{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OWMZVP4P3QPZOHONGSRPQ2QTDN","short_pith_number":"pith:OWMZVP4P","canonical_record":{"source":{"id":"1701.00477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-02T18:49:02Z","cross_cats_sorted":[],"title_canon_sha256":"ca9f6b3beef37f59f5b132f999981ffb000818737e9c2b364336d9bf1c4630fa","abstract_canon_sha256":"57c801d0e911c5cf0702268d6a4340313686f8c977e46a6173b2a51a980a54f9"},"schema_version":"1.0"},"canonical_sha256":"75999abf8fdc1f971dcd34a2f86a131b64458edfcec72fc4e7c9cb9c2408b00b","source":{"kind":"arxiv","id":"1701.00477","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00477","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00477v1","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00477","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"OWMZVP4P3QPZ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OWMZVP4P3QPZOHON","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OWMZVP4P","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OWMZVP4P3QPZOHONGSRPQ2QTDN","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-02T18:49:02Z","cross_cats_sorted":[],"title_canon_sha256":"ca9f6b3beef37f59f5b132f999981ffb000818737e9c2b364336d9bf1c4630fa","abstract_canon_sha256":"57c801d0e911c5cf0702268d6a4340313686f8c977e46a6173b2a51a980a54f9"},"schema_version":"1.0"},"canonical_sha256":"75999abf8fdc1f971dcd34a2f86a131b64458edfcec72fc4e7c9cb9c2408b00b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:35.497892Z","signature_b64":"jkjj90t1JhBKPMI1qPsdIarzocsOKQjFO6LFh1kYKjF0dywbUjf0Ep8cXB9zuH1f6OPHaYGnHmt4+awccjWpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75999abf8fdc1f971dcd34a2f86a131b64458edfcec72fc4e7c9cb9c2408b00b","last_reissued_at":"2026-05-18T00:53:35.497282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:35.497282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00477","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PJUDxb6CDwT6cg6q/qgdY6jc8Ldf4zmKmXeLruIsDYfrtj2tfwVoCSU16qXYmqU1BQ09DYYIJm21ztw3XbB9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:22:51.740940Z"},"content_sha256":"d5bb6515014fd50f2e6217a4cc3217039a2b915038d0f49e1bec96bbda4f3cb3","schema_version":"1.0","event_id":"sha256:d5bb6515014fd50f2e6217a4cc3217039a2b915038d0f49e1bec96bbda4f3cb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OWMZVP4P3QPZOHONGSRPQ2QTDN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Restriction of the Fourier transform to some oscillating curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dashan Fan, Lifeng Wang, Xianghong Chen","submitted_at":"2017-01-02T18:49:02Z","abstract_excerpt":"Let $\\phi$ be a smooth function on a compact interval $I$. Let $$\\gamma(t)=\\left (t,t^2,\\cdots,t^{n-1},\\phi(t)\\right).$$ In this paper, we show that $$\\left(\\int_I \\big|\\hat f(\\gamma(t))\\big|^q \\big|\\phi^{(n)}(t)\\big|^{\\frac{2}{n(n+1)}} dt\\right)^{1/q}\\le C\\|f\\|_{L^p(\\mathbb R^n)}$$ holds in the range $$1\\le p<\\frac{n^2+n+2}{n^2+n},\\quad 1\\le q<\\frac{2}{n^2+n}p'.$$ This generalizes an affine restriction theorem of Sj\\\"olin (1974) for $n=2$. Our proof relies on ideas of Sj\\\"olin (1974) and Drury (1985), and more recently Bak-Oberlin-Seeger (2008) and Stovall (2016), as well as a variation bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00477","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKoWTEDarze6Wo/rAX7+ZHATQo+TxYAOJlRzUPUysMEy4ZptvhNSjILwmRZFfukSnSUBaiRQNLI4fCsTClkFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:22:51.741478Z"},"content_sha256":"f853bc2ea7d94fa81e123e7b7221c48cf19bedfba8c7ca4495214c18f5a908c3","schema_version":"1.0","event_id":"sha256:f853bc2ea7d94fa81e123e7b7221c48cf19bedfba8c7ca4495214c18f5a908c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWMZVP4P3QPZOHONGSRPQ2QTDN/bundle.json","state_url":"https://pith.science/pith/OWMZVP4P3QPZOHONGSRPQ2QTDN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWMZVP4P3QPZOHONGSRPQ2QTDN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T10:22:51Z","links":{"resolver":"https://pith.science/pith/OWMZVP4P3QPZOHONGSRPQ2QTDN","bundle":"https://pith.science/pith/OWMZVP4P3QPZOHONGSRPQ2QTDN/bundle.json","state":"https://pith.science/pith/OWMZVP4P3QPZOHONGSRPQ2QTDN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWMZVP4P3QPZOHONGSRPQ2QTDN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OWMZVP4P3QPZOHONGSRPQ2QTDN","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":"57c801d0e911c5cf0702268d6a4340313686f8c977e46a6173b2a51a980a54f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-02T18:49:02Z","title_canon_sha256":"ca9f6b3beef37f59f5b132f999981ffb000818737e9c2b364336d9bf1c4630fa"},"schema_version":"1.0","source":{"id":"1701.00477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00477","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00477v1","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00477","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"OWMZVP4P3QPZ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OWMZVP4P3QPZOHON","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OWMZVP4P","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:f853bc2ea7d94fa81e123e7b7221c48cf19bedfba8c7ca4495214c18f5a908c3","target":"graph","created_at":"2026-05-18T00:53:35Z","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":"Let $\\phi$ be a smooth function on a compact interval $I$. Let $$\\gamma(t)=\\left (t,t^2,\\cdots,t^{n-1},\\phi(t)\\right).$$ In this paper, we show that $$\\left(\\int_I \\big|\\hat f(\\gamma(t))\\big|^q \\big|\\phi^{(n)}(t)\\big|^{\\frac{2}{n(n+1)}} dt\\right)^{1/q}\\le C\\|f\\|_{L^p(\\mathbb R^n)}$$ holds in the range $$1\\le p<\\frac{n^2+n+2}{n^2+n},\\quad 1\\le q<\\frac{2}{n^2+n}p'.$$ This generalizes an affine restriction theorem of Sj\\\"olin (1974) for $n=2$. Our proof relies on ideas of Sj\\\"olin (1974) and Drury (1985), and more recently Bak-Oberlin-Seeger (2008) and Stovall (2016), as well as a variation bound","authors_text":"Dashan Fan, Lifeng Wang, Xianghong Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-02T18:49:02Z","title":"Restriction of the Fourier transform to some oscillating curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00477","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:d5bb6515014fd50f2e6217a4cc3217039a2b915038d0f49e1bec96bbda4f3cb3","target":"record","created_at":"2026-05-18T00:53:35Z","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":"57c801d0e911c5cf0702268d6a4340313686f8c977e46a6173b2a51a980a54f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-02T18:49:02Z","title_canon_sha256":"ca9f6b3beef37f59f5b132f999981ffb000818737e9c2b364336d9bf1c4630fa"},"schema_version":"1.0","source":{"id":"1701.00477","kind":"arxiv","version":1}},"canonical_sha256":"75999abf8fdc1f971dcd34a2f86a131b64458edfcec72fc4e7c9cb9c2408b00b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75999abf8fdc1f971dcd34a2f86a131b64458edfcec72fc4e7c9cb9c2408b00b","first_computed_at":"2026-05-18T00:53:35.497282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:35.497282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jkjj90t1JhBKPMI1qPsdIarzocsOKQjFO6LFh1kYKjF0dywbUjf0Ep8cXB9zuH1f6OPHaYGnHmt4+awccjWpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:35.497892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5bb6515014fd50f2e6217a4cc3217039a2b915038d0f49e1bec96bbda4f3cb3","sha256:f853bc2ea7d94fa81e123e7b7221c48cf19bedfba8c7ca4495214c18f5a908c3"],"state_sha256":"6461b43cfb7371d5ca6ea4b016ad867911043febf9c6f4e09461900bee920319"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ew4oZ+OVadCPrlsjOYHFD74Pu2bGjWQUWbxLtgXo9TGhvR1FIKoWtDK29RcsD7bl2U2ipgiH+LaI8wLqu0oWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:22:51.743949Z","bundle_sha256":"c1ec43564ab95eb758a62b07d30607e7878c5c2bcb78878c24845469f1060d67"}}