{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:O4AUP5I2TOR27JFVBIYAZHFMU6","short_pith_number":"pith:O4AUP5I2","canonical_record":{"source":{"id":"1711.03479","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-09T17:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"9faef7aefa452a390d0feca22971d21093b8f713335f8f2a60de097a81d740b9","abstract_canon_sha256":"69f23546a6385d702c3e0b1193bb9836991ddce8a26be8ce036b1537c4dc7678"},"schema_version":"1.0"},"canonical_sha256":"770147f51a9ba3afa4b50a300c9caca7b7683b4ad33dffbc6172adf9561cf323","source":{"kind":"arxiv","id":"1711.03479","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03479","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03479v4","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03479","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"O4AUP5I2TOR2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O4AUP5I2TOR27JFV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O4AUP5I2","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:O4AUP5I2TOR27JFVBIYAZHFMU6","target":"record","payload":{"canonical_record":{"source":{"id":"1711.03479","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-09T17:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"9faef7aefa452a390d0feca22971d21093b8f713335f8f2a60de097a81d740b9","abstract_canon_sha256":"69f23546a6385d702c3e0b1193bb9836991ddce8a26be8ce036b1537c4dc7678"},"schema_version":"1.0"},"canonical_sha256":"770147f51a9ba3afa4b50a300c9caca7b7683b4ad33dffbc6172adf9561cf323","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:03.176222Z","signature_b64":"1U7jZtR1cebX0/ysp4ryI3u0LLkpCIyq6+xe0KVEjlSmoH8Ej9qvEBvWx9ZzlcrW675SG06AT9Cxnjiy/q6MAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"770147f51a9ba3afa4b50a300c9caca7b7683b4ad33dffbc6172adf9561cf323","last_reissued_at":"2026-05-17T23:54:03.175727Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:03.175727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.03479","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":"2026-05-17T23:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7exvJMu//df0KPPiB7hhogJNLiuSZZMqAznIufdOjTC7gYhWjUygVfcVkFUH2GBTpGAwSMRHdgceoQVd8lzHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:21:08.818935Z"},"content_sha256":"5512c8e6aaaa1899c7695dad93b74a144147ab078d8c04ffc9eb574390004f6c","schema_version":"1.0","event_id":"sha256:5512c8e6aaaa1899c7695dad93b74a144147ab078d8c04ffc9eb574390004f6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:O4AUP5I2TOR27JFVBIYAZHFMU6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recurrence of Markov chain traces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Itai Benjamini, Jonathan Hermon","submitted_at":"2017-11-09T17:22:55Z","abstract_excerpt":"It is shown that transient graphs for the simple random walk do not admit a nearest neighbor transient Markov chain (not necessarily a reversible one), that crosses all edges with positive probability, while there is such chain for the square grid $\\mathbb{Z}^2$. In particular, the $d$-dimensional grid $\\mathbb{Z}^d$ admits such a Markov chain only when $d=2$. For $d=2$ we present a relevant example due to Gady Kozma, while the general statement for transient graphs is obtained by proving that for every transient irreducible Markov chain on a countable state space, which admits a stationary me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03479","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":"2026-05-17T23:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwaGXbFy8eu74uWb3jMMoHyiBTE//S4sdCj4COvcANqsCYSdLQb5q91v1HsgjCYFmH1IMlR3zqEr2f0Qob6dDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:21:08.819658Z"},"content_sha256":"33dfb8426b7d7838a75ce34a4f1beb4cfedfb2648ffdebb1e1fa534be2077fc3","schema_version":"1.0","event_id":"sha256:33dfb8426b7d7838a75ce34a4f1beb4cfedfb2648ffdebb1e1fa534be2077fc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4AUP5I2TOR27JFVBIYAZHFMU6/bundle.json","state_url":"https://pith.science/pith/O4AUP5I2TOR27JFVBIYAZHFMU6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4AUP5I2TOR27JFVBIYAZHFMU6/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":"2026-05-26T13:21:08Z","links":{"resolver":"https://pith.science/pith/O4AUP5I2TOR27JFVBIYAZHFMU6","bundle":"https://pith.science/pith/O4AUP5I2TOR27JFVBIYAZHFMU6/bundle.json","state":"https://pith.science/pith/O4AUP5I2TOR27JFVBIYAZHFMU6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4AUP5I2TOR27JFVBIYAZHFMU6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O4AUP5I2TOR27JFVBIYAZHFMU6","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":"69f23546a6385d702c3e0b1193bb9836991ddce8a26be8ce036b1537c4dc7678","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-09T17:22:55Z","title_canon_sha256":"9faef7aefa452a390d0feca22971d21093b8f713335f8f2a60de097a81d740b9"},"schema_version":"1.0","source":{"id":"1711.03479","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03479","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03479v4","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03479","created_at":"2026-05-17T23:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"O4AUP5I2TOR2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O4AUP5I2TOR27JFV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O4AUP5I2","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:33dfb8426b7d7838a75ce34a4f1beb4cfedfb2648ffdebb1e1fa534be2077fc3","target":"graph","created_at":"2026-05-17T23:54:03Z","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":"It is shown that transient graphs for the simple random walk do not admit a nearest neighbor transient Markov chain (not necessarily a reversible one), that crosses all edges with positive probability, while there is such chain for the square grid $\\mathbb{Z}^2$. In particular, the $d$-dimensional grid $\\mathbb{Z}^d$ admits such a Markov chain only when $d=2$. For $d=2$ we present a relevant example due to Gady Kozma, while the general statement for transient graphs is obtained by proving that for every transient irreducible Markov chain on a countable state space, which admits a stationary me","authors_text":"Itai Benjamini, Jonathan Hermon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-09T17:22:55Z","title":"Recurrence of Markov chain traces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03479","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":"sha256:5512c8e6aaaa1899c7695dad93b74a144147ab078d8c04ffc9eb574390004f6c","target":"record","created_at":"2026-05-17T23:54:03Z","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":"69f23546a6385d702c3e0b1193bb9836991ddce8a26be8ce036b1537c4dc7678","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-09T17:22:55Z","title_canon_sha256":"9faef7aefa452a390d0feca22971d21093b8f713335f8f2a60de097a81d740b9"},"schema_version":"1.0","source":{"id":"1711.03479","kind":"arxiv","version":4}},"canonical_sha256":"770147f51a9ba3afa4b50a300c9caca7b7683b4ad33dffbc6172adf9561cf323","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"770147f51a9ba3afa4b50a300c9caca7b7683b4ad33dffbc6172adf9561cf323","first_computed_at":"2026-05-17T23:54:03.175727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:03.175727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1U7jZtR1cebX0/ysp4ryI3u0LLkpCIyq6+xe0KVEjlSmoH8Ej9qvEBvWx9ZzlcrW675SG06AT9Cxnjiy/q6MAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:03.176222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.03479","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5512c8e6aaaa1899c7695dad93b74a144147ab078d8c04ffc9eb574390004f6c","sha256:33dfb8426b7d7838a75ce34a4f1beb4cfedfb2648ffdebb1e1fa534be2077fc3"],"state_sha256":"c33b063c6e043b41892060760a1a58136e329f11f22bf7a38d132dfcae89a29b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bGjlEl2L7KconXx3iQM5adApESd+sTsLia4xhvOToTDvyLcOau9+oVJq49o7SDXi8sH35cB+N6v0R2bWQv18Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:21:08.822717Z","bundle_sha256":"6014844132d2dc92946395d718bcbabdf9c413cddbd6154a02d352b2959868c4"}}