{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XUGC2IVR7LQZ7TBL2IDDZOKJQS","short_pith_number":"pith:XUGC2IVR","canonical_record":{"source":{"id":"2008.07517","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-17T17:58:09Z","cross_cats_sorted":[],"title_canon_sha256":"17e7dc8ec0eb35d7654b9ae0efa81f59291af3cbc56c3ee248933091f6446742","abstract_canon_sha256":"01dc71ab38792bfd8407489c524e11ebfc5c26949cc78722869d6227ce128da7"},"schema_version":"1.0"},"canonical_sha256":"bd0c2d22b1fae19fcc2bd2063cb949849056b51c34f01012bad8226198266908","source":{"kind":"arxiv","id":"2008.07517","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.07517","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"arxiv_version","alias_value":"2008.07517v3","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.07517","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"pith_short_12","alias_value":"XUGC2IVR7LQZ","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"pith_short_16","alias_value":"XUGC2IVR7LQZ7TBL","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"pith_short_8","alias_value":"XUGC2IVR","created_at":"2026-07-05T09:37:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XUGC2IVR7LQZ7TBL2IDDZOKJQS","target":"record","payload":{"canonical_record":{"source":{"id":"2008.07517","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-17T17:58:09Z","cross_cats_sorted":[],"title_canon_sha256":"17e7dc8ec0eb35d7654b9ae0efa81f59291af3cbc56c3ee248933091f6446742","abstract_canon_sha256":"01dc71ab38792bfd8407489c524e11ebfc5c26949cc78722869d6227ce128da7"},"schema_version":"1.0"},"canonical_sha256":"bd0c2d22b1fae19fcc2bd2063cb949849056b51c34f01012bad8226198266908","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:37:27.000043Z","signature_b64":"CkYWBV09H6H44BDQN9YcExruSpHCbRklDhMyWCK6u4xdPdcoTtvYYuLGyvelN2IeLDFDfN/Yjyk/xL9HSMlOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd0c2d22b1fae19fcc2bd2063cb949849056b51c34f01012bad8226198266908","last_reissued_at":"2026-07-05T09:37:26.999627Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:37:26.999627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.07517","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:37:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iq7aO1rhBxudaPcIFmHbIqnJIQWMC2HzXLnLKXHYjvyznZTcqIR2XTTjQrfYBp477aH9GsIGmNnV97DrDSL1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:04:25.341478Z"},"content_sha256":"910092505bb2e1ea80f9fbf79326c9e8038806a1f2ef7279a9e5b075fdf1d3db","schema_version":"1.0","event_id":"sha256:910092505bb2e1ea80f9fbf79326c9e8038806a1f2ef7279a9e5b075fdf1d3db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XUGC2IVR7LQZ7TBL2IDDZOKJQS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sensitivity of mixing times of Cayley graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gady Kozma, Jonathan Hermon","submitted_at":"2020-08-17T17:58:09Z","abstract_excerpt":"We show that the total variation mixing time is not quasi-isometry invariant, even for Cayley graphs. Namely, we construct a sequence of pairs of Cayley graphs with maps between them that twist the metric in a bounded way, while the ratio of the two mixing times goes to infinity. The Cayley graphs serving as an example have unbounded degrees.\n  For non-transitive graphs we construct bounded degree graphs for which the mixing time from the worst starting point for one graph is asymptotically smaller than the mixing time from the best starting point of the random walk on a network obtained by in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07517","kind":"arxiv","version":3},"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/2008.07517/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":"2026-07-05T09:37:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QqF2o+2t7cHm+cqZk4WjJJTRPrbCI6Rs4G8F7olY5U2PXrXzX3/HoY/jimxasuxqOFgP+IEDwrAymDPbayK5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:04:25.342029Z"},"content_sha256":"78340306506ddc593ea196751ebd3592f0a6d3b251ae00fe44952d02ed4b37bc","schema_version":"1.0","event_id":"sha256:78340306506ddc593ea196751ebd3592f0a6d3b251ae00fe44952d02ed4b37bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUGC2IVR7LQZ7TBL2IDDZOKJQS/bundle.json","state_url":"https://pith.science/pith/XUGC2IVR7LQZ7TBL2IDDZOKJQS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUGC2IVR7LQZ7TBL2IDDZOKJQS/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":"2026-08-16T12:04:25Z","links":{"resolver":"https://pith.science/pith/XUGC2IVR7LQZ7TBL2IDDZOKJQS","bundle":"https://pith.science/pith/XUGC2IVR7LQZ7TBL2IDDZOKJQS/bundle.json","state":"https://pith.science/pith/XUGC2IVR7LQZ7TBL2IDDZOKJQS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUGC2IVR7LQZ7TBL2IDDZOKJQS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XUGC2IVR7LQZ7TBL2IDDZOKJQS","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":"01dc71ab38792bfd8407489c524e11ebfc5c26949cc78722869d6227ce128da7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-17T17:58:09Z","title_canon_sha256":"17e7dc8ec0eb35d7654b9ae0efa81f59291af3cbc56c3ee248933091f6446742"},"schema_version":"1.0","source":{"id":"2008.07517","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.07517","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"arxiv_version","alias_value":"2008.07517v3","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.07517","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"pith_short_12","alias_value":"XUGC2IVR7LQZ","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"pith_short_16","alias_value":"XUGC2IVR7LQZ7TBL","created_at":"2026-07-05T09:37:26Z"},{"alias_kind":"pith_short_8","alias_value":"XUGC2IVR","created_at":"2026-07-05T09:37:26Z"}],"graph_snapshots":[{"event_id":"sha256:78340306506ddc593ea196751ebd3592f0a6d3b251ae00fe44952d02ed4b37bc","target":"graph","created_at":"2026-07-05T09:37:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.07517/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the total variation mixing time is not quasi-isometry invariant, even for Cayley graphs. Namely, we construct a sequence of pairs of Cayley graphs with maps between them that twist the metric in a bounded way, while the ratio of the two mixing times goes to infinity. The Cayley graphs serving as an example have unbounded degrees.\n  For non-transitive graphs we construct bounded degree graphs for which the mixing time from the worst starting point for one graph is asymptotically smaller than the mixing time from the best starting point of the random walk on a network obtained by in","authors_text":"Gady Kozma, Jonathan Hermon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-17T17:58:09Z","title":"Sensitivity of mixing times of Cayley graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07517","kind":"arxiv","version":3},"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":"sha256:910092505bb2e1ea80f9fbf79326c9e8038806a1f2ef7279a9e5b075fdf1d3db","target":"record","created_at":"2026-07-05T09:37:26Z","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":"01dc71ab38792bfd8407489c524e11ebfc5c26949cc78722869d6227ce128da7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-08-17T17:58:09Z","title_canon_sha256":"17e7dc8ec0eb35d7654b9ae0efa81f59291af3cbc56c3ee248933091f6446742"},"schema_version":"1.0","source":{"id":"2008.07517","kind":"arxiv","version":3}},"canonical_sha256":"bd0c2d22b1fae19fcc2bd2063cb949849056b51c34f01012bad8226198266908","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd0c2d22b1fae19fcc2bd2063cb949849056b51c34f01012bad8226198266908","first_computed_at":"2026-07-05T09:37:26.999627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:37:26.999627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CkYWBV09H6H44BDQN9YcExruSpHCbRklDhMyWCK6u4xdPdcoTtvYYuLGyvelN2IeLDFDfN/Yjyk/xL9HSMlOBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:37:27.000043Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.07517","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:910092505bb2e1ea80f9fbf79326c9e8038806a1f2ef7279a9e5b075fdf1d3db","sha256:78340306506ddc593ea196751ebd3592f0a6d3b251ae00fe44952d02ed4b37bc"],"state_sha256":"b15fd4abd6cf4bf31de0ea68f5b0316cbd924ed122e0ed9fadd9c5111e719ebd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKnqkC7Db0yCK9EV+YU1Ro4CxNgFSn1yN9auID7FSVB1TiJKh3wfQhF8Xz6tFBBjlms3LwJ03nMCwMDF+jRuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:04:25.347818Z","bundle_sha256":"556c64ae589d7dbfa30a15bb7bd138ed8565cb983bae641f2e943d1586c39406"}}