{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MPCZWM7HUSY2UCP6LNACAGLNAB","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":"540459d835be70e0716148348bc2644b14b3f66c85f381de952bb1c1b1fa69e7","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2025-06-05T07:06:28Z","title_canon_sha256":"f06564b58ebc1ae2eb79946cc8424c9551b54cfd45f9024e1132df64402fba50"},"schema_version":"1.0","source":{"id":"2506.04686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04686","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04686v1","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04686","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"MPCZWM7HUSY2","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_16","alias_value":"MPCZWM7HUSY2UCP6","created_at":"2026-07-05T11:19:07Z"},{"alias_kind":"pith_short_8","alias_value":"MPCZWM7H","created_at":"2026-07-05T11:19:07Z"}],"graph_snapshots":[{"event_id":"sha256:837087d00fcc77ea480cf5e04b314b5bd68e492d41e3c3c84d3ec018c3c4f43c","target":"graph","created_at":"2026-07-05T11:19:07Z","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/2506.04686/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then the underlying space is also isomorphic to a Hilbert space.","authors_text":"Gerd Wachsmuth, Nicolas Borchard","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2025-06-05T07:06:28Z","title":"Characterization of Hilbertizable spaces via convex functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04686","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":"sha256:9d61514d1541dee5bba7b01f337f2848391d60e1c47aa277a6cbd7b8d1796721","target":"record","created_at":"2026-07-05T11:19:07Z","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":"540459d835be70e0716148348bc2644b14b3f66c85f381de952bb1c1b1fa69e7","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2025-06-05T07:06:28Z","title_canon_sha256":"f06564b58ebc1ae2eb79946cc8424c9551b54cfd45f9024e1132df64402fba50"},"schema_version":"1.0","source":{"id":"2506.04686","kind":"arxiv","version":1}},"canonical_sha256":"63c59b33e7a4b1aa09fe5b4020196d004444b4bcf0c6b4c59f4e978b7b7219b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63c59b33e7a4b1aa09fe5b4020196d004444b4bcf0c6b4c59f4e978b7b7219b6","first_computed_at":"2026-07-05T11:19:07.915186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:07.915186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"69bSXQZZD9ZIfhlTDHNnPTHL3E0cWwBgU+68do2wzsKFOlZUL/ELl4SWJU3sYPgFJQiEYVF8Yp3D0kCmbJRUCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:07.915696Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d61514d1541dee5bba7b01f337f2848391d60e1c47aa277a6cbd7b8d1796721","sha256:837087d00fcc77ea480cf5e04b314b5bd68e492d41e3c3c84d3ec018c3c4f43c"],"state_sha256":"42a452eea447feda246b455429c8846ba2b3bcca1824f19cc4f6659205921074"}