{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PCTZLVNAHSX336QEZM2WAXXO5Q","short_pith_number":"pith:PCTZLVNA","canonical_record":{"source":{"id":"1509.01431","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-04T12:49:38Z","cross_cats_sorted":[],"title_canon_sha256":"2ef97921c2dd3e1389d8b41d73a016cabfe18e3d2f5a19a4b9f4c63cbcca9d64","abstract_canon_sha256":"55f8cf6d9f274916133584f94d152d7e826c465d0f9106822cc194641e5ab762"},"schema_version":"1.0"},"canonical_sha256":"78a795d5a03cafbdfa04cb35605eeeec1a2bf3cd7e5d64876436739c96b87bc9","source":{"kind":"arxiv","id":"1509.01431","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01431","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01431v4","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01431","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"PCTZLVNAHSX3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PCTZLVNAHSX336QE","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PCTZLVNA","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PCTZLVNAHSX336QEZM2WAXXO5Q","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01431","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-04T12:49:38Z","cross_cats_sorted":[],"title_canon_sha256":"2ef97921c2dd3e1389d8b41d73a016cabfe18e3d2f5a19a4b9f4c63cbcca9d64","abstract_canon_sha256":"55f8cf6d9f274916133584f94d152d7e826c465d0f9106822cc194641e5ab762"},"schema_version":"1.0"},"canonical_sha256":"78a795d5a03cafbdfa04cb35605eeeec1a2bf3cd7e5d64876436739c96b87bc9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:57.421650Z","signature_b64":"E3URj0gBRuT8VJKaddQsD9Qfkjcya5GyFz2yOTsnL2rmlKr569tFYO6trZyFm+Rxn5rTa9NuGBqzqNl/0Af1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78a795d5a03cafbdfa04cb35605eeeec1a2bf3cd7e5d64876436739c96b87bc9","last_reissued_at":"2026-05-18T00:23:57.420981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:57.420981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01431","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ukgUxFkb2pdecjqBc1iSuXxGELgJ+3c8eXtqEp+nHW/XD8vpvdK4dspWFw5B8Qt87Xy//+OD08TFLnVfzx6rCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:53:59.053420Z"},"content_sha256":"865a4f4d8450a26b49cd2e45c975e88400352b5a07cf47c827088ce1e53eaea0","schema_version":"1.0","event_id":"sha256:865a4f4d8450a26b49cd2e45c975e88400352b5a07cf47c827088ce1e53eaea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PCTZLVNAHSX336QEZM2WAXXO5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved mixing rates of directed cycles by added connection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bal\\'azs Gerencs\\'er, Julien Hendrickx","submitted_at":"2015-09-04T12:49:38Z","abstract_excerpt":"We investigate the mixing rate of a Markov chain where a combination of long distance edges and non-reversibility is introduced: as a first step, we focus here on the following graphs: starting from the cycle graph, we select random nodes and add all edges connecting them. We prove a square factor improvement of the mixing rate compared to the reversible version of the Markov chain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01431","kind":"arxiv","version":4},"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":"2026-05-18T00:23:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6RTAL3Uh55fricciMCEPF35xKedNVB29oKRlF8AADFbm17jQ/3tLJ5U1TFOXnCyP2+KeDNus7amdYWKOtzOZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:53:59.054120Z"},"content_sha256":"eb094f218def838df81e137ed085fe7994b3ea8a8ab32df03a90654e89ce6704","schema_version":"1.0","event_id":"sha256:eb094f218def838df81e137ed085fe7994b3ea8a8ab32df03a90654e89ce6704"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCTZLVNAHSX336QEZM2WAXXO5Q/bundle.json","state_url":"https://pith.science/pith/PCTZLVNAHSX336QEZM2WAXXO5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCTZLVNAHSX336QEZM2WAXXO5Q/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":"2026-05-31T14:53:59Z","links":{"resolver":"https://pith.science/pith/PCTZLVNAHSX336QEZM2WAXXO5Q","bundle":"https://pith.science/pith/PCTZLVNAHSX336QEZM2WAXXO5Q/bundle.json","state":"https://pith.science/pith/PCTZLVNAHSX336QEZM2WAXXO5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCTZLVNAHSX336QEZM2WAXXO5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PCTZLVNAHSX336QEZM2WAXXO5Q","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":"55f8cf6d9f274916133584f94d152d7e826c465d0f9106822cc194641e5ab762","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-04T12:49:38Z","title_canon_sha256":"2ef97921c2dd3e1389d8b41d73a016cabfe18e3d2f5a19a4b9f4c63cbcca9d64"},"schema_version":"1.0","source":{"id":"1509.01431","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01431","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01431v4","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01431","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"PCTZLVNAHSX3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PCTZLVNAHSX336QE","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PCTZLVNA","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:eb094f218def838df81e137ed085fe7994b3ea8a8ab32df03a90654e89ce6704","target":"graph","created_at":"2026-05-18T00:23:57Z","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 investigate the mixing rate of a Markov chain where a combination of long distance edges and non-reversibility is introduced: as a first step, we focus here on the following graphs: starting from the cycle graph, we select random nodes and add all edges connecting them. We prove a square factor improvement of the mixing rate compared to the reversible version of the Markov chain.","authors_text":"Bal\\'azs Gerencs\\'er, Julien Hendrickx","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-04T12:49:38Z","title":"Improved mixing rates of directed cycles by added connection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01431","kind":"arxiv","version":4},"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":"sha256:865a4f4d8450a26b49cd2e45c975e88400352b5a07cf47c827088ce1e53eaea0","target":"record","created_at":"2026-05-18T00:23:57Z","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":"55f8cf6d9f274916133584f94d152d7e826c465d0f9106822cc194641e5ab762","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-04T12:49:38Z","title_canon_sha256":"2ef97921c2dd3e1389d8b41d73a016cabfe18e3d2f5a19a4b9f4c63cbcca9d64"},"schema_version":"1.0","source":{"id":"1509.01431","kind":"arxiv","version":4}},"canonical_sha256":"78a795d5a03cafbdfa04cb35605eeeec1a2bf3cd7e5d64876436739c96b87bc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78a795d5a03cafbdfa04cb35605eeeec1a2bf3cd7e5d64876436739c96b87bc9","first_computed_at":"2026-05-18T00:23:57.420981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:57.420981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E3URj0gBRuT8VJKaddQsD9Qfkjcya5GyFz2yOTsnL2rmlKr569tFYO6trZyFm+Rxn5rTa9NuGBqzqNl/0Af1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:57.421650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01431","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:865a4f4d8450a26b49cd2e45c975e88400352b5a07cf47c827088ce1e53eaea0","sha256:eb094f218def838df81e137ed085fe7994b3ea8a8ab32df03a90654e89ce6704"],"state_sha256":"40e340bd23faaf38c9655af4234391ddbc575b3a4f0598cebf574d8e3fcd7da3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2Ufd91rLVt1Vb+hK/7KVgag2ZTs7UtNB2GkfLqm/yNOo4kGuBmuK1uUfhTNppbQQbzuG71o9iXbwAcuQXf8Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:53:59.057888Z","bundle_sha256":"f862a8a5255e7d01d39f4624eb3cf2c5747d5e56ba0cc13616866417d56df5bb"}}