{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZVHJJUOZO625BTCTS6DIHCJ3U7","short_pith_number":"pith:ZVHJJUOZ","canonical_record":{"source":{"id":"1006.3246","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-16T15:24:54Z","cross_cats_sorted":["cs.SC","q-bio.QM"],"title_canon_sha256":"b76060009de4122bb566f6a60271e9890cf7b65ed2dfc23f98f716dda499f2df","abstract_canon_sha256":"8d7b8a021260719cf9b93acd7ed60676894ac7333cd5b2078c55c7a59a1b91fa"},"schema_version":"1.0"},"canonical_sha256":"cd4e94d1d977b5d0cc53978683893ba7cfa990ec0b26bb3472940eebeb2e5392","source":{"kind":"arxiv","id":"1006.3246","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3246","created_at":"2026-05-18T03:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3246v4","created_at":"2026-05-18T03:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3246","created_at":"2026-05-18T03:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZVHJJUOZO625","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZVHJJUOZO625BTCT","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZVHJJUOZ","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZVHJJUOZO625BTCTS6DIHCJ3U7","target":"record","payload":{"canonical_record":{"source":{"id":"1006.3246","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-16T15:24:54Z","cross_cats_sorted":["cs.SC","q-bio.QM"],"title_canon_sha256":"b76060009de4122bb566f6a60271e9890cf7b65ed2dfc23f98f716dda499f2df","abstract_canon_sha256":"8d7b8a021260719cf9b93acd7ed60676894ac7333cd5b2078c55c7a59a1b91fa"},"schema_version":"1.0"},"canonical_sha256":"cd4e94d1d977b5d0cc53978683893ba7cfa990ec0b26bb3472940eebeb2e5392","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:26.020214Z","signature_b64":"ieGjuR1pekfjqgb5KHilUgac+duKf79HA/sIqpc1HRSKkYoaQTcbWs720fbKWukGNE6PqQZeFvrnw6rLp7QABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd4e94d1d977b5d0cc53978683893ba7cfa990ec0b26bb3472940eebeb2e5392","last_reissued_at":"2026-05-18T03:25:26.019744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:26.019744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.3246","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":"2026-05-18T03:25:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzXfUE3RHd5c4dAq53JA8V1fUxoGPJBk+6LlPsIlJXmZuxR1w3VWGqPCknI6A7T4QVPS+VXiajugnf2ypFLCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:43:29.696035Z"},"content_sha256":"6b8b128917c270f0d4d281d615a3f5c9f3fe7f5f3f079babf2c1693763eb1411","schema_version":"1.0","event_id":"sha256:6b8b128917c270f0d4d281d615a3f5c9f3fe7f5f3f079babf2c1693763eb1411"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZVHJJUOZO625BTCTS6DIHCJ3U7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","q-bio.QM"],"primary_cat":"math.PR","authors_text":"Gr\\'egory Nuel (MAP5), Jean-Guillaume Dumas (LJK)","submitted_at":"2010-06-16T15:24:54Z","abstract_excerpt":"We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a partial recursion after a fast computation of the second largest eigenvalue of the transition matrix of a Markov chain embedding. The second approach uses fast Taylor expansions of an exact bivariate rational reconstruction of the distribution. We illustrate the interest of both approaches on a simple toy-example and two biological applications: the transcr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3246","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":""},"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":"2026-05-18T03:25:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"013HNFyyYO3U5ESm6YJ1kTHRBKHOo9Ka64Z7gbM/GyJm8foEUlgmVw7pneqKYlbbQXVy9tLuYC7AGJsuWOhrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:43:29.696394Z"},"content_sha256":"24f87d24db25a09b8825c9ff182e03024e43bf3b16e1af8d925255e7c00e526c","schema_version":"1.0","event_id":"sha256:24f87d24db25a09b8825c9ff182e03024e43bf3b16e1af8d925255e7c00e526c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZVHJJUOZO625BTCTS6DIHCJ3U7/bundle.json","state_url":"https://pith.science/pith/ZVHJJUOZO625BTCTS6DIHCJ3U7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZVHJJUOZO625BTCTS6DIHCJ3U7/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":"2026-06-03T05:43:29Z","links":{"resolver":"https://pith.science/pith/ZVHJJUOZO625BTCTS6DIHCJ3U7","bundle":"https://pith.science/pith/ZVHJJUOZO625BTCTS6DIHCJ3U7/bundle.json","state":"https://pith.science/pith/ZVHJJUOZO625BTCTS6DIHCJ3U7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZVHJJUOZO625BTCTS6DIHCJ3U7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZVHJJUOZO625BTCTS6DIHCJ3U7","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":"8d7b8a021260719cf9b93acd7ed60676894ac7333cd5b2078c55c7a59a1b91fa","cross_cats_sorted":["cs.SC","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-16T15:24:54Z","title_canon_sha256":"b76060009de4122bb566f6a60271e9890cf7b65ed2dfc23f98f716dda499f2df"},"schema_version":"1.0","source":{"id":"1006.3246","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3246","created_at":"2026-05-18T03:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3246v4","created_at":"2026-05-18T03:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3246","created_at":"2026-05-18T03:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZVHJJUOZO625","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZVHJJUOZO625BTCT","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZVHJJUOZ","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:24f87d24db25a09b8825c9ff182e03024e43bf3b16e1af8d925255e7c00e526c","target":"graph","created_at":"2026-05-18T03:25:26Z","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":"We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a partial recursion after a fast computation of the second largest eigenvalue of the transition matrix of a Markov chain embedding. The second approach uses fast Taylor expansions of an exact bivariate rational reconstruction of the distribution. We illustrate the interest of both approaches on a simple toy-example and two biological applications: the transcr","authors_text":"Gr\\'egory Nuel (MAP5), Jean-Guillaume Dumas (LJK)","cross_cats":["cs.SC","q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-16T15:24:54Z","title":"Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3246","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":"sha256:6b8b128917c270f0d4d281d615a3f5c9f3fe7f5f3f079babf2c1693763eb1411","target":"record","created_at":"2026-05-18T03:25:26Z","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":"8d7b8a021260719cf9b93acd7ed60676894ac7333cd5b2078c55c7a59a1b91fa","cross_cats_sorted":["cs.SC","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-16T15:24:54Z","title_canon_sha256":"b76060009de4122bb566f6a60271e9890cf7b65ed2dfc23f98f716dda499f2df"},"schema_version":"1.0","source":{"id":"1006.3246","kind":"arxiv","version":4}},"canonical_sha256":"cd4e94d1d977b5d0cc53978683893ba7cfa990ec0b26bb3472940eebeb2e5392","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd4e94d1d977b5d0cc53978683893ba7cfa990ec0b26bb3472940eebeb2e5392","first_computed_at":"2026-05-18T03:25:26.019744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:26.019744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ieGjuR1pekfjqgb5KHilUgac+duKf79HA/sIqpc1HRSKkYoaQTcbWs720fbKWukGNE6PqQZeFvrnw6rLp7QABw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:26.020214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3246","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b8b128917c270f0d4d281d615a3f5c9f3fe7f5f3f079babf2c1693763eb1411","sha256:24f87d24db25a09b8825c9ff182e03024e43bf3b16e1af8d925255e7c00e526c"],"state_sha256":"e1d01d6126cb413e30025005772093b86a910d5d785221b8981330c73e9cc12a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eikByUwMfp/FslhxISdXfILcJeP/HDD+xRl8AuXTbReEU2qP46xKVZbXW/6cbyN5x8KnHuKSUIff3XkL8CLtBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:43:29.698306Z","bundle_sha256":"34e0468649056944260d7373b4e445fda61c78c0c16a3954bcafba418dfdb0fa"}}