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We study this question for the smooth, positive-definite 4-manifolds $M_n:=\\#_n\\mathbb{CP}^2$. Even though every isometry of $H_2(M_n;\\mathbb{Z})$ is induced by some orientation-preserving diffeomorphism, not necessarily of finite order, we show that Nielsen realization is sparse: as $n\\to\\infty$, a random"},"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":"2605.27537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-26T18:10:11Z","cross_cats_sorted":[],"title_canon_sha256":"b3250b89ee041723b099f786c4b3af7918ed867b2b5b73c0eb2fb39100371eee","abstract_canon_sha256":"243998ed054a291d8286b376e271fb81156c8cba1d19d7cbccd8bbb29e8eb941"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:14.695516Z","signature_b64":"SpF3wYFOs8+Q1rsxbKQBDtG76Ydd6Pd528KP+a6O8KzSJsxCVis+Gk09ShSwSFnVYNjzwC3WWgrs2mJRYIzoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee8ef0987804b2c4fca865f39235e5adc67e907c74a1249ef6586bb8b084ebd4","last_reissued_at":"2026-05-28T01:04:14.694539Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:14.694539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homological Nielsen realization for the manifolds $\\#_n \\mathbb{CP}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ethan Pesikoff","submitted_at":"2026-05-26T18:10:11Z","abstract_excerpt":"Given a smooth, oriented, simply-connected $4$-manifold $M$, the homological Nielsen realization problem asks: when does a finite group of isometries $G\\leq O(H_2(M;\\mathbb{Z}))$ preserving the intersection form lift isomorphically to a finite group of orientation-preserving diffeomorphisms? We study this question for the smooth, positive-definite 4-manifolds $M_n:=\\#_n\\mathbb{CP}^2$. Even though every isometry of $H_2(M_n;\\mathbb{Z})$ is induced by some orientation-preserving diffeomorphism, not necessarily of finite order, we show that Nielsen realization is sparse: as $n\\to\\infty$, a random"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27537","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/2605.27537/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":"2605.27537","created_at":"2026-05-28T01:04:14.694640+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.27537v1","created_at":"2026-05-28T01:04:14.694640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27537","created_at":"2026-05-28T01:04:14.694640+00:00"},{"alias_kind":"pith_short_12","alias_value":"52HPBGDYASZM","created_at":"2026-05-28T01:04:14.694640+00:00"},{"alias_kind":"pith_short_16","alias_value":"52HPBGDYASZMJ7FI","created_at":"2026-05-28T01:04:14.694640+00:00"},{"alias_kind":"pith_short_8","alias_value":"52HPBGDY","created_at":"2026-05-28T01:04:14.694640+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/52HPBGDYASZMJ7FIMXZZENPFVX","json":"https://pith.science/pith/52HPBGDYASZMJ7FIMXZZENPFVX.json","graph_json":"https://pith.science/api/pith-number/52HPBGDYASZMJ7FIMXZZENPFVX/graph.json","events_json":"https://pith.science/api/pith-number/52HPBGDYASZMJ7FIMXZZENPFVX/events.json","paper":"https://pith.science/paper/52HPBGDY"},"agent_actions":{"view_html":"https://pith.science/pith/52HPBGDYASZMJ7FIMXZZENPFVX","download_json":"https://pith.science/pith/52HPBGDYASZMJ7FIMXZZENPFVX.json","view_paper":"https://pith.science/paper/52HPBGDY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.27537&json=true","fetch_graph":"https://pith.science/api/pith-number/52HPBGDYASZMJ7FIMXZZENPFVX/graph.json","fetch_events":"https://pith.science/api/pith-number/52HPBGDYASZMJ7FIMXZZENPFVX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/52HPBGDYASZMJ7FIMXZZENPFVX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/52HPBGDYASZMJ7FIMXZZENPFVX/action/storage_attestation","attest_author":"https://pith.science/pith/52HPBGDYASZMJ7FIMXZZENPFVX/action/author_attestation","sign_citation":"https://pith.science/pith/52HPBGDYASZMJ7FIMXZZENPFVX/action/citation_signature","submit_replication":"https://pith.science/pith/52HPBGDYASZMJ7FIMXZZENPFVX/action/replication_record"}},"created_at":"2026-05-28T01:04:14.694640+00:00","updated_at":"2026-05-28T01:04:14.694640+00:00"}