{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:H7ROYTUMQK26EIXZIJC35OH5H6","short_pith_number":"pith:H7ROYTUM","canonical_record":{"source":{"id":"1610.02709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-09T19:36:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"971d8c9cda9d8bd9d90ae36474f0881035fa3880f795782c25358ec55f2354d2","abstract_canon_sha256":"88ea35d16eda4ed7770072b8dfc39eae20043f714c9774a6d129a39c1ecfef10"},"schema_version":"1.0"},"canonical_sha256":"3fe2ec4e8c82b5e222f94245beb8fd3f883cf443949464ec181cd5d82a5d294a","source":{"kind":"arxiv","id":"1610.02709","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02709","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02709v2","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02709","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"pith_short_12","alias_value":"H7ROYTUMQK26","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H7ROYTUMQK26EIXZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H7ROYTUM","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:H7ROYTUMQK26EIXZIJC35OH5H6","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-09T19:36:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"971d8c9cda9d8bd9d90ae36474f0881035fa3880f795782c25358ec55f2354d2","abstract_canon_sha256":"88ea35d16eda4ed7770072b8dfc39eae20043f714c9774a6d129a39c1ecfef10"},"schema_version":"1.0"},"canonical_sha256":"3fe2ec4e8c82b5e222f94245beb8fd3f883cf443949464ec181cd5d82a5d294a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:33.950363Z","signature_b64":"N3p/6/RHHsNqVg3Hrv0a6096R520ZcI+bsLq4o5HO/bl+k0LpeyqF6XI9bNQyvEyjbnHDK2xrxuwfy3YXtzuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fe2ec4e8c82b5e222f94245beb8fd3f883cf443949464ec181cd5d82a5d294a","last_reissued_at":"2026-05-18T00:52:33.949907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:33.949907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02709","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":"2026-05-18T00:52:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uRBl/Dxo2ZADSRl1StN4gxLZe8AQguKmLsb+alQVm7NnWVeLiVJU4B0V9cWRDoBFn1KrxFcFNzUyei8nMhHXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:03:50.389794Z"},"content_sha256":"be0b023984802973ab52c8c2adf60ae8bfba7c1525b37ceac768f7bf05b5e28a","schema_version":"1.0","event_id":"sha256:be0b023984802973ab52c8c2adf60ae8bfba7c1525b37ceac768f7bf05b5e28a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:H7ROYTUMQK26EIXZIJC35OH5H6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Empirical scaling of the length of the longest increasing subsequences of random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"J. Ricardo G. Mendon\\c{c}a","submitted_at":"2016-10-09T19:36:32Z","abstract_excerpt":"We provide Monte Carlo estimates of the scaling of the length $L_{n}$ of the longest increasing subsequences of $n$-steps random walks for several different distributions of step lengths, short and heavy-tailed. Our simulations indicate that, barring possible logarithmic corrections, $L_{n} \\sim n^{\\theta}$ with the leading scaling exponent $0.60 \\lesssim \\theta \\lesssim 0.69$ for the heavy-tailed distributions of step lengths examined, with values increasing as the distribution becomes more heavy-tailed, and $\\theta \\simeq 0.57$ for distributions of finite variance, irrespective of the partic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02709","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":"2026-05-18T00:52:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ai6ie0OWQ3Sm7ex6WteNYws/PLH0+H2GjBunLDHWm9RwcRumk3WkBpiMS0Ow59p80oWadC2s/SdM9P57opi1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:03:50.390136Z"},"content_sha256":"b1d670aed5fe8da3bbd447dcbb68ea89e5631862dbce2fa0ead7acc5a9b737b2","schema_version":"1.0","event_id":"sha256:b1d670aed5fe8da3bbd447dcbb68ea89e5631862dbce2fa0ead7acc5a9b737b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H7ROYTUMQK26EIXZIJC35OH5H6/bundle.json","state_url":"https://pith.science/pith/H7ROYTUMQK26EIXZIJC35OH5H6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H7ROYTUMQK26EIXZIJC35OH5H6/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":"2026-06-27T15:03:50Z","links":{"resolver":"https://pith.science/pith/H7ROYTUMQK26EIXZIJC35OH5H6","bundle":"https://pith.science/pith/H7ROYTUMQK26EIXZIJC35OH5H6/bundle.json","state":"https://pith.science/pith/H7ROYTUMQK26EIXZIJC35OH5H6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H7ROYTUMQK26EIXZIJC35OH5H6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H7ROYTUMQK26EIXZIJC35OH5H6","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":"88ea35d16eda4ed7770072b8dfc39eae20043f714c9774a6d129a39c1ecfef10","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-09T19:36:32Z","title_canon_sha256":"971d8c9cda9d8bd9d90ae36474f0881035fa3880f795782c25358ec55f2354d2"},"schema_version":"1.0","source":{"id":"1610.02709","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02709","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02709v2","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02709","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"pith_short_12","alias_value":"H7ROYTUMQK26","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H7ROYTUMQK26EIXZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H7ROYTUM","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:b1d670aed5fe8da3bbd447dcbb68ea89e5631862dbce2fa0ead7acc5a9b737b2","target":"graph","created_at":"2026-05-18T00:52:33Z","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 provide Monte Carlo estimates of the scaling of the length $L_{n}$ of the longest increasing subsequences of $n$-steps random walks for several different distributions of step lengths, short and heavy-tailed. Our simulations indicate that, barring possible logarithmic corrections, $L_{n} \\sim n^{\\theta}$ with the leading scaling exponent $0.60 \\lesssim \\theta \\lesssim 0.69$ for the heavy-tailed distributions of step lengths examined, with values increasing as the distribution becomes more heavy-tailed, and $\\theta \\simeq 0.57$ for distributions of finite variance, irrespective of the partic","authors_text":"J. Ricardo G. Mendon\\c{c}a","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-09T19:36:32Z","title":"Empirical scaling of the length of the longest increasing subsequences of random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02709","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:be0b023984802973ab52c8c2adf60ae8bfba7c1525b37ceac768f7bf05b5e28a","target":"record","created_at":"2026-05-18T00:52:33Z","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":"88ea35d16eda4ed7770072b8dfc39eae20043f714c9774a6d129a39c1ecfef10","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-09T19:36:32Z","title_canon_sha256":"971d8c9cda9d8bd9d90ae36474f0881035fa3880f795782c25358ec55f2354d2"},"schema_version":"1.0","source":{"id":"1610.02709","kind":"arxiv","version":2}},"canonical_sha256":"3fe2ec4e8c82b5e222f94245beb8fd3f883cf443949464ec181cd5d82a5d294a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fe2ec4e8c82b5e222f94245beb8fd3f883cf443949464ec181cd5d82a5d294a","first_computed_at":"2026-05-18T00:52:33.949907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:33.949907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N3p/6/RHHsNqVg3Hrv0a6096R520ZcI+bsLq4o5HO/bl+k0LpeyqF6XI9bNQyvEyjbnHDK2xrxuwfy3YXtzuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:33.950363Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02709","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be0b023984802973ab52c8c2adf60ae8bfba7c1525b37ceac768f7bf05b5e28a","sha256:b1d670aed5fe8da3bbd447dcbb68ea89e5631862dbce2fa0ead7acc5a9b737b2"],"state_sha256":"5173b42c5bcd069a6f4e6aebf23257b36e7adc430afba1543dd02ccb33db2f0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bns5fAK7vSnUEJQg80FID1kePy34Vtwl63RRRhdpcjg/ZRLU00R8TTj6TR853GRqGEP1mHWjsAy7CjWzjVIaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:03:50.392062Z","bundle_sha256":"0fde6cdebaa37986c0c56ae412f73fb72908537f2fef2118e24459f833af3cc7"}}