{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6LZ4KHB3CJJWOXBXMDBFGQ3T6Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0af1f3906c979e137859f7a375049552be33c501df8e882c2bfd7057b5dd7163","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-12-10T12:17:17Z","title_canon_sha256":"4a2f16ca740e38f0d04335c56c1ac3ab17fc4ae4267e9cdb5aba576e8d098e24"},"schema_version":"1.0","source":{"id":"1012.2246","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2246","created_at":"2026-05-18T02:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2246v2","created_at":"2026-05-18T02:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2246","created_at":"2026-05-18T02:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"6LZ4KHB3CJJW","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6LZ4KHB3CJJWOXBX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6LZ4KHB3","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:ccab71536337ef0d6a2dc98cf0226fed44f819393efaec8fa6940e49fd6da0b0","target":"graph","created_at":"2026-05-18T02:04:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain exponent appearing in the equations, constructing solutions of these sub-critical equations and then in letting the exponent tend to its true value. We prove that the solutions of the sub-critical equations remain bounded which yields solutions of the constraint equation unless a certain limit equation admits a non-trivial solution. Finally, we give conditions which ensure that the limit equation admit","authors_text":"Anna Sakovich, Romain Gicquaud","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-12-10T12:17:17Z","title":"A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2246","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9a9c8275a5ab488bb57168827d4a15aa9965b485ce6f620d2e3820f2e2c1815b","target":"record","created_at":"2026-05-18T02:04:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0af1f3906c979e137859f7a375049552be33c501df8e882c2bfd7057b5dd7163","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-12-10T12:17:17Z","title_canon_sha256":"4a2f16ca740e38f0d04335c56c1ac3ab17fc4ae4267e9cdb5aba576e8d098e24"},"schema_version":"1.0","source":{"id":"1012.2246","kind":"arxiv","version":2}},"canonical_sha256":"f2f3c51c3b1253675c3760c2534373f42bc9e59217151f8433a511f2912e4301","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2f3c51c3b1253675c3760c2534373f42bc9e59217151f8433a511f2912e4301","first_computed_at":"2026-05-18T02:04:30.613799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:30.613799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4pF8/jQb950Lky1IH4WYKrY0obYLgCEgHvXrHM1QchpOYH0tYP3Bvmz1zMMHWzxf95jfMSh2YtXMBonevUqkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:30.616701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2246","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a9c8275a5ab488bb57168827d4a15aa9965b485ce6f620d2e3820f2e2c1815b","sha256:ccab71536337ef0d6a2dc98cf0226fed44f819393efaec8fa6940e49fd6da0b0"],"state_sha256":"e7bc27d664a98f041e26618c19e39b39f33ef541fbc6a3e347e570d1fb7b9c69"}