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Both the ECH of Y and the Seiberg-Witten Floer cohomology of Y admit absolute gradings by homotopy classes of oriented two-plane fields. We show that Taubes' isomorphism preserves these gradings. To do this, we prove another result relating the expected dimension of any component of the Seiberg-Witten moduli space over a completed connec"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.3010","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-08-15T01:34:15Z","cross_cats_sorted":[],"title_canon_sha256":"0cb22e853c652e993f29d81d06fd6784bebd17069f9372aef3527efd01f1563e","abstract_canon_sha256":"c771fb02e516765740fba1da0189c70851c145eac28e37a000b37168d4ae8db0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:06.668419Z","signature_b64":"XjqyDKHnah3HqYwdtEkodKYonOSKj2y5/XAFZSYUIGY65C3AFHhTxWhT86HEMCHr50N9nqTp3gqJmQs8fty4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a50d7c87c6440d45e3c64fc8355d5636a11d0f4eb401f7e5795abec391f0e07","last_reissued_at":"2026-05-18T03:31:06.667797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:06.667797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The absolute gradings on embedded contact homology and Seiberg-Witten Floer cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Daniel Cristofaro-Gardiner","submitted_at":"2012-08-15T01:34:15Z","abstract_excerpt":"Let Y be a closed connected contact 3-manifold. 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