{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:RFB75TVN7SG46D4V3UXLSCEPA4","short_pith_number":"pith:RFB75TVN","canonical_record":{"source":{"id":"2506.18827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-23T16:41:47Z","cross_cats_sorted":[],"title_canon_sha256":"3f0148481afb61700f270fdc7646f52a2e6e19b84a38faa1b2952e30896b4584","abstract_canon_sha256":"1bcac8c8ddd3033793f885c7bd230f528214e74707d6256561f21d3a17f023ce"},"schema_version":"1.0"},"canonical_sha256":"8943feceadfc8dcf0f95dd2eb9088f072f12d4a15f17035eb9c2607bee55d1e5","source":{"kind":"arxiv","id":"2506.18827","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18827","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18827v2","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18827","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"RFB75TVN7SG4","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"pith_short_16","alias_value":"RFB75TVN7SG46D4V","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"pith_short_8","alias_value":"RFB75TVN","created_at":"2026-07-01T01:17:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:RFB75TVN7SG46D4V3UXLSCEPA4","target":"record","payload":{"canonical_record":{"source":{"id":"2506.18827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-23T16:41:47Z","cross_cats_sorted":[],"title_canon_sha256":"3f0148481afb61700f270fdc7646f52a2e6e19b84a38faa1b2952e30896b4584","abstract_canon_sha256":"1bcac8c8ddd3033793f885c7bd230f528214e74707d6256561f21d3a17f023ce"},"schema_version":"1.0"},"canonical_sha256":"8943feceadfc8dcf0f95dd2eb9088f072f12d4a15f17035eb9c2607bee55d1e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:17:10.087756Z","signature_b64":"htPHYvQaX2YOv4AEqLDJqrmmlhdrP51aBECdWjL8Nie82gWpbjtN5LlbOllP083gRP8nz0ksgMighRpmcKy/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8943feceadfc8dcf0f95dd2eb9088f072f12d4a15f17035eb9c2607bee55d1e5","last_reissued_at":"2026-07-01T01:17:10.087243Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:17:10.087243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.18827","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":"2026-07-01T01:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+vVYiAVIlwyhmI34MMUSN26s4morwq7WpvfAB4GEZAtZ8/meTlxs/nMNyu/SaAUCKtwfzZO8QojSAPr9LG3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T02:00:52.705567Z"},"content_sha256":"64e4430c01bd5622f3abf922a6d66891f7607ba03c615e480bafa28a0d65b7c6","schema_version":"1.0","event_id":"sha256:64e4430c01bd5622f3abf922a6d66891f7607ba03c615e480bafa28a0d65b7c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:RFB75TVN7SG46D4V3UXLSCEPA4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Jinwoo Sung","submitted_at":"2025-06-23T16:41:47Z","abstract_excerpt":"Let $\\mathcal G$ be an infinite graph -- not necessarily one-ended -- on which the simple random walk is transient. We define a variant of the continuous-time random walk on $\\mathcal G$ which reaches $\\infty$ in finite time and \"reflects off of $\\infty$\" infinitely many times.\n  We show that the Aldous-Broder algorithm for the random walk reflected off of $\\infty$ gives the free uniform spanning forest (FUSF) on $\\mathcal G$. Furthermore, Wilson's algorithm for the random walk reflected off of $\\infty$ gives the FUSF on $\\mathcal G$ on the event that the FUSF is connected, but not in general."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18827","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.18827/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-01T01:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XG2ZKehH2meOGEzHtSZdytU1eBkKLfrRdteJ0LYutq5NedR9URmzxUZRYvDx6N7OR7TheZjVinvbBtQD+CuVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T02:00:52.706096Z"},"content_sha256":"6f19d94b3de47673dc15651e0f33f6e09778723a97c956cdb3e435a600903161","schema_version":"1.0","event_id":"sha256:6f19d94b3de47673dc15651e0f33f6e09778723a97c956cdb3e435a600903161"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RFB75TVN7SG46D4V3UXLSCEPA4/bundle.json","state_url":"https://pith.science/pith/RFB75TVN7SG46D4V3UXLSCEPA4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RFB75TVN7SG46D4V3UXLSCEPA4/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":"2026-08-16T02:00:52Z","links":{"resolver":"https://pith.science/pith/RFB75TVN7SG46D4V3UXLSCEPA4","bundle":"https://pith.science/pith/RFB75TVN7SG46D4V3UXLSCEPA4/bundle.json","state":"https://pith.science/pith/RFB75TVN7SG46D4V3UXLSCEPA4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RFB75TVN7SG46D4V3UXLSCEPA4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RFB75TVN7SG46D4V3UXLSCEPA4","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":"1bcac8c8ddd3033793f885c7bd230f528214e74707d6256561f21d3a17f023ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-23T16:41:47Z","title_canon_sha256":"3f0148481afb61700f270fdc7646f52a2e6e19b84a38faa1b2952e30896b4584"},"schema_version":"1.0","source":{"id":"2506.18827","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18827","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18827v2","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18827","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"RFB75TVN7SG4","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"pith_short_16","alias_value":"RFB75TVN7SG46D4V","created_at":"2026-07-01T01:17:10Z"},{"alias_kind":"pith_short_8","alias_value":"RFB75TVN","created_at":"2026-07-01T01:17:10Z"}],"graph_snapshots":[{"event_id":"sha256:6f19d94b3de47673dc15651e0f33f6e09778723a97c956cdb3e435a600903161","target":"graph","created_at":"2026-07-01T01:17:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.18827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal G$ be an infinite graph -- not necessarily one-ended -- on which the simple random walk is transient. We define a variant of the continuous-time random walk on $\\mathcal G$ which reaches $\\infty$ in finite time and \"reflects off of $\\infty$\" infinitely many times.\n  We show that the Aldous-Broder algorithm for the random walk reflected off of $\\infty$ gives the free uniform spanning forest (FUSF) on $\\mathcal G$. Furthermore, Wilson's algorithm for the random walk reflected off of $\\infty$ gives the FUSF on $\\mathcal G$ on the event that the FUSF is connected, but not in general.","authors_text":"Ewain Gwynne, Jinwoo Sung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-23T16:41:47Z","title":"Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18827","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":"sha256:64e4430c01bd5622f3abf922a6d66891f7607ba03c615e480bafa28a0d65b7c6","target":"record","created_at":"2026-07-01T01:17:10Z","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":"1bcac8c8ddd3033793f885c7bd230f528214e74707d6256561f21d3a17f023ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-23T16:41:47Z","title_canon_sha256":"3f0148481afb61700f270fdc7646f52a2e6e19b84a38faa1b2952e30896b4584"},"schema_version":"1.0","source":{"id":"2506.18827","kind":"arxiv","version":2}},"canonical_sha256":"8943feceadfc8dcf0f95dd2eb9088f072f12d4a15f17035eb9c2607bee55d1e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8943feceadfc8dcf0f95dd2eb9088f072f12d4a15f17035eb9c2607bee55d1e5","first_computed_at":"2026-07-01T01:17:10.087243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:10.087243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"htPHYvQaX2YOv4AEqLDJqrmmlhdrP51aBECdWjL8Nie82gWpbjtN5LlbOllP083gRP8nz0ksgMighRpmcKy/Aw==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:10.087756Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.18827","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64e4430c01bd5622f3abf922a6d66891f7607ba03c615e480bafa28a0d65b7c6","sha256:6f19d94b3de47673dc15651e0f33f6e09778723a97c956cdb3e435a600903161"],"state_sha256":"5ec5be67a85d4dc7b0f114a73ac728aa06a8a36ac97278ee3f87e7b28ff00588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RxWeZ77wFFDzNJioQRyeau+7Sts8tzWP0Kt3oU3o1GPNOi108rjSE+0OwS6S10EJJzUTOpqGpcYkc3WU53P/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T02:00:52.709663Z","bundle_sha256":"8d1c4c2d38ba931fd0e1dbec03afc91dfa1795b6308b9f2713aa67245e644a6b"}}