{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:JMAOOGTX2TGKVCYBDSBZ42J3ZG","short_pith_number":"pith:JMAOOGTX","schema_version":"1.0","canonical_sha256":"4b00e71a77d4ccaa8b011c839e693bc98f82b5e438dd87f2bcf2c869931a5441","source":{"kind":"arxiv","id":"2502.06754","version":4},"attestation_state":"computed","paper":{"title":"A switching identity for cable-graph loop soups and Gaussian free fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Wendelin Werner","submitted_at":"2025-02-10T18:32:10Z","abstract_excerpt":"We derive a \"switching identity\" that can be stated for critical Brownian loop-soups or for the Gaussian free field on a cable graph: It basically says that at the level of cluster configurations and at the more general level of the occupation time fields, conditioning two points on the cable-graph to belong to the same cluster of Brownian loops (or equivalently to the same sign-cluster of the GFF) amounts to adding a random odd number of independent Brownian excursions between these points to an otherwise unconditioned configuration. This explicit simple description of the conditional law of "},"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":"2502.06754","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-02-10T18:32:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fcebb93902db9ac8e36546b397907085794cd4636a4196b7d0147e9705472446","abstract_canon_sha256":"b37fdc3f8c4012c8604a48c6a81f13264048d78032a41cf4cb5d9196fecd1046"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:26.569526Z","signature_b64":"exx15MJsSs11EY0mFcfxhdtamsryBiFaKUSpPcfY8SQzplJPvdTQNhQsfXGSS4Xad07msiwdjC4KYwNNSumcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b00e71a77d4ccaa8b011c839e693bc98f82b5e438dd87f2bcf2c869931a5441","last_reissued_at":"2026-07-05T11:31:26.569067Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:26.569067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A switching identity for cable-graph loop soups and Gaussian free fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Wendelin Werner","submitted_at":"2025-02-10T18:32:10Z","abstract_excerpt":"We derive a \"switching identity\" that can be stated for critical Brownian loop-soups or for the Gaussian free field on a cable graph: It basically says that at the level of cluster configurations and at the more general level of the occupation time fields, conditioning two points on the cable-graph to belong to the same cluster of Brownian loops (or equivalently to the same sign-cluster of the GFF) amounts to adding a random odd number of independent Brownian excursions between these points to an otherwise unconditioned configuration. This explicit simple description of the conditional law of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06754","kind":"arxiv","version":4},"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/2502.06754/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":"2502.06754","created_at":"2026-07-05T11:31:26.569122+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.06754v4","created_at":"2026-07-05T11:31:26.569122+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06754","created_at":"2026-07-05T11:31:26.569122+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMAOOGTX2TGK","created_at":"2026-07-05T11:31:26.569122+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMAOOGTX2TGKVCYB","created_at":"2026-07-05T11:31:26.569122+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMAOOGTX","created_at":"2026-07-05T11:31:26.569122+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.17494","citing_title":"Generalized intersection exponents and local cut points for three-dimensional Brownian loop soup","ref_index":31,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG","json":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG.json","graph_json":"https://pith.science/api/pith-number/JMAOOGTX2TGKVCYBDSBZ42J3ZG/graph.json","events_json":"https://pith.science/api/pith-number/JMAOOGTX2TGKVCYBDSBZ42J3ZG/events.json","paper":"https://pith.science/paper/JMAOOGTX"},"agent_actions":{"view_html":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG","download_json":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG.json","view_paper":"https://pith.science/paper/JMAOOGTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.06754&json=true","fetch_graph":"https://pith.science/api/pith-number/JMAOOGTX2TGKVCYBDSBZ42J3ZG/graph.json","fetch_events":"https://pith.science/api/pith-number/JMAOOGTX2TGKVCYBDSBZ42J3ZG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG/action/storage_attestation","attest_author":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG/action/author_attestation","sign_citation":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG/action/citation_signature","submit_replication":"https://pith.science/pith/JMAOOGTX2TGKVCYBDSBZ42J3ZG/action/replication_record"}},"created_at":"2026-07-05T11:31:26.569122+00:00","updated_at":"2026-07-05T11:31:26.569122+00:00"}