{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4F3ZYBIE3DAIU2FN6XVBBO54LM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a196d20ccab497b0a20e125098dd4ad8bae05f9cc593de09891b7866a5d594a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-23T11:08:20Z","title_canon_sha256":"51fb8f490f3bbc1b9bc8e36a57e2e5d5795cb8ed3211836e5f65877904c445c4"},"schema_version":"1.0","source":{"id":"1704.06908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06908","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06908v1","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06908","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"4F3ZYBIE3DAI","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4F3ZYBIE3DAIU2FN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4F3ZYBIE","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:570f0239a9cdffbb7175e7ccc3208a7301207beac8cf8c89441df6eadcc646e2","target":"graph","created_at":"2026-05-18T00:45:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"K. Sreenadh, T. Mukherjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-23T11:08:20Z","title":"On doubly nonlocal $p$-fractional coupled elliptic system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06908","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5a7343b722619f310425e7aba0bb93e0399010faff5c3538b2137b2a46db0958","target":"record","created_at":"2026-05-18T00:45:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a196d20ccab497b0a20e125098dd4ad8bae05f9cc593de09891b7866a5d594a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-23T11:08:20Z","title_canon_sha256":"51fb8f490f3bbc1b9bc8e36a57e2e5d5795cb8ed3211836e5f65877904c445c4"},"schema_version":"1.0","source":{"id":"1704.06908","kind":"arxiv","version":1}},"canonical_sha256":"e1779c0504d8c08a68adf5ea10bbbc5b2856e57dda0fd6b8ed088372df80a32b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1779c0504d8c08a68adf5ea10bbbc5b2856e57dda0fd6b8ed088372df80a32b","first_computed_at":"2026-05-18T00:45:55.407587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:55.407587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WmSO5xYF7/j12hSZ4hhy27kKuceCGdH36eUT2LYaV7Q8CVyuE0E7/UYF5wbgxXi5V/SdT3YauCPs+8UNfYcdCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:55.408136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a7343b722619f310425e7aba0bb93e0399010faff5c3538b2137b2a46db0958","sha256:570f0239a9cdffbb7175e7ccc3208a7301207beac8cf8c89441df6eadcc646e2"],"state_sha256":"d6c78ac6a3f238276aa10ef0ca528c0958caefb3794c1f2c8058c4cea455d002"}