{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LIVQOBRYZK4I74UCC4UF5AJYNQ","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":"1d57574c79a5e806744d75ae6ded011a07d73af1555d959f9e96a5eefe3a47a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T04:16:56Z","title_canon_sha256":"8d8343f022ecad4a0b65349e831acaaddcc5a54fd025fdbe2d876fafd060f648"},"schema_version":"1.0","source":{"id":"2411.14719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14719","created_at":"2026-05-20T00:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14719v2","created_at":"2026-05-20T00:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14719","created_at":"2026-05-20T00:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"LIVQOBRYZK4I","created_at":"2026-05-20T00:00:16Z"},{"alias_kind":"pith_short_16","alias_value":"LIVQOBRYZK4I74UC","created_at":"2026-05-20T00:00:16Z"},{"alias_kind":"pith_short_8","alias_value":"LIVQOBRY","created_at":"2026-05-20T00:00:16Z"}],"graph_snapshots":[{"event_id":"sha256:a0bc1e3137d8eb413f225c012bbc0ee1de1fa3843bf27af12479ef3035389195","target":"graph","created_at":"2026-05-20T00:00:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.14719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the higher-order Schr\\\"odinger equation with critical Sobolev exponent on the hyperbolic space $\\mathbb{H}^n$: $$P_m u + a(x)\\,u = |u|^{q-2}u, \\quad u \\in D^{m,2}(\\mathbb{H}^n),$$ where $P_m$ is the GJMS operator of order $2m$, $q = \\frac{2n}{n-2m}$ is the critical exponent, and $a(x) \\geq 0$ is a potential in $L^{n/2m}(\\mathbb{H}^n)$. This problem simultaneously generalizes the classical work of Benci--Cerami from second-order to arbitrary order and from Euclidean space to hyperbolic space.\n  We establish a global compactness theorem (profile decomposition) for Palais--Smale sequence","authors_text":"Jungang Li, Zhiwei Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T04:16:56Z","title":"Global Compactness and Existence for Higher Order Critical Equations on Hyperbolic Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14719","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:c73105344b34a1ac150f18656384fc02463356c526dc52c4629c6c1777d595d4","target":"record","created_at":"2026-05-20T00:00:16Z","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":"1d57574c79a5e806744d75ae6ded011a07d73af1555d959f9e96a5eefe3a47a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T04:16:56Z","title_canon_sha256":"8d8343f022ecad4a0b65349e831acaaddcc5a54fd025fdbe2d876fafd060f648"},"schema_version":"1.0","source":{"id":"2411.14719","kind":"arxiv","version":2}},"canonical_sha256":"5a2b070638cab88ff28217285e81386c30daafd24b342709ea61dce7e338c42b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a2b070638cab88ff28217285e81386c30daafd24b342709ea61dce7e338c42b","first_computed_at":"2026-05-20T00:00:16.754807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:16.754807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dodx6Lr2Se3W7WWDW5+cUNmJxpKmHq8d1kY8nMlNlACDHO0DHe5aJCgiFY1iRaJXIbFr/5rho4xY87X0t3dPDA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:16.755668Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c73105344b34a1ac150f18656384fc02463356c526dc52c4629c6c1777d595d4","sha256:a0bc1e3137d8eb413f225c012bbc0ee1de1fa3843bf27af12479ef3035389195"],"state_sha256":"1969ccd8bfe7393c20eb9968f18a1c1df2d6b1b01deb53c07956fa4873604d60"}