{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TMPFIIX5YJZSWZUUNDSPYGRKRC","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":"5c765e5d0481322d556f419c1b3b7c552d677ff95f6886252f81a49feb8f54d7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-11T12:15:18Z","title_canon_sha256":"e90a3e0a2483b7edf4db4e2d5afcdf1895d43626188c2fa0e403777c02019693"},"schema_version":"1.0","source":{"id":"1606.03584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03584","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03584v1","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03584","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"TMPFIIX5YJZS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TMPFIIX5YJZSWZUU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TMPFIIX5","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:4ec69eb393a4e312d4ea2d97f4c648cab4c99a7f6c74c66ce937361a265b9235","target":"graph","created_at":"2026-05-18T00:15:42Z","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 $H$ be either a complex inner product space of dimension at least two, or a real inner product space of dimension at least three. Let us fix an $\\alpha\\in \\left(0,\\tfrac{\\pi}{2}\\right)$. The purpose of this paper is to characterize all bijective transformations on the projective space $P(H)$ obtained from $H$ which preserves the angle $\\alpha$ between lines in both directions. (We emphasize that we do not assume anything about other angles). For real inner product spaces and when $H=\\mathbb{C}^2$ we do this for every $\\alpha$, and when $H$ is a complex inner product space of dimension at l","authors_text":"Gy\\\"orgy P\\'al Geh\\'er","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-11T12:15:18Z","title":"Symmetries of projective spaces and spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03584","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:f33e8c76175ea15c37b108b9218c5c234075237ef743928dff8e2d7261594828","target":"record","created_at":"2026-05-18T00:15:42Z","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":"5c765e5d0481322d556f419c1b3b7c552d677ff95f6886252f81a49feb8f54d7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-11T12:15:18Z","title_canon_sha256":"e90a3e0a2483b7edf4db4e2d5afcdf1895d43626188c2fa0e403777c02019693"},"schema_version":"1.0","source":{"id":"1606.03584","kind":"arxiv","version":1}},"canonical_sha256":"9b1e5422fdc2732b669468e4fc1a2a888903c145369ab007f528383ecd450636","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b1e5422fdc2732b669468e4fc1a2a888903c145369ab007f528383ecd450636","first_computed_at":"2026-05-18T00:15:42.414843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:42.414843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CJxaeoET2GUtXbLAcTnqAWnqjxeoS6fn1cNI1dVL6/P91BHJH1wh5UBF7TN/308F5dCf3FCxXgOvYSx2wLSqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:42.415386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f33e8c76175ea15c37b108b9218c5c234075237ef743928dff8e2d7261594828","sha256:4ec69eb393a4e312d4ea2d97f4c648cab4c99a7f6c74c66ce937361a265b9235"],"state_sha256":"ad0c6d6510be47db8c6cc501a5ab2afdde70348fbebd9e185a88d920b565c049"}