{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:IKDIG2372Q33POZJJMQPUQOFAB","short_pith_number":"pith:IKDIG237","schema_version":"1.0","canonical_sha256":"4286836b7fd437b7bb294b20fa41c5006c49187b63ee7885513e7593df24a450","source":{"kind":"arxiv","id":"2411.01256","version":1},"attestation_state":"computed","paper":{"title":"Ground states for the double weighted critical Kirchhoff equation on the unit ball in $\\mathbb{R}^3$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiabao Su, Yao Du","submitted_at":"2024-11-02T14:09:22Z","abstract_excerpt":"This paper deals with the existence of ground states for degenerative ($a=0$) and non-degenerative ($a>0$) double weighted critical Kirchhoff equation \\begin{eqnarray*} \\left\\{\n  \\begin{array}{ll} \\displaystyle-\\left(a+b\\int_B |\\nabla u|^2dx\\right)\\Delta u=|x|^{\\alpha_1} |u|^{4+2\\alpha_1}u+\\mu|x|^{\\alpha_2} |u|^{4+2\\alpha_2}u+\\lambda h(|x|) f(u) &{\\rm in}\\ B,\\\\ u=0 &{\\rm on}\\ \\partial B,\n  \\end{array} \\right. \\end{eqnarray*} where $B$ is a unit open ball in $\\mathbb{R}^3$ with center $0$, $a\\geq0, b>0, \\mu\\in \\mathbb{R}, \\lambda>0, \\alpha_1>\\alpha_2>-2$, $4+2\\alpha_i=2^*(\\alpha_i)-2\\ (i=1,2)$ "},"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":"2411.01256","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-02T14:09:22Z","cross_cats_sorted":[],"title_canon_sha256":"36f1b7ed0efbf887add11a64136a695ea1b32689d0075a3dd26879f972772e44","abstract_canon_sha256":"9b695aea0408c1111b0ffaf7f16dc88423ddaea3505645d29c4804cee2df339c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:30:27.576824Z","signature_b64":"RFF6uR/3HgpRM3NSfBcmCuDvB7H4lamVvRuQqYvyBZ6TIzbcVn900Av46o3s2C502rQvF5NqEgqIrGeRN9V9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4286836b7fd437b7bb294b20fa41c5006c49187b63ee7885513e7593df24a450","last_reissued_at":"2026-07-05T09:30:27.576352Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:30:27.576352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground states for the double weighted critical Kirchhoff equation on the unit ball in $\\mathbb{R}^3$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiabao Su, Yao Du","submitted_at":"2024-11-02T14:09:22Z","abstract_excerpt":"This paper deals with the existence of ground states for degenerative ($a=0$) and non-degenerative ($a>0$) double weighted critical Kirchhoff equation \\begin{eqnarray*} \\left\\{\n  \\begin{array}{ll} \\displaystyle-\\left(a+b\\int_B |\\nabla u|^2dx\\right)\\Delta u=|x|^{\\alpha_1} |u|^{4+2\\alpha_1}u+\\mu|x|^{\\alpha_2} |u|^{4+2\\alpha_2}u+\\lambda h(|x|) f(u) &{\\rm in}\\ B,\\\\ u=0 &{\\rm on}\\ \\partial B,\n  \\end{array} \\right. \\end{eqnarray*} where $B$ is a unit open ball in $\\mathbb{R}^3$ with center $0$, $a\\geq0, b>0, \\mu\\in \\mathbb{R}, \\lambda>0, \\alpha_1>\\alpha_2>-2$, $4+2\\alpha_i=2^*(\\alpha_i)-2\\ (i=1,2)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01256","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/2411.01256/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":"2411.01256","created_at":"2026-07-05T09:30:27.576406+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.01256v1","created_at":"2026-07-05T09:30:27.576406+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.01256","created_at":"2026-07-05T09:30:27.576406+00:00"},{"alias_kind":"pith_short_12","alias_value":"IKDIG2372Q33","created_at":"2026-07-05T09:30:27.576406+00:00"},{"alias_kind":"pith_short_16","alias_value":"IKDIG2372Q33POZJ","created_at":"2026-07-05T09:30:27.576406+00:00"},{"alias_kind":"pith_short_8","alias_value":"IKDIG237","created_at":"2026-07-05T09:30:27.576406+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.27505","citing_title":"TruEye: Fine-Grained Detection of AI-Generated Human Subjects in Images","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB","json":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB.json","graph_json":"https://pith.science/api/pith-number/IKDIG2372Q33POZJJMQPUQOFAB/graph.json","events_json":"https://pith.science/api/pith-number/IKDIG2372Q33POZJJMQPUQOFAB/events.json","paper":"https://pith.science/paper/IKDIG237"},"agent_actions":{"view_html":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB","download_json":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB.json","view_paper":"https://pith.science/paper/IKDIG237","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.01256&json=true","fetch_graph":"https://pith.science/api/pith-number/IKDIG2372Q33POZJJMQPUQOFAB/graph.json","fetch_events":"https://pith.science/api/pith-number/IKDIG2372Q33POZJJMQPUQOFAB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB/action/storage_attestation","attest_author":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB/action/author_attestation","sign_citation":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB/action/citation_signature","submit_replication":"https://pith.science/pith/IKDIG2372Q33POZJJMQPUQOFAB/action/replication_record"}},"created_at":"2026-07-05T09:30:27.576406+00:00","updated_at":"2026-07-05T09:30:27.576406+00:00"}