{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PUSN3BXZ6EEPAPURNL75UKWCHL","short_pith_number":"pith:PUSN3BXZ","canonical_record":{"source":{"id":"1306.4973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-20T19:46:48Z","cross_cats_sorted":[],"title_canon_sha256":"5a4ec9a20311c9764a7e395330ff6c09f2828dc82cbfd60286f5df6ff6749fb6","abstract_canon_sha256":"25b013f83fb47369359f0f7cdb91c1a677a65f8eb07691b2eb9440ff15daa9bd"},"schema_version":"1.0"},"canonical_sha256":"7d24dd86f9f108f03e916affda2ac23aec6edbaa132007a7beabc71872e93688","source":{"kind":"arxiv","id":"1306.4973","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4973","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4973v3","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4973","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"PUSN3BXZ6EEP","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PUSN3BXZ6EEPAPUR","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PUSN3BXZ","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PUSN3BXZ6EEPAPURNL75UKWCHL","target":"record","payload":{"canonical_record":{"source":{"id":"1306.4973","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-20T19:46:48Z","cross_cats_sorted":[],"title_canon_sha256":"5a4ec9a20311c9764a7e395330ff6c09f2828dc82cbfd60286f5df6ff6749fb6","abstract_canon_sha256":"25b013f83fb47369359f0f7cdb91c1a677a65f8eb07691b2eb9440ff15daa9bd"},"schema_version":"1.0"},"canonical_sha256":"7d24dd86f9f108f03e916affda2ac23aec6edbaa132007a7beabc71872e93688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:51.968875Z","signature_b64":"6MKTEWPoOqLFelKsYURYSJDLXhUGbNSi9QAHg0meaX2m6A/LauBDRm4egQYQj9gI5ItF5VPBulvA1F/Mnj1uDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d24dd86f9f108f03e916affda2ac23aec6edbaa132007a7beabc71872e93688","last_reissued_at":"2026-05-18T02:56:51.968423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:51.968423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.4973","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K25wSF19VBZ0u9mabT9DgaXnvD+eLi8SrUVIoU0r3me0nzN2ZZ/qLirSpu64uOa59u+n2jvAhmoLK/V2qkX5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:02:28.429501Z"},"content_sha256":"71fbc39abd8084287be77e55e7fa3813e75a26b601157e00cdae87dbbe1fcf6e","schema_version":"1.0","event_id":"sha256:71fbc39abd8084287be77e55e7fa3813e75a26b601157e00cdae87dbbe1fcf6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PUSN3BXZ6EEPAPURNL75UKWCHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strichartz estimates for Schr\\\"odinger equations on irrational tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tadahiro Oh, Yuzhao Wang, Zihua Guo","submitted_at":"2013-06-20T19:46:48Z","abstract_excerpt":"In this paper, we prove new Strichartz estimates for linear Schrodinger equations posed on d-dimensional irrational tori. Then, we use these estimates to prove subcritical and critical local well-posedness results for nonlinear Schrodinger equations (NLS) on irrational tori."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4973","kind":"arxiv","version":3},"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":"2026-05-18T02:56:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I+aIAtt1FN9+OFC71Xqr7t46priJVY9qaZBuO3iClV/dnycn+CUOC5SZUuokVGqIhPobSV3WsRiKVvon6noPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:02:28.430138Z"},"content_sha256":"775d8c66c75b70eaae141d3941c051df4fc56fd4940f63e658cd79eb74a091c0","schema_version":"1.0","event_id":"sha256:775d8c66c75b70eaae141d3941c051df4fc56fd4940f63e658cd79eb74a091c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PUSN3BXZ6EEPAPURNL75UKWCHL/bundle.json","state_url":"https://pith.science/pith/PUSN3BXZ6EEPAPURNL75UKWCHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PUSN3BXZ6EEPAPURNL75UKWCHL/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":"2026-06-11T06:02:28Z","links":{"resolver":"https://pith.science/pith/PUSN3BXZ6EEPAPURNL75UKWCHL","bundle":"https://pith.science/pith/PUSN3BXZ6EEPAPURNL75UKWCHL/bundle.json","state":"https://pith.science/pith/PUSN3BXZ6EEPAPURNL75UKWCHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PUSN3BXZ6EEPAPURNL75UKWCHL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PUSN3BXZ6EEPAPURNL75UKWCHL","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":"25b013f83fb47369359f0f7cdb91c1a677a65f8eb07691b2eb9440ff15daa9bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-20T19:46:48Z","title_canon_sha256":"5a4ec9a20311c9764a7e395330ff6c09f2828dc82cbfd60286f5df6ff6749fb6"},"schema_version":"1.0","source":{"id":"1306.4973","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4973","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4973v3","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4973","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"PUSN3BXZ6EEP","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PUSN3BXZ6EEPAPUR","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PUSN3BXZ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:775d8c66c75b70eaae141d3941c051df4fc56fd4940f63e658cd79eb74a091c0","target":"graph","created_at":"2026-05-18T02:56:51Z","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 paper, we prove new Strichartz estimates for linear Schrodinger equations posed on d-dimensional irrational tori. Then, we use these estimates to prove subcritical and critical local well-posedness results for nonlinear Schrodinger equations (NLS) on irrational tori.","authors_text":"Tadahiro Oh, Yuzhao Wang, Zihua Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-20T19:46:48Z","title":"Strichartz estimates for Schr\\\"odinger equations on irrational tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4973","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":"sha256:71fbc39abd8084287be77e55e7fa3813e75a26b601157e00cdae87dbbe1fcf6e","target":"record","created_at":"2026-05-18T02:56:51Z","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":"25b013f83fb47369359f0f7cdb91c1a677a65f8eb07691b2eb9440ff15daa9bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-20T19:46:48Z","title_canon_sha256":"5a4ec9a20311c9764a7e395330ff6c09f2828dc82cbfd60286f5df6ff6749fb6"},"schema_version":"1.0","source":{"id":"1306.4973","kind":"arxiv","version":3}},"canonical_sha256":"7d24dd86f9f108f03e916affda2ac23aec6edbaa132007a7beabc71872e93688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d24dd86f9f108f03e916affda2ac23aec6edbaa132007a7beabc71872e93688","first_computed_at":"2026-05-18T02:56:51.968423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:51.968423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6MKTEWPoOqLFelKsYURYSJDLXhUGbNSi9QAHg0meaX2m6A/LauBDRm4egQYQj9gI5ItF5VPBulvA1F/Mnj1uDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:51.968875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4973","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71fbc39abd8084287be77e55e7fa3813e75a26b601157e00cdae87dbbe1fcf6e","sha256:775d8c66c75b70eaae141d3941c051df4fc56fd4940f63e658cd79eb74a091c0"],"state_sha256":"20720fa0fb314a02e0e8180ca8e18db83f43a60b89195b2fda05c0bf3f50062c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HS5ycDZLJHyXS25dpS4T+ViILRzLywlqp66Fxx1I2yKPi45qafxuhGo99MeURCTe4obviTdegJR3jXDlrydcBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:02:28.434008Z","bundle_sha256":"afb3af07ddce7d2ecb2de8e879a2c435b50f23cdc96a2a546a227366bce0cec8"}}