{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:Y2HXMKWQOSSNYFKSWQRMLPZLU6","short_pith_number":"pith:Y2HXMKWQ","schema_version":"1.0","canonical_sha256":"c68f762ad074a4dc1552b422c5bf2ba7a3ddb98a1d9c396ccc0f5bccacf4a664","source":{"kind":"arxiv","id":"2606.10973","version":1},"attestation_state":"computed","paper":{"title":"Quasisymmetric rigidity of the Brownian sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MG","math.MP"],"primary_cat":"math.PR","authors_text":"Jason Miller, Yi Tian","submitted_at":"2026-06-09T15:13:28Z","abstract_excerpt":"The Brownian sphere, also known as the Brownian map, is a canonical random metric measure space homeomorphic to the two-dimensional sphere $\\mathbf S^2$. It can be interpreted as the uniform measure on surfaces homeomorphic to $\\mathbf S^2$, in the sense that it arises as the scaling limit of many natural models of random planar maps chosen uniformly from a given class. It is also equivalent to the $\\sqrt{8/3}$-Liouville quantum gravity sphere. We prove that the Brownian sphere is quasisymmetrically rigid, meaning that, almost surely, it has no nontrivial quasisymmetric automorphisms. We also "},"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":"2606.10973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-09T15:13:28Z","cross_cats_sorted":["math-ph","math.CV","math.MG","math.MP"],"title_canon_sha256":"4479114cbab2d46266f2bad8bb2ce3e71c2238bdb4e4e9fb1cdd43d3619e9821","abstract_canon_sha256":"1d06960426ea92da8a88a43f45a8437dba6c7b48df3eae98fd49d4caa6ca1db9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:50.765034Z","signature_b64":"zvrU9JYYehbVPTn8wPnV61JCJytuJwN+GFXt7oujObGedzGjFUmhY76LtXaZ69tVEiW8SNb6+BF0f8qbl27uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c68f762ad074a4dc1552b422c5bf2ba7a3ddb98a1d9c396ccc0f5bccacf4a664","last_reissued_at":"2026-06-10T01:10:50.764285Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:50.764285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasisymmetric rigidity of the Brownian sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MG","math.MP"],"primary_cat":"math.PR","authors_text":"Jason Miller, Yi Tian","submitted_at":"2026-06-09T15:13:28Z","abstract_excerpt":"The Brownian sphere, also known as the Brownian map, is a canonical random metric measure space homeomorphic to the two-dimensional sphere $\\mathbf S^2$. It can be interpreted as the uniform measure on surfaces homeomorphic to $\\mathbf S^2$, in the sense that it arises as the scaling limit of many natural models of random planar maps chosen uniformly from a given class. It is also equivalent to the $\\sqrt{8/3}$-Liouville quantum gravity sphere. We prove that the Brownian sphere is quasisymmetrically rigid, meaning that, almost surely, it has no nontrivial quasisymmetric automorphisms. We also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10973","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/2606.10973/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":"2606.10973","created_at":"2026-06-10T01:10:50.764466+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10973v1","created_at":"2026-06-10T01:10:50.764466+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10973","created_at":"2026-06-10T01:10:50.764466+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2HXMKWQOSSN","created_at":"2026-06-10T01:10:50.764466+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2HXMKWQOSSNYFKS","created_at":"2026-06-10T01:10:50.764466+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2HXMKWQ","created_at":"2026-06-10T01:10:50.764466+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/Y2HXMKWQOSSNYFKSWQRMLPZLU6","json":"https://pith.science/pith/Y2HXMKWQOSSNYFKSWQRMLPZLU6.json","graph_json":"https://pith.science/api/pith-number/Y2HXMKWQOSSNYFKSWQRMLPZLU6/graph.json","events_json":"https://pith.science/api/pith-number/Y2HXMKWQOSSNYFKSWQRMLPZLU6/events.json","paper":"https://pith.science/paper/Y2HXMKWQ"},"agent_actions":{"view_html":"https://pith.science/pith/Y2HXMKWQOSSNYFKSWQRMLPZLU6","download_json":"https://pith.science/pith/Y2HXMKWQOSSNYFKSWQRMLPZLU6.json","view_paper":"https://pith.science/paper/Y2HXMKWQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10973&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2HXMKWQOSSNYFKSWQRMLPZLU6/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2HXMKWQOSSNYFKSWQRMLPZLU6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2HXMKWQOSSNYFKSWQRMLPZLU6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2HXMKWQOSSNYFKSWQRMLPZLU6/action/storage_attestation","attest_author":"https://pith.science/pith/Y2HXMKWQOSSNYFKSWQRMLPZLU6/action/author_attestation","sign_citation":"https://pith.science/pith/Y2HXMKWQOSSNYFKSWQRMLPZLU6/action/citation_signature","submit_replication":"https://pith.science/pith/Y2HXMKWQOSSNYFKSWQRMLPZLU6/action/replication_record"}},"created_at":"2026-06-10T01:10:50.764466+00:00","updated_at":"2026-06-10T01:10:50.764466+00:00"}