{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4F3ZYBIE3DAIU2FN6XVBBO54LM","short_pith_number":"pith:4F3ZYBIE","schema_version":"1.0","canonical_sha256":"e1779c0504d8c08a68adf5ea10bbbc5b2856e57dda0fd6b8ed088372df80a32b","source":{"kind":"arxiv","id":"1704.06908","version":1},"attestation_state":"computed","paper":{"title":"On doubly nonlocal $p$-fractional coupled elliptic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, T. Mukherjee","submitted_at":"2017-04-23T11:08:20Z","abstract_excerpt":"\\noi We study the following nonlinear system with perturbations involving p-fractional Laplacian \\begin{equation*} (P)\\left\\{ \\begin{split} (-\\De)^s_p u+ a_1(x)u|u|^{p-2} &= \\alpha(|x|^{-\\mu}*|u|^q)|u|^{q-2}u+ \\beta (|x|^{-\\mu}*|v|^q)|u|^{q-2}u+ f_1(x)\\; \\text{in}\\; \\mb R^n,\\\\ (-\\De)^s_p v+ a_2(x)v|v|^{p-2} &= \\gamma(|x|^{-\\mu}*|v|^q)|v|^{q-2}v+ \\beta (|x|^{-\\mu}*|u|^q)|v|^{q-2}v+ f_2(x)\\; \\text{in}\\; \\mb R^n, \\end{split} \\right. \\end{equation*} where $n>sp$, $0<s<1$, $p\\geq2$, $\\mu \\in (0,n)$, $\\frac{p}{2}\\left( 2-\\frac{\\mu}{n}\\right) < q <\\frac{p^*_s}{2}\\left( 2-\\frac{\\mu}{n}\\right)$, $\\alph"},"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":"1704.06908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-23T11:08:20Z","cross_cats_sorted":[],"title_canon_sha256":"51fb8f490f3bbc1b9bc8e36a57e2e5d5795cb8ed3211836e5f65877904c445c4","abstract_canon_sha256":"a196d20ccab497b0a20e125098dd4ad8bae05f9cc593de09891b7866a5d594a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:55.408136Z","signature_b64":"WmSO5xYF7/j12hSZ4hhy27kKuceCGdH36eUT2LYaV7Q8CVyuE0E7/UYF5wbgxXi5V/SdT3YauCPs+8UNfYcdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1779c0504d8c08a68adf5ea10bbbc5b2856e57dda0fd6b8ed088372df80a32b","last_reissued_at":"2026-05-18T00:45:55.407587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:55.407587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On doubly nonlocal $p$-fractional coupled elliptic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, T. Mukherjee","submitted_at":"2017-04-23T11:08:20Z","abstract_excerpt":"\\noi We study the following nonlinear system with perturbations involving p-fractional Laplacian \\begin{equation*} (P)\\left\\{ \\begin{split} (-\\De)^s_p u+ a_1(x)u|u|^{p-2} &= \\alpha(|x|^{-\\mu}*|u|^q)|u|^{q-2}u+ \\beta (|x|^{-\\mu}*|v|^q)|u|^{q-2}u+ f_1(x)\\; \\text{in}\\; \\mb R^n,\\\\ (-\\De)^s_p v+ a_2(x)v|v|^{p-2} &= \\gamma(|x|^{-\\mu}*|v|^q)|v|^{q-2}v+ \\beta (|x|^{-\\mu}*|u|^q)|v|^{q-2}v+ f_2(x)\\; \\text{in}\\; \\mb R^n, \\end{split} \\right. \\end{equation*} where $n>sp$, $0<s<1$, $p\\geq2$, $\\mu \\in (0,n)$, $\\frac{p}{2}\\left( 2-\\frac{\\mu}{n}\\right) < q <\\frac{p^*_s}{2}\\left( 2-\\frac{\\mu}{n}\\right)$, $\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06908","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":""},"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":"1704.06908","created_at":"2026-05-18T00:45:55.407656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.06908v1","created_at":"2026-05-18T00:45:55.407656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06908","created_at":"2026-05-18T00:45:55.407656+00:00"},{"alias_kind":"pith_short_12","alias_value":"4F3ZYBIE3DAI","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"4F3ZYBIE3DAIU2FN","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"4F3ZYBIE","created_at":"2026-05-18T12:30:58.224056+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM","json":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM.json","graph_json":"https://pith.science/api/pith-number/4F3ZYBIE3DAIU2FN6XVBBO54LM/graph.json","events_json":"https://pith.science/api/pith-number/4F3ZYBIE3DAIU2FN6XVBBO54LM/events.json","paper":"https://pith.science/paper/4F3ZYBIE"},"agent_actions":{"view_html":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM","download_json":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM.json","view_paper":"https://pith.science/paper/4F3ZYBIE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.06908&json=true","fetch_graph":"https://pith.science/api/pith-number/4F3ZYBIE3DAIU2FN6XVBBO54LM/graph.json","fetch_events":"https://pith.science/api/pith-number/4F3ZYBIE3DAIU2FN6XVBBO54LM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM/action/storage_attestation","attest_author":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM/action/author_attestation","sign_citation":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM/action/citation_signature","submit_replication":"https://pith.science/pith/4F3ZYBIE3DAIU2FN6XVBBO54LM/action/replication_record"}},"created_at":"2026-05-18T00:45:55.407656+00:00","updated_at":"2026-05-18T00:45:55.407656+00:00"}