{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BBYTFSTMXYC3TFNIASW6U6KPIB","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":"0f8f0188e1f779801196bc430dff328996176243ceb5da3bf075212e8a66aaa2","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2007-05-08T19:00:43Z","title_canon_sha256":"379b7f7ffae0adda323596599c54a89a111467bb7c45cc3b720810770ca20822"},"schema_version":"1.0","source":{"id":"0705.1143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.1143","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"0705.1143v1","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.1143","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"BBYTFSTMXYC3","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BBYTFSTMXYC3TFNI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BBYTFSTM","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:187436ba4f021f5fe5c4bd4df85dba9d1e2327e600d8257579d9dd0904d4a08d","target":"graph","created_at":"2026-05-18T01:22:31Z","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":"Harer, Kas and Kirby have conjectured that every handle decomposition of the elliptic surface $E(1)_{2,3}$ requires both 1- and 3-handles. In this article, we construct a smooth 4-manifold which has the same Seiberg-Witten invariant as $E(1)_{2,3}$ and admits neither 1- nor 3-handles, by using rational blow-downs and Kirby calculus. Our manifold gives the first example of either a counterexample to the Harer-Kas-Kirby conjecture or a homeomorphic but non-diffeomorphic pair of simply connected closed smooth 4-manifolds with the same non-vanishing Seiberg-Witten invariants.","authors_text":"Kouichi Yasui","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2007-05-08T19:00:43Z","title":"Exotic rational elliptic surfaces without 1-handles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.1143","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":"sha256:59a09dc89d9399ee60b315b7a9a9620845fc7895a521c49d7bca3d49fbcff752","target":"record","created_at":"2026-05-18T01:22:31Z","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":"0f8f0188e1f779801196bc430dff328996176243ceb5da3bf075212e8a66aaa2","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2007-05-08T19:00:43Z","title_canon_sha256":"379b7f7ffae0adda323596599c54a89a111467bb7c45cc3b720810770ca20822"},"schema_version":"1.0","source":{"id":"0705.1143","kind":"arxiv","version":1}},"canonical_sha256":"087132ca6cbe05b995a804adea794f404e04064b616c088749e71461f6a88970","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"087132ca6cbe05b995a804adea794f404e04064b616c088749e71461f6a88970","first_computed_at":"2026-05-18T01:22:31.257388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:31.257388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CinsGQlSXCgQclFnH3xLy442war9NfmXikNFeQhID4FcLZB/Q62oMy/aS1CkZ98oTX8U6U5aIasnc8hTHVfKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:31.257916Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.1143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59a09dc89d9399ee60b315b7a9a9620845fc7895a521c49d7bca3d49fbcff752","sha256:187436ba4f021f5fe5c4bd4df85dba9d1e2327e600d8257579d9dd0904d4a08d"],"state_sha256":"0fbe5c3b6b6c6cc7459f3dca99143800ac58b1f8a99681abb00345b2e7117f31"}