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Conditional on the event that both branches from $x_1^{\\delta}$ and $x_2^{\\delta}$ hit the boundary through $x_3^{\\delta}$, the two branches meet at a point $\\trifurcation^{\\delta}$ which we call trifurcation, and the union 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":"2511.11151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-11-14T10:29:47Z","cross_cats_sorted":[],"title_canon_sha256":"b623328d172953c578e04e6bc847d60d1a31f4097ac02bd526a0a48911e3eccc","abstract_canon_sha256":"4fe4b5d6bf430f3ff56a3a494f7e7d93f6516d184f1afa74080f641146e4ff16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:38.458532Z","signature_b64":"fI2X/JbWPe+ZOqLw0vLxBQaBCL4MfRoWhdQmZ7FART57ZC2pz/f9p2OLw03iBwah2mwD9V0ZathLX/HXD8NPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e85bf64db7718f6c34b8f210a82aab19764b22a08445340f552226e9b7e39d7e","last_reissued_at":"2026-06-02T01:03:38.458035Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:38.458035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tripod in uniform spanning tree and three-sided radial SLE$_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hao Wu, Jiacheng Ding, Mingchang Liu","submitted_at":"2025-11-14T10:29:47Z","abstract_excerpt":"Fix a bounded $3$-polygon $(\\Omega; x_1, x_2, x_3)$ with three marked boundary points $x_1, x_2, x_3\\in\\partial\\Omega$ and suppose $(\\Omega^{\\delta}; x_1^{\\delta}, x_2^{\\delta}, x_3^{\\delta})$ is an approximation of $(\\Omega; x_1, x_2, x_3)$ on $\\delta$-scaled hexagonal lattice. We consider uniform spanning tree (UST) in $\\Omega^{\\delta}$ with wired boundary conditions. Conditional on the event that both branches from $x_1^{\\delta}$ and $x_2^{\\delta}$ hit the boundary through $x_3^{\\delta}$, the two branches meet at a point $\\trifurcation^{\\delta}$ which we call trifurcation, and the union of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.11151","kind":"arxiv","version":2},"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/2511.11151/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":"2511.11151","created_at":"2026-06-02T01:03:38.458098+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.11151v2","created_at":"2026-06-02T01:03:38.458098+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.11151","created_at":"2026-06-02T01:03:38.458098+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BN7MTNXOGHW","created_at":"2026-06-02T01:03:38.458098+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BN7MTNXOGHWYNFY","created_at":"2026-06-02T01:03:38.458098+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BN7MTNX","created_at":"2026-06-02T01:03:38.458098+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/5BN7MTNXOGHWYNFY6IIKQKVLDF","json":"https://pith.science/pith/5BN7MTNXOGHWYNFY6IIKQKVLDF.json","graph_json":"https://pith.science/api/pith-number/5BN7MTNXOGHWYNFY6IIKQKVLDF/graph.json","events_json":"https://pith.science/api/pith-number/5BN7MTNXOGHWYNFY6IIKQKVLDF/events.json","paper":"https://pith.science/paper/5BN7MTNX"},"agent_actions":{"view_html":"https://pith.science/pith/5BN7MTNXOGHWYNFY6IIKQKVLDF","download_json":"https://pith.science/pith/5BN7MTNXOGHWYNFY6IIKQKVLDF.json","view_paper":"https://pith.science/paper/5BN7MTNX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.11151&json=true","fetch_graph":"https://pith.science/api/pith-number/5BN7MTNXOGHWYNFY6IIKQKVLDF/graph.json","fetch_events":"https://pith.science/api/pith-number/5BN7MTNXOGHWYNFY6IIKQKVLDF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BN7MTNXOGHWYNFY6IIKQKVLDF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BN7MTNXOGHWYNFY6IIKQKVLDF/action/storage_attestation","attest_author":"https://pith.science/pith/5BN7MTNXOGHWYNFY6IIKQKVLDF/action/author_attestation","sign_citation":"https://pith.science/pith/5BN7MTNXOGHWYNFY6IIKQKVLDF/action/citation_signature","submit_replication":"https://pith.science/pith/5BN7MTNXOGHWYNFY6IIKQKVLDF/action/replication_record"}},"created_at":"2026-06-02T01:03:38.458098+00:00","updated_at":"2026-06-02T01:03:38.458098+00:00"}