{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FIDXJ6JLPUFKWUOHVC6X5RVHLP","short_pith_number":"pith:FIDXJ6JL","canonical_record":{"source":{"id":"1003.4330","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-23T03:07:33Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"e5fecffd962552bc8aff3edc91c3559a760e2a26bf41c814655ba9aea7b65775","abstract_canon_sha256":"84e7ab9eef55cb4b0e8a2d11f1465a4149ed232c1d94129ea52ea562e4069b56"},"schema_version":"1.0"},"canonical_sha256":"2a0774f92b7d0aab51c7a8bd7ec6a75bfcc9a1e7b4c6c67cd775194ae3688ac9","source":{"kind":"arxiv","id":"1003.4330","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4330","created_at":"2026-05-18T04:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4330v5","created_at":"2026-05-18T04:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4330","created_at":"2026-05-18T04:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"FIDXJ6JLPUFK","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FIDXJ6JLPUFKWUOH","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FIDXJ6JL","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FIDXJ6JLPUFKWUOHVC6X5RVHLP","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4330","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-23T03:07:33Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"e5fecffd962552bc8aff3edc91c3559a760e2a26bf41c814655ba9aea7b65775","abstract_canon_sha256":"84e7ab9eef55cb4b0e8a2d11f1465a4149ed232c1d94129ea52ea562e4069b56"},"schema_version":"1.0"},"canonical_sha256":"2a0774f92b7d0aab51c7a8bd7ec6a75bfcc9a1e7b4c6c67cd775194ae3688ac9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:05.048940Z","signature_b64":"k0PXXCNZTZwKQw6CD0ucsZaeFsmg62fPkitg4veoygDeFlwQaof0VbQUvgYYSzFL32C6KxdsWAFYKW5iju2yDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a0774f92b7d0aab51c7a8bd7ec6a75bfcc9a1e7b4c6c67cd775194ae3688ac9","last_reissued_at":"2026-05-18T04:35:05.048298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:05.048298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4330","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zz7jI+5D0WjL86Ec7wX55S5WxMT+puYARq00MBVy2oYAaXzgMIXmmQCwEusbhkZEITSKatqG79Zoss+9wCduCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T18:31:22.889853Z"},"content_sha256":"d701e0a217f109597181d711c9ef96db23e5dc06c2a0a28881a1d65319565307","schema_version":"1.0","event_id":"sha256:d701e0a217f109597181d711c9ef96db23e5dc06c2a0a28881a1d65319565307"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FIDXJ6JLPUFKWUOHVC6X5RVHLP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical Proofs Of Kato Type Smoothing Estimates for The Schr\\\"odinger Equation with Quadratic Potential in R^n+1 with application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Xuwen Chen","submitted_at":"2010-03-23T03:07:33Z","abstract_excerpt":"This paper applies Hermite function techniques to give elementary proofs of Kato type smoothing estimates for the Schr\\\"odinger equation with quadratic potential in R^n+1. This is equivalent to proving a uniform L^2(R^n) to L^2(R^n) boundedness for a family of singularized Hermite projection kernels. As an applicationas the above estimate, we also prove the R^9 collapsing variable type Strichartz estimate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4330","kind":"arxiv","version":5},"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":"2026-05-18T04:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvZJHiuskXe67k3QI8N3kRbWj2m7xFyo/4fZBIzQUxEyehNogutF+Tvt6kzH6q3r636k5m3EQaj4X24aw94YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T18:31:22.890568Z"},"content_sha256":"498c4156d3f2c496d675a0d9c29fffcc98c76b26a7bc82367fd9ba31d76eef4c","schema_version":"1.0","event_id":"sha256:498c4156d3f2c496d675a0d9c29fffcc98c76b26a7bc82367fd9ba31d76eef4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FIDXJ6JLPUFKWUOHVC6X5RVHLP/bundle.json","state_url":"https://pith.science/pith/FIDXJ6JLPUFKWUOHVC6X5RVHLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FIDXJ6JLPUFKWUOHVC6X5RVHLP/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":"2026-05-23T18:31:22Z","links":{"resolver":"https://pith.science/pith/FIDXJ6JLPUFKWUOHVC6X5RVHLP","bundle":"https://pith.science/pith/FIDXJ6JLPUFKWUOHVC6X5RVHLP/bundle.json","state":"https://pith.science/pith/FIDXJ6JLPUFKWUOHVC6X5RVHLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FIDXJ6JLPUFKWUOHVC6X5RVHLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FIDXJ6JLPUFKWUOHVC6X5RVHLP","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":"84e7ab9eef55cb4b0e8a2d11f1465a4149ed232c1d94129ea52ea562e4069b56","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-23T03:07:33Z","title_canon_sha256":"e5fecffd962552bc8aff3edc91c3559a760e2a26bf41c814655ba9aea7b65775"},"schema_version":"1.0","source":{"id":"1003.4330","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4330","created_at":"2026-05-18T04:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4330v5","created_at":"2026-05-18T04:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4330","created_at":"2026-05-18T04:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"FIDXJ6JLPUFK","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FIDXJ6JLPUFKWUOH","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FIDXJ6JL","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:498c4156d3f2c496d675a0d9c29fffcc98c76b26a7bc82367fd9ba31d76eef4c","target":"graph","created_at":"2026-05-18T04:35:05Z","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":"This paper applies Hermite function techniques to give elementary proofs of Kato type smoothing estimates for the Schr\\\"odinger equation with quadratic potential in R^n+1. This is equivalent to proving a uniform L^2(R^n) to L^2(R^n) boundedness for a family of singularized Hermite projection kernels. As an applicationas the above estimate, we also prove the R^9 collapsing variable type Strichartz estimate.","authors_text":"Xuwen Chen","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-23T03:07:33Z","title":"Classical Proofs Of Kato Type Smoothing Estimates for The Schr\\\"odinger Equation with Quadratic Potential in R^n+1 with application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4330","kind":"arxiv","version":5},"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:d701e0a217f109597181d711c9ef96db23e5dc06c2a0a28881a1d65319565307","target":"record","created_at":"2026-05-18T04:35:05Z","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":"84e7ab9eef55cb4b0e8a2d11f1465a4149ed232c1d94129ea52ea562e4069b56","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-23T03:07:33Z","title_canon_sha256":"e5fecffd962552bc8aff3edc91c3559a760e2a26bf41c814655ba9aea7b65775"},"schema_version":"1.0","source":{"id":"1003.4330","kind":"arxiv","version":5}},"canonical_sha256":"2a0774f92b7d0aab51c7a8bd7ec6a75bfcc9a1e7b4c6c67cd775194ae3688ac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a0774f92b7d0aab51c7a8bd7ec6a75bfcc9a1e7b4c6c67cd775194ae3688ac9","first_computed_at":"2026-05-18T04:35:05.048298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:05.048298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k0PXXCNZTZwKQw6CD0ucsZaeFsmg62fPkitg4veoygDeFlwQaof0VbQUvgYYSzFL32C6KxdsWAFYKW5iju2yDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:05.048940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4330","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d701e0a217f109597181d711c9ef96db23e5dc06c2a0a28881a1d65319565307","sha256:498c4156d3f2c496d675a0d9c29fffcc98c76b26a7bc82367fd9ba31d76eef4c"],"state_sha256":"0c4a69b57912b20a63029d39add87e53bdeb5a7b044f41edcdcbe7015ea5e577"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1EFfjOa5hKq0GEx1d0vGrxrgleOCFxySUopa/iwDWfffUQrZuDReUvuJVCOP6YGTry3/CNoMbi7StnL8LVjrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T18:31:22.894609Z","bundle_sha256":"85ec9211f574dd27d8fdd481dbf4dd8bf09c19838c241e17b61b2581d3c24237"}}