{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:64RP2WJZJW7UGHO2FQZW35MZOC","short_pith_number":"pith:64RP2WJZ","schema_version":"1.0","canonical_sha256":"f722fd59394dbf431dda2c336df59970b0b02461b78b56c61445ad072aab2663","source":{"kind":"arxiv","id":"math/0603431","version":2},"attestation_state":"computed","paper":{"title":"Singular Kahler-Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Ahmed Zeriahi (IMT), Philippe Eyssidieux (IF), Vincent Guedj (LATP)","submitted_at":"2006-03-17T15:20:53Z","abstract_excerpt":"We study degenerate complex Monge-Amp\\`ere equations of the form $(\\omega+dd^c \\varphi)^n = e^{t \\varphi} \\mu$ where $\\omega$ is a big semi-positive form on a compact K\\\"ahler manifold $X$ of dimension $n$, $t \\in \\R^+$, and $\\mu=f\\omega^n$ is a positive measure with density $f\\in L^p(X,\\omega^n)$, $p>1$. We prove the existence and unicity of bounded $\\omega$-plurisubharmonic solutions. We also prove that the solution is continuous under a further technical condition.\n  In case $X$ is projective and $\\omega=\\psi^*\\omega'$, where $\\psi:X\\to V$ is a proper birational morphism to a normal project"},"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":"math/0603431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2006-03-17T15:20:53Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"7f21b826c9b1b0511d0feb421ff0619e98e435846d9d083f1bdd56705364c171","abstract_canon_sha256":"e87f9ebe6b940563198d4822f3331d377c532ea5fef630ef64ea3d310f250450"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:14:33.245591Z","signature_b64":"uCfXPlzl9STi8paJ3Xlm7IitBz3aa4WrhxGuDL1UXsvecPqxc+XMD4uuqvsgPJqqSXLGYhw5i/DWlvMvjlQJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f722fd59394dbf431dda2c336df59970b0b02461b78b56c61445ad072aab2663","last_reissued_at":"2026-07-04T15:14:33.245218Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:14:33.245218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular Kahler-Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Ahmed Zeriahi (IMT), Philippe Eyssidieux (IF), Vincent Guedj (LATP)","submitted_at":"2006-03-17T15:20:53Z","abstract_excerpt":"We study degenerate complex Monge-Amp\\`ere equations of the form $(\\omega+dd^c \\varphi)^n = e^{t \\varphi} \\mu$ where $\\omega$ is a big semi-positive form on a compact K\\\"ahler manifold $X$ of dimension $n$, $t \\in \\R^+$, and $\\mu=f\\omega^n$ is a positive measure with density $f\\in L^p(X,\\omega^n)$, $p>1$. We prove the existence and unicity of bounded $\\omega$-plurisubharmonic solutions. We also prove that the solution is continuous under a further technical condition.\n  In case $X$ is projective and $\\omega=\\psi^*\\omega'$, where $\\psi:X\\to V$ is a proper birational morphism to a normal project"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603431","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0603431/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":"math/0603431","created_at":"2026-07-04T15:14:33.245277+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0603431v2","created_at":"2026-07-04T15:14:33.245277+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603431","created_at":"2026-07-04T15:14:33.245277+00:00"},{"alias_kind":"pith_short_12","alias_value":"64RP2WJZJW7U","created_at":"2026-07-04T15:14:33.245277+00:00"},{"alias_kind":"pith_short_16","alias_value":"64RP2WJZJW7UGHO2","created_at":"2026-07-04T15:14:33.245277+00:00"},{"alias_kind":"pith_short_8","alias_value":"64RP2WJZ","created_at":"2026-07-04T15:14:33.245277+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.19313","citing_title":"Calabi-Yau threefolds across quadratic singularities","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC","json":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC.json","graph_json":"https://pith.science/api/pith-number/64RP2WJZJW7UGHO2FQZW35MZOC/graph.json","events_json":"https://pith.science/api/pith-number/64RP2WJZJW7UGHO2FQZW35MZOC/events.json","paper":"https://pith.science/paper/64RP2WJZ"},"agent_actions":{"view_html":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC","download_json":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC.json","view_paper":"https://pith.science/paper/64RP2WJZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0603431&json=true","fetch_graph":"https://pith.science/api/pith-number/64RP2WJZJW7UGHO2FQZW35MZOC/graph.json","fetch_events":"https://pith.science/api/pith-number/64RP2WJZJW7UGHO2FQZW35MZOC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC/action/storage_attestation","attest_author":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC/action/author_attestation","sign_citation":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC/action/citation_signature","submit_replication":"https://pith.science/pith/64RP2WJZJW7UGHO2FQZW35MZOC/action/replication_record"}},"created_at":"2026-07-04T15:14:33.245277+00:00","updated_at":"2026-07-04T15:14:33.245277+00:00"}