{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7VISEYKN54HYCBVNEOR57VRYGT","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":"9ae38f1f86071ef0cd2f2be276c8c357cc8b5d147f124f5f0f597bb462dc7e0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-12T21:17:37Z","title_canon_sha256":"8959e9d842d9273762e83879de4538575e779c39ba68819bcdb5e49ef55082aa"},"schema_version":"1.0","source":{"id":"1308.2701","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2701","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2701v2","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2701","created_at":"2026-05-18T03:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"7VISEYKN54HY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7VISEYKN54HYCBVN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7VISEYKN","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:5aaf4bdab849b1f15d60963c4a89c1d30b66efd8ac7462e715c5e71eb203e6cd","target":"graph","created_at":"2026-05-18T03:07:43Z","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":"Several stochastic processes related to transient L\\'evy processes with potential densities $u(x,y)=u(y-x)$, that need not be symmetric nor bounded on the diagonal, are defined and studied.\n  They are real valued processes on a space of measures $V$ endowed with a metric $d$. Sufficient conditions are obtained for the continuity of these processes on $(V,d)$. The processes include $n$-fold self-intersection local times of transient L\\'evy processes and permanental chaoses, which are `loop soup $n$-fold self-intersection local times' constructed from the loop soup of the L\\'evy process. Loop so","authors_text":"Jay Rosen, Michael B. Marcus, Yves Le Jan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-12T21:17:37Z","title":"Intersection local times, loop soups and permanental Wick powers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2701","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":"sha256:86015c75d9e0b1f7a574bb2f9d9b3965f7fbfb6e6b2c4af6c5784c23dbfd4e23","target":"record","created_at":"2026-05-18T03:07:43Z","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":"9ae38f1f86071ef0cd2f2be276c8c357cc8b5d147f124f5f0f597bb462dc7e0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-12T21:17:37Z","title_canon_sha256":"8959e9d842d9273762e83879de4538575e779c39ba68819bcdb5e49ef55082aa"},"schema_version":"1.0","source":{"id":"1308.2701","kind":"arxiv","version":2}},"canonical_sha256":"fd5122614def0f8106ad23a3dfd63834e08d6366aa8b7062e67e29ab003a754e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd5122614def0f8106ad23a3dfd63834e08d6366aa8b7062e67e29ab003a754e","first_computed_at":"2026-05-18T03:07:43.067957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:43.067957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QdUMnrz7n+lresdMRozY1hQ9RD4P9Hcbo1aaTXa+guiepWAjsF+/mmw5CKK0XJsZsQp58WvZidPh9GewQiMjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:43.068547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2701","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86015c75d9e0b1f7a574bb2f9d9b3965f7fbfb6e6b2c4af6c5784c23dbfd4e23","sha256:5aaf4bdab849b1f15d60963c4a89c1d30b66efd8ac7462e715c5e71eb203e6cd"],"state_sha256":"31f4f18d5216713e795b17d3319299b7a7802ba9be2202900ce39b60cf4a95d7"}