{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:23MK23OC4MCP7EUFSQSER2IB52","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":"872d34472476e9e17655c897bddadaaf78254d2900b624c089eea29f11157414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-30T14:41:27Z","title_canon_sha256":"1f36b5b697a04e7cad80e4da7e52c5aae1980f20e0aa0ae59659338cfab3008d"},"schema_version":"1.0","source":{"id":"2208.00236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.00236","created_at":"2026-07-05T04:44:49Z"},{"alias_kind":"arxiv_version","alias_value":"2208.00236v1","created_at":"2026-07-05T04:44:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.00236","created_at":"2026-07-05T04:44:49Z"},{"alias_kind":"pith_short_12","alias_value":"23MK23OC4MCP","created_at":"2026-07-05T04:44:49Z"},{"alias_kind":"pith_short_16","alias_value":"23MK23OC4MCP7EUF","created_at":"2026-07-05T04:44:49Z"},{"alias_kind":"pith_short_8","alias_value":"23MK23OC","created_at":"2026-07-05T04:44:49Z"}],"graph_snapshots":[{"event_id":"sha256:5bf9cda0fb26034ad550e12b3c807dd69af4f1eb008804912ee6de1c07978cca","target":"graph","created_at":"2026-07-05T04:44:49Z","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/2208.00236/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the nonlinear Choquard equation \\begin{eqnarray*} \\Delta^{2}u-\\Delta u+(1+\\lambda a(x))u=(R_{\\alpha}\\ast|u|^{p})|u|^{p-2}u \\end{eqnarray*} on a Cayley graph of a discrete group of polynomial growth with the homogeneous dimension $N\\geq 2$, where $\\alpha\\in(0,N),\\,p>\\frac{N+\\alpha}{N},\\,\\lambda$ is a positive parameter and $R_\\alpha$ stands for the Green's function of the discrete fractional Laplacian, which has same asymptotics as the Riesz potential. Under some assumptions on $a(x)$, we establish the existence and asymptotic behavior of ground state solutions for the n","authors_text":"Lidan Wang, Ruowei Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-30T14:41:27Z","title":"The existence and convergence of solutions for the nonlinear Choquard equations on groups of polynomial growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.00236","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":"sha256:6804a88cd1d1efab9a409882e3c50abf8172ef16f346512ba48578c99653c1ae","target":"record","created_at":"2026-07-05T04:44:49Z","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":"872d34472476e9e17655c897bddadaaf78254d2900b624c089eea29f11157414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-30T14:41:27Z","title_canon_sha256":"1f36b5b697a04e7cad80e4da7e52c5aae1980f20e0aa0ae59659338cfab3008d"},"schema_version":"1.0","source":{"id":"2208.00236","kind":"arxiv","version":1}},"canonical_sha256":"d6d8ad6dc2e304ff9285942448e901eeba879b61ab5ac9693a4213c6e1f670cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6d8ad6dc2e304ff9285942448e901eeba879b61ab5ac9693a4213c6e1f670cb","first_computed_at":"2026-07-05T04:44:49.322365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:44:49.322365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M20TVbdvFoFsX2sgNZhR9FUBHaCm5fnMsePiIQY8UsVZtErs6gX1jKCCjkDUaQxyXmnXZrE7f6Q0PbCwG7bwBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:44:49.322762Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.00236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6804a88cd1d1efab9a409882e3c50abf8172ef16f346512ba48578c99653c1ae","sha256:5bf9cda0fb26034ad550e12b3c807dd69af4f1eb008804912ee6de1c07978cca"],"state_sha256":"c8de941ecaeaa2944cb2b43721c4d7fde8a59c0f620e288a17f846735c57a2dc"}