{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:B34ABRT66KDLLOMAUXG376JQ5N","short_pith_number":"pith:B34ABRT6","canonical_record":{"source":{"id":"0902.0115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-01T23:07:00Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"74ab170722ba73647552f34930dd572e16633e20a09c816704391dde251c3545","abstract_canon_sha256":"71b63cfc67e0c0485712236232e8ff0cbf683c82b6d44c99773bbc99f5c18115"},"schema_version":"1.0"},"canonical_sha256":"0ef800c67ef286b5b980a5cdbff930eb434b3506f032e4e5ec862a0ff56fa0de","source":{"kind":"arxiv","id":"0902.0115","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0115","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0115v2","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0115","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"B34ABRT66KDL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"B34ABRT66KDLLOMA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"B34ABRT6","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:B34ABRT66KDLLOMAUXG376JQ5N","target":"record","payload":{"canonical_record":{"source":{"id":"0902.0115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-01T23:07:00Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"74ab170722ba73647552f34930dd572e16633e20a09c816704391dde251c3545","abstract_canon_sha256":"71b63cfc67e0c0485712236232e8ff0cbf683c82b6d44c99773bbc99f5c18115"},"schema_version":"1.0"},"canonical_sha256":"0ef800c67ef286b5b980a5cdbff930eb434b3506f032e4e5ec862a0ff56fa0de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:45.506188Z","signature_b64":"j52RtQiN1gXreoj0pbfoG6Yl3QfU/WgTDxslO+iQoeozr9SiKI3avrxBjVvPmryVPcTOAjBLVfoQSEWcjZv7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ef800c67ef286b5b980a5cdbff930eb434b3506f032e4e5ec862a0ff56fa0de","last_reissued_at":"2026-05-18T04:24:45.505715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:45.505715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.0115","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGP4V4FQ5w0JmSl3KMSL+qRy5GBB33mff/kgJVdWebcpv31Xk4NArbhz2J2Y0G9DPIUZ4s8F3PDtPpi3JNo8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:39:52.064450Z"},"content_sha256":"c61b2881a86e9518c911a56ebf22f943bc2529ce48b6b0ecc599dd6cf70ca592","schema_version":"1.0","event_id":"sha256:c61b2881a86e9518c911a56ebf22f943bc2529ce48b6b0ecc599dd6cf70ca592"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:B34ABRT66KDLLOMAUXG376JQ5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cutpoints and resistance of random walk paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Itai Benjamini, Oded Schramm, Ori Gurel-Gurevich","submitted_at":"2009-02-01T23:07:00Z","abstract_excerpt":"We construct a bounded degree graph $G$, such that a simple random walk on it is transient but the random walk path (i.e., the subgraph of all the edges the random walk has crossed) has only finitely many cutpoints, almost surely. We also prove that the expected number of cutpoints of any transient Markov chain is infinite. This answers two questions of James, Lyons and Peres [A Transient Markov Chain With Finitely Many Cutpoints (2007) Festschrift for David Freedman]. Additionally, we consider a simple random walk on a finite connected graph $G$ that starts at some fixed vertex $x$ and is sto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0115","kind":"arxiv","version":2},"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":"2026-05-18T04:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rau2p5mMI+/t1z5tBL1ukzf15gU85dpuZUEqE1GuCd1gneW99rcY1uVVO1nCsWZGbSbpe4roK5SjrWXmKL6ECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:39:52.065155Z"},"content_sha256":"084c3be34ca0c80361da091e479b601b1df56fb8a4529ffcfac726d3132952ad","schema_version":"1.0","event_id":"sha256:084c3be34ca0c80361da091e479b601b1df56fb8a4529ffcfac726d3132952ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B34ABRT66KDLLOMAUXG376JQ5N/bundle.json","state_url":"https://pith.science/pith/B34ABRT66KDLLOMAUXG376JQ5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B34ABRT66KDLLOMAUXG376JQ5N/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":"2026-05-25T23:39:52Z","links":{"resolver":"https://pith.science/pith/B34ABRT66KDLLOMAUXG376JQ5N","bundle":"https://pith.science/pith/B34ABRT66KDLLOMAUXG376JQ5N/bundle.json","state":"https://pith.science/pith/B34ABRT66KDLLOMAUXG376JQ5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B34ABRT66KDLLOMAUXG376JQ5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:B34ABRT66KDLLOMAUXG376JQ5N","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":"71b63cfc67e0c0485712236232e8ff0cbf683c82b6d44c99773bbc99f5c18115","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-01T23:07:00Z","title_canon_sha256":"74ab170722ba73647552f34930dd572e16633e20a09c816704391dde251c3545"},"schema_version":"1.0","source":{"id":"0902.0115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0115","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0115v2","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0115","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"B34ABRT66KDL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"B34ABRT66KDLLOMA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"B34ABRT6","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:084c3be34ca0c80361da091e479b601b1df56fb8a4529ffcfac726d3132952ad","target":"graph","created_at":"2026-05-18T04:24:45Z","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 construct a bounded degree graph $G$, such that a simple random walk on it is transient but the random walk path (i.e., the subgraph of all the edges the random walk has crossed) has only finitely many cutpoints, almost surely. We also prove that the expected number of cutpoints of any transient Markov chain is infinite. This answers two questions of James, Lyons and Peres [A Transient Markov Chain With Finitely Many Cutpoints (2007) Festschrift for David Freedman]. Additionally, we consider a simple random walk on a finite connected graph $G$ that starts at some fixed vertex $x$ and is sto","authors_text":"Itai Benjamini, Oded Schramm, Ori Gurel-Gurevich","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-01T23:07:00Z","title":"Cutpoints and resistance of random walk paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0115","kind":"arxiv","version":2},"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:c61b2881a86e9518c911a56ebf22f943bc2529ce48b6b0ecc599dd6cf70ca592","target":"record","created_at":"2026-05-18T04:24:45Z","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":"71b63cfc67e0c0485712236232e8ff0cbf683c82b6d44c99773bbc99f5c18115","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-02-01T23:07:00Z","title_canon_sha256":"74ab170722ba73647552f34930dd572e16633e20a09c816704391dde251c3545"},"schema_version":"1.0","source":{"id":"0902.0115","kind":"arxiv","version":2}},"canonical_sha256":"0ef800c67ef286b5b980a5cdbff930eb434b3506f032e4e5ec862a0ff56fa0de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ef800c67ef286b5b980a5cdbff930eb434b3506f032e4e5ec862a0ff56fa0de","first_computed_at":"2026-05-18T04:24:45.505715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:45.505715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j52RtQiN1gXreoj0pbfoG6Yl3QfU/WgTDxslO+iQoeozr9SiKI3avrxBjVvPmryVPcTOAjBLVfoQSEWcjZv7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:45.506188Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c61b2881a86e9518c911a56ebf22f943bc2529ce48b6b0ecc599dd6cf70ca592","sha256:084c3be34ca0c80361da091e479b601b1df56fb8a4529ffcfac726d3132952ad"],"state_sha256":"1c00ea54bef9e97fa48d970e32078e58271ad7de5a768ba9565a4d75f512880e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"puRmM/cEvr/nTky6LhjiFw+fV55Bg5mIjjgx6uHEI/FZ312DZXeZ5MXubMAq5caJK4Nqyh6T7SmPvDEtmSl6DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:39:52.069250Z","bundle_sha256":"4444bee3e8997c33f5fb08681e5a3c1b8ed7a46f6d741cb64da4f038e1885820"}}