{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DI4DQS2M6A24NVGUCPI2SJELLR","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":"15817312eeb2d8887e6632d8fd04bf392029e0ba89acab6157cd7946254c190b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T10:43:54Z","title_canon_sha256":"69bc497eba46466aea360f0928b85ac6e0a11c628b696e8c5b30dd28853782d8"},"schema_version":"1.0","source":{"id":"1609.07305","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07305","created_at":"2026-05-18T00:33:00Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07305v3","created_at":"2026-05-18T00:33:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07305","created_at":"2026-05-18T00:33:00Z"},{"alias_kind":"pith_short_12","alias_value":"DI4DQS2M6A24","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DI4DQS2M6A24NVGU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DI4DQS2M","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:3f22a15c41b28b22388d62f24707b30a965290f16c1c44008d44fbd67a9e5a4e","target":"graph","created_at":"2026-05-18T00:33:00Z","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 firstly prove Strichartz estimates for the fractional Schr\\\"odinger equations on $\\mathbb{R}^d$ endowed with a smooth bounded metric $g$. We then prove Strichartz estimates for the fractional Schr\\\"odinger and wave equations on compact Riemannian manifolds without boundary $(M,g)$. We finally give applications of Strichartz estimates for the local well-posedness of the pure power-type nonlinear fractional Schr\\\"odinger and wave equations posed on $(M,g)$.","authors_text":"Van Duong Dinh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T10:43:54Z","title":"Strichartz estimates for the fractional Schr\\\"odinger and wave equations on compact manifolds without boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07305","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:f6b0340a8948dec59cad1c0cbad684285c1e470dbd61b5401d6d44669665fdc6","target":"record","created_at":"2026-05-18T00:33:00Z","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":"15817312eeb2d8887e6632d8fd04bf392029e0ba89acab6157cd7946254c190b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T10:43:54Z","title_canon_sha256":"69bc497eba46466aea360f0928b85ac6e0a11c628b696e8c5b30dd28853782d8"},"schema_version":"1.0","source":{"id":"1609.07305","kind":"arxiv","version":3}},"canonical_sha256":"1a38384b4cf035c6d4d413d1a9248b5c41cf914da0ed54d61f2d42b4bc2b4b99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a38384b4cf035c6d4d413d1a9248b5c41cf914da0ed54d61f2d42b4bc2b4b99","first_computed_at":"2026-05-18T00:33:00.018728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:00.018728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yw9FUZLqjZwIcyN0blrekCyT+N6RUW8n1k1PzisKwlWR/OUQ2CWXj/fbXVmOv+6fd6v9jiZUTSwr9ATGtA7jDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:00.019355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07305","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6b0340a8948dec59cad1c0cbad684285c1e470dbd61b5401d6d44669665fdc6","sha256:3f22a15c41b28b22388d62f24707b30a965290f16c1c44008d44fbd67a9e5a4e"],"state_sha256":"f17428c548c3c1df49a3c5bcd56c20ab8ffc97405c2179c7e92c2d75287cabcf"}