{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:IW45T3IIQFLMWVUTNJ2KEAKOIJ","short_pith_number":"pith:IW45T3II","schema_version":"1.0","canonical_sha256":"45b9d9ed088156cb56936a74a2014e427826492bc9af65787fb1b1e356b9847d","source":{"kind":"arxiv","id":"2310.08611","version":1},"attestation_state":"computed","paper":{"title":"Energy estimates for the Einstein-Yang-Mills fields and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"math.AP","authors_text":"Sari Ghanem","submitted_at":"2023-10-12T00:57:19Z","abstract_excerpt":"We prove exterior energy estimates for tensorial non-linear wave equations, where the background metric is a perturbation of the Minkowski space-time, and where the derivatives are the Minkowski covariant derivatives. We obtain bounds in the exterior region of the Minkowski space-time, for the weighted $L^2$ norm on each component, separately, of the covariant derivative of the tensorial solutions, and we also control a space-time integral in the exterior of the covariant tangential derivatives of the solutions. As a special application, we use here these energy estimates to prove the exterior"},"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":"2310.08611","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-10-12T00:57:19Z","cross_cats_sorted":["gr-qc","math.DG"],"title_canon_sha256":"da45ebe1b1bd1de81199024ab313622ca5206a05e79470a2943b41bd20ce1f2d","abstract_canon_sha256":"a2c20e9c375d97d6c3ddf5997ee947f67f3108682ab312d8732aedc9e616d245"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:00:30.777773Z","signature_b64":"n2jXQqJrf2re0BzXycs/YhuHpZN3eQYU4wfH9/99vGBLktuyvuvH8SPeHOjvRTzYof214MYHLVm1KiF51IbdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45b9d9ed088156cb56936a74a2014e427826492bc9af65787fb1b1e356b9847d","last_reissued_at":"2026-07-05T07:00:30.777296Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:00:30.777296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy estimates for the Einstein-Yang-Mills fields and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"math.AP","authors_text":"Sari Ghanem","submitted_at":"2023-10-12T00:57:19Z","abstract_excerpt":"We prove exterior energy estimates for tensorial non-linear wave equations, where the background metric is a perturbation of the Minkowski space-time, and where the derivatives are the Minkowski covariant derivatives. We obtain bounds in the exterior region of the Minkowski space-time, for the weighted $L^2$ norm on each component, separately, of the covariant derivative of the tensorial solutions, and we also control a space-time integral in the exterior of the covariant tangential derivatives of the solutions. As a special application, we use here these energy estimates to prove the exterior"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.08611","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/2310.08611/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":"2310.08611","created_at":"2026-07-05T07:00:30.777466+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.08611v1","created_at":"2026-07-05T07:00:30.777466+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.08611","created_at":"2026-07-05T07:00:30.777466+00:00"},{"alias_kind":"pith_short_12","alias_value":"IW45T3IIQFLM","created_at":"2026-07-05T07:00:30.777466+00:00"},{"alias_kind":"pith_short_16","alias_value":"IW45T3IIQFLMWVUT","created_at":"2026-07-05T07:00:30.777466+00:00"},{"alias_kind":"pith_short_8","alias_value":"IW45T3II","created_at":"2026-07-05T07:00:30.777466+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.00071","citing_title":"Overview of the proof of the exterior stability of the $(1+3)$-Minkowski space-time governed by the Einstein-Yang-Mills system in the Lorenz gauge","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ","json":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ.json","graph_json":"https://pith.science/api/pith-number/IW45T3IIQFLMWVUTNJ2KEAKOIJ/graph.json","events_json":"https://pith.science/api/pith-number/IW45T3IIQFLMWVUTNJ2KEAKOIJ/events.json","paper":"https://pith.science/paper/IW45T3II"},"agent_actions":{"view_html":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ","download_json":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ.json","view_paper":"https://pith.science/paper/IW45T3II","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.08611&json=true","fetch_graph":"https://pith.science/api/pith-number/IW45T3IIQFLMWVUTNJ2KEAKOIJ/graph.json","fetch_events":"https://pith.science/api/pith-number/IW45T3IIQFLMWVUTNJ2KEAKOIJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ/action/storage_attestation","attest_author":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ/action/author_attestation","sign_citation":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ/action/citation_signature","submit_replication":"https://pith.science/pith/IW45T3IIQFLMWVUTNJ2KEAKOIJ/action/replication_record"}},"created_at":"2026-07-05T07:00:30.777466+00:00","updated_at":"2026-07-05T07:00:30.777466+00:00"}