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\\text{in}\\; \\Omega\n  (-\\Delta)^sv &= \\delta |v|^{q-2}v + \\left(\\int_{\\Om}\\frac{|u(y)|^{2^*_\\mu}}{|x-y|^\\mu}~\\mathrm{d}y \\right) |v|^{2^*_\\mu-2}v \\; \\text{in}\\; \\Omega\n  u &=v=0\\; \\text{in}\\; \\mb R^n\\setminus\\Omega, \\end{spl"},"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":"1711.02835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-08T05:21:04Z","cross_cats_sorted":[],"title_canon_sha256":"7ec661a1f4c58f4e50555e62cd888ded5678760262fa5b1dcdc6599254a72907","abstract_canon_sha256":"1729dd3710a391ddf308c288c3aaae9c8b4c5bf1cc4099925836f41f0c8c52ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:01.557876Z","signature_b64":"UL29Xr29rWEpx+wle6xkuMlESzT1Sh/7yaH5H3KLF/DQn9a3IzGR4Ow7giO9+dex3w0H8WN/ad5jUb5bBSKwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beae573dbd4b60e47ac656e6129607c8bb62cd7db432bf391cb1860aca2a3a07","last_reissued_at":"2026-05-18T00:31:01.556453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:01.556453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Doubly nonlocal system with Hardy-Littlewood-Sobolev critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J.Giacomoni, K.Sreenadh, Tuhina Mukherjee","submitted_at":"2017-11-08T05:21:04Z","abstract_excerpt":"This article concerns about the existence and multiplicity of weak solutions for the following nonlinear doubly nonlocal problem with critical nonlinearity in the sense of Hardy-Littlewood-Sobolev inequality \\begin{equation*} \\left\\{ \\begin{split} (-\\Delta)^su &= \\lambda |u|^{q-2}u + \\left(\\int_{\\Omega}\\frac{|v(y)|^{2^*_\\mu}}{|x-y|^\\mu}~\\mathrm{d}y\\right) |u|^{2^*_\\mu-2}u\\; \\text{in}\\; \\Omega\n  (-\\Delta)^sv &= \\delta |v|^{q-2}v + \\left(\\int_{\\Om}\\frac{|u(y)|^{2^*_\\mu}}{|x-y|^\\mu}~\\mathrm{d}y \\right) |v|^{2^*_\\mu-2}v \\; \\text{in}\\; \\Omega\n  u &=v=0\\; \\text{in}\\; \\mb R^n\\setminus\\Omega, \\end{spl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02835","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":"1711.02835","created_at":"2026-05-18T00:31:01.556562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.02835v1","created_at":"2026-05-18T00:31:01.556562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02835","created_at":"2026-05-18T00:31:01.556562+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2XFOPN5JNQO","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2XFOPN5JNQOI6WG","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2XFOPN5","created_at":"2026-05-18T12:31:53.515858+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/X2XFOPN5JNQOI6WGK3TBFFQHZC","json":"https://pith.science/pith/X2XFOPN5JNQOI6WGK3TBFFQHZC.json","graph_json":"https://pith.science/api/pith-number/X2XFOPN5JNQOI6WGK3TBFFQHZC/graph.json","events_json":"https://pith.science/api/pith-number/X2XFOPN5JNQOI6WGK3TBFFQHZC/events.json","paper":"https://pith.science/paper/X2XFOPN5"},"agent_actions":{"view_html":"https://pith.science/pith/X2XFOPN5JNQOI6WGK3TBFFQHZC","download_json":"https://pith.science/pith/X2XFOPN5JNQOI6WGK3TBFFQHZC.json","view_paper":"https://pith.science/paper/X2XFOPN5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.02835&json=true","fetch_graph":"https://pith.science/api/pith-number/X2XFOPN5JNQOI6WGK3TBFFQHZC/graph.json","fetch_events":"https://pith.science/api/pith-number/X2XFOPN5JNQOI6WGK3TBFFQHZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2XFOPN5JNQOI6WGK3TBFFQHZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2XFOPN5JNQOI6WGK3TBFFQHZC/action/storage_attestation","attest_author":"https://pith.science/pith/X2XFOPN5JNQOI6WGK3TBFFQHZC/action/author_attestation","sign_citation":"https://pith.science/pith/X2XFOPN5JNQOI6WGK3TBFFQHZC/action/citation_signature","submit_replication":"https://pith.science/pith/X2XFOPN5JNQOI6WGK3TBFFQHZC/action/replication_record"}},"created_at":"2026-05-18T00:31:01.556562+00:00","updated_at":"2026-05-18T00:31:01.556562+00:00"}