{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:COZMTQDZ5J5TPX72C25VOFM2X5","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":"b5643b3f0f4c6f0140a1e9e80f015cd8fff5c6c0aa08cae3a7421b40a77ef685","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1994-11-16T22:08:45Z","title_canon_sha256":"bb36cd974b0e830c504fa01b4c6018dd568ef30d10d4e8b975fd9e8092e42c76"},"schema_version":"1.0","source":{"id":"math/9411210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9411210","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9411210v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9411210","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"COZMTQDZ5J5T","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"COZMTQDZ5J5TPX72","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"COZMTQDZ","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:81337bedeff51ce8387157b27f209372f92e408ef9adc4e63787b4cccaa24d86","target":"graph","created_at":"2026-05-18T01:05:50Z","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":"Let $X$ be a (real or complex) rearrangement-in\\-va\\-riant function space on $\\Om$ (where $\\Om = [0,1]$ or $\\Om \\subseteq \\bbN$) whose norm is not proportional to the $L_2$-norm. Let $H$ be a separable Hilbert space. We characterize surjective isometries of $X(H).$ We prove that if $T$ is such an isometry then there exist Borel maps $a:\\Om\\to\\bbK$ and $\\sigma:\\Om\\lra\\Om$ and a strongly measurable operator map $S$ of $\\Om$ into $\\calB(H)$ so that for almost all $\\om$ $S(\\om)$ is a surjective isometry of $H$\n  and for any $f\\in X(H)$ $$Tf(\\om)=a(\\om)S(\\om)(f(\\sigma(\\om))) \\text{ a.e.}$$\n  As a c","authors_text":"Beata Randrianantoanina","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1994-11-16T22:08:45Z","title":"Isometries of Hilbert space valued function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9411210","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":"sha256:974a7632cac709e21c515d78bfa60bed53a14e59e53c7284594c4a27bec53e4d","target":"record","created_at":"2026-05-18T01:05:50Z","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":"b5643b3f0f4c6f0140a1e9e80f015cd8fff5c6c0aa08cae3a7421b40a77ef685","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1994-11-16T22:08:45Z","title_canon_sha256":"bb36cd974b0e830c504fa01b4c6018dd568ef30d10d4e8b975fd9e8092e42c76"},"schema_version":"1.0","source":{"id":"math/9411210","kind":"arxiv","version":1}},"canonical_sha256":"13b2c9c079ea7b37dffa16bb57159abf5dbe6cca4b7fb16b1b383364cb12b0d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13b2c9c079ea7b37dffa16bb57159abf5dbe6cca4b7fb16b1b383364cb12b0d3","first_computed_at":"2026-05-18T01:05:50.895187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.895187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OYxdnYi9weAJVdG9N/WhqrM9jLcKNQkXMztx1S6uDB1z1I2gZDHmCzA7MKiv7dPsWteS2qA23JfFcLSaIzgCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.895790Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9411210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:974a7632cac709e21c515d78bfa60bed53a14e59e53c7284594c4a27bec53e4d","sha256:81337bedeff51ce8387157b27f209372f92e408ef9adc4e63787b4cccaa24d86"],"state_sha256":"183061af46c2899806c716cf3ea26297b2e8cedb7bae3eeef91bc15630c3e585"}