{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MPQXRT7E4CJUI76ZEV26GOSQE4","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":"5b8fd189dd714e25215a692980188fd32c128c88f5cfa6516e775ad6a1987494","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-13T15:41:08Z","title_canon_sha256":"9b70a298f7b27879b9aaf11f9d4a1b9d22cdde4429ea9c40e2b9b9e442398c00"},"schema_version":"1.0","source":{"id":"1503.04111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04111","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04111v1","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04111","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"MPQXRT7E4CJU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MPQXRT7E4CJUI76Z","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MPQXRT7E","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:57a592be55b9244dc38147edb430ef0094ae6137c6c0c41bd788029f6d2bc045","target":"graph","created_at":"2026-05-18T01:22:21Z","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":"In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solutions to the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.","authors_text":"Maria del Mar Gonzalez, Yi Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-13T15:41:08Z","title":"Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04111","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":"sha256:5c7b5b3d2680e643d0fa3481f5f927b2748cd09dbbabf37957089ac907e40dde","target":"record","created_at":"2026-05-18T01:22:21Z","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":"5b8fd189dd714e25215a692980188fd32c128c88f5cfa6516e775ad6a1987494","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-13T15:41:08Z","title_canon_sha256":"9b70a298f7b27879b9aaf11f9d4a1b9d22cdde4429ea9c40e2b9b9e442398c00"},"schema_version":"1.0","source":{"id":"1503.04111","kind":"arxiv","version":1}},"canonical_sha256":"63e178cfe4e093447fd92575e33a50271e0072e129a7e357543fc7ab18314110","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63e178cfe4e093447fd92575e33a50271e0072e129a7e357543fc7ab18314110","first_computed_at":"2026-05-18T01:22:21.332499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:21.332499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tn8qXzQ3bbenJFqvyP49uMHZiUv56Gl70El7NF1wun9z39mZTll3janD2Z7krU+4FiL+NbXkhp3GiUYe49yUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:21.333175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c7b5b3d2680e643d0fa3481f5f927b2748cd09dbbabf37957089ac907e40dde","sha256:57a592be55b9244dc38147edb430ef0094ae6137c6c0c41bd788029f6d2bc045"],"state_sha256":"6b28cd1d1c758613ae6eb639342bbbe5f59ee5a232f3c536ac9cc37358adcc79"}