{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OFKHJGRYTLMONSZHRHQJ7HLIMM","short_pith_number":"pith:OFKHJGRY","canonical_record":{"source":{"id":"1003.5505","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-29T11:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"7d09d3a14530daf07f44947608ef5f80114d5c0e676a0161cfc1df0cd81c242a","abstract_canon_sha256":"be3793e26213c69e1132c9721ba714dd45f6156d5bd50363f66afdfbd27b4ce5"},"schema_version":"1.0"},"canonical_sha256":"7154749a389ad8e6cb2789e09f9d68632347fca3a76101a5cacfcfe16603c132","source":{"kind":"arxiv","id":"1003.5505","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5505","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5505v5","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5505","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"OFKHJGRYTLMO","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OFKHJGRYTLMONSZH","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OFKHJGRY","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OFKHJGRYTLMONSZHRHQJ7HLIMM","target":"record","payload":{"canonical_record":{"source":{"id":"1003.5505","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-29T11:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"7d09d3a14530daf07f44947608ef5f80114d5c0e676a0161cfc1df0cd81c242a","abstract_canon_sha256":"be3793e26213c69e1132c9721ba714dd45f6156d5bd50363f66afdfbd27b4ce5"},"schema_version":"1.0"},"canonical_sha256":"7154749a389ad8e6cb2789e09f9d68632347fca3a76101a5cacfcfe16603c132","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:26.283347Z","signature_b64":"0K/TY2m7TeX3IZhVxpF+aknt1XojjI9V4WION+zaPYk8fz6Ly9a5gp35+d2d5QrFWgUG2689mhhgjWpkAI5+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7154749a389ad8e6cb2789e09f9d68632347fca3a76101a5cacfcfe16603c132","last_reissued_at":"2026-05-18T02:24:26.282851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:26.282851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.5505","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aoa7/r10pdLR4HXn35D89qVlHCDi1Ufpsw/lnFfvpEvms8R98favExbygF3tjxodJWKmRviUPh8A2j/q5XIxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:34.044801Z"},"content_sha256":"720b81f9de9d2c59c4d3f7601c465e79c89a932b03a8571c1312a7fecbbba3f8","schema_version":"1.0","event_id":"sha256:720b81f9de9d2c59c4d3f7601c465e79c89a932b03a8571c1312a7fecbbba3f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OFKHJGRYTLMONSZHRHQJ7HLIMM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost sure convergence for stochastically biased random walks on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gabriel Faraud, Yueyun Hu, Zhan Shi","submitted_at":"2010-03-29T11:32:19Z","abstract_excerpt":"We are interested in the biased random walk on a supercritical Galton--Watson tree in the sense of Lyons, Pemantle and Peres, and study a phenomenon of slow movement. In order to observe such a slow movement, the bias needs to be random; the resulting random walk is then a tree-valued random walk in random environment. We investigate the recurrent case, and prove, under suitable general integrability assumptions, that upon the system's non-extinction, the maximal displacement of the walk in the first n steps, divided by (log n)^3, converges almost surely to a known positive constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5505","kind":"arxiv","version":5},"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":"2026-05-18T02:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hFFaLJAH7PhNlv1VIoxS5V2LTT1tgFbKPkvCg6Rokz83SEn5sOLitHFgt+J35zS8D2GzeWNDzgq81UbOopr+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:02:34.045513Z"},"content_sha256":"94fdbc7f4c1f3a785ae57f041f5d7cef53ff49502fe109b49d19c96768e5aec7","schema_version":"1.0","event_id":"sha256:94fdbc7f4c1f3a785ae57f041f5d7cef53ff49502fe109b49d19c96768e5aec7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFKHJGRYTLMONSZHRHQJ7HLIMM/bundle.json","state_url":"https://pith.science/pith/OFKHJGRYTLMONSZHRHQJ7HLIMM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFKHJGRYTLMONSZHRHQJ7HLIMM/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":"2026-06-11T23:02:34Z","links":{"resolver":"https://pith.science/pith/OFKHJGRYTLMONSZHRHQJ7HLIMM","bundle":"https://pith.science/pith/OFKHJGRYTLMONSZHRHQJ7HLIMM/bundle.json","state":"https://pith.science/pith/OFKHJGRYTLMONSZHRHQJ7HLIMM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFKHJGRYTLMONSZHRHQJ7HLIMM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OFKHJGRYTLMONSZHRHQJ7HLIMM","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":"be3793e26213c69e1132c9721ba714dd45f6156d5bd50363f66afdfbd27b4ce5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-29T11:32:19Z","title_canon_sha256":"7d09d3a14530daf07f44947608ef5f80114d5c0e676a0161cfc1df0cd81c242a"},"schema_version":"1.0","source":{"id":"1003.5505","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5505","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5505v5","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5505","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"OFKHJGRYTLMO","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OFKHJGRYTLMONSZH","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OFKHJGRY","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:94fdbc7f4c1f3a785ae57f041f5d7cef53ff49502fe109b49d19c96768e5aec7","target":"graph","created_at":"2026-05-18T02:24:26Z","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 are interested in the biased random walk on a supercritical Galton--Watson tree in the sense of Lyons, Pemantle and Peres, and study a phenomenon of slow movement. In order to observe such a slow movement, the bias needs to be random; the resulting random walk is then a tree-valued random walk in random environment. We investigate the recurrent case, and prove, under suitable general integrability assumptions, that upon the system's non-extinction, the maximal displacement of the walk in the first n steps, divided by (log n)^3, converges almost surely to a known positive constant.","authors_text":"Gabriel Faraud, Yueyun Hu, Zhan Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-29T11:32:19Z","title":"Almost sure convergence for stochastically biased random walks on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5505","kind":"arxiv","version":5},"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":"sha256:720b81f9de9d2c59c4d3f7601c465e79c89a932b03a8571c1312a7fecbbba3f8","target":"record","created_at":"2026-05-18T02:24:26Z","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":"be3793e26213c69e1132c9721ba714dd45f6156d5bd50363f66afdfbd27b4ce5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-29T11:32:19Z","title_canon_sha256":"7d09d3a14530daf07f44947608ef5f80114d5c0e676a0161cfc1df0cd81c242a"},"schema_version":"1.0","source":{"id":"1003.5505","kind":"arxiv","version":5}},"canonical_sha256":"7154749a389ad8e6cb2789e09f9d68632347fca3a76101a5cacfcfe16603c132","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7154749a389ad8e6cb2789e09f9d68632347fca3a76101a5cacfcfe16603c132","first_computed_at":"2026-05-18T02:24:26.282851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:26.282851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0K/TY2m7TeX3IZhVxpF+aknt1XojjI9V4WION+zaPYk8fz6Ly9a5gp35+d2d5QrFWgUG2689mhhgjWpkAI5+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:26.283347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5505","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:720b81f9de9d2c59c4d3f7601c465e79c89a932b03a8571c1312a7fecbbba3f8","sha256:94fdbc7f4c1f3a785ae57f041f5d7cef53ff49502fe109b49d19c96768e5aec7"],"state_sha256":"1f8659c659a10d085b82f7b55df16026d25939fd3ac442c04274d60aad6c7de8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CrdXuloDRPIsT4P07Uw7kuSn11XmiaHCr5QRLbfpqr2rfM6zyG44jRr3Lt1zmeCCBobYJqDmpqr1vUorNNnBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:02:34.049435Z","bundle_sha256":"e9222ccba031e9026e1dc1db0609b68423b0c2c43e8a5d1e7856848471d4308e"}}