{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:J2AXPARHMA4KCH7YRKKSG4JUE2","short_pith_number":"pith:J2AXPARH","schema_version":"1.0","canonical_sha256":"4e817782276038a11ff88a9523713426aea1ced720e080373dc50128d5e70f07","source":{"kind":"arxiv","id":"2506.13546","version":1},"attestation_state":"computed","paper":{"title":"p-K\\\"ahler structures on compact complex manifolds","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ettore Lo Giudice","submitted_at":"2025-06-16T14:33:33Z","abstract_excerpt":"Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-K\\\"ahler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-K\\\"ahler nilmanifolds equipped with nilpotent complex structures and holomorphically parallelizable nilmanifolds. We also derive necessary conditions for the existence of smooth curves of $p$-K\\\"ahler structures, starting from a fixed $p$-K\\\"ahler structure, along a differentiable family of compact complex manifolds. In addition, we study the cohomology classes of $p$-K"},"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":"2506.13546","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2025-06-16T14:33:33Z","cross_cats_sorted":[],"title_canon_sha256":"dc66839616adc1dfbd56d13ff36ce470c64b6febec75de01a9bc98540bd5867f","abstract_canon_sha256":"cbad237c2d1de363da2ba993397fd3486238cf99d0fa46cd09e24d7ad6586ff1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:21.977931Z","signature_b64":"Rc78TusRRycVZJAdQDDW38t0g6sAF1Np38yqutI867S4z5l4Iy3fhwLk9tJNMY95Sixo6MXPtBOwgSSugEs2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e817782276038a11ff88a9523713426aea1ced720e080373dc50128d5e70f07","last_reissued_at":"2026-07-05T11:22:21.977436Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:21.977436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"p-K\\\"ahler structures on compact complex manifolds","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ettore Lo Giudice","submitted_at":"2025-06-16T14:33:33Z","abstract_excerpt":"Let $(M,J)$ be a complex manifold of complex dimension $n$. A $p$-K\\\"ahler structure on $(M,J)$ is a real, closed $(p,p)$-transverse form. In this paper, we address the conjecture of L. Alessandrini and G. Bassanelli on $(n-2)$-K\\\"ahler nilmanifolds equipped with nilpotent complex structures and holomorphically parallelizable nilmanifolds. We also derive necessary conditions for the existence of smooth curves of $p$-K\\\"ahler structures, starting from a fixed $p$-K\\\"ahler structure, along a differentiable family of compact complex manifolds. In addition, we study the cohomology classes of $p$-K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13546","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/2506.13546/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":"2506.13546","created_at":"2026-07-05T11:22:21.977495+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.13546v1","created_at":"2026-07-05T11:22:21.977495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13546","created_at":"2026-07-05T11:22:21.977495+00:00"},{"alias_kind":"pith_short_12","alias_value":"J2AXPARHMA4K","created_at":"2026-07-05T11:22:21.977495+00:00"},{"alias_kind":"pith_short_16","alias_value":"J2AXPARHMA4KCH7Y","created_at":"2026-07-05T11:22:21.977495+00:00"},{"alias_kind":"pith_short_8","alias_value":"J2AXPARH","created_at":"2026-07-05T11:22:21.977495+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/J2AXPARHMA4KCH7YRKKSG4JUE2","json":"https://pith.science/pith/J2AXPARHMA4KCH7YRKKSG4JUE2.json","graph_json":"https://pith.science/api/pith-number/J2AXPARHMA4KCH7YRKKSG4JUE2/graph.json","events_json":"https://pith.science/api/pith-number/J2AXPARHMA4KCH7YRKKSG4JUE2/events.json","paper":"https://pith.science/paper/J2AXPARH"},"agent_actions":{"view_html":"https://pith.science/pith/J2AXPARHMA4KCH7YRKKSG4JUE2","download_json":"https://pith.science/pith/J2AXPARHMA4KCH7YRKKSG4JUE2.json","view_paper":"https://pith.science/paper/J2AXPARH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.13546&json=true","fetch_graph":"https://pith.science/api/pith-number/J2AXPARHMA4KCH7YRKKSG4JUE2/graph.json","fetch_events":"https://pith.science/api/pith-number/J2AXPARHMA4KCH7YRKKSG4JUE2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J2AXPARHMA4KCH7YRKKSG4JUE2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J2AXPARHMA4KCH7YRKKSG4JUE2/action/storage_attestation","attest_author":"https://pith.science/pith/J2AXPARHMA4KCH7YRKKSG4JUE2/action/author_attestation","sign_citation":"https://pith.science/pith/J2AXPARHMA4KCH7YRKKSG4JUE2/action/citation_signature","submit_replication":"https://pith.science/pith/J2AXPARHMA4KCH7YRKKSG4JUE2/action/replication_record"}},"created_at":"2026-07-05T11:22:21.977495+00:00","updated_at":"2026-07-05T11:22:21.977495+00:00"}