{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:T77SAJ46RFEEALJLJJHSK7LZI2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d26e43d0739ff7970885053c3f4ed514abb5470484d451b23ad6d5cfdf534ba8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-30T09:51:59Z","title_canon_sha256":"e52d9609c21267d85b683e077afb69f6cc216b38c328ae025620842afceca80f"},"schema_version":"1.0","source":{"id":"2507.22525","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.22525","created_at":"2026-07-05T12:07:40Z"},{"alias_kind":"arxiv_version","alias_value":"2507.22525v2","created_at":"2026-07-05T12:07:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.22525","created_at":"2026-07-05T12:07:40Z"},{"alias_kind":"pith_short_12","alias_value":"T77SAJ46RFEE","created_at":"2026-07-05T12:07:40Z"},{"alias_kind":"pith_short_16","alias_value":"T77SAJ46RFEEALJL","created_at":"2026-07-05T12:07:40Z"},{"alias_kind":"pith_short_8","alias_value":"T77SAJ46","created_at":"2026-07-05T12:07:40Z"}],"graph_snapshots":[{"event_id":"sha256:eaacbc7bd924cb4930d4d1798138a326b75d76d4d8f2866804ac0420cf3ca109","target":"graph","created_at":"2026-07-05T12:07:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.22525/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study finite abelian group actions on weakly Lefschetz cohomologically symplectic (WLS) manifolds, a collection of manifolds that includes all compact connected Kaehler manifolds. We prove that for any WLS manifold $X$ there exists a number $C$ such that, for any integer $m\\geq C$, if $({\\mathbf Z}/m)^k$ acts freely on $X$, then $\\sum_j b_j(X;{\\mathbf Q})\\geq 2^k$.\n  We also prove a structure theorem for effective actions on WLS manifolds of $({\\mathbf Z}/p)^r$, where $p$ is a big enough prime, analogous to some results for tori of Lupton and Oprea, and we find bounds on the discrete degree","authors_text":"Ignasi Mundet i Riera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-30T09:51:59Z","title":"Finite abelian group actions on weakly Lefschetz cohomologically symplectic manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.22525","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d52ec2c17d2b3e80b2670d6cce328b55398da82a9ba454bb961fefff5d382351","target":"record","created_at":"2026-07-05T12:07:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d26e43d0739ff7970885053c3f4ed514abb5470484d451b23ad6d5cfdf534ba8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-07-30T09:51:59Z","title_canon_sha256":"e52d9609c21267d85b683e077afb69f6cc216b38c328ae025620842afceca80f"},"schema_version":"1.0","source":{"id":"2507.22525","kind":"arxiv","version":2}},"canonical_sha256":"9fff20279e8948402d2b4a4f257d7946a9ce8ffaf2b9f0c12448b20ca804541c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fff20279e8948402d2b4a4f257d7946a9ce8ffaf2b9f0c12448b20ca804541c","first_computed_at":"2026-07-05T12:07:40.208245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:40.208245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u9ynME3iOH9HQunihcxmf3q4Ks75W8C6S9eHESGhr8xGYOhmI0Wc3ZBqVPaa2IPlSKxYcEf0AnSjfQtDl2cbBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:40.208963Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.22525","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d52ec2c17d2b3e80b2670d6cce328b55398da82a9ba454bb961fefff5d382351","sha256:eaacbc7bd924cb4930d4d1798138a326b75d76d4d8f2866804ac0420cf3ca109"],"state_sha256":"98a571cea408d25c4fc6d6c4eb83216cfd4c3bce2ad5543a498b310f002e98de"}