{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QPNXN34JPMFBY3CHLXG7IVHET5","short_pith_number":"pith:QPNXN34J","schema_version":"1.0","canonical_sha256":"83db76ef897b0a1c6c475dcdf454e49f6ccbddc3e44d2077d0425c3a75dda424","source":{"kind":"arxiv","id":"1010.2387","version":1},"attestation_state":"computed","paper":{"title":"Solutions of quasi-linear wave equations polyhomogeneous at null infinity in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Piotr T. Chru\\'sciel, Roger Tagne Wafo","submitted_at":"2010-10-12T13:35:11Z","abstract_excerpt":"We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in space-time dimensions $n+1\\ge 7$. Similarly we prove propagation of polyhomogeneity in dimensions $n+1\\ge 9$. As a byproduct we obtain, in those last dimensions, polyhomogeneity at null infinity of small data solutions of vacuum Einstein, or Einstein-Maxwell equations evolving out of initial data which are stationary outside of a ball."},"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":"1010.2387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-12T13:35:11Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"1e350b8e909d99700458c03262a3ec81c4427597cfe281a586cff654cceaa6c4","abstract_canon_sha256":"8eab1b96b221aad961be2413f15d2695345ad5ae278958a81ecc62c93155e6fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:28.107672Z","signature_b64":"z7skKsaAKj+BtK36sY9y95cNKMVTgVBDtndkV3evwU5XOGu4gSvjb6VRQDHs+eFFtnosVk3i+2jdI+wvo8S2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83db76ef897b0a1c6c475dcdf454e49f6ccbddc3e44d2077d0425c3a75dda424","last_reissued_at":"2026-05-18T04:39:28.107111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:28.107111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solutions of quasi-linear wave equations polyhomogeneous at null infinity in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Piotr T. Chru\\'sciel, Roger Tagne Wafo","submitted_at":"2010-10-12T13:35:11Z","abstract_excerpt":"We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in space-time dimensions $n+1\\ge 7$. Similarly we prove propagation of polyhomogeneity in dimensions $n+1\\ge 9$. As a byproduct we obtain, in those last dimensions, polyhomogeneity at null infinity of small data solutions of vacuum Einstein, or Einstein-Maxwell equations evolving out of initial data which are stationary outside of a ball."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2387","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":""},"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":"1010.2387","created_at":"2026-05-18T04:39:28.107210+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.2387v1","created_at":"2026-05-18T04:39:28.107210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2387","created_at":"2026-05-18T04:39:28.107210+00:00"},{"alias_kind":"pith_short_12","alias_value":"QPNXN34JPMFB","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"QPNXN34JPMFBY3CH","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"QPNXN34J","created_at":"2026-05-18T12:26:12.377268+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5","json":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5.json","graph_json":"https://pith.science/api/pith-number/QPNXN34JPMFBY3CHLXG7IVHET5/graph.json","events_json":"https://pith.science/api/pith-number/QPNXN34JPMFBY3CHLXG7IVHET5/events.json","paper":"https://pith.science/paper/QPNXN34J"},"agent_actions":{"view_html":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5","download_json":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5.json","view_paper":"https://pith.science/paper/QPNXN34J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.2387&json=true","fetch_graph":"https://pith.science/api/pith-number/QPNXN34JPMFBY3CHLXG7IVHET5/graph.json","fetch_events":"https://pith.science/api/pith-number/QPNXN34JPMFBY3CHLXG7IVHET5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5/action/storage_attestation","attest_author":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5/action/author_attestation","sign_citation":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5/action/citation_signature","submit_replication":"https://pith.science/pith/QPNXN34JPMFBY3CHLXG7IVHET5/action/replication_record"}},"created_at":"2026-05-18T04:39:28.107210+00:00","updated_at":"2026-05-18T04:39:28.107210+00:00"}