{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YTIEJIGJTSAL5ZWQNTCLWRUFZ5","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":"d1d2d2fc77cd30d165816878b7db031a34cde4a22a38eb4667785fbc68749763","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T15:37:20Z","title_canon_sha256":"a9f1d79663c2e0d81ee0ba711c52de69ace27b647a4a1011e5e51219af883bf3"},"schema_version":"1.0","source":{"id":"1810.04076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04076","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04076v1","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04076","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"YTIEJIGJTSAL","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YTIEJIGJTSAL5ZWQ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YTIEJIGJ","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:3141bc2bfb65e154b7e9fdb9371bdef68761c143697386fb0c1c087f005ab067","target":"graph","created_at":"2026-05-18T00:03:42Z","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":"We study the Cauchy problem for fractional Schr\\\"odinger equation with cubic convolution nonlinearity ($i\\partial_t u - (-\\Delta)^{\\frac{\\alpha}{2}}u\\pm (K\\ast |u|^2) u =0$) with Cauchy data in the modulation spaces $M^{p,q}(\\mathbb R^{d}).$ For $K(x)= |x|^{-\\gamma}$ $ (0< \\gamma< \\text{min} \\{\\alpha, d/2\\})$, we establish global well-posedness results in $M^{p,q}(\\mathbb R^{d}) (1\\leq p \\leq 2, 1\\leq q < 2d/ (d+\\gamma))$ when $\\alpha =2, d\\geq 1$, and with radial Cauchy data when $d\\geq 2, \\frac{2d}{2d-1}< \\alpha < 2. $ Similar results are proven in Fourier algebra $\\mathcal{F}L^1(\\mathbb R^d","authors_text":"Divyang G. Bhimani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T15:37:20Z","title":"Global well-posedness for fractional Hartree equation on modulation spaces and Fourier algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04076","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":"sha256:9f97b3b1bed84037973b998c1eb4fbba48900ab4961ac8e8205126db895800df","target":"record","created_at":"2026-05-18T00:03:42Z","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":"d1d2d2fc77cd30d165816878b7db031a34cde4a22a38eb4667785fbc68749763","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T15:37:20Z","title_canon_sha256":"a9f1d79663c2e0d81ee0ba711c52de69ace27b647a4a1011e5e51219af883bf3"},"schema_version":"1.0","source":{"id":"1810.04076","kind":"arxiv","version":1}},"canonical_sha256":"c4d044a0c99c80bee6d06cc4bb4685cf4cf1713d7862273d8c5ebf12f1a839dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4d044a0c99c80bee6d06cc4bb4685cf4cf1713d7862273d8c5ebf12f1a839dc","first_computed_at":"2026-05-18T00:03:42.315006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:42.315006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8BUN2JOg6/kBGnDHgz+X3FNMx4+Uc2bfVIG6oaY2pYvTRUWlE8jBKL+AGgno1xzTkNrQsMyP4EHkBBCve4+wDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:42.315477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f97b3b1bed84037973b998c1eb4fbba48900ab4961ac8e8205126db895800df","sha256:3141bc2bfb65e154b7e9fdb9371bdef68761c143697386fb0c1c087f005ab067"],"state_sha256":"23efc1cbe23407757101eb5cb1c0187226745a289acdfb95246db8009f6e377f"}