{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CJBXAX7AKWGIGUSA5VNVFR4A33","short_pith_number":"pith:CJBXAX7A","canonical_record":{"source":{"id":"1005.0193","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-05-03T06:21:36Z","cross_cats_sorted":[],"title_canon_sha256":"8f326d8a81ea0fb5eab167554a478f21255284ee1cf3b3f7e721618d596ec21d","abstract_canon_sha256":"7685cc89ed1ef71de14ec2c1659947259cac81b4f56e5751fa168e0a2236dd5d"},"schema_version":"1.0"},"canonical_sha256":"1243705fe0558c835240ed5b52c780def4ff9f6533bd7f6f25cf5e6e9303572f","source":{"kind":"arxiv","id":"1005.0193","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.0193","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1005.0193v5","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0193","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"CJBXAX7AKWGI","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CJBXAX7AKWGIGUSA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CJBXAX7A","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CJBXAX7AKWGIGUSA5VNVFR4A33","target":"record","payload":{"canonical_record":{"source":{"id":"1005.0193","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-05-03T06:21:36Z","cross_cats_sorted":[],"title_canon_sha256":"8f326d8a81ea0fb5eab167554a478f21255284ee1cf3b3f7e721618d596ec21d","abstract_canon_sha256":"7685cc89ed1ef71de14ec2c1659947259cac81b4f56e5751fa168e0a2236dd5d"},"schema_version":"1.0"},"canonical_sha256":"1243705fe0558c835240ed5b52c780def4ff9f6533bd7f6f25cf5e6e9303572f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:33.719506Z","signature_b64":"cjd0Igc36NjNHA4tC6XxFSt2y3Smrv+sxK29rozWFJTqTvhKRRD+m59tcR/9l9hgID1NQdISKMt+WYUK3i+PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1243705fe0558c835240ed5b52c780def4ff9f6533bd7f6f25cf5e6e9303572f","last_reissued_at":"2026-05-18T01:16:33.718866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:33.718866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.0193","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkTRK1CaXw92YoBCIdGQE5FBR2kAee4gAw3SFiLwvhpbRAXorDUWc1fjQPeD/XD6jnzjgNzuVUKygEE0xs8HCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:27:30.640697Z"},"content_sha256":"8d66ed9f3db8639c649808cab3cb506f72fbe95a0fd812099eb37558ecea1472","schema_version":"1.0","event_id":"sha256:8d66ed9f3db8639c649808cab3cb506f72fbe95a0fd812099eb37558ecea1472"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CJBXAX7AKWGIGUSA5VNVFR4A33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semifree Hamiltonian circle actions on 6-dimensional symplectic manifolds with non-isolated fixed point set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dong Youp Suh, Taekgyu Hwang, Yunhyung Cho","submitted_at":"2010-05-03T06:21:36Z","abstract_excerpt":"Let $(M, \\omega)$ be a 6-dimensional closed symplectic manifold with a symplectic $S^1$-action with $M^{S^1} \\neq \\emptyset$ and $\\dim M^{S^1} \\leq 2$. Assume that $\\omega$ is integral with a generalized moment map $\\mu$. We first prove that the action is Hamiltonian if and only if $b_2^+(M_{\\red})=1$, where $M_{\\red}$ is any reduced space with respect to $\\mu$. It means that if the action is non-Hamiltonian, then $b_2^+(M_{\\red}) \\geq 2$. Secondly, we focus on the case when the action is semifree and Hamiltonian. We prove that if $M^{S^1}$ consists of surfaces, then the number $k$ of fixed su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0193","kind":"arxiv","version":5},"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":"2026-05-18T01:16:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oKZmP63MYnjydApoRBCLNVob5G7AOG1BcEc+RZ3i/uZTb6nuI13hgty3RD+iXKxq+zglmiQU8+dSvLLPeuE0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:27:30.641047Z"},"content_sha256":"c2cd98977e28eea4e41685aea602c3d368193442514882087800b01b56f9db0d","schema_version":"1.0","event_id":"sha256:c2cd98977e28eea4e41685aea602c3d368193442514882087800b01b56f9db0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJBXAX7AKWGIGUSA5VNVFR4A33/bundle.json","state_url":"https://pith.science/pith/CJBXAX7AKWGIGUSA5VNVFR4A33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJBXAX7AKWGIGUSA5VNVFR4A33/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":"2026-06-02T23:27:30Z","links":{"resolver":"https://pith.science/pith/CJBXAX7AKWGIGUSA5VNVFR4A33","bundle":"https://pith.science/pith/CJBXAX7AKWGIGUSA5VNVFR4A33/bundle.json","state":"https://pith.science/pith/CJBXAX7AKWGIGUSA5VNVFR4A33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJBXAX7AKWGIGUSA5VNVFR4A33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CJBXAX7AKWGIGUSA5VNVFR4A33","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":"7685cc89ed1ef71de14ec2c1659947259cac81b4f56e5751fa168e0a2236dd5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-05-03T06:21:36Z","title_canon_sha256":"8f326d8a81ea0fb5eab167554a478f21255284ee1cf3b3f7e721618d596ec21d"},"schema_version":"1.0","source":{"id":"1005.0193","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.0193","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1005.0193v5","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0193","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"CJBXAX7AKWGI","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CJBXAX7AKWGIGUSA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CJBXAX7A","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:c2cd98977e28eea4e41685aea602c3d368193442514882087800b01b56f9db0d","target":"graph","created_at":"2026-05-18T01:16:33Z","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":"Let $(M, \\omega)$ be a 6-dimensional closed symplectic manifold with a symplectic $S^1$-action with $M^{S^1} \\neq \\emptyset$ and $\\dim M^{S^1} \\leq 2$. Assume that $\\omega$ is integral with a generalized moment map $\\mu$. We first prove that the action is Hamiltonian if and only if $b_2^+(M_{\\red})=1$, where $M_{\\red}$ is any reduced space with respect to $\\mu$. It means that if the action is non-Hamiltonian, then $b_2^+(M_{\\red}) \\geq 2$. Secondly, we focus on the case when the action is semifree and Hamiltonian. We prove that if $M^{S^1}$ consists of surfaces, then the number $k$ of fixed su","authors_text":"Dong Youp Suh, Taekgyu Hwang, Yunhyung Cho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-05-03T06:21:36Z","title":"Semifree Hamiltonian circle actions on 6-dimensional symplectic manifolds with non-isolated fixed point set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0193","kind":"arxiv","version":5},"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":"sha256:8d66ed9f3db8639c649808cab3cb506f72fbe95a0fd812099eb37558ecea1472","target":"record","created_at":"2026-05-18T01:16:33Z","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":"7685cc89ed1ef71de14ec2c1659947259cac81b4f56e5751fa168e0a2236dd5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-05-03T06:21:36Z","title_canon_sha256":"8f326d8a81ea0fb5eab167554a478f21255284ee1cf3b3f7e721618d596ec21d"},"schema_version":"1.0","source":{"id":"1005.0193","kind":"arxiv","version":5}},"canonical_sha256":"1243705fe0558c835240ed5b52c780def4ff9f6533bd7f6f25cf5e6e9303572f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1243705fe0558c835240ed5b52c780def4ff9f6533bd7f6f25cf5e6e9303572f","first_computed_at":"2026-05-18T01:16:33.718866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:33.718866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cjd0Igc36NjNHA4tC6XxFSt2y3Smrv+sxK29rozWFJTqTvhKRRD+m59tcR/9l9hgID1NQdISKMt+WYUK3i+PBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:33.719506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.0193","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d66ed9f3db8639c649808cab3cb506f72fbe95a0fd812099eb37558ecea1472","sha256:c2cd98977e28eea4e41685aea602c3d368193442514882087800b01b56f9db0d"],"state_sha256":"59a07ed0ac2c1daac700aa8fcfcdaba0d480093888dbd25c125fbc0c55f2c32d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnMYspuibAJUy/QsY7kjji7uSqqkVflY0yAHSrpZL+lc35qih36OtBrgE3RY1OUulOM/3w+J3b3uY3SbscpHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:27:30.643184Z","bundle_sha256":"3b693fd087df8b2a4de04f1fba3f3059f4073709c9e7b950e908bf68bfb2062d"}}