{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Z3KQYI6LEMTT4WY6ZXMRYO2R4M","short_pith_number":"pith:Z3KQYI6L","canonical_record":{"source":{"id":"1602.05560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-17T20:23:43Z","cross_cats_sorted":[],"title_canon_sha256":"f4ac3e5558a5003a5b3330a0ee6ed24d160c660a58bbddb3ce98b4f054dbe856","abstract_canon_sha256":"c74979579fcd42b8578e036381072671895dbad0882353bdb43169d3ba8a358a"},"schema_version":"1.0"},"canonical_sha256":"ced50c23cb23273e5b1ecdd91c3b51e3038aff251cc9a472ba276c245f15d4b9","source":{"kind":"arxiv","id":"1602.05560","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05560","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05560v2","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05560","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"Z3KQYI6LEMTT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z3KQYI6LEMTT4WY6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z3KQYI6L","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Z3KQYI6LEMTT4WY6ZXMRYO2R4M","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-17T20:23:43Z","cross_cats_sorted":[],"title_canon_sha256":"f4ac3e5558a5003a5b3330a0ee6ed24d160c660a58bbddb3ce98b4f054dbe856","abstract_canon_sha256":"c74979579fcd42b8578e036381072671895dbad0882353bdb43169d3ba8a358a"},"schema_version":"1.0"},"canonical_sha256":"ced50c23cb23273e5b1ecdd91c3b51e3038aff251cc9a472ba276c245f15d4b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:23.751012Z","signature_b64":"eV6xiWRPdqYjrX4ktY0l4G8t1EVXGzFlvX5lYx75OHlsN2dfPFLv63F0hqIZ8HgyTk2h5O5iTsQvWOaI0pPnBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ced50c23cb23273e5b1ecdd91c3b51e3038aff251cc9a472ba276c245f15d4b9","last_reissued_at":"2026-05-18T01:20:23.750421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:23.750421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05560","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":"2026-05-18T01:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9mueLbaaQ9dAJwukHR7CydKkzhpVZsm66w/TdGRmrNkJOASwTOqMYcw4uB9/xOJMaWSnWpj2nPuqxKQxUxqBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:56:55.687729Z"},"content_sha256":"ebcc95ef965f4925246291401165b3b8d79b0113656b45297efedf35ec6d1911","schema_version":"1.0","event_id":"sha256:ebcc95ef965f4925246291401165b3b8d79b0113656b45297efedf35ec6d1911"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Z3KQYI6LEMTT4WY6ZXMRYO2R4M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower bounds for moments of global scores of pairwise Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Zucca, Heinrich Matzinger, Joonas Sova, J\\\"uri Lember","submitted_at":"2016-02-17T20:23:43Z","abstract_excerpt":"Let $X_1,X_2,\\ldots$ and $Y_1,Y_2,\\ldots$ be two random sequences so that every random variable takes values in a finite set $\\mathbb{A}$. We consider a global similarity score $L_n:=L(X_1,\\ldots,X_n;Y_1,\\ldots,Y_n)$ that measures the homology (relatedness) of words $(X_1,\\ldots,X_n)$ and $(Y_1,\\ldots,Y_n)$. A typical example of such score is the length of the longest common subsequence. We study the order of central absolute moment $E|L_n-EL_n|^r$ in the case where two-dimensional process $(X_1,Y_1),(X_2,Y_2),\\ldots$ is a Markov chain on $\\mathbb{A}\\times \\mathbb{A}$. This is a very general m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05560","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":"2026-05-18T01:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+vw+pKsoRQpNP05xV59IltZrYwiOuczyCX0ssPYJnI76h364Nmz/JjEzHiOIK4gbORjIqjMiKnd7X3mn26IIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:56:55.688103Z"},"content_sha256":"999a9ab126448baea80650718a6af793987251bb55443f06c6aad8b3a0ba629f","schema_version":"1.0","event_id":"sha256:999a9ab126448baea80650718a6af793987251bb55443f06c6aad8b3a0ba629f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3KQYI6LEMTT4WY6ZXMRYO2R4M/bundle.json","state_url":"https://pith.science/pith/Z3KQYI6LEMTT4WY6ZXMRYO2R4M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3KQYI6LEMTT4WY6ZXMRYO2R4M/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":"2026-06-04T17:56:55Z","links":{"resolver":"https://pith.science/pith/Z3KQYI6LEMTT4WY6ZXMRYO2R4M","bundle":"https://pith.science/pith/Z3KQYI6LEMTT4WY6ZXMRYO2R4M/bundle.json","state":"https://pith.science/pith/Z3KQYI6LEMTT4WY6ZXMRYO2R4M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3KQYI6LEMTT4WY6ZXMRYO2R4M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z3KQYI6LEMTT4WY6ZXMRYO2R4M","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":"c74979579fcd42b8578e036381072671895dbad0882353bdb43169d3ba8a358a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-17T20:23:43Z","title_canon_sha256":"f4ac3e5558a5003a5b3330a0ee6ed24d160c660a58bbddb3ce98b4f054dbe856"},"schema_version":"1.0","source":{"id":"1602.05560","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05560","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05560v2","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05560","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"Z3KQYI6LEMTT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z3KQYI6LEMTT4WY6","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z3KQYI6L","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:999a9ab126448baea80650718a6af793987251bb55443f06c6aad8b3a0ba629f","target":"graph","created_at":"2026-05-18T01:20:23Z","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":"Let $X_1,X_2,\\ldots$ and $Y_1,Y_2,\\ldots$ be two random sequences so that every random variable takes values in a finite set $\\mathbb{A}$. We consider a global similarity score $L_n:=L(X_1,\\ldots,X_n;Y_1,\\ldots,Y_n)$ that measures the homology (relatedness) of words $(X_1,\\ldots,X_n)$ and $(Y_1,\\ldots,Y_n)$. A typical example of such score is the length of the longest common subsequence. We study the order of central absolute moment $E|L_n-EL_n|^r$ in the case where two-dimensional process $(X_1,Y_1),(X_2,Y_2),\\ldots$ is a Markov chain on $\\mathbb{A}\\times \\mathbb{A}$. This is a very general m","authors_text":"Fabio Zucca, Heinrich Matzinger, Joonas Sova, J\\\"uri Lember","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-17T20:23:43Z","title":"Lower bounds for moments of global scores of pairwise Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05560","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:ebcc95ef965f4925246291401165b3b8d79b0113656b45297efedf35ec6d1911","target":"record","created_at":"2026-05-18T01:20:23Z","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":"c74979579fcd42b8578e036381072671895dbad0882353bdb43169d3ba8a358a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-17T20:23:43Z","title_canon_sha256":"f4ac3e5558a5003a5b3330a0ee6ed24d160c660a58bbddb3ce98b4f054dbe856"},"schema_version":"1.0","source":{"id":"1602.05560","kind":"arxiv","version":2}},"canonical_sha256":"ced50c23cb23273e5b1ecdd91c3b51e3038aff251cc9a472ba276c245f15d4b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ced50c23cb23273e5b1ecdd91c3b51e3038aff251cc9a472ba276c245f15d4b9","first_computed_at":"2026-05-18T01:20:23.750421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:23.750421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eV6xiWRPdqYjrX4ktY0l4G8t1EVXGzFlvX5lYx75OHlsN2dfPFLv63F0hqIZ8HgyTk2h5O5iTsQvWOaI0pPnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:23.751012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05560","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebcc95ef965f4925246291401165b3b8d79b0113656b45297efedf35ec6d1911","sha256:999a9ab126448baea80650718a6af793987251bb55443f06c6aad8b3a0ba629f"],"state_sha256":"cd3b2ff31304ffff5e2c3a210a1f0786f31e8ffd022f8646808eee28c0456768"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"26EBeeLVEln5YWiNLn3QA8XK7hM6l9qhgb2gGbTF7QE8SL58UPM2z6ioAfTHCacb78dt9JuXQl1MrYIY7tRnBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:56:55.690346Z","bundle_sha256":"eb0e961b332a23e1821abc146fd134f349c2ba05f082876373f94aefce2c8c78"}}