{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WIVY5H4GW3TRN6AG7WKW2CICEI","short_pith_number":"pith:WIVY5H4G","schema_version":"1.0","canonical_sha256":"b22b8e9f86b6e716f806fd956d0902223d2d9bd6090bc605ae038100cf26ef4f","source":{"kind":"arxiv","id":"1011.3363","version":2},"attestation_state":"computed","paper":{"title":"Degeneration of Kaehler structures and half-form quantization of toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jo\\~ao P. Nunes, Jos\\'e M. Mour\\~ao, William D. Kirwin","submitted_at":"2010-11-15T12:42:32Z","abstract_excerpt":"We study the half-form Kaehler quantization of a smooth symplectic toric manifold $(X,\\omega)$, such that $[\\omega/2\\pi]-c_{1}(X)/2 \\in H^{2}(X,{\\mathbb{Z}})$ and is nonnegative. We define the half-form corrected quantization of $(X,\\omega)$ to be given by holomorphic sections of a certain hermitian line bundle $L\\rightarrow X$ with Chern class $[\\omega/ 2\\pi]-c_{1}(X)/2$. These sections then correspond to integral points of a \"corrected\" polytope $P_{L}$ with integral vertices. For a suitably translated moment polytope $P_{X}$ for $(X,\\omega)$, we have that $P_{L}\\subset P_{X}$ is obtained fr"},"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":"1011.3363","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-15T12:42:32Z","cross_cats_sorted":[],"title_canon_sha256":"dbcc8ba573a299fbe25d0338669fb80abd83d82929d096675da86a9b506d3de3","abstract_canon_sha256":"cc7563740f56f747fb6ea5eb81c4b36e3b66b9ee55265a7840ebf778ff7dff66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:56.431104Z","signature_b64":"kKf9ztC8KRCDrDoeleBD705Oxi3sybq0RWO1p8OS2/aFCIR5yOVN1N2jqn0abpOJ7lOGDhoeJri/wPmyxB3sDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b22b8e9f86b6e716f806fd956d0902223d2d9bd6090bc605ae038100cf26ef4f","last_reissued_at":"2026-05-18T03:38:56.430637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:56.430637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degeneration of Kaehler structures and half-form quantization of toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jo\\~ao P. Nunes, Jos\\'e M. Mour\\~ao, William D. Kirwin","submitted_at":"2010-11-15T12:42:32Z","abstract_excerpt":"We study the half-form Kaehler quantization of a smooth symplectic toric manifold $(X,\\omega)$, such that $[\\omega/2\\pi]-c_{1}(X)/2 \\in H^{2}(X,{\\mathbb{Z}})$ and is nonnegative. We define the half-form corrected quantization of $(X,\\omega)$ to be given by holomorphic sections of a certain hermitian line bundle $L\\rightarrow X$ with Chern class $[\\omega/ 2\\pi]-c_{1}(X)/2$. These sections then correspond to integral points of a \"corrected\" polytope $P_{L}$ with integral vertices. For a suitably translated moment polytope $P_{X}$ for $(X,\\omega)$, we have that $P_{L}\\subset P_{X}$ is obtained fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3363","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":"1011.3363","created_at":"2026-05-18T03:38:56.430711+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3363v2","created_at":"2026-05-18T03:38:56.430711+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3363","created_at":"2026-05-18T03:38:56.430711+00:00"},{"alias_kind":"pith_short_12","alias_value":"WIVY5H4GW3TR","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"WIVY5H4GW3TRN6AG","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"WIVY5H4G","created_at":"2026-05-18T12:26:15.391820+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/WIVY5H4GW3TRN6AG7WKW2CICEI","json":"https://pith.science/pith/WIVY5H4GW3TRN6AG7WKW2CICEI.json","graph_json":"https://pith.science/api/pith-number/WIVY5H4GW3TRN6AG7WKW2CICEI/graph.json","events_json":"https://pith.science/api/pith-number/WIVY5H4GW3TRN6AG7WKW2CICEI/events.json","paper":"https://pith.science/paper/WIVY5H4G"},"agent_actions":{"view_html":"https://pith.science/pith/WIVY5H4GW3TRN6AG7WKW2CICEI","download_json":"https://pith.science/pith/WIVY5H4GW3TRN6AG7WKW2CICEI.json","view_paper":"https://pith.science/paper/WIVY5H4G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3363&json=true","fetch_graph":"https://pith.science/api/pith-number/WIVY5H4GW3TRN6AG7WKW2CICEI/graph.json","fetch_events":"https://pith.science/api/pith-number/WIVY5H4GW3TRN6AG7WKW2CICEI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WIVY5H4GW3TRN6AG7WKW2CICEI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WIVY5H4GW3TRN6AG7WKW2CICEI/action/storage_attestation","attest_author":"https://pith.science/pith/WIVY5H4GW3TRN6AG7WKW2CICEI/action/author_attestation","sign_citation":"https://pith.science/pith/WIVY5H4GW3TRN6AG7WKW2CICEI/action/citation_signature","submit_replication":"https://pith.science/pith/WIVY5H4GW3TRN6AG7WKW2CICEI/action/replication_record"}},"created_at":"2026-05-18T03:38:56.430711+00:00","updated_at":"2026-05-18T03:38:56.430711+00:00"}