{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EIDIH23DOAAUZLTJJET5T6SRZ6","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":"01105cbbd5b75abdaa2ff39faef6aba09b8305554d4af33cb2f18e685480020c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-10T11:07:30Z","title_canon_sha256":"f8b6ead9fd949de3f5e5c2c0464e050e46bfd1746ddeeea638582aa7744917de"},"schema_version":"1.0","source":{"id":"1503.02862","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02862","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02862v1","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02862","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"EIDIH23DOAAU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EIDIH23DOAAUZLTJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EIDIH23D","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:253e36eccfb08e3ed072e4882c463dccfddb5696aaed367598141c17d61fda50","target":"graph","created_at":"2026-05-18T02:25:12Z","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 prove some existence results for the fractional Yamabe problem in the case that the boundary manifold is umbilic, thus covering some of the cases not considered by Gonzalez and Qing. These are inspired by the work of Coda-Marques on the boundary Yamabe problem but, in addition, a careful understanding of the behavior at infinity for asymptotically hyperbolic metrics is required.","authors_text":"Maria del Mar Gonzalez, Meng Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-10T11:07:30Z","title":"Further results on the fractional Yamabe problem: the umbilic case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02862","kind":"arxiv","version":1},"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":"sha256:558b1423a7c1d59b174fa2c463d824cb1adbe39ae315a26b191ab77fcd2058e5","target":"record","created_at":"2026-05-18T02:25:12Z","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":"01105cbbd5b75abdaa2ff39faef6aba09b8305554d4af33cb2f18e685480020c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-10T11:07:30Z","title_canon_sha256":"f8b6ead9fd949de3f5e5c2c0464e050e46bfd1746ddeeea638582aa7744917de"},"schema_version":"1.0","source":{"id":"1503.02862","kind":"arxiv","version":1}},"canonical_sha256":"220683eb6370014cae694927d9fa51cfa69b4e26a98b2d24d703da75df92d1b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"220683eb6370014cae694927d9fa51cfa69b4e26a98b2d24d703da75df92d1b3","first_computed_at":"2026-05-18T02:25:12.909924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:12.909924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qHWjt1rj6T8sGWdXkibFU80oN9WyxgNUwes+XC0SQxdQuR9Q3pQDPu25ZOtICqOY1q085ThzEH/XIiH1vvLHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:12.910447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:558b1423a7c1d59b174fa2c463d824cb1adbe39ae315a26b191ab77fcd2058e5","sha256:253e36eccfb08e3ed072e4882c463dccfddb5696aaed367598141c17d61fda50"],"state_sha256":"af58615dc85813d303a470f85278f4dd61380b20cd7be08dde933617dc59d408"}