{"paper":{"title":"Parity-violating spatially covariant gravity at total derivative order $d=5$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Jin-Jian Song, Xian Gao","submitted_at":"2026-07-22T16:04:07Z","abstract_excerpt":"We extend the polynomial construction of parity-violating spatially covariant gravity (SCG) to total derivative order $d=5$, where $d=d_{\\mathrm{t}}+d_{\\mathrm{s}}$ counts the total number of temporal and spatial derivatives. After organizing the monomials by $(d_{\\mathrm{t}},d_{\\mathrm{s}})$ and reducing them using integrations by parts, tensor symmetries, three-dimensional curvature identities, the Schouten identity, and the Cayley-Hamilton relation, we obtain a $59$-element basis: $2$, $40$, and $17$ monomials in the sectors $(0,5)$, $(2,3)$, and $(4,1)$, respectively. A direct inspection s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20317","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.20317/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}