{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:W6WXU5HXCVNJPF33B4OJSZHFGL","short_pith_number":"pith:W6WXU5HX","canonical_record":{"source":{"id":"1303.0848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-04T21:02:27Z","cross_cats_sorted":[],"title_canon_sha256":"a883fdb2df8aba56e795d7640b0c1dda1787914bbba9d543bf8abc50262d87d7","abstract_canon_sha256":"ca22ca876662eae802acaa0164ed9ddac9e20c690064c48b96c32bdb8bf82ff9"},"schema_version":"1.0"},"canonical_sha256":"b7ad7a74f7155a97977b0f1c9964e532d140f809b73ee01d1cad5dc80cd21220","source":{"kind":"arxiv","id":"1303.0848","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0848","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0848v1","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0848","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"W6WXU5HXCVNJ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W6WXU5HXCVNJPF33","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W6WXU5HX","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:W6WXU5HXCVNJPF33B4OJSZHFGL","target":"record","payload":{"canonical_record":{"source":{"id":"1303.0848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-04T21:02:27Z","cross_cats_sorted":[],"title_canon_sha256":"a883fdb2df8aba56e795d7640b0c1dda1787914bbba9d543bf8abc50262d87d7","abstract_canon_sha256":"ca22ca876662eae802acaa0164ed9ddac9e20c690064c48b96c32bdb8bf82ff9"},"schema_version":"1.0"},"canonical_sha256":"b7ad7a74f7155a97977b0f1c9964e532d140f809b73ee01d1cad5dc80cd21220","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:53.616797Z","signature_b64":"OyoiIe8zfGhx0sf6NSqZFnLih86XqkgOr3oSkJyFGXQ5VFtmMvs0ofchh4ovP/mDnzItja+x8pCMpFMkIn3dBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7ad7a74f7155a97977b0f1c9964e532d140f809b73ee01d1cad5dc80cd21220","last_reissued_at":"2026-05-18T03:31:53.616129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:53.616129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.0848","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVkb/sTaM60IfH9qzEdxSeUtfbWs8lzhNt7PNTgBBZcXSaF0llfQpvoeQv58mVuk/oWBtpaZjrz0O9TuzgNLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:09:25.411034Z"},"content_sha256":"01234626e4f657d248d3f9ec62b6be1a8547b17cd2731b121f0b90d472fae6ea","schema_version":"1.0","event_id":"sha256:01234626e4f657d248d3f9ec62b6be1a8547b17cd2731b121f0b90d472fae6ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:W6WXU5HXCVNJPF33B4OJSZHFGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hurwitz-type bound, knot surgery, and smooth $\\s^1$-four-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Weimin Chen","submitted_at":"2013-03-04T21:02:27Z","abstract_excerpt":"In this paper we prove several related results concerning smooth $\\Z_p$ or $\\s^1$ actions on 4-manifolds. We show that there exists an infinite sequence of smooth 4-manifolds $X_n$, $n\\geq 2$, which have the same integral homology and intersection form and the same Seiberg-Witten invariant, such that each $X_n$ supports no smooth $\\s^1$-actions but admits a smooth $\\Z_n$-action. In order to construct such manifolds, we devise a method for annihilating smooth $\\s^1$-actions on 4-manifolds using Fintushel-Stern knot surgery, and apply it to the Kodaira-Thurston manifold in an equivariant setting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0848","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WpKwU3KNogOem9U7H5JxxScycccLRq1vFa1PqiD4YJ7cSxYxx++xBxsZPNhiznXwi7lHshuj2KOizEhV/nubDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:09:25.411689Z"},"content_sha256":"68b2f1ba06528598a6b99f87fab64b59f95a3023eed0351e6e1579d0577f8a0c","schema_version":"1.0","event_id":"sha256:68b2f1ba06528598a6b99f87fab64b59f95a3023eed0351e6e1579d0577f8a0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W6WXU5HXCVNJPF33B4OJSZHFGL/bundle.json","state_url":"https://pith.science/pith/W6WXU5HXCVNJPF33B4OJSZHFGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W6WXU5HXCVNJPF33B4OJSZHFGL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T19:09:25Z","links":{"resolver":"https://pith.science/pith/W6WXU5HXCVNJPF33B4OJSZHFGL","bundle":"https://pith.science/pith/W6WXU5HXCVNJPF33B4OJSZHFGL/bundle.json","state":"https://pith.science/pith/W6WXU5HXCVNJPF33B4OJSZHFGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W6WXU5HXCVNJPF33B4OJSZHFGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W6WXU5HXCVNJPF33B4OJSZHFGL","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":"ca22ca876662eae802acaa0164ed9ddac9e20c690064c48b96c32bdb8bf82ff9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-04T21:02:27Z","title_canon_sha256":"a883fdb2df8aba56e795d7640b0c1dda1787914bbba9d543bf8abc50262d87d7"},"schema_version":"1.0","source":{"id":"1303.0848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0848","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0848v1","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0848","created_at":"2026-05-18T03:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"W6WXU5HXCVNJ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W6WXU5HXCVNJPF33","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W6WXU5HX","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:68b2f1ba06528598a6b99f87fab64b59f95a3023eed0351e6e1579d0577f8a0c","target":"graph","created_at":"2026-05-18T03:31:53Z","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":"In this paper we prove several related results concerning smooth $\\Z_p$ or $\\s^1$ actions on 4-manifolds. We show that there exists an infinite sequence of smooth 4-manifolds $X_n$, $n\\geq 2$, which have the same integral homology and intersection form and the same Seiberg-Witten invariant, such that each $X_n$ supports no smooth $\\s^1$-actions but admits a smooth $\\Z_n$-action. In order to construct such manifolds, we devise a method for annihilating smooth $\\s^1$-actions on 4-manifolds using Fintushel-Stern knot surgery, and apply it to the Kodaira-Thurston manifold in an equivariant setting","authors_text":"Weimin Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-04T21:02:27Z","title":"Hurwitz-type bound, knot surgery, and smooth $\\s^1$-four-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0848","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":"sha256:01234626e4f657d248d3f9ec62b6be1a8547b17cd2731b121f0b90d472fae6ea","target":"record","created_at":"2026-05-18T03:31:53Z","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":"ca22ca876662eae802acaa0164ed9ddac9e20c690064c48b96c32bdb8bf82ff9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-04T21:02:27Z","title_canon_sha256":"a883fdb2df8aba56e795d7640b0c1dda1787914bbba9d543bf8abc50262d87d7"},"schema_version":"1.0","source":{"id":"1303.0848","kind":"arxiv","version":1}},"canonical_sha256":"b7ad7a74f7155a97977b0f1c9964e532d140f809b73ee01d1cad5dc80cd21220","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7ad7a74f7155a97977b0f1c9964e532d140f809b73ee01d1cad5dc80cd21220","first_computed_at":"2026-05-18T03:31:53.616129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:53.616129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OyoiIe8zfGhx0sf6NSqZFnLih86XqkgOr3oSkJyFGXQ5VFtmMvs0ofchh4ovP/mDnzItja+x8pCMpFMkIn3dBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:53.616797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01234626e4f657d248d3f9ec62b6be1a8547b17cd2731b121f0b90d472fae6ea","sha256:68b2f1ba06528598a6b99f87fab64b59f95a3023eed0351e6e1579d0577f8a0c"],"state_sha256":"16707aa6b189a4d476d77d5af8ac0389b49f4b00b9d543a2da53656508f664fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bSNcx8ruEQKgJE7MGT8uHhxLaj0O3ZyZHi9mPEcwM2Q3denRTaZfm2Poavq/55kcCTbL2/QAO0jNBLDDiSxLCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:09:25.414904Z","bundle_sha256":"80237ab756594cac403b8563c900d7d086ce37b9beb32db2e254d63877ad4df6"}}