{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DB2WDBWPC7YTB73ELNSU435HEE","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":"0574f0702c5955ad89d606aef18151e72b5813773d382ddff5cec902dd6cf2fc","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-02-11T00:25:14Z","title_canon_sha256":"de173c732285cc441cd7bb05043827832661e7a290031cf16e186f7394ca257a"},"schema_version":"1.0","source":{"id":"0902.1784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1784","created_at":"2026-05-18T04:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1784v2","created_at":"2026-05-18T04:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1784","created_at":"2026-05-18T04:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"DB2WDBWPC7YT","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DB2WDBWPC7YTB73E","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DB2WDBWP","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:6cc7323f774c73dda6c375d860362dde39a50cecdddf902aafa2e5382d208d53","target":"graph","created_at":"2026-05-18T04:14:18Z","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":"A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a bounded representation in a real or complex Hilbert space is orthogonalizable or unitarizable (that is similar to an orthogonal or unitary representation), respectively, provided the representation has an invariant indefinite quadratic form with finitely many negative squares.","authors_text":"L. Turowska, M.I. Ostrovskii, V.S. Shulman","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-02-11T00:25:14Z","title":"Fixed points of holomorphic transformations of operator balls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1784","kind":"arxiv","version":2},"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":"sha256:1a9f2fc49721187f20ccf4cc8aec5dfd1a8b5bd0b65666d035ac595f118f125f","target":"record","created_at":"2026-05-18T04:14:18Z","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":"0574f0702c5955ad89d606aef18151e72b5813773d382ddff5cec902dd6cf2fc","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-02-11T00:25:14Z","title_canon_sha256":"de173c732285cc441cd7bb05043827832661e7a290031cf16e186f7394ca257a"},"schema_version":"1.0","source":{"id":"0902.1784","kind":"arxiv","version":2}},"canonical_sha256":"18756186cf17f130ff645b654e6fa7213afa93737ddbcb1ff9295fde9ae7e23b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18756186cf17f130ff645b654e6fa7213afa93737ddbcb1ff9295fde9ae7e23b","first_computed_at":"2026-05-18T04:14:18.357651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:18.357651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86YBk0fTGdSHZiyctsiyrJhUfl0NKyD9F9c0pR/JjBqNpKK8Qq2c17jFNfpdhSsel7nniSNO95CifTbg9FP/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:18.358176Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.1784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a9f2fc49721187f20ccf4cc8aec5dfd1a8b5bd0b65666d035ac595f118f125f","sha256:6cc7323f774c73dda6c375d860362dde39a50cecdddf902aafa2e5382d208d53"],"state_sha256":"7ae0e4e06d75b97c7cf2d53add78945b03b86ca83e3cf442b7dad1d705ddd4b3"}