{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D6XHMBBJE5PLOKLZ5Z5BNOOLTL","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":"80e745638449b9a0d870b32d211139ad005fb9f8a7d3466853d3de2d794e6025","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-21T10:35:24Z","title_canon_sha256":"09c2b7077de46450ece21a29ca33bf8f9d33f2ba041a667c6a55cdc6e2a83f96"},"schema_version":"1.0","source":{"id":"1111.4818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4818","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4818v1","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4818","created_at":"2026-05-18T04:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"D6XHMBBJE5PL","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D6XHMBBJE5PLOKLZ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D6XHMBBJ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:0374313f4c3a260600e51fca77783440458d54a1a4d69917bf083b4c04041183","target":"graph","created_at":"2026-05-18T04:02:13Z","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 consider continuous-time random interlacements on a transient weighted graph. We prove an identity in law relating the field of occupation times of random interlacements at level u to the Gaussian free field on the weighted graph. This identity is closely linked to the generalized second Ray-Knight theorem, and uniquely determines the law of occupation times of random interlacements at level u.","authors_text":"Alain-Sol Sznitman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-21T10:35:24Z","title":"An isomorphism theorem for random interlacements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4818","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":"sha256:68007fb16d2045156d3e31b299a4a5f4c20f8d668195033c0ee3ca1c7a790491","target":"record","created_at":"2026-05-18T04:02:13Z","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":"80e745638449b9a0d870b32d211139ad005fb9f8a7d3466853d3de2d794e6025","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-21T10:35:24Z","title_canon_sha256":"09c2b7077de46450ece21a29ca33bf8f9d33f2ba041a667c6a55cdc6e2a83f96"},"schema_version":"1.0","source":{"id":"1111.4818","kind":"arxiv","version":1}},"canonical_sha256":"1fae760429275eb72979ee7a16b9cb9af50a2730155de119d7261227b27457aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fae760429275eb72979ee7a16b9cb9af50a2730155de119d7261227b27457aa","first_computed_at":"2026-05-18T04:02:13.352176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:13.352176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H7I4ZnbTVEypWWHA3NIZNIiviX1bi+8BS4C5RVcoG/3Eq0b5tPhoNisGvvwhr8dzEa2gkEc4BvA9A5IWS/PsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:13.353056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68007fb16d2045156d3e31b299a4a5f4c20f8d668195033c0ee3ca1c7a790491","sha256:0374313f4c3a260600e51fca77783440458d54a1a4d69917bf083b4c04041183"],"state_sha256":"e78a62327f841341da574e9438095ea251a555838e341c278eee8ee833f281ab"}