{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AWVDMVIFKD7IA2NJ6OVHZ56RYZ","short_pith_number":"pith:AWVDMVIF","canonical_record":{"source":{"id":"1702.08034","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T14:01:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8d3897111f37b39997c69a4f178e87e4bbccf34c27f8db143dafc3c9763c67e1","abstract_canon_sha256":"2daa325763b00b9e699551e75ac75a20ce72d432a6e70f596344abc75b1a09a6"},"schema_version":"1.0"},"canonical_sha256":"05aa36550550fe8069a9f3aa7cf7d1c64cdf60dcf1c6ab135f68b961a83f2619","source":{"kind":"arxiv","id":"1702.08034","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08034","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08034v3","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08034","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"AWVDMVIFKD7I","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AWVDMVIFKD7IA2NJ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AWVDMVIF","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AWVDMVIFKD7IA2NJ6OVHZ56RYZ","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08034","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T14:01:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"8d3897111f37b39997c69a4f178e87e4bbccf34c27f8db143dafc3c9763c67e1","abstract_canon_sha256":"2daa325763b00b9e699551e75ac75a20ce72d432a6e70f596344abc75b1a09a6"},"schema_version":"1.0"},"canonical_sha256":"05aa36550550fe8069a9f3aa7cf7d1c64cdf60dcf1c6ab135f68b961a83f2619","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:01.062416Z","signature_b64":"tfttPd65pKo6pXPJJ1r5JEwZgyHRa0ZrC3gz/r9nTJQxC3+dwrKSBfTAJ3gLYNm/EnLTW8RZTBy9VDg/+SXDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05aa36550550fe8069a9f3aa7cf7d1c64cdf60dcf1c6ab135f68b961a83f2619","last_reissued_at":"2026-05-18T00:26:01.061801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:01.061801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08034","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":"2026-05-18T00:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvwMaK5u9NQD+cIlfqAFq8ub+wGT5KkAZwt4pgF6ubbI5KI2YnidYIyUYRtJ3gQIzYVCKQqcCW2jl0rwG6BfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:50:44.137756Z"},"content_sha256":"3aa236e519b8c7727113546c0bac7e7bcab38c7f5121b40d63cc39829875f9ad","schema_version":"1.0","event_id":"sha256:3aa236e519b8c7727113546c0bac7e7bcab38c7f5121b40d63cc39829875f9ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AWVDMVIFKD7IA2NJ6OVHZ56RYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cutoff for Ramanujan graphs via degree inflation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Jonathan Hermon","submitted_at":"2017-02-26T14:01:02Z","abstract_excerpt":"Recently Lubetzky and Peres showed that simple random walks on a sequence of $d$-regular Ramanujan graphs $G_n=(V_n,E_n)$ of increasing sizes exhibit cutoff in total variation around the diameter lower bound $\\frac{d}{d-2}\\log_{d-1}|V_n| $. We provide a different argument under the assumption that for some $r(n) \\gg 1$ the maximal number of simple cycles in a ball of radius $r(n)$ in $G_n$ is uniformly bounded in $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08034","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":""},"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":"2026-05-18T00:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NwoLDz7AsDX6tskujVseF2D67cOwmC43rakuGWHShjTGz/Ubn0omhGTQOg6of2vkCtWDnhqOIJ/HVnUcXA6+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:50:44.138105Z"},"content_sha256":"72f1d70fe8e1d2c00e2e24cc9456801c71a1afc882bb1b707c1882c2a9a2cbae","schema_version":"1.0","event_id":"sha256:72f1d70fe8e1d2c00e2e24cc9456801c71a1afc882bb1b707c1882c2a9a2cbae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWVDMVIFKD7IA2NJ6OVHZ56RYZ/bundle.json","state_url":"https://pith.science/pith/AWVDMVIFKD7IA2NJ6OVHZ56RYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWVDMVIFKD7IA2NJ6OVHZ56RYZ/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":"2026-06-30T03:50:44Z","links":{"resolver":"https://pith.science/pith/AWVDMVIFKD7IA2NJ6OVHZ56RYZ","bundle":"https://pith.science/pith/AWVDMVIFKD7IA2NJ6OVHZ56RYZ/bundle.json","state":"https://pith.science/pith/AWVDMVIFKD7IA2NJ6OVHZ56RYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWVDMVIFKD7IA2NJ6OVHZ56RYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AWVDMVIFKD7IA2NJ6OVHZ56RYZ","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":"2daa325763b00b9e699551e75ac75a20ce72d432a6e70f596344abc75b1a09a6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T14:01:02Z","title_canon_sha256":"8d3897111f37b39997c69a4f178e87e4bbccf34c27f8db143dafc3c9763c67e1"},"schema_version":"1.0","source":{"id":"1702.08034","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08034","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08034v3","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08034","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"AWVDMVIFKD7I","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AWVDMVIFKD7IA2NJ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AWVDMVIF","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:72f1d70fe8e1d2c00e2e24cc9456801c71a1afc882bb1b707c1882c2a9a2cbae","target":"graph","created_at":"2026-05-18T00:26:01Z","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":"Recently Lubetzky and Peres showed that simple random walks on a sequence of $d$-regular Ramanujan graphs $G_n=(V_n,E_n)$ of increasing sizes exhibit cutoff in total variation around the diameter lower bound $\\frac{d}{d-2}\\log_{d-1}|V_n| $. We provide a different argument under the assumption that for some $r(n) \\gg 1$ the maximal number of simple cycles in a ball of radius $r(n)$ in $G_n$ is uniformly bounded in $n$.","authors_text":"Jonathan Hermon","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T14:01:02Z","title":"Cutoff for Ramanujan graphs via degree inflation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08034","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":"sha256:3aa236e519b8c7727113546c0bac7e7bcab38c7f5121b40d63cc39829875f9ad","target":"record","created_at":"2026-05-18T00:26:01Z","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":"2daa325763b00b9e699551e75ac75a20ce72d432a6e70f596344abc75b1a09a6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T14:01:02Z","title_canon_sha256":"8d3897111f37b39997c69a4f178e87e4bbccf34c27f8db143dafc3c9763c67e1"},"schema_version":"1.0","source":{"id":"1702.08034","kind":"arxiv","version":3}},"canonical_sha256":"05aa36550550fe8069a9f3aa7cf7d1c64cdf60dcf1c6ab135f68b961a83f2619","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05aa36550550fe8069a9f3aa7cf7d1c64cdf60dcf1c6ab135f68b961a83f2619","first_computed_at":"2026-05-18T00:26:01.061801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:01.061801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tfttPd65pKo6pXPJJ1r5JEwZgyHRa0ZrC3gz/r9nTJQxC3+dwrKSBfTAJ3gLYNm/EnLTW8RZTBy9VDg/+SXDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:01.062416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08034","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3aa236e519b8c7727113546c0bac7e7bcab38c7f5121b40d63cc39829875f9ad","sha256:72f1d70fe8e1d2c00e2e24cc9456801c71a1afc882bb1b707c1882c2a9a2cbae"],"state_sha256":"66b91a461005c4db344483ea8ad729461bb5b11373bedf8f564e680b3965e0d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bYhEmz96JnKusbjjkOZ5jPH4vGkFkg/eGq7/2R/f3gZpc+HILMxEFax5OLe7BuEsj/TTXFNZKJu/TO2/a+2+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T03:50:44.140538Z","bundle_sha256":"238da559307ae2b2c035edefec6ccbbb025ae80db8f96ce914d387372b5a1e77"}}