{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NPHAGYWWASTMHOJRPCQDF256N4","short_pith_number":"pith:NPHAGYWW","canonical_record":{"source":{"id":"1309.7910","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-30T16:29:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bc5c4eb0bf41e86f0449cbb1894bf3d0303fe848ccce38022edff369334b817a","abstract_canon_sha256":"cf88e4445e03634999001c23bd3919eba6d194c3643f930c67f97f4a0c5ceb5f"},"schema_version":"1.0"},"canonical_sha256":"6bce0362d604a6c3b93178a032ebbe6f03f02d828e1753ff922400b25d6e6468","source":{"kind":"arxiv","id":"1309.7910","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7910","created_at":"2026-05-18T00:58:16Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7910v3","created_at":"2026-05-18T00:58:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7910","created_at":"2026-05-18T00:58:16Z"},{"alias_kind":"pith_short_12","alias_value":"NPHAGYWWASTM","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NPHAGYWWASTMHOJR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NPHAGYWW","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NPHAGYWWASTMHOJRPCQDF256N4","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7910","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-30T16:29:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bc5c4eb0bf41e86f0449cbb1894bf3d0303fe848ccce38022edff369334b817a","abstract_canon_sha256":"cf88e4445e03634999001c23bd3919eba6d194c3643f930c67f97f4a0c5ceb5f"},"schema_version":"1.0"},"canonical_sha256":"6bce0362d604a6c3b93178a032ebbe6f03f02d828e1753ff922400b25d6e6468","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:16.763766Z","signature_b64":"2aaLyGdUe6dbIS30zsp/bBNwFrUa03Y/NoMoeqSDht5fm7UOAlIFFmk+SNuGX3a/XHRsPi3YFU8FhCqXu/RoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bce0362d604a6c3b93178a032ebbe6f03f02d828e1753ff922400b25d6e6468","last_reissued_at":"2026-05-18T00:58:16.763045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:16.763045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7910","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fEiBvTdmLiwdi1maFfBP7i31tQmslkIdiPnRCAfh8+tuLeX1la5XkxkzOen1Ij4PSxdKa/fBsteLlW8aqRoFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:51:38.548943Z"},"content_sha256":"4bdd374dd852baf99d985600ef3398075cb1d0053a58aff36757fab229fb77ba","schema_version":"1.0","event_id":"sha256:4bdd374dd852baf99d985600ef3398075cb1d0053a58aff36757fab229fb77ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NPHAGYWWASTMHOJRPCQDF256N4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Arvind Yedla, Henry D. Pfister, Phong S. Nguyen, Yung-Yih Jian","submitted_at":"2013-09-30T16:29:43Z","abstract_excerpt":"Low-density parity-check (LDPC) convolutional codes (or spatially-coupled codes) were recently shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this spectacular performance is now called threshold saturation via spatial coupling. This new phenomenon is characterized by the belief-propagation threshold of the spatially-coupled ensemble increasing to an intrinsic noise threshold defined by the uncoupled system. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7910","kind":"arxiv","version":3},"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":"2026-05-18T00:58:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BdbtLPTR3Cmjg/BVb2q2MMDHSlWGPJaN/y2doTbfM9nTL2Vv/2ZDLKbyC2MGBpaFj9c2FxgrHCJV/OHTAUlKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:51:38.549676Z"},"content_sha256":"693c18a4dfa521a3fd52b765c59da83b9876d297596c45ee59df48e01b105db2","schema_version":"1.0","event_id":"sha256:693c18a4dfa521a3fd52b765c59da83b9876d297596c45ee59df48e01b105db2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPHAGYWWASTMHOJRPCQDF256N4/bundle.json","state_url":"https://pith.science/pith/NPHAGYWWASTMHOJRPCQDF256N4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPHAGYWWASTMHOJRPCQDF256N4/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":"2026-05-27T09:51:38Z","links":{"resolver":"https://pith.science/pith/NPHAGYWWASTMHOJRPCQDF256N4","bundle":"https://pith.science/pith/NPHAGYWWASTMHOJRPCQDF256N4/bundle.json","state":"https://pith.science/pith/NPHAGYWWASTMHOJRPCQDF256N4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPHAGYWWASTMHOJRPCQDF256N4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NPHAGYWWASTMHOJRPCQDF256N4","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":"cf88e4445e03634999001c23bd3919eba6d194c3643f930c67f97f4a0c5ceb5f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-30T16:29:43Z","title_canon_sha256":"bc5c4eb0bf41e86f0449cbb1894bf3d0303fe848ccce38022edff369334b817a"},"schema_version":"1.0","source":{"id":"1309.7910","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7910","created_at":"2026-05-18T00:58:16Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7910v3","created_at":"2026-05-18T00:58:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7910","created_at":"2026-05-18T00:58:16Z"},{"alias_kind":"pith_short_12","alias_value":"NPHAGYWWASTM","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NPHAGYWWASTMHOJR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NPHAGYWW","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:693c18a4dfa521a3fd52b765c59da83b9876d297596c45ee59df48e01b105db2","target":"graph","created_at":"2026-05-18T00:58:16Z","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 (or spatially-coupled codes) were recently shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this spectacular performance is now called threshold saturation via spatial coupling. This new phenomenon is characterized by the belief-propagation threshold of the spatially-coupled ensemble increasing to an intrinsic noise threshold defined by the uncoupled system. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled","authors_text":"Arvind Yedla, Henry D. Pfister, Phong S. Nguyen, Yung-Yih Jian","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-30T16:29:43Z","title":"A Simple Proof of Maxwell Saturation for Coupled Scalar Recursions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7910","kind":"arxiv","version":3},"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":"sha256:4bdd374dd852baf99d985600ef3398075cb1d0053a58aff36757fab229fb77ba","target":"record","created_at":"2026-05-18T00:58:16Z","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":"cf88e4445e03634999001c23bd3919eba6d194c3643f930c67f97f4a0c5ceb5f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-30T16:29:43Z","title_canon_sha256":"bc5c4eb0bf41e86f0449cbb1894bf3d0303fe848ccce38022edff369334b817a"},"schema_version":"1.0","source":{"id":"1309.7910","kind":"arxiv","version":3}},"canonical_sha256":"6bce0362d604a6c3b93178a032ebbe6f03f02d828e1753ff922400b25d6e6468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bce0362d604a6c3b93178a032ebbe6f03f02d828e1753ff922400b25d6e6468","first_computed_at":"2026-05-18T00:58:16.763045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:16.763045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2aaLyGdUe6dbIS30zsp/bBNwFrUa03Y/NoMoeqSDht5fm7UOAlIFFmk+SNuGX3a/XHRsPi3YFU8FhCqXu/RoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:16.763766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7910","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bdd374dd852baf99d985600ef3398075cb1d0053a58aff36757fab229fb77ba","sha256:693c18a4dfa521a3fd52b765c59da83b9876d297596c45ee59df48e01b105db2"],"state_sha256":"23cf67e72ba65610a959022d7c56f1ff4eb4be4fec747b69c7e79c48e35550dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XdyWKkL4xpiTPqy4/B0IQeEaaPtDN3TPPua74fHdMsXzQy3nrJtKcegqiQymql1Mfp9mzSDNSvhcxbq7cA4AAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:51:38.554226Z","bundle_sha256":"9a251560a9137243e0da37b9acde6e701a81d1086628992f28f37278d906db33"}}