{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:B4O72ECS7LDDQVIDQGSQUYPYAB","short_pith_number":"pith:B4O72ECS","schema_version":"1.0","canonical_sha256":"0f1dfd1052fac638550381a50a61f800605001a76ba7a53e70443ccfd7d0a9d9","source":{"kind":"arxiv","id":"2306.05620","version":2},"attestation_state":"computed","paper":{"title":"Stability for Line Bundles and Deformed Hermitian-Yang-Mills Equation on Some Elliptic Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jason Lo, Shing-Tung Yau, Tristan C. Collins, Yun Shi","submitted_at":"2023-06-09T01:49:21Z","abstract_excerpt":"We study the twisted ampleness criterion due to Collins, Jacob and Yau on surfaces, which is equivalent to the existence of solutions to the deformed Hermitian-Yang-Mills (dHYM) equation. When $X$ is a Weierstrass elliptic K3 surface, and $\\omega$ an ample class such that $\\omega$ lies in the span of a section class and the fiber class, we show that for a class of line bundles $L$ with fiber degree 1 and $\\omega c_1(L)>0$, the twisted ampleness of $L$ respect to $\\omega$, always implies the $\\sigma_{\\omega, 0}$-stability (Bridgeland stability) of $L$. This answers a question by Collins and Yau"},"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":"2306.05620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-09T01:49:21Z","cross_cats_sorted":[],"title_canon_sha256":"d1d4b2bc1be90220d681e7e01133e526227bb3ccce74463ccdb386f5afc915c2","abstract_canon_sha256":"da39fa6aa4c46701c74951fc9715d86134a355f64b7b4414f2f214b9682edabb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:52.427641Z","signature_b64":"qSXaXZFLp2O33ceVi4vzC9zEldAAg4+IU2ZHBltTPUB/7p5RmidNxLsd0L0Chaf58iM7ZC6uw31SM/LCoUpHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f1dfd1052fac638550381a50a61f800605001a76ba7a53e70443ccfd7d0a9d9","last_reissued_at":"2026-07-05T09:09:52.427156Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:52.427156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability for Line Bundles and Deformed Hermitian-Yang-Mills Equation on Some Elliptic Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jason Lo, Shing-Tung Yau, Tristan C. Collins, Yun Shi","submitted_at":"2023-06-09T01:49:21Z","abstract_excerpt":"We study the twisted ampleness criterion due to Collins, Jacob and Yau on surfaces, which is equivalent to the existence of solutions to the deformed Hermitian-Yang-Mills (dHYM) equation. When $X$ is a Weierstrass elliptic K3 surface, and $\\omega$ an ample class such that $\\omega$ lies in the span of a section class and the fiber class, we show that for a class of line bundles $L$ with fiber degree 1 and $\\omega c_1(L)>0$, the twisted ampleness of $L$ respect to $\\omega$, always implies the $\\sigma_{\\omega, 0}$-stability (Bridgeland stability) of $L$. This answers a question by Collins and Yau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05620","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/2306.05620/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":"2306.05620","created_at":"2026-07-05T09:09:52.427209+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.05620v2","created_at":"2026-07-05T09:09:52.427209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.05620","created_at":"2026-07-05T09:09:52.427209+00:00"},{"alias_kind":"pith_short_12","alias_value":"B4O72ECS7LDD","created_at":"2026-07-05T09:09:52.427209+00:00"},{"alias_kind":"pith_short_16","alias_value":"B4O72ECS7LDDQVID","created_at":"2026-07-05T09:09:52.427209+00:00"},{"alias_kind":"pith_short_8","alias_value":"B4O72ECS","created_at":"2026-07-05T09:09:52.427209+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08622","citing_title":"Deformed Hermitian-Yang-Mills equation on the manifold of full flags","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2507.02787","citing_title":"Stability of non-supersymmetric vacua from calibrations","ref_index":43,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB","json":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB.json","graph_json":"https://pith.science/api/pith-number/B4O72ECS7LDDQVIDQGSQUYPYAB/graph.json","events_json":"https://pith.science/api/pith-number/B4O72ECS7LDDQVIDQGSQUYPYAB/events.json","paper":"https://pith.science/paper/B4O72ECS"},"agent_actions":{"view_html":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB","download_json":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB.json","view_paper":"https://pith.science/paper/B4O72ECS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.05620&json=true","fetch_graph":"https://pith.science/api/pith-number/B4O72ECS7LDDQVIDQGSQUYPYAB/graph.json","fetch_events":"https://pith.science/api/pith-number/B4O72ECS7LDDQVIDQGSQUYPYAB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB/action/storage_attestation","attest_author":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB/action/author_attestation","sign_citation":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB/action/citation_signature","submit_replication":"https://pith.science/pith/B4O72ECS7LDDQVIDQGSQUYPYAB/action/replication_record"}},"created_at":"2026-07-05T09:09:52.427209+00:00","updated_at":"2026-07-05T09:09:52.427209+00:00"}