{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AR453VY3RJHGEPID3HOT7FAMK3","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":"df6cf47a67dfb2adc43639058385547d912e553c4eb147d4e7045f5a23339c8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-06-29T13:04:42Z","title_canon_sha256":"204b9dcc726463b9f88f177699bbde06c0d49774fd8fcf85de80f7e6fa4b8a3f"},"schema_version":"1.0","source":{"id":"1006.5600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5600","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5600v1","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5600","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"AR453VY3RJHG","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AR453VY3RJHGEPID","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AR453VY3","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:ec5a27721611a192d5e6d9c110db64fdf3f36b6b4bf2bbb6523378a648da2a5f","target":"graph","created_at":"2026-05-18T03:59:49Z","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 note we provide dispersive estimates for Fourier integrals with parameter-dependent phase functions in terms of geometric quantities of associated families of Fresnel surfaces. The results are based on a multi-dimensional van der Corput lemma due to the first author.\n  Applications to dispersive estimates for hyperbolic systems and scalar higher order hyperbolic equations are also discussed.","authors_text":"Jens Wirth, Michael Ruzhansky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-06-29T13:04:42Z","title":"Dispersive type estimates for Fourier integrals and applications to hyperbolic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5600","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":"sha256:5d2365eda7e7e33304ee76da28b1d2faa745428567d74e992b53423ee73c08f6","target":"record","created_at":"2026-05-18T03:59:49Z","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":"df6cf47a67dfb2adc43639058385547d912e553c4eb147d4e7045f5a23339c8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-06-29T13:04:42Z","title_canon_sha256":"204b9dcc726463b9f88f177699bbde06c0d49774fd8fcf85de80f7e6fa4b8a3f"},"schema_version":"1.0","source":{"id":"1006.5600","kind":"arxiv","version":1}},"canonical_sha256":"0479ddd71b8a4e623d03d9dd3f940c56d770b6e97beffb210aff4e878b1b4dd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0479ddd71b8a4e623d03d9dd3f940c56d770b6e97beffb210aff4e878b1b4dd8","first_computed_at":"2026-05-18T03:59:49.643361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:49.643361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ntJD1Lldh2BQisUOoVOxKIuhTX7yyKMq2h5DC4XSYfGKwlIlMEeTHsZdBs+zGqQOc/uJgTdJJNsxTr1RPTQkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:49.643735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d2365eda7e7e33304ee76da28b1d2faa745428567d74e992b53423ee73c08f6","sha256:ec5a27721611a192d5e6d9c110db64fdf3f36b6b4bf2bbb6523378a648da2a5f"],"state_sha256":"49859a669601a021261041b7a089d9f7016869d19e28eba372c6be1b7ae4f765"}