{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I24H4VR6DPGKTVVHE7FOAEAXOB","short_pith_number":"pith:I24H4VR6","canonical_record":{"source":{"id":"1608.03633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-11T23:05:04Z","cross_cats_sorted":[],"title_canon_sha256":"92826ea901c38913e3a54160745f812fbcfb7503df27ca0e957edcdb0ba685c6","abstract_canon_sha256":"6cfd093b544c1d9e6900e9023f3f01c8eb5202f86a34db03fb0933351c6bd91c"},"schema_version":"1.0"},"canonical_sha256":"46b87e563e1bcca9d6a727cae0101770608e59aa9390e31794d57b8471248e93","source":{"kind":"arxiv","id":"1608.03633","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03633","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03633v1","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03633","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"I24H4VR6DPGK","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I24H4VR6DPGKTVVH","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I24H4VR6","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I24H4VR6DPGKTVVHE7FOAEAXOB","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-11T23:05:04Z","cross_cats_sorted":[],"title_canon_sha256":"92826ea901c38913e3a54160745f812fbcfb7503df27ca0e957edcdb0ba685c6","abstract_canon_sha256":"6cfd093b544c1d9e6900e9023f3f01c8eb5202f86a34db03fb0933351c6bd91c"},"schema_version":"1.0"},"canonical_sha256":"46b87e563e1bcca9d6a727cae0101770608e59aa9390e31794d57b8471248e93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:19.861176Z","signature_b64":"c0hFi78d/JxuV4NwyjGg+1V6XAmpyOHpqBov17bGMx4sw41KViNTi//hhror58tx0jMrSt8lFie3YQUaoKrRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b87e563e1bcca9d6a727cae0101770608e59aa9390e31794d57b8471248e93","last_reissued_at":"2026-05-18T00:54:19.860673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:19.860673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03633","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":"2026-05-18T00:54:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"en2TgK8knaFwUQHxwxVsMNwKlnULgz53C9e1re/5mYL/ikDqmEC5uxrk4fNX38XtrrIuAbIbUVc7XEkgEE2HAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:51:17.378332Z"},"content_sha256":"0210cd68548192d3ea6fd4dee3090f89c3c05ff55687084b69f20524b250a602","schema_version":"1.0","event_id":"sha256:0210cd68548192d3ea6fd4dee3090f89c3c05ff55687084b69f20524b250a602"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I24H4VR6DPGKTVVHE7FOAEAXOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing of the exclusion process with small bias","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David A. Levin, Yuval Peres","submitted_at":"2016-08-11T23:05:04Z","abstract_excerpt":"We analyze the mixing behavior of the biased exclusion process on a path of length $n$ as the bias $\\beta_n$ tends to $0$ as $n \\to \\infty$. We show that the sequence of chains has a pre-cutoff, and interpolates between the unbiased exclusion and the process with constant bias. As the bias increases, the mixing time undergoes two phase transitions: one when $\\beta_n$ is of order $1/n$, and the other when $\\beta_n$ is order $\\log n/n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03633","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":""},"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":"2026-05-18T00:54:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bp2RgfzA9u6VpIOzcpZYJe8JVBaKCYqPP+lYcSDnjGqxItzT2Or6m6Mmupsb1v2H3wjcZovfaZejT4VObnjVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:51:17.378693Z"},"content_sha256":"0ec2084b891ec9ff38879bad1127326dbe55e8c38defcc3514332af0e631ae1f","schema_version":"1.0","event_id":"sha256:0ec2084b891ec9ff38879bad1127326dbe55e8c38defcc3514332af0e631ae1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I24H4VR6DPGKTVVHE7FOAEAXOB/bundle.json","state_url":"https://pith.science/pith/I24H4VR6DPGKTVVHE7FOAEAXOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I24H4VR6DPGKTVVHE7FOAEAXOB/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":"2026-06-26T13:51:17Z","links":{"resolver":"https://pith.science/pith/I24H4VR6DPGKTVVHE7FOAEAXOB","bundle":"https://pith.science/pith/I24H4VR6DPGKTVVHE7FOAEAXOB/bundle.json","state":"https://pith.science/pith/I24H4VR6DPGKTVVHE7FOAEAXOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I24H4VR6DPGKTVVHE7FOAEAXOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I24H4VR6DPGKTVVHE7FOAEAXOB","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":"6cfd093b544c1d9e6900e9023f3f01c8eb5202f86a34db03fb0933351c6bd91c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-11T23:05:04Z","title_canon_sha256":"92826ea901c38913e3a54160745f812fbcfb7503df27ca0e957edcdb0ba685c6"},"schema_version":"1.0","source":{"id":"1608.03633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03633","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03633v1","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03633","created_at":"2026-05-18T00:54:19Z"},{"alias_kind":"pith_short_12","alias_value":"I24H4VR6DPGK","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I24H4VR6DPGKTVVH","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I24H4VR6","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:0ec2084b891ec9ff38879bad1127326dbe55e8c38defcc3514332af0e631ae1f","target":"graph","created_at":"2026-05-18T00:54:19Z","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 analyze the mixing behavior of the biased exclusion process on a path of length $n$ as the bias $\\beta_n$ tends to $0$ as $n \\to \\infty$. We show that the sequence of chains has a pre-cutoff, and interpolates between the unbiased exclusion and the process with constant bias. As the bias increases, the mixing time undergoes two phase transitions: one when $\\beta_n$ is of order $1/n$, and the other when $\\beta_n$ is order $\\log n/n$.","authors_text":"David A. Levin, Yuval Peres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-11T23:05:04Z","title":"Mixing of the exclusion process with small bias"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03633","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":"sha256:0210cd68548192d3ea6fd4dee3090f89c3c05ff55687084b69f20524b250a602","target":"record","created_at":"2026-05-18T00:54:19Z","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":"6cfd093b544c1d9e6900e9023f3f01c8eb5202f86a34db03fb0933351c6bd91c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-11T23:05:04Z","title_canon_sha256":"92826ea901c38913e3a54160745f812fbcfb7503df27ca0e957edcdb0ba685c6"},"schema_version":"1.0","source":{"id":"1608.03633","kind":"arxiv","version":1}},"canonical_sha256":"46b87e563e1bcca9d6a727cae0101770608e59aa9390e31794d57b8471248e93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46b87e563e1bcca9d6a727cae0101770608e59aa9390e31794d57b8471248e93","first_computed_at":"2026-05-18T00:54:19.860673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:19.860673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c0hFi78d/JxuV4NwyjGg+1V6XAmpyOHpqBov17bGMx4sw41KViNTi//hhror58tx0jMrSt8lFie3YQUaoKrRAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:19.861176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0210cd68548192d3ea6fd4dee3090f89c3c05ff55687084b69f20524b250a602","sha256:0ec2084b891ec9ff38879bad1127326dbe55e8c38defcc3514332af0e631ae1f"],"state_sha256":"17d9d32aff86c893f4dde212769de8a806128ff28c3f486e579c13f1bb687e85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8x5B9KyX6qrQFZk2wGxngSxFDNQPFE5SR/KcKf23JKhsxQLBAdotH3wLIBnPyIde+ZQWL1jRTLPBPNVDbB0hBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:51:17.380771Z","bundle_sha256":"b9fa819dd417f3488951445006c475f325c0dd5bbf4a97b246251ab9e9ffca35"}}