{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TJIRXRLKVBIYN3FCGRFZMB7IYD","short_pith_number":"pith:TJIRXRLK","schema_version":"1.0","canonical_sha256":"9a511bc56aa85186eca2344b9607e8c0d866ae2826a45d863f57bec7114b6a74","source":{"kind":"arxiv","id":"2607.22387","version":1},"attestation_state":"computed","paper":{"title":"Super-Brownian limits and the $k$-point function for high-dimensional percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Arthur Blanc-Renaudie, Tom Hutchcroft","submitted_at":"2026-07-24T15:12:59Z","abstract_excerpt":"We prove that there exist positive constants $A$ and $V$ such that the high-dimensional critical percolation $k$-point function is given by \\[ T_{p_c}(x_1,x_2,\\ldots,x_{k}) \\sim V^{k-2} A^{2k-3} \\sum_{T\\in \\mathsf{Tr}(k)} \\sum_{\\substack{\\Phi:V(T)\\to \\mathbb{Z}^d \\\\ \\Phi(i)=x_i \\forall 1\\leq i \\leq k}} \\prod_{\\substack{u,v\\in V(T)\\\\u\\sim v}}G(\\Phi(u),\\Phi(v)) \\] as $\\min_{i\\neq j}\\|x_i-x_j\\|\\to \\infty$, where $\\mathsf{Tr}(k)$ is a set of isomorphism class representatives of trees with $k$ labelled leaves $\\{1,\\ldots,k\\}$ and unlabelled internal vertices all of which have degree $3$ and $G$ is "},"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":"2607.22387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-24T15:12:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"527e5c74f191909df19305f551a11d819dc44429512f559611abc20885793645","abstract_canon_sha256":"581d9542514df62b4c72dc8ea8bbb3066b6999d9293aab58bedb1799c5509f09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-27T01:21:17.823529Z","signature_b64":"UBZ/dJos96Pl/4/kSxOlnZvBgFJaTCZXzs6DAuybUGGDOXhNIP1mVNKGk/+sEzUWJ5Otykqxo4RObberXxNaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a511bc56aa85186eca2344b9607e8c0d866ae2826a45d863f57bec7114b6a74","last_reissued_at":"2026-07-27T01:21:17.822669Z","signature_status":"signed_v1","first_computed_at":"2026-07-27T01:21:17.822669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Super-Brownian limits and the $k$-point function for high-dimensional percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Arthur Blanc-Renaudie, Tom Hutchcroft","submitted_at":"2026-07-24T15:12:59Z","abstract_excerpt":"We prove that there exist positive constants $A$ and $V$ such that the high-dimensional critical percolation $k$-point function is given by \\[ T_{p_c}(x_1,x_2,\\ldots,x_{k}) \\sim V^{k-2} A^{2k-3} \\sum_{T\\in \\mathsf{Tr}(k)} \\sum_{\\substack{\\Phi:V(T)\\to \\mathbb{Z}^d \\\\ \\Phi(i)=x_i \\forall 1\\leq i \\leq k}} \\prod_{\\substack{u,v\\in V(T)\\\\u\\sim v}}G(\\Phi(u),\\Phi(v)) \\] as $\\min_{i\\neq j}\\|x_i-x_j\\|\\to \\infty$, where $\\mathsf{Tr}(k)$ is a set of isomorphism class representatives of trees with $k$ labelled leaves $\\{1,\\ldots,k\\}$ and unlabelled internal vertices all of which have degree $3$ and $G$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22387","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/2607.22387/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":"2607.22387","created_at":"2026-07-27T01:21:17.823109+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.22387v1","created_at":"2026-07-27T01:21:17.823109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22387","created_at":"2026-07-27T01:21:17.823109+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJIRXRLKVBIY","created_at":"2026-07-27T01:21:17.823109+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJIRXRLKVBIYN3FC","created_at":"2026-07-27T01:21:17.823109+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJIRXRLK","created_at":"2026-07-27T01:21:17.823109+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/TJIRXRLKVBIYN3FCGRFZMB7IYD","json":"https://pith.science/pith/TJIRXRLKVBIYN3FCGRFZMB7IYD.json","graph_json":"https://pith.science/api/pith-number/TJIRXRLKVBIYN3FCGRFZMB7IYD/graph.json","events_json":"https://pith.science/api/pith-number/TJIRXRLKVBIYN3FCGRFZMB7IYD/events.json","paper":"https://pith.science/paper/TJIRXRLK"},"agent_actions":{"view_html":"https://pith.science/pith/TJIRXRLKVBIYN3FCGRFZMB7IYD","download_json":"https://pith.science/pith/TJIRXRLKVBIYN3FCGRFZMB7IYD.json","view_paper":"https://pith.science/paper/TJIRXRLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.22387&json=true","fetch_graph":"https://pith.science/api/pith-number/TJIRXRLKVBIYN3FCGRFZMB7IYD/graph.json","fetch_events":"https://pith.science/api/pith-number/TJIRXRLKVBIYN3FCGRFZMB7IYD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJIRXRLKVBIYN3FCGRFZMB7IYD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJIRXRLKVBIYN3FCGRFZMB7IYD/action/storage_attestation","attest_author":"https://pith.science/pith/TJIRXRLKVBIYN3FCGRFZMB7IYD/action/author_attestation","sign_citation":"https://pith.science/pith/TJIRXRLKVBIYN3FCGRFZMB7IYD/action/citation_signature","submit_replication":"https://pith.science/pith/TJIRXRLKVBIYN3FCGRFZMB7IYD/action/replication_record"}},"created_at":"2026-07-27T01:21:17.823109+00:00","updated_at":"2026-07-27T01:21:17.823109+00:00"}