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Such a situation arises generically in bimetric or massive gravity (including the recently discussed version of de Rham, Gabadadze and Tolley), as well as in perturbative quantum gravity where one vielbein parametrizes the background space-time and the other the dynamical degrees of freedom. We determine the conditions under which the relation $g^{\\mu\\nu} E^{A}{}_{\\mu} L^{B}{}_{\\nu} = g^{\\mu\\nu} E^{B}{}_{\\mu} L^{A}{}_{\\nu}$ can be"},"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":"1208.4493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-08-22T13:11:33Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4ac5a2e8a6d845a3509e910da4f1eb106d780cba8d488904c5256999489c2e07","abstract_canon_sha256":"ade5fbdf06247919d52f63d3ae20d327444b384d339a0d8012db4452bf70ea3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:59.691889Z","signature_b64":"Hg3NhiBZg4fy1JWKrtexKpxhGW0ZabboU/Q+Y17NN2d88z+fMKK9MKI0umABECdw5JEOag3RfVwE+z9ecD0QDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65cad2151bddb2a383cec2cfc235ac1acc01539b7663ecc1ae4a34312393b89d","last_reissued_at":"2026-05-18T01:54:59.691143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:59.691143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on \"symmetric\" vielbeins in bimetric, massive, perturbative and non perturbative gravities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Cedric Deffayet, George Zahariade, Jihad Mourad","submitted_at":"2012-08-22T13:11:33Z","abstract_excerpt":"We consider a manifold endowed with two different vielbeins $E^{A}{}_{\\mu}$ and $L^{A}{}_{\\mu}$ corresponding to two different metrics $g_{\\mu\\nu}$ and $f_{\\mu\\nu}$. 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