{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:7YL4P74ZZVBQOL2GQ55Y7YBQ7U","short_pith_number":"pith:7YL4P74Z","canonical_record":{"source":{"id":"1902.06987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-19T10:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"b75048cf08e05faaabf0a1203556722b4b77b0ab9db4d5f9db9e93827e5389b4","abstract_canon_sha256":"2a0ee6d63d28510c97173dd2eaa1d3378e7acadf7c7f6f77910b460a54293865"},"schema_version":"1.0"},"canonical_sha256":"fe17c7ff99cd43072f46877b8fe030fd1c841fdc432b20b255124e20658e09d4","source":{"kind":"arxiv","id":"1902.06987","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06987","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06987v1","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06987","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"7YL4P74ZZVBQ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7YL4P74ZZVBQOL2G","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7YL4P74Z","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:7YL4P74ZZVBQOL2GQ55Y7YBQ7U","target":"record","payload":{"canonical_record":{"source":{"id":"1902.06987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-19T10:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"b75048cf08e05faaabf0a1203556722b4b77b0ab9db4d5f9db9e93827e5389b4","abstract_canon_sha256":"2a0ee6d63d28510c97173dd2eaa1d3378e7acadf7c7f6f77910b460a54293865"},"schema_version":"1.0"},"canonical_sha256":"fe17c7ff99cd43072f46877b8fe030fd1c841fdc432b20b255124e20658e09d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:40.248094Z","signature_b64":"6F8B/5baq1rjXeOnNwXQWIID1COx8tOtbPYtPtERBFn12g21/siKXtyOVNdAORI6egG6sW+M8rNRUeiRML+YDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe17c7ff99cd43072f46877b8fe030fd1c841fdc432b20b255124e20658e09d4","last_reissued_at":"2026-05-17T23:53:40.247444Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:40.247444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.06987","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":"2026-05-17T23:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K/YV0MNsAbQMcqX3dZfx7VdQLBUpmiRJSsFbHa74W+vETvEHdphWgHbKTMWh4Cme/MsXQi+0ycutu/Ijjjr3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:30:33.049143Z"},"content_sha256":"d195e6560ecbb09894dfff55887c63882715a691ff08cbfeb5bd5a2d38b3f22e","schema_version":"1.0","event_id":"sha256:d195e6560ecbb09894dfff55887c63882715a691ff08cbfeb5bd5a2d38b3f22e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:7YL4P74ZZVBQOL2GQ55Y7YBQ7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomization improved Strichartz estimates and global well-posedness for supercritical data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joachim Krieger, Nicolas Burq","submitted_at":"2019-02-19T10:52:25Z","abstract_excerpt":"We introduce a novel data randomisation for the free wave equation which leads to the same range of Strichartz estimates as for radial data, albeit in a non-radial context. We then use these estimates to establish global well-posedness for a wave maps type nonlinear wave equation for certain supercritical data, provided the data are suitably small and randomised."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06987","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":"2026-05-17T23:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLwDMtPQZr2si8aRZFgX8QsAShUdRjojGmeBIfAym/YEumIu56NSi/0oOTCoRrYJLDPrJMG79y3O16KoZYu/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:30:33.049838Z"},"content_sha256":"9621987f90193ec6c5c878f7f0b0640fead7a6c08aabee6f548251694e62e94c","schema_version":"1.0","event_id":"sha256:9621987f90193ec6c5c878f7f0b0640fead7a6c08aabee6f548251694e62e94c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7YL4P74ZZVBQOL2GQ55Y7YBQ7U/bundle.json","state_url":"https://pith.science/pith/7YL4P74ZZVBQOL2GQ55Y7YBQ7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7YL4P74ZZVBQOL2GQ55Y7YBQ7U/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":"2026-05-25T20:30:33Z","links":{"resolver":"https://pith.science/pith/7YL4P74ZZVBQOL2GQ55Y7YBQ7U","bundle":"https://pith.science/pith/7YL4P74ZZVBQOL2GQ55Y7YBQ7U/bundle.json","state":"https://pith.science/pith/7YL4P74ZZVBQOL2GQ55Y7YBQ7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7YL4P74ZZVBQOL2GQ55Y7YBQ7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7YL4P74ZZVBQOL2GQ55Y7YBQ7U","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":"2a0ee6d63d28510c97173dd2eaa1d3378e7acadf7c7f6f77910b460a54293865","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-19T10:52:25Z","title_canon_sha256":"b75048cf08e05faaabf0a1203556722b4b77b0ab9db4d5f9db9e93827e5389b4"},"schema_version":"1.0","source":{"id":"1902.06987","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06987","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06987v1","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06987","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"7YL4P74ZZVBQ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7YL4P74ZZVBQOL2G","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7YL4P74Z","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:9621987f90193ec6c5c878f7f0b0640fead7a6c08aabee6f548251694e62e94c","target":"graph","created_at":"2026-05-17T23:53:40Z","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 introduce a novel data randomisation for the free wave equation which leads to the same range of Strichartz estimates as for radial data, albeit in a non-radial context. We then use these estimates to establish global well-posedness for a wave maps type nonlinear wave equation for certain supercritical data, provided the data are suitably small and randomised.","authors_text":"Joachim Krieger, Nicolas Burq","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-19T10:52:25Z","title":"Randomization improved Strichartz estimates and global well-posedness for supercritical data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06987","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:d195e6560ecbb09894dfff55887c63882715a691ff08cbfeb5bd5a2d38b3f22e","target":"record","created_at":"2026-05-17T23:53:40Z","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":"2a0ee6d63d28510c97173dd2eaa1d3378e7acadf7c7f6f77910b460a54293865","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-19T10:52:25Z","title_canon_sha256":"b75048cf08e05faaabf0a1203556722b4b77b0ab9db4d5f9db9e93827e5389b4"},"schema_version":"1.0","source":{"id":"1902.06987","kind":"arxiv","version":1}},"canonical_sha256":"fe17c7ff99cd43072f46877b8fe030fd1c841fdc432b20b255124e20658e09d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe17c7ff99cd43072f46877b8fe030fd1c841fdc432b20b255124e20658e09d4","first_computed_at":"2026-05-17T23:53:40.247444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:40.247444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6F8B/5baq1rjXeOnNwXQWIID1COx8tOtbPYtPtERBFn12g21/siKXtyOVNdAORI6egG6sW+M8rNRUeiRML+YDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:40.248094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06987","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d195e6560ecbb09894dfff55887c63882715a691ff08cbfeb5bd5a2d38b3f22e","sha256:9621987f90193ec6c5c878f7f0b0640fead7a6c08aabee6f548251694e62e94c"],"state_sha256":"2d86278df18e00b0390f0efd1bb93a73def61428500e668c6b8b4a3a327b8a10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqbPKFVgdIXlG2/6Cf6oPGBfHA0leMmUp/wzQfbmsjxA9X1QV0pbDG5OVqPdujQbN2DDMC+lvuchz5wjXLD0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:30:33.053380Z","bundle_sha256":"313113598b7fee1b7f6307fe6143e97b04665ba667b8f4d47dc9800a81ee2968"}}