{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RTFFXCPZW6XD37TPR4QFFMMOSL","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":"a2a9269d6e031469c31dd737f923cfd6c40c86ca118b0e59a2827cedf342ac2c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-23T05:07:47Z","title_canon_sha256":"019f9f17ec18ab2b32f0c4b226921c07a770f87d3551b5388274505ef7aa7c59"},"schema_version":"1.0","source":{"id":"1605.06896","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06896","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06896v3","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06896","created_at":"2026-05-18T00:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"RTFFXCPZW6XD","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RTFFXCPZW6XD37TP","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RTFFXCPZ","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:fd8bdfb1df6cffdfc45166e740d0b2770a37799bee7d6214e036504c7cc4cd17","target":"graph","created_at":"2026-05-18T00:42:39Z","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":"In this article, we first employ the concentration compactness techniques to prove existence and stability results of standing waves for nonlinear fractional Schr\\\"{o}dinger-Choquard equation \\[ i\\partial_t\\Psi + (-\\Delta)^{\\alpha}\\Psi = a |\\Psi|^{s-2}\\Psi+\\lambda \\left( \\frac{1}{|x|^{N-\\beta}} \\star |\\Psi|^p \\right)|\\Psi|^{p-2}\\Psi\\ \\ \\ \\mathrm{in}\\ \\mathbb{R}^{N+1}, \\] where $N\\geq 2$, $\\alpha\\in (0,1)$, $\\beta\\in (0, N)$, $s\\in (2, 2+\\frac{4\\alpha}{N})$, $p\\in [2, 1+\\frac{2\\alpha+\\beta}{N})$, and the constants $a, \\lambda$ are nonnegative satisfying $a+\\lambda > 0.$ We then extend the argum","authors_text":"Santosh Bhattarai","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-23T05:07:47Z","title":"On fractional Schrodinger systems of Choquard type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06896","kind":"arxiv","version":3},"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:dad2ba3005dbc16f7c329ea0d36eb4d6fce92edeeed5f93be58a2946f6311d4a","target":"record","created_at":"2026-05-18T00:42:39Z","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":"a2a9269d6e031469c31dd737f923cfd6c40c86ca118b0e59a2827cedf342ac2c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-23T05:07:47Z","title_canon_sha256":"019f9f17ec18ab2b32f0c4b226921c07a770f87d3551b5388274505ef7aa7c59"},"schema_version":"1.0","source":{"id":"1605.06896","kind":"arxiv","version":3}},"canonical_sha256":"8cca5b89f9b7ae3dfe6f8f2052b18e92ff75a6cb6090101ab1d2eed8cf3315ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cca5b89f9b7ae3dfe6f8f2052b18e92ff75a6cb6090101ab1d2eed8cf3315ea","first_computed_at":"2026-05-18T00:42:39.509346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:39.509346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggvyQ0mCIXvzkzRn3LFjlkrxxGjc/T/letDuIjAfFx/9USY9hcAQ/aTgBR39y7RKvIx5MWVoc4llXBNNDIphDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:39.510062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06896","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dad2ba3005dbc16f7c329ea0d36eb4d6fce92edeeed5f93be58a2946f6311d4a","sha256:fd8bdfb1df6cffdfc45166e740d0b2770a37799bee7d6214e036504c7cc4cd17"],"state_sha256":"5190c0e781be01149f08c65963541b690b70b53700adbf9726ee4eb53096a168"}