{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SJNXKQAMOBCXVHYG4ANE3MMG2A","short_pith_number":"pith:SJNXKQAM","schema_version":"1.0","canonical_sha256":"925b75400c70457a9f06e01a4db186d02ee711647903d3285bf9be4e80467ffe","source":{"kind":"arxiv","id":"2607.18070","version":1},"attestation_state":"computed","paper":{"title":"The Brownian loop-catcher","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Gefei Cai","submitted_at":"2026-07-20T15:37:43Z","abstract_excerpt":"We introduce a family of random connected closed subsets of planar Brownian motion, called Brownian loop-catchers, which interpolate between the continuum loop-erased random-walk (LERW) and the Brownian trace. This provides the canonical continuation of Brownian loop soup clusters to central charges $-2\\le c<0$. For each such $c$, the corresponding loop-catcher satisfies the following recovery property: adding all loops from an independent Brownian loop soup of intensity $-c/2$ that intersect it recovers the Brownian trace. Furthermore, no such law exists for $c<-2$. We also show that its oute"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.18070","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-20T15:37:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f864d39e44605be4584af36f89378b8e0f9d03935d610361854154c8144b6e53","abstract_canon_sha256":"83808f31984a65400f06836be4c3a2c3807c5cff96e9af164df34adf9fdff221"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T02:22:14.698178Z","signature_b64":"0wyPOVJs6Pl2P8GlJS64a+vpaSBidx4kqz4JKezsCGw/J4PP6shPbzCMq/1Wu+kx8P54p85LAhaFDdgaaroPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"925b75400c70457a9f06e01a4db186d02ee711647903d3285bf9be4e80467ffe","last_reissued_at":"2026-07-21T02:22:14.697351Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T02:22:14.697351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Brownian loop-catcher","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Gefei Cai","submitted_at":"2026-07-20T15:37:43Z","abstract_excerpt":"We introduce a family of random connected closed subsets of planar Brownian motion, called Brownian loop-catchers, which interpolate between the continuum loop-erased random-walk (LERW) and the Brownian trace. This provides the canonical continuation of Brownian loop soup clusters to central charges $-2\\le c<0$. For each such $c$, the corresponding loop-catcher satisfies the following recovery property: adding all loops from an independent Brownian loop soup of intensity $-c/2$ that intersect it recovers the Brownian trace. Furthermore, no such law exists for $c<-2$. We also show that its oute"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18070","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.18070/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.18070","created_at":"2026-07-21T02:22:14.697786+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.18070v1","created_at":"2026-07-21T02:22:14.697786+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18070","created_at":"2026-07-21T02:22:14.697786+00:00"},{"alias_kind":"pith_short_12","alias_value":"SJNXKQAMOBCX","created_at":"2026-07-21T02:22:14.697786+00:00"},{"alias_kind":"pith_short_16","alias_value":"SJNXKQAMOBCXVHYG","created_at":"2026-07-21T02:22:14.697786+00:00"},{"alias_kind":"pith_short_8","alias_value":"SJNXKQAM","created_at":"2026-07-21T02:22:14.697786+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A","json":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A.json","graph_json":"https://pith.science/api/pith-number/SJNXKQAMOBCXVHYG4ANE3MMG2A/graph.json","events_json":"https://pith.science/api/pith-number/SJNXKQAMOBCXVHYG4ANE3MMG2A/events.json","paper":"https://pith.science/paper/SJNXKQAM"},"agent_actions":{"view_html":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A","download_json":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A.json","view_paper":"https://pith.science/paper/SJNXKQAM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.18070&json=true","fetch_graph":"https://pith.science/api/pith-number/SJNXKQAMOBCXVHYG4ANE3MMG2A/graph.json","fetch_events":"https://pith.science/api/pith-number/SJNXKQAMOBCXVHYG4ANE3MMG2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A/action/storage_attestation","attest_author":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A/action/author_attestation","sign_citation":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A/action/citation_signature","submit_replication":"https://pith.science/pith/SJNXKQAMOBCXVHYG4ANE3MMG2A/action/replication_record"}},"created_at":"2026-07-21T02:22:14.697786+00:00","updated_at":"2026-07-21T02:22:14.697786+00:00"}