{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3UHBTN3TFWIUHJMRO3WZ6O43DV","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":"21c72b3f0cf18d7bb2f4fb3287ef903bda66964fb4b5a3172cacc64f4ac55eb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-07T17:57:27Z","title_canon_sha256":"99ce9e2a1296d1bb2d4fefba848eb411edfc6d58c9c2ea86625459a281ae0548"},"schema_version":"1.0","source":{"id":"1902.05121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05121","created_at":"2026-05-17T23:54:01Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05121v1","created_at":"2026-05-17T23:54:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05121","created_at":"2026-05-17T23:54:01Z"},{"alias_kind":"pith_short_12","alias_value":"3UHBTN3TFWIU","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"3UHBTN3TFWIUHJMR","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"3UHBTN3T","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:586745c25ba67e987e604ab1410936f3d55bf0fb1b560db2b6f3c95d25ffe66a","target":"graph","created_at":"2026-05-17T23:54:01Z","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":"Given a weighted graph, we show how to define two types of natural interactions which correspond to local interactions between two Fock spaces. The first type of interaction involves loop ensembles and spanning trees. The second type of interaction involves loop holonomies and random connections.","authors_text":"Yves Le Jan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-07T17:57:27Z","title":"Loop interactions and their representations in Fock space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05121","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":"sha256:27785fed9f0d1d6a85691961369bfb63960eb947be64a8e0e8cc6b3572f64bc8","target":"record","created_at":"2026-05-17T23:54:01Z","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":"21c72b3f0cf18d7bb2f4fb3287ef903bda66964fb4b5a3172cacc64f4ac55eb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-07T17:57:27Z","title_canon_sha256":"99ce9e2a1296d1bb2d4fefba848eb411edfc6d58c9c2ea86625459a281ae0548"},"schema_version":"1.0","source":{"id":"1902.05121","kind":"arxiv","version":1}},"canonical_sha256":"dd0e19b7732d9143a59176ed9f3b9b1d602c3ef96443dcda651a0a988ca62f7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd0e19b7732d9143a59176ed9f3b9b1d602c3ef96443dcda651a0a988ca62f7b","first_computed_at":"2026-05-17T23:54:01.877858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:01.877858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8PCj6KGoFzW+prNFnm3RgbRDhKEn3Dtwmgn9avBz+qlsd+NNReLR7nbkTqtw+5UmCvfu4mwSxqCaLZXJnioCAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:01.878475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27785fed9f0d1d6a85691961369bfb63960eb947be64a8e0e8cc6b3572f64bc8","sha256:586745c25ba67e987e604ab1410936f3d55bf0fb1b560db2b6f3c95d25ffe66a"],"state_sha256":"4da1c7e72d08f4f90e32633086a872296d36d0b1c7c7cc849dfaf1370da58095"}