{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:V4TJFLCHIXFSXVVZCHR3FVYHUZ","short_pith_number":"pith:V4TJFLCH","schema_version":"1.0","canonical_sha256":"af2692ac4745cb2bd6b911e3b2d707a66328a7de73d3e0383a817c3408c11b71","source":{"kind":"arxiv","id":"1202.4267","version":2},"attestation_state":"computed","paper":{"title":"Sticky central limit theorems on open books","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Ezra Miller, Huiling Le, James Nolen, Jonathan C. Mattingly, J. S. Marron, Megan Owen, Sean Skwerer, Stephan Huckemann, Thomas Hotz, Vic Patrangenaru","submitted_at":"2012-02-20T09:37:54Z","abstract_excerpt":"Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fr\\'{e}chet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension $1$ and hence measure $0$) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine. We also state versions o"},"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":"1202.4267","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-20T09:37:54Z","cross_cats_sorted":["math.MG","math.ST","stat.TH"],"title_canon_sha256":"b0cb1e432a046185ed4fbf36cfb1d15380cd0cbd7c8df251520e02a772c949fa","abstract_canon_sha256":"4c6f88a5a22570465f37c36d42833612a288e68d4c6ffc716eb0d94f71ceb73e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:44.853909Z","signature_b64":"scP4Y+N/E0clOWqiIwx4DtFJSlp93vWV066aTv3hEGmvPar/Tw4OAndr97tU6ki++7vbS8Z1ccpZYZmT9ntJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af2692ac4745cb2bd6b911e3b2d707a66328a7de73d3e0383a817c3408c11b71","last_reissued_at":"2026-05-18T03:05:44.853189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:44.853189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sticky central limit theorems on open books","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Ezra Miller, Huiling Le, James Nolen, Jonathan C. Mattingly, J. S. Marron, Megan Owen, Sean Skwerer, Stephan Huckemann, Thomas Hotz, Vic Patrangenaru","submitted_at":"2012-02-20T09:37:54Z","abstract_excerpt":"Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fr\\'{e}chet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension $1$ and hence measure $0$) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine. We also state versions o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4267","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":""},"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":"1202.4267","created_at":"2026-05-18T03:05:44.853309+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4267v2","created_at":"2026-05-18T03:05:44.853309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4267","created_at":"2026-05-18T03:05:44.853309+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4TJFLCHIXFS","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4TJFLCHIXFSXVVZ","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4TJFLCH","created_at":"2026-05-18T12:27:25.539911+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/V4TJFLCHIXFSXVVZCHR3FVYHUZ","json":"https://pith.science/pith/V4TJFLCHIXFSXVVZCHR3FVYHUZ.json","graph_json":"https://pith.science/api/pith-number/V4TJFLCHIXFSXVVZCHR3FVYHUZ/graph.json","events_json":"https://pith.science/api/pith-number/V4TJFLCHIXFSXVVZCHR3FVYHUZ/events.json","paper":"https://pith.science/paper/V4TJFLCH"},"agent_actions":{"view_html":"https://pith.science/pith/V4TJFLCHIXFSXVVZCHR3FVYHUZ","download_json":"https://pith.science/pith/V4TJFLCHIXFSXVVZCHR3FVYHUZ.json","view_paper":"https://pith.science/paper/V4TJFLCH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4267&json=true","fetch_graph":"https://pith.science/api/pith-number/V4TJFLCHIXFSXVVZCHR3FVYHUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/V4TJFLCHIXFSXVVZCHR3FVYHUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4TJFLCHIXFSXVVZCHR3FVYHUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4TJFLCHIXFSXVVZCHR3FVYHUZ/action/storage_attestation","attest_author":"https://pith.science/pith/V4TJFLCHIXFSXVVZCHR3FVYHUZ/action/author_attestation","sign_citation":"https://pith.science/pith/V4TJFLCHIXFSXVVZCHR3FVYHUZ/action/citation_signature","submit_replication":"https://pith.science/pith/V4TJFLCHIXFSXVVZCHR3FVYHUZ/action/replication_record"}},"created_at":"2026-05-18T03:05:44.853309+00:00","updated_at":"2026-05-18T03:05:44.853309+00:00"}