proof of Threshold Saturation for Spatially-Coupled LDPC Codes on BMS Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6111","kind":"arxiv","version":2},"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:e30f6dd35eaee577d4ed4363f66869f5cadd6d87154d4c20caf180bfe4dbcc5b","target":"record","created_at":"2026-05-18T03:03:55Z","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":"ebe433d558aa4199d5d5343e3061e573b5772b54d2155a4b9042c2669d35e203","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T18:13:53Z","title_canon_sha256":"cc65cfe3e16f490814524db62a8a1fd10798eba7973110f438603bfccea9f4d5"},"schema_version":"1.0","source":{"id":"1301.6111","kind":"arxiv","version":2}},"canonical_sha256":"b83d3957b572792407a256230955909dafd138bd4cfa1d581881fd9de8e2bf8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b83d3957b572792407a256230955909dafd138bd4cfa1d581881fd9de8e2bf8f","first_computed_at":"2026-05-18T03:03:55.037142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:55.037142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cKNKgZM/oMMH47KE7/uJAYrJvU78nFtWaZrMgCygZ5OyoOoZHweFfz3pBtC+E4VEQd6YYufTYCdbSytpBpEfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:55.037848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6111","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e30f6dd35eaee577d4ed4363f66869f5cadd6d87154d4c20caf180bfe4dbcc5b","sha256:155c99d60bf45d7b524e0116f251b2f45755c688bec087450e5eb70f8ebe9ea5"],"state_sha256":"e11530e51e1afc536466ccd6247a6554c99fe3ac90db05523859ccf824e5d258"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8m8lofezS0WFzUEsP8XqiZSoalIMRkaW9JWpHNHBEKv87+fPTaLGpNyELJgY9qx/kaNKbfjSdlCvTT6U/tzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:35:18.526200Z","bundle_sha256":"2962efa11c2b74f27f12225d03d8d0c26ccc9d4bfd7674beb7325fb6b039976e"}}