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We show that a certain weighted sum of Bergman kernels for ${Sym}^i {E} \\otimes \\det({E})^{k+j}$ as $i$ and $j$ vary over a finite set admit an asymptotic expansion. This extends a similar result for cyclic K\\\"ahler orbifolds."},"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":"2605.24572","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-23T13:22:59Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"be03bc9f0143edffbf14f0e9095ca6634f21aacc769c843504b7952ec88f9ab5","abstract_canon_sha256":"ae0acbcbb6ba35509d486ef5c2693d531d9e083a87be2a52a493148899e1cc5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:46.932728Z","signature_b64":"UrOkDR2jGTVQJkzbsJJk3kf8ZAhJrN01tsvtLWiiDUOvBSaIGHk3gVT2CRkSteEotClF64ws6bI+VsLBqrYDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e33b6ad3c87f9a62282306c81c9cc07a234b1d0bdd9288ed3b5cfade49db1733","last_reissued_at":"2026-05-26T01:03:46.931875Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:46.931875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orbifold Bergman Kernels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Julius Ross, Shin Kim","submitted_at":"2026-05-23T13:22:59Z","abstract_excerpt":"Let $({X}, \\omega)$ be a compact $n$-dimensional K\\\"ahler orbifold, the stabilizer groups of which are abelian and have rank at most two. Let ${E}$ be an orbi-ample vector bundle of rank $2$ over ${X}$ and let $H$ be a Hermitian metric on ${E}$ such that the curvature form of $\\det H$ is $-2\\pi \\sqrt{-1} \\omega$. We show that a certain weighted sum of Bergman kernels for ${Sym}^i {E} \\otimes \\det({E})^{k+j}$ as $i$ and $j$ vary over a finite set admit an asymptotic expansion. This extends a similar result for cyclic K\\\"ahler orbifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24572","kind":"arxiv","version":1},"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/2605.24572/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":"2605.24572","created_at":"2026-05-26T01:03:46.932025+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.24572v1","created_at":"2026-05-26T01:03:46.932025+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24572","created_at":"2026-05-26T01:03:46.932025+00:00"},{"alias_kind":"pith_short_12","alias_value":"4M5WVU6IP6NG","created_at":"2026-05-26T01:03:46.932025+00:00"},{"alias_kind":"pith_short_16","alias_value":"4M5WVU6IP6NGEKBD","created_at":"2026-05-26T01:03:46.932025+00:00"},{"alias_kind":"pith_short_8","alias_value":"4M5WVU6I","created_at":"2026-05-26T01:03:46.932025+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/4M5WVU6IP6NGEKBDA3EBZHGAPI","json":"https://pith.science/pith/4M5WVU6IP6NGEKBDA3EBZHGAPI.json","graph_json":"https://pith.science/api/pith-number/4M5WVU6IP6NGEKBDA3EBZHGAPI/graph.json","events_json":"https://pith.science/api/pith-number/4M5WVU6IP6NGEKBDA3EBZHGAPI/events.json","paper":"https://pith.science/paper/4M5WVU6I"},"agent_actions":{"view_html":"https://pith.science/pith/4M5WVU6IP6NGEKBDA3EBZHGAPI","download_json":"https://pith.science/pith/4M5WVU6IP6NGEKBDA3EBZHGAPI.json","view_paper":"https://pith.science/paper/4M5WVU6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.24572&json=true","fetch_graph":"https://pith.science/api/pith-number/4M5WVU6IP6NGEKBDA3EBZHGAPI/graph.json","fetch_events":"https://pith.science/api/pith-number/4M5WVU6IP6NGEKBDA3EBZHGAPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4M5WVU6IP6NGEKBDA3EBZHGAPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4M5WVU6IP6NGEKBDA3EBZHGAPI/action/storage_attestation","attest_author":"https://pith.science/pith/4M5WVU6IP6NGEKBDA3EBZHGAPI/action/author_attestation","sign_citation":"https://pith.science/pith/4M5WVU6IP6NGEKBDA3EBZHGAPI/action/citation_signature","submit_replication":"https://pith.science/pith/4M5WVU6IP6NGEKBDA3EBZHGAPI/action/replication_record"}},"created_at":"2026-05-26T01:03:46.932025+00:00","updated_at":"2026-05-26T01:03:46.932025+00:00"}