{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:VJSBAXEDNT267K2HUKN6VHFQ7V","short_pith_number":"pith:VJSBAXED","schema_version":"1.0","canonical_sha256":"aa64105c836cf5efab47a29bea9cb0fd64d20fb4a4c32f559f946f7e7b0933ad","source":{"kind":"arxiv","id":"0912.0481","version":1},"attestation_state":"computed","paper":{"title":"Vector theories in cosmology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"gr-qc","authors_text":"Cyril Pitrou, Gilles Esposito-Farese, Jean-Philippe Uzan","submitted_at":"2009-12-02T18:14:48Z","abstract_excerpt":"This article provides a general study of the Hamiltonian stability and the hyperbolicity of vector field models involving both a general function of the Faraday tensor and its dual, $f(F^2,F\\tilde F)$, as well as a Proca potential for the vector field, $V(A^2)$. In particular it is demonstrated that theories involving only $f(F^2)$ do not satisfy the hyperbolicity conditions. It is then shown that in this class of models, the cosmological dynamics always dilutes the vector field. In the case of a nonminimal coupling to gravity, it is established that theories involving $R f(A^2)$ or $Rf(F^2)$ "},"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":"0912.0481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-12-02T18:14:48Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"c25e6eb59c2d30ae13a1e4e91ecff581eb1570009440b8f6e54dc9611a23adad","abstract_canon_sha256":"f44e5be2d2b48b43580d12b5050be8bcea586d5a096f928fa0b520ffb319e935"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:27:29.198478Z","signature_b64":"aK4snWHtkWGA4de4x8jSapfnMMnlFK3rA+vI0yherHDSB/g9OZch1SQXwjwUJHaOQK+uGXFQKMXtYgIOAZeyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa64105c836cf5efab47a29bea9cb0fd64d20fb4a4c32f559f946f7e7b0933ad","last_reissued_at":"2026-07-04T17:27:29.198044Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:27:29.198044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vector theories in cosmology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"gr-qc","authors_text":"Cyril Pitrou, Gilles Esposito-Farese, Jean-Philippe Uzan","submitted_at":"2009-12-02T18:14:48Z","abstract_excerpt":"This article provides a general study of the Hamiltonian stability and the hyperbolicity of vector field models involving both a general function of the Faraday tensor and its dual, $f(F^2,F\\tilde F)$, as well as a Proca potential for the vector field, $V(A^2)$. In particular it is demonstrated that theories involving only $f(F^2)$ do not satisfy the hyperbolicity conditions. It is then shown that in this class of models, the cosmological dynamics always dilutes the vector field. In the case of a nonminimal coupling to gravity, it is established that theories involving $R f(A^2)$ or $Rf(F^2)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0481","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/0912.0481/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0912.0481","created_at":"2026-07-04T17:27:29.198111+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.0481v1","created_at":"2026-07-04T17:27:29.198111+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0481","created_at":"2026-07-04T17:27:29.198111+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJSBAXEDNT26","created_at":"2026-07-04T17:27:29.198111+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJSBAXEDNT267K2H","created_at":"2026-07-04T17:27:29.198111+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJSBAXED","created_at":"2026-07-04T17:27:29.198111+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2606.23731","citing_title":"Potentially healthy time evolution in interacting $p$-form fields","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2512.04349","citing_title":"Cosmological implications of Bumblebee theory on an FLRW background","ref_index":43,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V","json":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V.json","graph_json":"https://pith.science/api/pith-number/VJSBAXEDNT267K2HUKN6VHFQ7V/graph.json","events_json":"https://pith.science/api/pith-number/VJSBAXEDNT267K2HUKN6VHFQ7V/events.json","paper":"https://pith.science/paper/VJSBAXED"},"agent_actions":{"view_html":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V","download_json":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V.json","view_paper":"https://pith.science/paper/VJSBAXED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.0481&json=true","fetch_graph":"https://pith.science/api/pith-number/VJSBAXEDNT267K2HUKN6VHFQ7V/graph.json","fetch_events":"https://pith.science/api/pith-number/VJSBAXEDNT267K2HUKN6VHFQ7V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V/action/storage_attestation","attest_author":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V/action/author_attestation","sign_citation":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V/action/citation_signature","submit_replication":"https://pith.science/pith/VJSBAXEDNT267K2HUKN6VHFQ7V/action/replication_record"}},"created_at":"2026-07-04T17:27:29.198111+00:00","updated_at":"2026-07-04T17:27:29.198111+00:00"}