{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MXZO4CDQ5H26KQOXBI4FAGTK3K","short_pith_number":"pith:MXZO4CDQ","canonical_record":{"source":{"id":"1908.02898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-08T01:39:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bc3aabf810c33362802a73fb98be946f028a5b7e53fe121eb214262ba9517603","abstract_canon_sha256":"b1b0472ce2f13e5eb1c5480602def8a6192bbcd3209c5b835b4ceac949999aec"},"schema_version":"1.0"},"canonical_sha256":"65f2ee0870e9f5e541d70a38501a6adaac25a2d80de5b1107e32670a74735c19","source":{"kind":"arxiv","id":"1908.02898","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02898","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02898v1","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02898","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"MXZO4CDQ5H26","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_16","alias_value":"MXZO4CDQ5H26KQOX","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_8","alias_value":"MXZO4CDQ","created_at":"2026-07-04T23:52:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MXZO4CDQ5H26KQOXBI4FAGTK3K","target":"record","payload":{"canonical_record":{"source":{"id":"1908.02898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-08T01:39:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bc3aabf810c33362802a73fb98be946f028a5b7e53fe121eb214262ba9517603","abstract_canon_sha256":"b1b0472ce2f13e5eb1c5480602def8a6192bbcd3209c5b835b4ceac949999aec"},"schema_version":"1.0"},"canonical_sha256":"65f2ee0870e9f5e541d70a38501a6adaac25a2d80de5b1107e32670a74735c19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:24.546020Z","signature_b64":"xg3yjOt+cFMPQhiI7c7zfvTZLl6DHso9kNHSMdO3QPwNs1l805qrjDNNiV2/Q3CXiAvxURUh5kaJij0O4sE0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65f2ee0870e9f5e541d70a38501a6adaac25a2d80de5b1107e32670a74735c19","last_reissued_at":"2026-07-04T23:52:24.545254Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:24.545254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.02898","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":"2026-07-04T23:52:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nrPM1pMrrK13kLWIF5N+WJ59em3fqTOsbs/uGfiwcVmGDaPikKjiuSWJpniCA/u/Zsz5RaRV90I8gHvFgGAnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T04:10:00.237972Z"},"content_sha256":"475b6c987caf909a2da3e751333c38e351340ceba1f46fd5d7dbb050bf999c5b","schema_version":"1.0","event_id":"sha256:475b6c987caf909a2da3e751333c38e351340ceba1f46fd5d7dbb050bf999c5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MXZO4CDQ5H26KQOXBI4FAGTK3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cutoff for random lifts of weighted graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Guillaume Conchon--Kerjan","submitted_at":"2019-08-08T01:39:55Z","abstract_excerpt":"We prove a cutoff for the random walk on random $n$-lifts of finite weighted graphs, even when the random walk on the base graph $\\mathcal{G}$ of the lift is not reversible. The mixing time is w.h.p. $t_{mix}=h^{-1}\\log n$, where $h$ is a constant associated to $\\mathcal{G}$, namely the entropy of its universal cover. Moreover, this mixing time is the smallest possible among all $n$-lifts of $\\mathcal{G}$. In the particular case where the base graph is a vertex with $d/2$ loops, $d$ even, we obtain a cutoff for a $d$-regular random graph (as did Lubetzky and Sly in \\cite{cutoffregular} with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02898","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/1908.02898/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":"2026-07-04T23:52:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TPrLrUHYod6NtgjFLcKt8ywWjx4Dc8pzbNst1iJKMkviA7F/wApu2gtztDXehGzVYWgaXNmM5eVUcL3m1DyXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T04:10:00.238493Z"},"content_sha256":"5a0a584d8850d2ece4f2ab06bebb179681c6ff5c53cf503e1e7dbd810007fa16","schema_version":"1.0","event_id":"sha256:5a0a584d8850d2ece4f2ab06bebb179681c6ff5c53cf503e1e7dbd810007fa16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXZO4CDQ5H26KQOXBI4FAGTK3K/bundle.json","state_url":"https://pith.science/pith/MXZO4CDQ5H26KQOXBI4FAGTK3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXZO4CDQ5H26KQOXBI4FAGTK3K/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":"2026-08-16T04:10:00Z","links":{"resolver":"https://pith.science/pith/MXZO4CDQ5H26KQOXBI4FAGTK3K","bundle":"https://pith.science/pith/MXZO4CDQ5H26KQOXBI4FAGTK3K/bundle.json","state":"https://pith.science/pith/MXZO4CDQ5H26KQOXBI4FAGTK3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXZO4CDQ5H26KQOXBI4FAGTK3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MXZO4CDQ5H26KQOXBI4FAGTK3K","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":"b1b0472ce2f13e5eb1c5480602def8a6192bbcd3209c5b835b4ceac949999aec","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-08T01:39:55Z","title_canon_sha256":"bc3aabf810c33362802a73fb98be946f028a5b7e53fe121eb214262ba9517603"},"schema_version":"1.0","source":{"id":"1908.02898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02898","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02898v1","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02898","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"MXZO4CDQ5H26","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_16","alias_value":"MXZO4CDQ5H26KQOX","created_at":"2026-07-04T23:52:24Z"},{"alias_kind":"pith_short_8","alias_value":"MXZO4CDQ","created_at":"2026-07-04T23:52:24Z"}],"graph_snapshots":[{"event_id":"sha256:5a0a584d8850d2ece4f2ab06bebb179681c6ff5c53cf503e1e7dbd810007fa16","target":"graph","created_at":"2026-07-04T23:52:24Z","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/1908.02898/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a cutoff for the random walk on random $n$-lifts of finite weighted graphs, even when the random walk on the base graph $\\mathcal{G}$ of the lift is not reversible. The mixing time is w.h.p. $t_{mix}=h^{-1}\\log n$, where $h$ is a constant associated to $\\mathcal{G}$, namely the entropy of its universal cover. Moreover, this mixing time is the smallest possible among all $n$-lifts of $\\mathcal{G}$. In the particular case where the base graph is a vertex with $d/2$ loops, $d$ even, we obtain a cutoff for a $d$-regular random graph (as did Lubetzky and Sly in \\cite{cutoffregular} with a ","authors_text":"Guillaume Conchon--Kerjan","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-08T01:39:55Z","title":"Cutoff for random lifts of weighted graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02898","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":"sha256:475b6c987caf909a2da3e751333c38e351340ceba1f46fd5d7dbb050bf999c5b","target":"record","created_at":"2026-07-04T23:52:24Z","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":"b1b0472ce2f13e5eb1c5480602def8a6192bbcd3209c5b835b4ceac949999aec","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-08T01:39:55Z","title_canon_sha256":"bc3aabf810c33362802a73fb98be946f028a5b7e53fe121eb214262ba9517603"},"schema_version":"1.0","source":{"id":"1908.02898","kind":"arxiv","version":1}},"canonical_sha256":"65f2ee0870e9f5e541d70a38501a6adaac25a2d80de5b1107e32670a74735c19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65f2ee0870e9f5e541d70a38501a6adaac25a2d80de5b1107e32670a74735c19","first_computed_at":"2026-07-04T23:52:24.545254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:24.545254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xg3yjOt+cFMPQhiI7c7zfvTZLl6DHso9kNHSMdO3QPwNs1l805qrjDNNiV2/Q3CXiAvxURUh5kaJij0O4sE0Ag==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:24.546020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:475b6c987caf909a2da3e751333c38e351340ceba1f46fd5d7dbb050bf999c5b","sha256:5a0a584d8850d2ece4f2ab06bebb179681c6ff5c53cf503e1e7dbd810007fa16"],"state_sha256":"e5bbb779150a6adf170606ce22056b14287956bd6d5914b7566d565d568e693c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfVXT7uVmSmaZv8klHgYna04EB5E3d4rafWBKIu9bXoyEQcqebhPkk2i0vKpIrrflEOwqVQVYRwnghNEyfFiBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T04:10:00.242555Z","bundle_sha256":"ac403754e696facf39ed118bb74c95786c842f8a0ec9b06fa509aae7e2f2fae0"}}