{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:I7VEHDV6FHU2NHCP2ACABEUKXB","short_pith_number":"pith:I7VEHDV6","canonical_record":{"source":{"id":"1404.4249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-16T14:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"184f85ad6e66e423a6f6027ce537e119df1454797f187212c0785ddefedb229d","abstract_canon_sha256":"41447b048bfcae22bbc0fdb49c4aa6e4c83899de80e1baf46c951dfc0ca35d71"},"schema_version":"1.0"},"canonical_sha256":"47ea438ebe29e9a69c4fd00400928ab840447970a4278c523ac7a8a2ffc02aa5","source":{"kind":"arxiv","id":"1404.4249","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4249","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4249v1","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4249","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"I7VEHDV6FHU2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I7VEHDV6FHU2NHCP","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I7VEHDV6","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:I7VEHDV6FHU2NHCP2ACABEUKXB","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-16T14:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"184f85ad6e66e423a6f6027ce537e119df1454797f187212c0785ddefedb229d","abstract_canon_sha256":"41447b048bfcae22bbc0fdb49c4aa6e4c83899de80e1baf46c951dfc0ca35d71"},"schema_version":"1.0"},"canonical_sha256":"47ea438ebe29e9a69c4fd00400928ab840447970a4278c523ac7a8a2ffc02aa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:05.824306Z","signature_b64":"ZYX0SG4F8aIlIMzYwTjzyznPRcwKvzJwivOSZBxjEDqu9dzo8Pym1mLXbP6xFceSXb2AyDFuGEXx3SSLk67eCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47ea438ebe29e9a69c4fd00400928ab840447970a4278c523ac7a8a2ffc02aa5","last_reissued_at":"2026-05-18T02:54:05.823729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:05.823729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4249","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":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1MWwZ31TSapMlJVp0Tey8pXG+6iOmdypLjbbwftFmZuZ51DmO9dB2GHcWsHwWhxf5LwoPJfUNCre3+7TtSwDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:20:14.208604Z"},"content_sha256":"85d364c30137cf204eb2188777d7950f5e30d84a068436d7193d4f01bc4686aa","schema_version":"1.0","event_id":"sha256:85d364c30137cf204eb2188777d7950f5e30d84a068436d7193d4f01bc4686aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:I7VEHDV6FHU2NHCP2ACABEUKXB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Broder's Chain Is Not Rapidly Mixing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Annabell Berger, Steffen Rechner","submitted_at":"2014-04-16T14:05:29Z","abstract_excerpt":"We prove that Broder's Markov chain for approximate sampling near-perfect and perfect matchings is not rapidly mixing for Hamiltonian, regular, threshold and planar bipartite graphs, filling a gap in the literature. In the second part we experimentally compare Broder's chain with the Markov chain by Jerrum, Sinclair and Vigoda from 2004. For the first time, we provide a systematic experimental investigation of mixing time bounds for these Markov chains. We observe that the exact total mixing time is in many cases significantly lower than known upper bounds using canonical path or multicommodit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4249","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":"2026-05-18T02:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L9hP8ZvmTqhYZxsX8sQHTDveQDiaYUlD28XLVEdKBYESiH3U535OCsq51LsBxxFRX/JxQxOm4xWBUXI7+xAKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:20:14.209214Z"},"content_sha256":"2ab5ab373ad44c6fc375df04957b241e885cc39be5b8be02f27e906728fe502e","schema_version":"1.0","event_id":"sha256:2ab5ab373ad44c6fc375df04957b241e885cc39be5b8be02f27e906728fe502e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I7VEHDV6FHU2NHCP2ACABEUKXB/bundle.json","state_url":"https://pith.science/pith/I7VEHDV6FHU2NHCP2ACABEUKXB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I7VEHDV6FHU2NHCP2ACABEUKXB/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":"2026-05-31T10:20:14Z","links":{"resolver":"https://pith.science/pith/I7VEHDV6FHU2NHCP2ACABEUKXB","bundle":"https://pith.science/pith/I7VEHDV6FHU2NHCP2ACABEUKXB/bundle.json","state":"https://pith.science/pith/I7VEHDV6FHU2NHCP2ACABEUKXB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I7VEHDV6FHU2NHCP2ACABEUKXB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I7VEHDV6FHU2NHCP2ACABEUKXB","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":"41447b048bfcae22bbc0fdb49c4aa6e4c83899de80e1baf46c951dfc0ca35d71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-16T14:05:29Z","title_canon_sha256":"184f85ad6e66e423a6f6027ce537e119df1454797f187212c0785ddefedb229d"},"schema_version":"1.0","source":{"id":"1404.4249","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4249","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4249v1","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4249","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"I7VEHDV6FHU2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I7VEHDV6FHU2NHCP","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I7VEHDV6","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:2ab5ab373ad44c6fc375df04957b241e885cc39be5b8be02f27e906728fe502e","target":"graph","created_at":"2026-05-18T02:54:05Z","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 prove that Broder's Markov chain for approximate sampling near-perfect and perfect matchings is not rapidly mixing for Hamiltonian, regular, threshold and planar bipartite graphs, filling a gap in the literature. In the second part we experimentally compare Broder's chain with the Markov chain by Jerrum, Sinclair and Vigoda from 2004. For the first time, we provide a systematic experimental investigation of mixing time bounds for these Markov chains. We observe that the exact total mixing time is in many cases significantly lower than known upper bounds using canonical path or multicommodit","authors_text":"Annabell Berger, Steffen Rechner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-16T14:05:29Z","title":"Broder's Chain Is Not Rapidly Mixing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4249","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":"sha256:85d364c30137cf204eb2188777d7950f5e30d84a068436d7193d4f01bc4686aa","target":"record","created_at":"2026-05-18T02:54:05Z","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":"41447b048bfcae22bbc0fdb49c4aa6e4c83899de80e1baf46c951dfc0ca35d71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-16T14:05:29Z","title_canon_sha256":"184f85ad6e66e423a6f6027ce537e119df1454797f187212c0785ddefedb229d"},"schema_version":"1.0","source":{"id":"1404.4249","kind":"arxiv","version":1}},"canonical_sha256":"47ea438ebe29e9a69c4fd00400928ab840447970a4278c523ac7a8a2ffc02aa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47ea438ebe29e9a69c4fd00400928ab840447970a4278c523ac7a8a2ffc02aa5","first_computed_at":"2026-05-18T02:54:05.823729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:05.823729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZYX0SG4F8aIlIMzYwTjzyznPRcwKvzJwivOSZBxjEDqu9dzo8Pym1mLXbP6xFceSXb2AyDFuGEXx3SSLk67eCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:05.824306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4249","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85d364c30137cf204eb2188777d7950f5e30d84a068436d7193d4f01bc4686aa","sha256:2ab5ab373ad44c6fc375df04957b241e885cc39be5b8be02f27e906728fe502e"],"state_sha256":"5e9c86157e52bee76de4d381006ed39226701ae245e827fb5489155533b4bbe0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMFdTdZld2bHsz7bT+soU44BzgicCZu5LPpW1LW1kybjXtUDGnTJZjDaigPJGhANvoMMOZGeL19UeRhZ5X8lBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:20:14.212499Z","bundle_sha256":"a4139df3a17a1eddd8a58bc79bea5f62c5c35174b57150747b3574bcf3c5a365"}}