{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6PT3QVA45APPZX4WN5PCJBCLEA","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":"40893bae9814ba7ce0467048230993de37cc660e60de5e3b91f7a518a6201f51","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-08-05T02:42:51Z","title_canon_sha256":"6c2d810d59e8fc9339f0d923cef407341ad3d4a4b0d18dbd28fe364a50c4f973"},"schema_version":"1.0","source":{"id":"1908.01448","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01448","created_at":"2026-07-05T06:13:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01448v5","created_at":"2026-07-05T06:13:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01448","created_at":"2026-07-05T06:13:13Z"},{"alias_kind":"pith_short_12","alias_value":"6PT3QVA45APP","created_at":"2026-07-05T06:13:13Z"},{"alias_kind":"pith_short_16","alias_value":"6PT3QVA45APPZX4W","created_at":"2026-07-05T06:13:13Z"},{"alias_kind":"pith_short_8","alias_value":"6PT3QVA4","created_at":"2026-07-05T06:13:13Z"}],"graph_snapshots":[{"event_id":"sha256:8510ade5972a832ac4d6d0ecc8915365a406f125d5eaba44b81a50e49653f551","target":"graph","created_at":"2026-07-05T06:13:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.01448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Hardy spaces for Fourier integral operators $\\mathcal{H}_{FIO}^{p}(\\mathbb{R}^{n})$, for $1\\leq p\\leq \\infty$, were introduced by Smith in [Smith,1998] and Hassell et al. in [Hassell-Portal-Rozendaal,2020]. In this article, we give several equivalent characterizations of $\\mathcal{H}_{FIO}^{1}(\\mathbb{R}^{n})$, for example in terms of Littlewood--Paley $g$ functions and maximal functions. This answers a question from [Rozendaal,2021]. We also give several applications of the characterizations.","authors_text":"Jan Rozendaal, Liang Song, Naijia Liu, Zhijie Fan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-08-05T02:42:51Z","title":"Characterizations of the Hardy space $\\mathcal{H}_{FIO}^{1}(\\mathbb{R}^{n})$ for Fourier integral operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01448","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":"sha256:862a8c22d749ee432a38c98f37653d9ee4bea55f1ca157533daeb21fcca1fc66","target":"record","created_at":"2026-07-05T06:13:13Z","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":"40893bae9814ba7ce0467048230993de37cc660e60de5e3b91f7a518a6201f51","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-08-05T02:42:51Z","title_canon_sha256":"6c2d810d59e8fc9339f0d923cef407341ad3d4a4b0d18dbd28fe364a50c4f973"},"schema_version":"1.0","source":{"id":"1908.01448","kind":"arxiv","version":5}},"canonical_sha256":"f3e7b8541ce81efcdf966f5e24844b2002d3ee804d578aba79b598261ba15908","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3e7b8541ce81efcdf966f5e24844b2002d3ee804d578aba79b598261ba15908","first_computed_at":"2026-07-05T06:13:13.552875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:13:13.552875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o7wkSo4AGN40EXExRodFYZgLRpqYU6azDbBfQDFV6tKCu0ptjvRNX9WN6ePWaZmfGewwtD1lYsoWVGiCNyS2BA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:13:13.553343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01448","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:862a8c22d749ee432a38c98f37653d9ee4bea55f1ca157533daeb21fcca1fc66","sha256:8510ade5972a832ac4d6d0ecc8915365a406f125d5eaba44b81a50e49653f551"],"state_sha256":"f6c267d79b3efdcce2b37920312a9af91aee8829dcabf0598d71d5db45660301"}