{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:NE36GSWDM36HMVLBALACWHU4EF","short_pith_number":"pith:NE36GSWD","schema_version":"1.0","canonical_sha256":"6937e34ac366fc76556102c02b1e9c2166823bbc9b0f55821419b1216db1eafb","source":{"kind":"arxiv","id":"2502.09774","version":2},"attestation_state":"computed","paper":{"title":"The period-index problem for hyper-K\\\"ahler varieties via hyperholomorphic bundles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Davesh Maulik, James Hotchkiss, Junliang Shen, Qizheng Yin, Ruxuan Zhang","submitted_at":"2025-02-13T21:09:08Z","abstract_excerpt":"We prove new bounds for the period-index problem for hyper-K\\\"ahler varieties of $K3^{[n]}$-type using projectively hyperholomorphic bundles constructed by Markman. We show that $\\mathrm{dim}(X)$ is a bound for any $X$ of $K3^{[n]}$-type. We also show that $\\frac{1}{2}\\mathrm{dim}(X)$ is a bound for most Brauer classes when the Picard rank of $X$ is at least two, providing evidence for a conjecture of Huybrechts."},"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":"2502.09774","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-02-13T21:09:08Z","cross_cats_sorted":[],"title_canon_sha256":"80192503a0f7411c8a49863d427eff5aad2bb1da1b0364d60ded5acddce4d2ae","abstract_canon_sha256":"e3aab50e54cd6141add32aeec3dd3e3bafb3cff2463052240fcce721b534536c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:08.036773Z","signature_b64":"HC8pyLsOAXZtL0pHBqlVlHbrn5auPmA7yD0UlaS2qfEPIbAaBuUpJHByj2lje1ebAK5VFbtIrD5iMbyg+JehCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6937e34ac366fc76556102c02b1e9c2166823bbc9b0f55821419b1216db1eafb","last_reissued_at":"2026-07-05T11:25:08.036284Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:08.036284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The period-index problem for hyper-K\\\"ahler varieties via hyperholomorphic bundles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Davesh Maulik, James Hotchkiss, Junliang Shen, Qizheng Yin, Ruxuan Zhang","submitted_at":"2025-02-13T21:09:08Z","abstract_excerpt":"We prove new bounds for the period-index problem for hyper-K\\\"ahler varieties of $K3^{[n]}$-type using projectively hyperholomorphic bundles constructed by Markman. We show that $\\mathrm{dim}(X)$ is a bound for any $X$ of $K3^{[n]}$-type. We also show that $\\frac{1}{2}\\mathrm{dim}(X)$ is a bound for most Brauer classes when the Picard rank of $X$ is at least two, providing evidence for a conjecture of Huybrechts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.09774","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/2502.09774/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":"2502.09774","created_at":"2026-07-05T11:25:08.036350+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.09774v2","created_at":"2026-07-05T11:25:08.036350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.09774","created_at":"2026-07-05T11:25:08.036350+00:00"},{"alias_kind":"pith_short_12","alias_value":"NE36GSWDM36H","created_at":"2026-07-05T11:25:08.036350+00:00"},{"alias_kind":"pith_short_16","alias_value":"NE36GSWDM36HMVLB","created_at":"2026-07-05T11:25:08.036350+00:00"},{"alias_kind":"pith_short_8","alias_value":"NE36GSWD","created_at":"2026-07-05T11:25:08.036350+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.23622","citing_title":"On moduli spaces of vector bundles on $K3^{[n]}$-type IHS manifolds","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2606.18357","citing_title":"Irreducible symplectic varieties via K3-del Pezzo double covers","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2603.23033","citing_title":"Hyper-K\\\"ahler varieties: Lagrangian fibrations, atomic sheaves, and categories","ref_index":66,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF","json":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF.json","graph_json":"https://pith.science/api/pith-number/NE36GSWDM36HMVLBALACWHU4EF/graph.json","events_json":"https://pith.science/api/pith-number/NE36GSWDM36HMVLBALACWHU4EF/events.json","paper":"https://pith.science/paper/NE36GSWD"},"agent_actions":{"view_html":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF","download_json":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF.json","view_paper":"https://pith.science/paper/NE36GSWD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.09774&json=true","fetch_graph":"https://pith.science/api/pith-number/NE36GSWDM36HMVLBALACWHU4EF/graph.json","fetch_events":"https://pith.science/api/pith-number/NE36GSWDM36HMVLBALACWHU4EF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF/action/storage_attestation","attest_author":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF/action/author_attestation","sign_citation":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF/action/citation_signature","submit_replication":"https://pith.science/pith/NE36GSWDM36HMVLBALACWHU4EF/action/replication_record"}},"created_at":"2026-07-05T11:25:08.036350+00:00","updated_at":"2026-07-05T11:25:08.036350+00:00"}