{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:52HPBGDYASZMJ7FIMXZZENPFVX","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":"243998ed054a291d8286b376e271fb81156c8cba1d19d7cbccd8bbb29e8eb941","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-26T18:10:11Z","title_canon_sha256":"b3250b89ee041723b099f786c4b3af7918ed867b2b5b73c0eb2fb39100371eee"},"schema_version":"1.0","source":{"id":"2605.27537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27537","created_at":"2026-05-28T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27537v1","created_at":"2026-05-28T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27537","created_at":"2026-05-28T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"52HPBGDYASZM","created_at":"2026-05-28T01:04:14Z"},{"alias_kind":"pith_short_16","alias_value":"52HPBGDYASZMJ7FI","created_at":"2026-05-28T01:04:14Z"},{"alias_kind":"pith_short_8","alias_value":"52HPBGDY","created_at":"2026-05-28T01:04:14Z"}],"graph_snapshots":[{"event_id":"sha256:d780d76b387c620f056ccce9236a880a1992174f8b6a418443997185b24024a2","target":"graph","created_at":"2026-05-28T01:04:14Z","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/2605.27537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Ethan Pesikoff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-26T18:10:11Z","title":"Homological Nielsen realization for the manifolds $\\#_n \\mathbb{CP}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27537","kind":"arxiv","version":1},"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:aff30546cfd7ee33086c80331d6845a20818a6d471b0e894ccbaa342206e0c3d","target":"record","created_at":"2026-05-28T01:04:14Z","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":"243998ed054a291d8286b376e271fb81156c8cba1d19d7cbccd8bbb29e8eb941","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-26T18:10:11Z","title_canon_sha256":"b3250b89ee041723b099f786c4b3af7918ed867b2b5b73c0eb2fb39100371eee"},"schema_version":"1.0","source":{"id":"2605.27537","kind":"arxiv","version":1}},"canonical_sha256":"ee8ef0987804b2c4fca865f39235e5adc67e907c74a1249ef6586bb8b084ebd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee8ef0987804b2c4fca865f39235e5adc67e907c74a1249ef6586bb8b084ebd4","first_computed_at":"2026-05-28T01:04:14.694539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:14.694539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SpF3wYFOs8+Q1rsxbKQBDtG76Ydd6Pd528KP+a6O8KzSJsxCVis+Gk09ShSwSFnVYNjzwC3WWgrs2mJRYIzoCg==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:14.695516Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aff30546cfd7ee33086c80331d6845a20818a6d471b0e894ccbaa342206e0c3d","sha256:d780d76b387c620f056ccce9236a880a1992174f8b6a418443997185b24024a2"],"state_sha256":"59831ac0410f59822a3f681adc987e3cd02f8c41419541d538d8f3e7631c81fb"}