{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DJVB7UCMHOAPWIDF4FHXGU7PX3","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":"da9a2e8c944d288cba358a4b18f4f73e5cbe0f5aad979ca09571c64754d3fa03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-07T18:35:40Z","title_canon_sha256":"81f5b78034e691004bcb3180815f947657462d9cc9cd528ec2857581a660e46c"},"schema_version":"1.0","source":{"id":"1706.02329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02329","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02329v1","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02329","created_at":"2026-05-18T00:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"DJVB7UCMHOAP","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DJVB7UCMHOAPWIDF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DJVB7UCM","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:97198afd39290530d51073f3071017d7d64fe6e84d64f5e62429d62431ba8458","target":"graph","created_at":"2026-05-18T00:42:45Z","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":"Wigner's celebrated theorem, which is particularly important in the mathematical foundations of quantum mechanics, states that every bijective transformation on the set of all rank-one projections of a complex Hilbert space which preserves the transition probability is induced by a unitary or an antiunitary operator. This vital theorem has been generalised in various ways by several scientists. In 2001, Moln\\'ar provided a natural generalisation, namely, he provided a characterisation of (not necessarily bijective) maps which act on the Grassmann space of all rank-$n$ projections and leave the","authors_text":"Gy\\\"orgy P\\'al Geh\\'er","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-07T18:35:40Z","title":"Wigner's theorem on Grassmann spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02329","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:f4ea4578f22e8055cbb4aa55abd9cc731bcc77e72c0dd20ecec7c2aa787990fe","target":"record","created_at":"2026-05-18T00:42:45Z","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":"da9a2e8c944d288cba358a4b18f4f73e5cbe0f5aad979ca09571c64754d3fa03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-07T18:35:40Z","title_canon_sha256":"81f5b78034e691004bcb3180815f947657462d9cc9cd528ec2857581a660e46c"},"schema_version":"1.0","source":{"id":"1706.02329","kind":"arxiv","version":1}},"canonical_sha256":"1a6a1fd04c3b80fb2065e14f7353efbefd96fa88ab510cddd17f20621dbf5aa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a6a1fd04c3b80fb2065e14f7353efbefd96fa88ab510cddd17f20621dbf5aa6","first_computed_at":"2026-05-18T00:42:45.745506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:45.745506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"clRG/0lhCm1bCZh9/VsNIOs2MKt0Q+lMBcPf0vCaOTt5FrpewWiY0aUHQ9b0E6JDxc53y4un7ni1fG8HmcNFCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:45.746158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4ea4578f22e8055cbb4aa55abd9cc731bcc77e72c0dd20ecec7c2aa787990fe","sha256:97198afd39290530d51073f3071017d7d64fe6e84d64f5e62429d62431ba8458"],"state_sha256":"add0ea2aa685eb554df22b15a3f47082ed1792613887c63c44c61fad1b74b1d2"}