{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:VRFOFLBPF7SW3SLGEKP6T6BOYT","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":"f0329ac87dc09059c68308671cc63b1d47803f227363f3a5ca3bd3ae903a1e7e","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"2005-01-02T05:10:51Z","title_canon_sha256":"f5fadda7ba05233892b4e67e7109599187ca6458942e1aa80e8ba707eb9e0917"},"schema_version":"1.0","source":{"id":"math/0501011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501011","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501011v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501011","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"VRFOFLBPF7SW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"VRFOFLBPF7SW3SLG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"VRFOFLBP","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:8ce02d47571deb2502a5c76898dc16d290c4d3f135c93f4e11359892fd29dccb","target":"graph","created_at":"2026-05-18T04:16:31Z","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"},"paper":{"abstract_excerpt":"A manifold obtained by k simultaneous symplectic blow-ups of CP^2 of equal sizes epsilon (where the size of CP^1 \\subset CP^2 is one) admits an effective two dimensional torus action if k <= 3 and admits an effective circle action if (k-1)epsilon < 1. We show that these bounds are sharp if 1/epsilon is an integer.","authors_text":"Liat Kessler, Yael Karshon","cross_cats":[],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2005-01-02T05:10:51Z","title":"Circle and torus actions on equal symplectic blow-ups of CP^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501011","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:bd3de595d1957675bf1aa0a7fc4eddcc511cff689082e11b82c43accdbaa9542","target":"record","created_at":"2026-05-18T04:16:31Z","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":"f0329ac87dc09059c68308671cc63b1d47803f227363f3a5ca3bd3ae903a1e7e","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"2005-01-02T05:10:51Z","title_canon_sha256":"f5fadda7ba05233892b4e67e7109599187ca6458942e1aa80e8ba707eb9e0917"},"schema_version":"1.0","source":{"id":"math/0501011","kind":"arxiv","version":1}},"canonical_sha256":"ac4ae2ac2f2fe56dc966229fe9f82ec4d8fb92c8b2b35ea90a39c39fd2e6df31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4ae2ac2f2fe56dc966229fe9f82ec4d8fb92c8b2b35ea90a39c39fd2e6df31","first_computed_at":"2026-05-18T04:16:31.133207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:31.133207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zdd0NSv4GMQ5h6BEGZrdhnik4Nh6EEDneoF2KMbGAt2cTgA1ctypDbf2+eTleChZKc7JUiTxGFRuiPDtVeHxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:31.133597Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd3de595d1957675bf1aa0a7fc4eddcc511cff689082e11b82c43accdbaa9542","sha256:8ce02d47571deb2502a5c76898dc16d290c4d3f135c93f4e11359892fd29dccb"],"state_sha256":"b59dc53dd9b4eb54d136db1b46d2d2d058e1cc4b225754b9896f2c24e02e7690"}