{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:7PFMWSZDKDSENTFGC3UF2YA2MO","short_pith_number":"pith:7PFMWSZD","schema_version":"1.0","canonical_sha256":"fbcacb4b2350e446cca616e85d601a6381cba816b3fb5c4c26f7267ca72c29f1","source":{"kind":"arxiv","id":"1210.2220","version":2},"attestation_state":"computed","paper":{"title":"Envelopes of positive metrics with prescribed singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Witt Nystrom, Julius Ross","submitted_at":"2012-10-08T10:37:04Z","abstract_excerpt":"We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C^{1,1} regularity of such envelopes, showing their Monge-Ampere measure is supported on a certain \"equilibrium set\" and connecting with the asymptotics of the partial Bergman functions coming from multiplier ideals. We investigate how these envelopes behave on certain products, and how they relate to the Legendre transform of a test curve of singularity types in the context of geodesic rays in the space of K\\\"ahler potentials. Finally we consider the ass"},"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":"1210.2220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-10-08T10:37:04Z","cross_cats_sorted":[],"title_canon_sha256":"078f61a4fd7827f23f1e527ef3dbe8590e7da3bb0aef321fd1c917ad307c07af","abstract_canon_sha256":"b242f0e80cbaf901c4d5d41b3db9878f59798c03719a0f4863447e61b4ebdae5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:03.661413Z","signature_b64":"XSAyL7GjcgkzPn4dFd32hiy+pjRRGEaDD6Vu+JGv2B5NQxmaxMSp0o2bll1AGWr3jEdbs8AdtP0nJJqAkutTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbcacb4b2350e446cca616e85d601a6381cba816b3fb5c4c26f7267ca72c29f1","last_reissued_at":"2026-05-18T01:11:03.660889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:03.660889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Envelopes of positive metrics with prescribed singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Witt Nystrom, Julius Ross","submitted_at":"2012-10-08T10:37:04Z","abstract_excerpt":"We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C^{1,1} regularity of such envelopes, showing their Monge-Ampere measure is supported on a certain \"equilibrium set\" and connecting with the asymptotics of the partial Bergman functions coming from multiplier ideals. We investigate how these envelopes behave on certain products, and how they relate to the Legendre transform of a test curve of singularity types in the context of geodesic rays in the space of K\\\"ahler potentials. Finally we consider the ass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2220","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":"1210.2220","created_at":"2026-05-18T01:11:03.660959+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2220v2","created_at":"2026-05-18T01:11:03.660959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2220","created_at":"2026-05-18T01:11:03.660959+00:00"},{"alias_kind":"pith_short_12","alias_value":"7PFMWSZDKDSE","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"7PFMWSZDKDSENTFG","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"7PFMWSZD","created_at":"2026-05-18T12:26:58.693483+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/7PFMWSZDKDSENTFGC3UF2YA2MO","json":"https://pith.science/pith/7PFMWSZDKDSENTFGC3UF2YA2MO.json","graph_json":"https://pith.science/api/pith-number/7PFMWSZDKDSENTFGC3UF2YA2MO/graph.json","events_json":"https://pith.science/api/pith-number/7PFMWSZDKDSENTFGC3UF2YA2MO/events.json","paper":"https://pith.science/paper/7PFMWSZD"},"agent_actions":{"view_html":"https://pith.science/pith/7PFMWSZDKDSENTFGC3UF2YA2MO","download_json":"https://pith.science/pith/7PFMWSZDKDSENTFGC3UF2YA2MO.json","view_paper":"https://pith.science/paper/7PFMWSZD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2220&json=true","fetch_graph":"https://pith.science/api/pith-number/7PFMWSZDKDSENTFGC3UF2YA2MO/graph.json","fetch_events":"https://pith.science/api/pith-number/7PFMWSZDKDSENTFGC3UF2YA2MO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7PFMWSZDKDSENTFGC3UF2YA2MO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7PFMWSZDKDSENTFGC3UF2YA2MO/action/storage_attestation","attest_author":"https://pith.science/pith/7PFMWSZDKDSENTFGC3UF2YA2MO/action/author_attestation","sign_citation":"https://pith.science/pith/7PFMWSZDKDSENTFGC3UF2YA2MO/action/citation_signature","submit_replication":"https://pith.science/pith/7PFMWSZDKDSENTFGC3UF2YA2MO/action/replication_record"}},"created_at":"2026-05-18T01:11:03.660959+00:00","updated_at":"2026-05-18T01:11:03.660959+00:00"}