{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GYMB3PHY4PRY3GC3CJGFW7JS76","short_pith_number":"pith:GYMB3PHY","canonical_record":{"source":{"id":"1903.07910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-19T10:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"b07afbd61b4bf9ceda3bcd39733960ac638ac805b4ba6fa92e72b83b05da2bc6","abstract_canon_sha256":"56172a41ba55c8cb971690d442bbfa44859bb9b24fe2988b1829b937e257d748"},"schema_version":"1.0"},"canonical_sha256":"36181dbcf8e3e38d985b124c5b7d32ff83a7f72f8b3363c06c9fca120e6f8fd2","source":{"kind":"arxiv","id":"1903.07910","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07910","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07910v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07910","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"GYMB3PHY4PRY","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GYMB3PHY4PRY3GC3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GYMB3PHY","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GYMB3PHY4PRY3GC3CJGFW7JS76","target":"record","payload":{"canonical_record":{"source":{"id":"1903.07910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-19T10:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"b07afbd61b4bf9ceda3bcd39733960ac638ac805b4ba6fa92e72b83b05da2bc6","abstract_canon_sha256":"56172a41ba55c8cb971690d442bbfa44859bb9b24fe2988b1829b937e257d748"},"schema_version":"1.0"},"canonical_sha256":"36181dbcf8e3e38d985b124c5b7d32ff83a7f72f8b3363c06c9fca120e6f8fd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:53.499523Z","signature_b64":"bPN4aUqwS3CKxnGCFFuF+bd5WO0hwCYxr1L1wcGQn45x1d54CbsaFkekGnGaIcA4MYUO70lSe1NlLq3TNSlFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36181dbcf8e3e38d985b124c5b7d32ff83a7f72f8b3363c06c9fca120e6f8fd2","last_reissued_at":"2026-05-17T23:50:53.498834Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:53.498834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.07910","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":"2026-05-17T23:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QQCeiJh6Ko5SotJGZoCD7GtosUTzmMrO+OtFuSS8RdaP+VS7nTVw3PLW/ZiGzQf44SIygCsuaBzVlo5OkXIoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:40:22.236440Z"},"content_sha256":"6f0c0d9608f810eb333e0d96d4a1b6965ee370796b1ea67e715a8ca16e6431b2","schema_version":"1.0","event_id":"sha256:6f0c0d9608f810eb333e0d96d4a1b6965ee370796b1ea67e715a8ca16e6431b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GYMB3PHY4PRY3GC3CJGFW7JS76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random interlacements for vertex-reinforced jump processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Franz Merkl, Pierre Tarr\\`es, Silke W.W. Rolles","submitted_at":"2019-03-19T10:01:43Z","abstract_excerpt":"We introduce random interlacements for transient vertex-reinforced jump processes on a general graph $G$. Using increasing finite subgraphs $G_n$ of $G$ with wired boundary conditions, we show convergence of the vertex-reinforced jump process on $G_n$ observed in a finite window to the random interlacement observed in the same window."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07910","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":"2026-05-17T23:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kTWdOLKalqWUS/pgVn6kq0QtPl9w2OkUB7fJgRv9hEOzaO2lmH6WrwAKqSQ38Trju9VVJ6LNl+FM84O6/K+HDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:40:22.236786Z"},"content_sha256":"5322d231ada2b4c0ca8c94cfabfb820cb4072b22845ea262de8f40b274402bf0","schema_version":"1.0","event_id":"sha256:5322d231ada2b4c0ca8c94cfabfb820cb4072b22845ea262de8f40b274402bf0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GYMB3PHY4PRY3GC3CJGFW7JS76/bundle.json","state_url":"https://pith.science/pith/GYMB3PHY4PRY3GC3CJGFW7JS76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GYMB3PHY4PRY3GC3CJGFW7JS76/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":"2026-06-03T14:40:22Z","links":{"resolver":"https://pith.science/pith/GYMB3PHY4PRY3GC3CJGFW7JS76","bundle":"https://pith.science/pith/GYMB3PHY4PRY3GC3CJGFW7JS76/bundle.json","state":"https://pith.science/pith/GYMB3PHY4PRY3GC3CJGFW7JS76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GYMB3PHY4PRY3GC3CJGFW7JS76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GYMB3PHY4PRY3GC3CJGFW7JS76","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":"56172a41ba55c8cb971690d442bbfa44859bb9b24fe2988b1829b937e257d748","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-19T10:01:43Z","title_canon_sha256":"b07afbd61b4bf9ceda3bcd39733960ac638ac805b4ba6fa92e72b83b05da2bc6"},"schema_version":"1.0","source":{"id":"1903.07910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07910","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07910v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07910","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"GYMB3PHY4PRY","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GYMB3PHY4PRY3GC3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GYMB3PHY","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:5322d231ada2b4c0ca8c94cfabfb820cb4072b22845ea262de8f40b274402bf0","target":"graph","created_at":"2026-05-17T23:50:53Z","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 introduce random interlacements for transient vertex-reinforced jump processes on a general graph $G$. Using increasing finite subgraphs $G_n$ of $G$ with wired boundary conditions, we show convergence of the vertex-reinforced jump process on $G_n$ observed in a finite window to the random interlacement observed in the same window.","authors_text":"Franz Merkl, Pierre Tarr\\`es, Silke W.W. Rolles","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-19T10:01:43Z","title":"Random interlacements for vertex-reinforced jump processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07910","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":"sha256:6f0c0d9608f810eb333e0d96d4a1b6965ee370796b1ea67e715a8ca16e6431b2","target":"record","created_at":"2026-05-17T23:50:53Z","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":"56172a41ba55c8cb971690d442bbfa44859bb9b24fe2988b1829b937e257d748","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-19T10:01:43Z","title_canon_sha256":"b07afbd61b4bf9ceda3bcd39733960ac638ac805b4ba6fa92e72b83b05da2bc6"},"schema_version":"1.0","source":{"id":"1903.07910","kind":"arxiv","version":1}},"canonical_sha256":"36181dbcf8e3e38d985b124c5b7d32ff83a7f72f8b3363c06c9fca120e6f8fd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36181dbcf8e3e38d985b124c5b7d32ff83a7f72f8b3363c06c9fca120e6f8fd2","first_computed_at":"2026-05-17T23:50:53.498834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:53.498834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bPN4aUqwS3CKxnGCFFuF+bd5WO0hwCYxr1L1wcGQn45x1d54CbsaFkekGnGaIcA4MYUO70lSe1NlLq3TNSlFBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:53.499523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f0c0d9608f810eb333e0d96d4a1b6965ee370796b1ea67e715a8ca16e6431b2","sha256:5322d231ada2b4c0ca8c94cfabfb820cb4072b22845ea262de8f40b274402bf0"],"state_sha256":"0a1ca058d3ed679d20ace425ae7ebb0459fccc603f27993587c20f3708e06af3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K/97fG0l0PEtFOesAChWsUZOmzyx8wU0ntPZWOCWF4m80njj9taCh+1c1d1ODuvodN2r0zmn0wDKiwpB0b9+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:40:22.238786Z","bundle_sha256":"c92a173f65a19abc6239cc0efd11793022652cf9a012e2e95e4c62720c889f35"}}