{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MAIJLOKPQYICD3UVDMEP7OEXAF","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":"1bc4c713381b2eba3ccff0923952617c69cab909c63027b5b062aeb539da9b47","cross_cats_sorted":["math.GT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-26T14:13:29Z","title_canon_sha256":"6b845c40e767537700603435a31262d60f2f4c2fb8280ae698c755ef5043e96b"},"schema_version":"1.0","source":{"id":"1506.08088","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08088","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08088v3","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08088","created_at":"2026-05-18T01:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"MAIJLOKPQYIC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MAIJLOKPQYICD3UV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MAIJLOKP","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:bb63798f4d2e4937287c4c7b85e819ccae9b54126132250b6b1c1dda54ad740f","target":"graph","created_at":"2026-05-18T01:11:51Z","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":"We define Seiberg-Witten equations on closed manifolds endowed with a Riemannian foliation of codimension 4. When the foliation is taut, we show compactness of the moduli space under some hypothesis satisfied for instance by closed K-contact manifolds. Furthermore, we prove some vanishing and non-vanishing results and we highlight that the invariants may be used to distinguish different foliations on diffeomorphic manifolds.","authors_text":"Mehdi Lejmi, Patrick Weber, Yuri Kordyukov","cross_cats":["math.GT","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-26T14:13:29Z","title":"Seiberg-Witten invariants on manifolds with Riemannian foliations of codimension 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08088","kind":"arxiv","version":3},"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":"sha256:93bdaf663915c628893800af6548dc3de4a60f3d9e27e9aafab575663755081b","target":"record","created_at":"2026-05-18T01:11:51Z","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":"1bc4c713381b2eba3ccff0923952617c69cab909c63027b5b062aeb539da9b47","cross_cats_sorted":["math.GT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-26T14:13:29Z","title_canon_sha256":"6b845c40e767537700603435a31262d60f2f4c2fb8280ae698c755ef5043e96b"},"schema_version":"1.0","source":{"id":"1506.08088","kind":"arxiv","version":3}},"canonical_sha256":"601095b94f861021ee951b08ffb89701648ec7b1341a95e95dfe07581ab4a654","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"601095b94f861021ee951b08ffb89701648ec7b1341a95e95dfe07581ab4a654","first_computed_at":"2026-05-18T01:11:51.573668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:51.573668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qHTb1qXqwj6ErFfv3gjxYlswiQAogsDxJWywMRtSBF+AbS4vObh/p2JTAH3GPvrM8WFxslisDSSmO9ljGXO3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:51.574004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08088","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93bdaf663915c628893800af6548dc3de4a60f3d9e27e9aafab575663755081b","sha256:bb63798f4d2e4937287c4c7b85e819ccae9b54126132250b6b1c1dda54ad740f"],"state_sha256":"4c1e151fe596b73a3ff61a62e19ac1aebc7e4d123bfa914396d0d7187b9807e4"}