{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2WMJL5P53EOM3ZISGFENXV5RNV","short_pith_number":"pith:2WMJL5P5","canonical_record":{"source":{"id":"1701.02379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-09T22:37:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a71d79147b4ef62fe3b696481503f04dfb7ce53bd4f61e72c5e2c4f1febf1973","abstract_canon_sha256":"e48ce4f14da8ef875c199bd5015ff39eb6e5699f6f47786ce748bc6599d0e942"},"schema_version":"1.0"},"canonical_sha256":"d59895f5fdd91ccde5123148dbd7b16d63973f603546c5539381eb4a6b91531f","source":{"kind":"arxiv","id":"1701.02379","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02379","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02379v2","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02379","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"2WMJL5P53EOM","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2WMJL5P53EOM3ZIS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2WMJL5P5","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2WMJL5P53EOM3ZISGFENXV5RNV","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-09T22:37:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a71d79147b4ef62fe3b696481503f04dfb7ce53bd4f61e72c5e2c4f1febf1973","abstract_canon_sha256":"e48ce4f14da8ef875c199bd5015ff39eb6e5699f6f47786ce748bc6599d0e942"},"schema_version":"1.0"},"canonical_sha256":"d59895f5fdd91ccde5123148dbd7b16d63973f603546c5539381eb4a6b91531f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:56.887330Z","signature_b64":"21vwhPt+uMkFQl7nKWgXwHkHjJX/5PGQnlnbF9Z9BbWvCuXAJJkBERMJi7ufI8YiTlKRCOIbP06eQ/ky6fs8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d59895f5fdd91ccde5123148dbd7b16d63973f603546c5539381eb4a6b91531f","last_reissued_at":"2026-05-18T00:23:56.886675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:56.886675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02379","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":"2026-05-18T00:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5L2nOcncFghzjvqRZX9I3fbEj7hgg83HxPlSzccBXKH8iyPn+taFg/jHMrtMWr1O9rU860KXtX507wlhZGXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:55:46.754739Z"},"content_sha256":"b72e8fbf926aab8a7db62b9a5dc77d9f26f5ce9252c56f7bb255ce5e49801417","schema_version":"1.0","event_id":"sha256:b72e8fbf926aab8a7db62b9a5dc77d9f26f5ce9252c56f7bb255ce5e49801417"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2WMJL5P53EOM3ZISGFENXV5RNV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Tanner Graph Cycle Distribution of Random LDPC, Random Protograph-Based LDPC, and Random Quasi-Cyclic LDPC Code Ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ali Dehghan, Amir H. Banihashemi","submitted_at":"2017-01-09T22:37:21Z","abstract_excerpt":"In this paper, we study the cycle distribution of random low-density parity-check (LDPC) codes, randomly constructed protograph-based LDPC codes, and random quasi-cyclic (QC) LDPC codes. We prove that for a random bipartite graph, with a given (irregular) degree distribution, the distributions of cycles of different length tend to independent Poisson distributions, as the size of the graph tends to infinity. We derive asymptotic upper and lower bounds on the expected values of the Poisson distributions that are independent of the size of the graph, and only depend on the degree distribution an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02379","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":"2026-05-18T00:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nwvh4h2ZelNltxY2xK0sct5JCOL6l8jmc1CG74EGm5xHJ8aeC2RlpW2fzix01uEiXE8GHhpkf4MJEL9PS8VwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:55:46.755081Z"},"content_sha256":"0c00f901ca279864a3997794ef5d0645ef29553ac48f74c0393b7da1a2b69c80","schema_version":"1.0","event_id":"sha256:0c00f901ca279864a3997794ef5d0645ef29553ac48f74c0393b7da1a2b69c80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2WMJL5P53EOM3ZISGFENXV5RNV/bundle.json","state_url":"https://pith.science/pith/2WMJL5P53EOM3ZISGFENXV5RNV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2WMJL5P53EOM3ZISGFENXV5RNV/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":"2026-06-02T17:55:46Z","links":{"resolver":"https://pith.science/pith/2WMJL5P53EOM3ZISGFENXV5RNV","bundle":"https://pith.science/pith/2WMJL5P53EOM3ZISGFENXV5RNV/bundle.json","state":"https://pith.science/pith/2WMJL5P53EOM3ZISGFENXV5RNV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2WMJL5P53EOM3ZISGFENXV5RNV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2WMJL5P53EOM3ZISGFENXV5RNV","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":"e48ce4f14da8ef875c199bd5015ff39eb6e5699f6f47786ce748bc6599d0e942","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-09T22:37:21Z","title_canon_sha256":"a71d79147b4ef62fe3b696481503f04dfb7ce53bd4f61e72c5e2c4f1febf1973"},"schema_version":"1.0","source":{"id":"1701.02379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02379","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02379v2","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02379","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"2WMJL5P53EOM","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2WMJL5P53EOM3ZIS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2WMJL5P5","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:0c00f901ca279864a3997794ef5d0645ef29553ac48f74c0393b7da1a2b69c80","target":"graph","created_at":"2026-05-18T00:23:56Z","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":"In this paper, we study the cycle distribution of random low-density parity-check (LDPC) codes, randomly constructed protograph-based LDPC codes, and random quasi-cyclic (QC) LDPC codes. We prove that for a random bipartite graph, with a given (irregular) degree distribution, the distributions of cycles of different length tend to independent Poisson distributions, as the size of the graph tends to infinity. We derive asymptotic upper and lower bounds on the expected values of the Poisson distributions that are independent of the size of the graph, and only depend on the degree distribution an","authors_text":"Ali Dehghan, Amir H. Banihashemi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-09T22:37:21Z","title":"On the Tanner Graph Cycle Distribution of Random LDPC, Random Protograph-Based LDPC, and Random Quasi-Cyclic LDPC Code Ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02379","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:b72e8fbf926aab8a7db62b9a5dc77d9f26f5ce9252c56f7bb255ce5e49801417","target":"record","created_at":"2026-05-18T00:23:56Z","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":"e48ce4f14da8ef875c199bd5015ff39eb6e5699f6f47786ce748bc6599d0e942","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-09T22:37:21Z","title_canon_sha256":"a71d79147b4ef62fe3b696481503f04dfb7ce53bd4f61e72c5e2c4f1febf1973"},"schema_version":"1.0","source":{"id":"1701.02379","kind":"arxiv","version":2}},"canonical_sha256":"d59895f5fdd91ccde5123148dbd7b16d63973f603546c5539381eb4a6b91531f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d59895f5fdd91ccde5123148dbd7b16d63973f603546c5539381eb4a6b91531f","first_computed_at":"2026-05-18T00:23:56.886675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:56.886675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"21vwhPt+uMkFQl7nKWgXwHkHjJX/5PGQnlnbF9Z9BbWvCuXAJJkBERMJi7ufI8YiTlKRCOIbP06eQ/ky6fs8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:56.887330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b72e8fbf926aab8a7db62b9a5dc77d9f26f5ce9252c56f7bb255ce5e49801417","sha256:0c00f901ca279864a3997794ef5d0645ef29553ac48f74c0393b7da1a2b69c80"],"state_sha256":"ee2e3533092a3f6009c3dc395bba065f0beb3bbacca38f18149d5784f5a6957e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"On7uGQOlX5j+7JSvUEmu425Y4xdRoGe1AZaVwa+dOHgneRYXCflMqOuG8zy5SjD3C2RH94C1yEWjVkysoL12Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:55:46.757060Z","bundle_sha256":"0f26b885051c51a8128c77d0522de2248aefc28f82d0733070a0e0a74fa24992"}}