{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C2KAUTMWPG7MXNNMDL33GIZPOD","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":"015f4178072283d4bdefac7934db1a96de9d97d17d4ecdd377d130ce5256042d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-23T12:57:25Z","title_canon_sha256":"ea2a909c70acda94406a55b662e53b5b7a4bb8137bb4c781fad8cb25e460710c"},"schema_version":"1.0","source":{"id":"1211.5489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5489","created_at":"2026-05-18T03:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5489v1","created_at":"2026-05-18T03:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5489","created_at":"2026-05-18T03:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"C2KAUTMWPG7M","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C2KAUTMWPG7MXNNM","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C2KAUTMW","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:d4069d9a477f1add8e3551f49b28a9c00a6aac3e5da6aa3145ce4fba71109041","target":"graph","created_at":"2026-05-18T03:40:04Z","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":"The problem of determining the correct order of fluctuation of the optimal alignment score of two random strings of length $n$ has been open for several decades. It is known that the biased expected effect of a random letter-change on the optimal score implies an order of fluctuation linear in $\\sqrt{n}$. However, in many situations where such a biased effect is observed empirically, it has been impossible to prove analytically. The main result of this paper shows that when the rescaled-limit of the optimal alignment score increases in a certain direction, then the biased effect exists. On the","authors_text":"Heinrich Matzinger, Raphael Hauser, Saba Amsalu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-23T12:57:25Z","title":"A Monte Carlo Approach to the Fluctuation Problem in Optimal Alignments of Random Strings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5489","kind":"arxiv","version":1},"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":"sha256:1facddda7dce9bc878ecef73dd94bce870f2c0f85cb749688c8cf682e8affb81","target":"record","created_at":"2026-05-18T03:40:04Z","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":"015f4178072283d4bdefac7934db1a96de9d97d17d4ecdd377d130ce5256042d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-23T12:57:25Z","title_canon_sha256":"ea2a909c70acda94406a55b662e53b5b7a4bb8137bb4c781fad8cb25e460710c"},"schema_version":"1.0","source":{"id":"1211.5489","kind":"arxiv","version":1}},"canonical_sha256":"16940a4d9679becbb5ac1af7b3232f70efcecb8111d93f10771dc120b7f05fb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16940a4d9679becbb5ac1af7b3232f70efcecb8111d93f10771dc120b7f05fb7","first_computed_at":"2026-05-18T03:40:04.281174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:04.281174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JFMWZUy/b785zNkKuVJdvEXWhPLN18mxiAv1vvFXo0brq2TttSQE0+GfYiiovctqGeRtwaHcEDW4gAQO6Zx5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:04.281832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1facddda7dce9bc878ecef73dd94bce870f2c0f85cb749688c8cf682e8affb81","sha256:d4069d9a477f1add8e3551f49b28a9c00a6aac3e5da6aa3145ce4fba71109041"],"state_sha256":"9484d18bd2f8e2d98e4e675180c526f31366dce24b5dd11afbfe7a7a983acc57"}