{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WV3CZBZTW4QA35EC2LEG7A3IPZ","short_pith_number":"pith:WV3CZBZT","schema_version":"1.0","canonical_sha256":"b5762c8733b7200df482d2c86f83687e40ac54b3827a4fcbe77f90bac3434bd2","source":{"kind":"arxiv","id":"1307.3634","version":2},"attestation_state":"computed","paper":{"title":"Kahler-Einstein metrics, canonical random point processes and birational geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.CV","math.MP"],"primary_cat":"math.DG","authors_text":"Robert J. Berman","submitted_at":"2013-07-13T09:24:30Z","abstract_excerpt":"In the present paper and the companion paper [8] a probabilistic (statistical mechanical) approach to the study of canonical metrics and measures on a complex algebraic variety X is introduced. On any such variety with positive Kodaira dimension a canonical (birationally invariant) random point processes is defined and shown to converge in probability towards a canonical deterministic measure on X, coinciding with the canonical measure of Song-Tian and Tsuji. The proof is based on new large deviation principle for Gibbs measures with singular Hamiltonians which relies on an asymptotic submean "},"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":"1307.3634","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-13T09:24:30Z","cross_cats_sorted":["math-ph","math.AG","math.CV","math.MP"],"title_canon_sha256":"76d8b54673bc329ff1c754f74fc7afc97df67b4d37abcd6dfc16f13635d6cfd5","abstract_canon_sha256":"a02cf1d224cfe1024e96bb2a5d1df944a222d969a3b3bf7991aadb9573364b1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:30.579899Z","signature_b64":"6rcUxfRmYWeUOUX0UcEbwb4PZA9UEPIRqZC/Z5kKmcBW9hO+71+20kIhmFRMh2DZbX3JWztTsccXTMU2DTtIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5762c8733b7200df482d2c86f83687e40ac54b3827a4fcbe77f90bac3434bd2","last_reissued_at":"2026-05-18T01:04:30.579071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:30.579071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kahler-Einstein metrics, canonical random point processes and birational geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.CV","math.MP"],"primary_cat":"math.DG","authors_text":"Robert J. Berman","submitted_at":"2013-07-13T09:24:30Z","abstract_excerpt":"In the present paper and the companion paper [8] a probabilistic (statistical mechanical) approach to the study of canonical metrics and measures on a complex algebraic variety X is introduced. On any such variety with positive Kodaira dimension a canonical (birationally invariant) random point processes is defined and shown to converge in probability towards a canonical deterministic measure on X, coinciding with the canonical measure of Song-Tian and Tsuji. The proof is based on new large deviation principle for Gibbs measures with singular Hamiltonians which relies on an asymptotic submean "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3634","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":"1307.3634","created_at":"2026-05-18T01:04:30.579215+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.3634v2","created_at":"2026-05-18T01:04:30.579215+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3634","created_at":"2026-05-18T01:04:30.579215+00:00"},{"alias_kind":"pith_short_12","alias_value":"WV3CZBZTW4QA","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WV3CZBZTW4QA35EC","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WV3CZBZT","created_at":"2026-05-18T12:28:04.890932+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/WV3CZBZTW4QA35EC2LEG7A3IPZ","json":"https://pith.science/pith/WV3CZBZTW4QA35EC2LEG7A3IPZ.json","graph_json":"https://pith.science/api/pith-number/WV3CZBZTW4QA35EC2LEG7A3IPZ/graph.json","events_json":"https://pith.science/api/pith-number/WV3CZBZTW4QA35EC2LEG7A3IPZ/events.json","paper":"https://pith.science/paper/WV3CZBZT"},"agent_actions":{"view_html":"https://pith.science/pith/WV3CZBZTW4QA35EC2LEG7A3IPZ","download_json":"https://pith.science/pith/WV3CZBZTW4QA35EC2LEG7A3IPZ.json","view_paper":"https://pith.science/paper/WV3CZBZT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.3634&json=true","fetch_graph":"https://pith.science/api/pith-number/WV3CZBZTW4QA35EC2LEG7A3IPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/WV3CZBZTW4QA35EC2LEG7A3IPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WV3CZBZTW4QA35EC2LEG7A3IPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WV3CZBZTW4QA35EC2LEG7A3IPZ/action/storage_attestation","attest_author":"https://pith.science/pith/WV3CZBZTW4QA35EC2LEG7A3IPZ/action/author_attestation","sign_citation":"https://pith.science/pith/WV3CZBZTW4QA35EC2LEG7A3IPZ/action/citation_signature","submit_replication":"https://pith.science/pith/WV3CZBZTW4QA35EC2LEG7A3IPZ/action/replication_record"}},"created_at":"2026-05-18T01:04:30.579215+00:00","updated_at":"2026-05-18T01:04:30.579215+00:00"}