{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:53DSV7SI5DANQ6LUE44MYVCSUU","short_pith_number":"pith:53DSV7SI","canonical_record":{"source":{"id":"2605.29185","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-27T23:48:04Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"4a2713cf148d822dad5ac653deb8b9d89c9605772afad78ce80b4301c935db18","abstract_canon_sha256":"be6b995c0d60b732403d8e7fd01285119830d104019a83156db2411540e1a71b"},"schema_version":"1.0"},"canonical_sha256":"eec72afe48e8c0d879742738cc5452a50dd6c21f480aa626fb17ddfca46530fe","source":{"kind":"arxiv","id":"2605.29185","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29185","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29185v1","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29185","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"53DSV7SI5DAN","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"pith_short_16","alias_value":"53DSV7SI5DANQ6LU","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"pith_short_8","alias_value":"53DSV7SI","created_at":"2026-05-29T01:05:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:53DSV7SI5DANQ6LUE44MYVCSUU","target":"record","payload":{"canonical_record":{"source":{"id":"2605.29185","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-27T23:48:04Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"4a2713cf148d822dad5ac653deb8b9d89c9605772afad78ce80b4301c935db18","abstract_canon_sha256":"be6b995c0d60b732403d8e7fd01285119830d104019a83156db2411540e1a71b"},"schema_version":"1.0"},"canonical_sha256":"eec72afe48e8c0d879742738cc5452a50dd6c21f480aa626fb17ddfca46530fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:05:23.246712Z","signature_b64":"Uq+k1GV0jXQ+VKQ7cAbZy7ZuhxdnADgGgq2l6IFReQkpYscXKhJ+/zw4AyDuxUeesnInIqWpdT6BuDkiJkPpBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eec72afe48e8c0d879742738cc5452a50dd6c21f480aa626fb17ddfca46530fe","last_reissued_at":"2026-05-29T01:05:23.245734Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:05:23.245734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.29185","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"94ayiweRsT96hC7R4fuckPyE1Zk1YN5SbfC21ge3cZYmyn3Iu7NosIYiqT7FObr+rLyC+OM2ufAxEbVvvDx+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:40:13.912888Z"},"content_sha256":"39135c915b0dfc81294f8a74ebc6f12a31009f02b0133a34a07a43272a9c9f20","schema_version":"1.0","event_id":"sha256:39135c915b0dfc81294f8a74ebc6f12a31009f02b0133a34a07a43272a9c9f20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:53DSV7SI5DANQ6LUE44MYVCSUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Records, drift, and the longest increasing subsequence of biased Gaussian random walks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"J. Ricardo G. Mendon\\c{c}a","submitted_at":"2026-05-27T23:48:04Z","abstract_excerpt":"The longest increasing subsequence (LIS) of a random walk has so far been studied mainly for zero-mean, symmetric step increments. We numerically investigate the LIS of biased Gaussian random walks, with unit-variance increments and positive drift $\\mu_{p} = \\Phi^{-1}(p)$, where $p = \\mathbb{P}(\\xi>0)$. In contrast with the symmetric case, we find that for every fixed $p>1/2$ the mean LIS length grows linearly, $\\langle L_{n}(p)\\rangle \\sim a(p)n$, with $a(p)$ increasing from $0$ at $p=1/2$ to $1$ as $p \\to 1$. The record count is also linear, with coefficient $\\lambda(p)$ given by Spitzer's f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29185","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29185/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-29T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G92T10DH5tErT9/648lkN/wXjOGzHiSVT8SwvQFEzXQoJt3ppnHbN62LsPZzplxcB0U3/4Zxym8YtEW1OIUsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:40:13.913262Z"},"content_sha256":"05039729ef0cb661c5bbe1d800ae6f314ed49552653414913a248dca3364d509","schema_version":"1.0","event_id":"sha256:05039729ef0cb661c5bbe1d800ae6f314ed49552653414913a248dca3364d509"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53DSV7SI5DANQ6LUE44MYVCSUU/bundle.json","state_url":"https://pith.science/pith/53DSV7SI5DANQ6LUE44MYVCSUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53DSV7SI5DANQ6LUE44MYVCSUU/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":"2026-06-27T13:40:13Z","links":{"resolver":"https://pith.science/pith/53DSV7SI5DANQ6LUE44MYVCSUU","bundle":"https://pith.science/pith/53DSV7SI5DANQ6LUE44MYVCSUU/bundle.json","state":"https://pith.science/pith/53DSV7SI5DANQ6LUE44MYVCSUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53DSV7SI5DANQ6LUE44MYVCSUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:53DSV7SI5DANQ6LUE44MYVCSUU","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":"be6b995c0d60b732403d8e7fd01285119830d104019a83156db2411540e1a71b","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-27T23:48:04Z","title_canon_sha256":"4a2713cf148d822dad5ac653deb8b9d89c9605772afad78ce80b4301c935db18"},"schema_version":"1.0","source":{"id":"2605.29185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29185","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29185v1","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29185","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"53DSV7SI5DAN","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"pith_short_16","alias_value":"53DSV7SI5DANQ6LU","created_at":"2026-05-29T01:05:23Z"},{"alias_kind":"pith_short_8","alias_value":"53DSV7SI","created_at":"2026-05-29T01:05:23Z"}],"graph_snapshots":[{"event_id":"sha256:05039729ef0cb661c5bbe1d800ae6f314ed49552653414913a248dca3364d509","target":"graph","created_at":"2026-05-29T01:05:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.29185/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The longest increasing subsequence (LIS) of a random walk has so far been studied mainly for zero-mean, symmetric step increments. We numerically investigate the LIS of biased Gaussian random walks, with unit-variance increments and positive drift $\\mu_{p} = \\Phi^{-1}(p)$, where $p = \\mathbb{P}(\\xi>0)$. In contrast with the symmetric case, we find that for every fixed $p>1/2$ the mean LIS length grows linearly, $\\langle L_{n}(p)\\rangle \\sim a(p)n$, with $a(p)$ increasing from $0$ at $p=1/2$ to $1$ as $p \\to 1$. The record count is also linear, with coefficient $\\lambda(p)$ given by Spitzer's f","authors_text":"J. Ricardo G. Mendon\\c{c}a","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-27T23:48:04Z","title":"Records, drift, and the longest increasing subsequence of biased Gaussian random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29185","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":"sha256:39135c915b0dfc81294f8a74ebc6f12a31009f02b0133a34a07a43272a9c9f20","target":"record","created_at":"2026-05-29T01:05:23Z","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":"be6b995c0d60b732403d8e7fd01285119830d104019a83156db2411540e1a71b","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-27T23:48:04Z","title_canon_sha256":"4a2713cf148d822dad5ac653deb8b9d89c9605772afad78ce80b4301c935db18"},"schema_version":"1.0","source":{"id":"2605.29185","kind":"arxiv","version":1}},"canonical_sha256":"eec72afe48e8c0d879742738cc5452a50dd6c21f480aa626fb17ddfca46530fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eec72afe48e8c0d879742738cc5452a50dd6c21f480aa626fb17ddfca46530fe","first_computed_at":"2026-05-29T01:05:23.245734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:23.245734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uq+k1GV0jXQ+VKQ7cAbZy7ZuhxdnADgGgq2l6IFReQkpYscXKhJ+/zw4AyDuxUeesnInIqWpdT6BuDkiJkPpBA==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:23.246712Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39135c915b0dfc81294f8a74ebc6f12a31009f02b0133a34a07a43272a9c9f20","sha256:05039729ef0cb661c5bbe1d800ae6f314ed49552653414913a248dca3364d509"],"state_sha256":"36e9d4041cf47483907e8e96564d68ca1731bf762d8781754d670f8ec740ddbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"195BXLBQIKKrDzMmRy0V/NjeSJJVBgbR/plmTQng37EfBViuXxfhru+9GTcD92I11RS+sZlqvVpMXmvzkyBhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:40:13.915349Z","bundle_sha256":"e3f5cec1e9f4b66822dc58323d9256cd0af52234a5a35b962baa9db868b7446b"}}