{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2RE35YZ7DSLV34BTVQ43BC4MSM","short_pith_number":"pith:2RE35YZ7","schema_version":"1.0","canonical_sha256":"d449bee33f1c975df033ac39b08b8c93301a2bd2b987e6832f2e58843933bbdc","source":{"kind":"arxiv","id":"2510.08947","version":4},"attestation_state":"computed","paper":{"title":"On positive solutions of Lane-Emden equations on the integer lattice graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bobo Hua, Feng Zhou, Huyuan Chen","submitted_at":"2025-10-10T02:57:53Z","abstract_excerpt":"In this paper, we investigate the existence and nonexistence of positive solutions to the Lane-Emden equations $$ -\\Delta u = Q |u|^{p-2}u $$ on the $d$-dimensional integer lattice graph $\\mathbb{Z}^d$, as well as in the half-space and quadrant domains, under the zero Dirichlet boundary condition in the latter two cases. Here, $d \\geq 2$, $p > 0$, and $Q$ denotes a Hardy-type positive potential satisfying $Q(x) \\sim (1+|x|)^{-\\alpha}$ with $\\alpha \\in [0, +\\infty]$. \\smallskip\n  We identify the Sobolev super-critical regions of the parameter pair $(\\alpha, p)$ for which the existence of positi"},"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":"2510.08947","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-10-10T02:57:53Z","cross_cats_sorted":[],"title_canon_sha256":"1b5a72c9a0fae08a8ee4106e1bc05c0882350737dc56af87a22b935a63689912","abstract_canon_sha256":"528db3f932343dc7ca5449a3d36f54c25325974553c53eae06cbcae8208602a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:14.466277Z","signature_b64":"AUhpJC4o4tLffiW39llkg4+VkhN+SFGFwgY1OTHpAlrBCb3U52W8SxiN0oCZDCpCdhMwtZtu9c19TIEbikSSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d449bee33f1c975df033ac39b08b8c93301a2bd2b987e6832f2e58843933bbdc","last_reissued_at":"2026-05-20T00:04:14.465559Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:14.465559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On positive solutions of Lane-Emden equations on the integer lattice graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bobo Hua, Feng Zhou, Huyuan Chen","submitted_at":"2025-10-10T02:57:53Z","abstract_excerpt":"In this paper, we investigate the existence and nonexistence of positive solutions to the Lane-Emden equations $$ -\\Delta u = Q |u|^{p-2}u $$ on the $d$-dimensional integer lattice graph $\\mathbb{Z}^d$, as well as in the half-space and quadrant domains, under the zero Dirichlet boundary condition in the latter two cases. Here, $d \\geq 2$, $p > 0$, and $Q$ denotes a Hardy-type positive potential satisfying $Q(x) \\sim (1+|x|)^{-\\alpha}$ with $\\alpha \\in [0, +\\infty]$. \\smallskip\n  We identify the Sobolev super-critical regions of the parameter pair $(\\alpha, p)$ for which the existence of positi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.08947","kind":"arxiv","version":4},"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/2510.08947/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":"2510.08947","created_at":"2026-05-20T00:04:14.465677+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.08947v4","created_at":"2026-05-20T00:04:14.465677+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.08947","created_at":"2026-05-20T00:04:14.465677+00:00"},{"alias_kind":"pith_short_12","alias_value":"2RE35YZ7DSLV","created_at":"2026-05-20T00:04:14.465677+00:00"},{"alias_kind":"pith_short_16","alias_value":"2RE35YZ7DSLV34BT","created_at":"2026-05-20T00:04:14.465677+00:00"},{"alias_kind":"pith_short_8","alias_value":"2RE35YZ7","created_at":"2026-05-20T00:04:14.465677+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.24932","citing_title":"Sharp Criteria for the existence of positive solutions to Lane-Emden-type inequalities on weighted graphs","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM","json":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM.json","graph_json":"https://pith.science/api/pith-number/2RE35YZ7DSLV34BTVQ43BC4MSM/graph.json","events_json":"https://pith.science/api/pith-number/2RE35YZ7DSLV34BTVQ43BC4MSM/events.json","paper":"https://pith.science/paper/2RE35YZ7"},"agent_actions":{"view_html":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM","download_json":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM.json","view_paper":"https://pith.science/paper/2RE35YZ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.08947&json=true","fetch_graph":"https://pith.science/api/pith-number/2RE35YZ7DSLV34BTVQ43BC4MSM/graph.json","fetch_events":"https://pith.science/api/pith-number/2RE35YZ7DSLV34BTVQ43BC4MSM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM/action/storage_attestation","attest_author":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM/action/author_attestation","sign_citation":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM/action/citation_signature","submit_replication":"https://pith.science/pith/2RE35YZ7DSLV34BTVQ43BC4MSM/action/replication_record"}},"created_at":"2026-05-20T00:04:14.465677+00:00","updated_at":"2026-05-20T00:04:14.465677+00:00"}