{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NKB4PQIRSNB5TUPASXX4RW5IX6","short_pith_number":"pith:NKB4PQIR","schema_version":"1.0","canonical_sha256":"6a83c7c1119343d9d1e095efc8dba8bf95f8dad462ae96af4c583732d0016047","source":{"kind":"arxiv","id":"1111.5259","version":3},"attestation_state":"computed","paper":{"title":"Toric partial density functions and stability of toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV","math.SG"],"primary_cat":"math.DG","authors_text":"Florian T. Pokorny, Michael Singer","submitted_at":"2011-11-22T17:32:19Z","abstract_excerpt":"Let $(L, h)\\to (X, \\omega)$ denote a polarized toric K\\\"ahler manifold. Fix a toric submanifold $Y$ and denote by $\\hat{\\rho}_{tk}:X\\to \\mathbb{R}$ the partial density function corresponding to the partial Bergman kernel projecting smooth sections of $L^k$ onto holomorphic sections of $L^k$ that vanish to order at least $tk$ along $Y$, for fixed $t>0$ such that $tk\\in \\mathbb{N}$. We prove the existence of a distributional expansion of $\\hat{\\rho}_{tk}$ as $k\\to \\infty$, including the identification of the coefficient of $k^{n-1}$ as a distribution on $X$. This expansion is used to give a dire"},"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":"1111.5259","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-22T17:32:19Z","cross_cats_sorted":["math.AG","math.CV","math.SG"],"title_canon_sha256":"f70b3f179951245b49d41cec7a93a2dbf602110eafff20c07815c897ffc021aa","abstract_canon_sha256":"f9cdbb359aeda2166989c45d0009a2532fd02af1e5157149bbcf974026d50700"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.094065Z","signature_b64":"OO58VdsBG15gmeoSe/soI2krxx3CTFisdkmAAXNae5ZOenttS3kjDqPYoSjeCjhsv/cFiapgEZ4iveTOy2ZYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a83c7c1119343d9d1e095efc8dba8bf95f8dad462ae96af4c583732d0016047","last_reissued_at":"2026-05-18T03:12:58.093485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.093485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toric partial density functions and stability of toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV","math.SG"],"primary_cat":"math.DG","authors_text":"Florian T. Pokorny, Michael Singer","submitted_at":"2011-11-22T17:32:19Z","abstract_excerpt":"Let $(L, h)\\to (X, \\omega)$ denote a polarized toric K\\\"ahler manifold. Fix a toric submanifold $Y$ and denote by $\\hat{\\rho}_{tk}:X\\to \\mathbb{R}$ the partial density function corresponding to the partial Bergman kernel projecting smooth sections of $L^k$ onto holomorphic sections of $L^k$ that vanish to order at least $tk$ along $Y$, for fixed $t>0$ such that $tk\\in \\mathbb{N}$. We prove the existence of a distributional expansion of $\\hat{\\rho}_{tk}$ as $k\\to \\infty$, including the identification of the coefficient of $k^{n-1}$ as a distribution on $X$. This expansion is used to give a dire"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5259","kind":"arxiv","version":3},"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":"1111.5259","created_at":"2026-05-18T03:12:58.093581+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.5259v3","created_at":"2026-05-18T03:12:58.093581+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5259","created_at":"2026-05-18T03:12:58.093581+00:00"},{"alias_kind":"pith_short_12","alias_value":"NKB4PQIRSNB5","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NKB4PQIRSNB5TUPA","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NKB4PQIR","created_at":"2026-05-18T12:26:37.096874+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/NKB4PQIRSNB5TUPASXX4RW5IX6","json":"https://pith.science/pith/NKB4PQIRSNB5TUPASXX4RW5IX6.json","graph_json":"https://pith.science/api/pith-number/NKB4PQIRSNB5TUPASXX4RW5IX6/graph.json","events_json":"https://pith.science/api/pith-number/NKB4PQIRSNB5TUPASXX4RW5IX6/events.json","paper":"https://pith.science/paper/NKB4PQIR"},"agent_actions":{"view_html":"https://pith.science/pith/NKB4PQIRSNB5TUPASXX4RW5IX6","download_json":"https://pith.science/pith/NKB4PQIRSNB5TUPASXX4RW5IX6.json","view_paper":"https://pith.science/paper/NKB4PQIR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.5259&json=true","fetch_graph":"https://pith.science/api/pith-number/NKB4PQIRSNB5TUPASXX4RW5IX6/graph.json","fetch_events":"https://pith.science/api/pith-number/NKB4PQIRSNB5TUPASXX4RW5IX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NKB4PQIRSNB5TUPASXX4RW5IX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NKB4PQIRSNB5TUPASXX4RW5IX6/action/storage_attestation","attest_author":"https://pith.science/pith/NKB4PQIRSNB5TUPASXX4RW5IX6/action/author_attestation","sign_citation":"https://pith.science/pith/NKB4PQIRSNB5TUPASXX4RW5IX6/action/citation_signature","submit_replication":"https://pith.science/pith/NKB4PQIRSNB5TUPASXX4RW5IX6/action/replication_record"}},"created_at":"2026-05-18T03:12:58.093581+00:00","updated_at":"2026-05-18T03:12:58.093581+00:00"}