{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:23MK23OC4MCP7EUFSQSER2IB52","short_pith_number":"pith:23MK23OC","schema_version":"1.0","canonical_sha256":"d6d8ad6dc2e304ff9285942448e901eeba879b61ab5ac9693a4213c6e1f670cb","source":{"kind":"arxiv","id":"2208.00236","version":1},"attestation_state":"computed","paper":{"title":"The existence and convergence of solutions for the nonlinear Choquard equations on groups of polynomial growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lidan Wang, Ruowei Li","submitted_at":"2022-07-30T14:41:27Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2208.00236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-30T14:41:27Z","cross_cats_sorted":[],"title_canon_sha256":"1f36b5b697a04e7cad80e4da7e52c5aae1980f20e0aa0ae59659338cfab3008d","abstract_canon_sha256":"872d34472476e9e17655c897bddadaaf78254d2900b624c089eea29f11157414"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:49.322762Z","signature_b64":"M20TVbdvFoFsX2sgNZhR9FUBHaCm5fnMsePiIQY8UsVZtErs6gX1jKCCjkDUaQxyXmnXZrE7f6Q0PbCwG7bwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6d8ad6dc2e304ff9285942448e901eeba879b61ab5ac9693a4213c6e1f670cb","last_reissued_at":"2026-07-05T04:44:49.322365Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:49.322365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The existence and convergence of solutions for the nonlinear Choquard equations on groups of polynomial growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lidan Wang, Ruowei Li","submitted_at":"2022-07-30T14:41:27Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.00236","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.00236/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2208.00236","created_at":"2026-07-05T04:44:49.322424+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.00236v1","created_at":"2026-07-05T04:44:49.322424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.00236","created_at":"2026-07-05T04:44:49.322424+00:00"},{"alias_kind":"pith_short_12","alias_value":"23MK23OC4MCP","created_at":"2026-07-05T04:44:49.322424+00:00"},{"alias_kind":"pith_short_16","alias_value":"23MK23OC4MCP7EUF","created_at":"2026-07-05T04:44:49.322424+00:00"},{"alias_kind":"pith_short_8","alias_value":"23MK23OC","created_at":"2026-07-05T04:44:49.322424+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.22552","citing_title":"Positive solutions to fractional $p$-Laplacian Choquard equation on lattice graphs","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52","json":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52.json","graph_json":"https://pith.science/api/pith-number/23MK23OC4MCP7EUFSQSER2IB52/graph.json","events_json":"https://pith.science/api/pith-number/23MK23OC4MCP7EUFSQSER2IB52/events.json","paper":"https://pith.science/paper/23MK23OC"},"agent_actions":{"view_html":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52","download_json":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52.json","view_paper":"https://pith.science/paper/23MK23OC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.00236&json=true","fetch_graph":"https://pith.science/api/pith-number/23MK23OC4MCP7EUFSQSER2IB52/graph.json","fetch_events":"https://pith.science/api/pith-number/23MK23OC4MCP7EUFSQSER2IB52/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52/action/timestamp_anchor","attest_storage":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52/action/storage_attestation","attest_author":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52/action/author_attestation","sign_citation":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52/action/citation_signature","submit_replication":"https://pith.science/pith/23MK23OC4MCP7EUFSQSER2IB52/action/replication_record"}},"created_at":"2026-07-05T04:44:49.322424+00:00","updated_at":"2026-07-05T04:44:49.322424+00:00"}