{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZFV626E5WZM53KRDXMDYRW2YK4","short_pith_number":"pith:ZFV626E5","canonical_record":{"source":{"id":"1211.4600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-19T21:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"647de0a362d7dc10b493a86436a1b569c727922f076b03b4c6e3b7dfa4e25cfd","abstract_canon_sha256":"a101daf5e29a080bef556d4aa4bf3736afc1b38fcfd4e7898c499faae1cf47e9"},"schema_version":"1.0"},"canonical_sha256":"c96bed789db659ddaa23bb0788db58573f18bca0f06ebb6e1cfb19c57f267c83","source":{"kind":"arxiv","id":"1211.4600","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4600","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4600v1","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4600","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"ZFV626E5WZM5","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZFV626E5WZM53KRD","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZFV626E5","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZFV626E5WZM53KRDXMDYRW2YK4","target":"record","payload":{"canonical_record":{"source":{"id":"1211.4600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-19T21:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"647de0a362d7dc10b493a86436a1b569c727922f076b03b4c6e3b7dfa4e25cfd","abstract_canon_sha256":"a101daf5e29a080bef556d4aa4bf3736afc1b38fcfd4e7898c499faae1cf47e9"},"schema_version":"1.0"},"canonical_sha256":"c96bed789db659ddaa23bb0788db58573f18bca0f06ebb6e1cfb19c57f267c83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:02.545448Z","signature_b64":"SKsz8MViJMMixoCU/g0FTISDw9aFORoYL5QUn1zWFjHgbz1+RoKBKQgaKeUYJVuyj7qrSGQxvSgLbKxRAU9SAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c96bed789db659ddaa23bb0788db58573f18bca0f06ebb6e1cfb19c57f267c83","last_reissued_at":"2026-05-18T03:40:02.544947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:02.544947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.4600","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vurSRoVEkbbD3akV4+8HNcYoqOECyal4nWsWlceDZrQ4P3ZPq/W2RlEGOOLqI+KyPtTk2wMQPbnnW3v3LCy2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:48:13.644877Z"},"content_sha256":"b9cf5c6ac0e88b8c1a5c1296bb6bc00bf34c56e32ac8b56dfff0546fad7e1845","schema_version":"1.0","event_id":"sha256:b9cf5c6ac0e88b8c1a5c1296bb6bc00bf34c56e32ac8b56dfff0546fad7e1845"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZFV626E5WZM53KRDXMDYRW2YK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wigner's theorem revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gyula Maksa, Zsolt P\\'ales","submitted_at":"2012-11-19T21:37:49Z","abstract_excerpt":"In this paper, we give the general solution of the functional equation $$\\big\\{\\|f(x)+f(y)\\|,\\|f(x)-f(y)\\|\\big\\}=\\big\\{\\|x+y\\|,\\|x-y\\|\\big\\}\\qquad(x,y\\in X)$$ where $f:X\\to Y$ and $X,Y$ are inner product spaces. Related equations are also considered. Our main tool is a real version of Wigner's unitary--antiunitary theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4600","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+SeYkrp6vzZMQlg+gx5sJnFZFDBDl7hYBzxc3oC79NmXYDt2tTIpwug0IyRctGksMMzpZ/EQc10Y1H3iCP2QCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:48:13.645616Z"},"content_sha256":"630e26e3dccb084c9c4fb3054d2ccfa1df244d298516d4e04b05295981074224","schema_version":"1.0","event_id":"sha256:630e26e3dccb084c9c4fb3054d2ccfa1df244d298516d4e04b05295981074224"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFV626E5WZM53KRDXMDYRW2YK4/bundle.json","state_url":"https://pith.science/pith/ZFV626E5WZM53KRDXMDYRW2YK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFV626E5WZM53KRDXMDYRW2YK4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T23:48:13Z","links":{"resolver":"https://pith.science/pith/ZFV626E5WZM53KRDXMDYRW2YK4","bundle":"https://pith.science/pith/ZFV626E5WZM53KRDXMDYRW2YK4/bundle.json","state":"https://pith.science/pith/ZFV626E5WZM53KRDXMDYRW2YK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFV626E5WZM53KRDXMDYRW2YK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZFV626E5WZM53KRDXMDYRW2YK4","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":"a101daf5e29a080bef556d4aa4bf3736afc1b38fcfd4e7898c499faae1cf47e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-19T21:37:49Z","title_canon_sha256":"647de0a362d7dc10b493a86436a1b569c727922f076b03b4c6e3b7dfa4e25cfd"},"schema_version":"1.0","source":{"id":"1211.4600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4600","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4600v1","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4600","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"ZFV626E5WZM5","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZFV626E5WZM53KRD","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZFV626E5","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:630e26e3dccb084c9c4fb3054d2ccfa1df244d298516d4e04b05295981074224","target":"graph","created_at":"2026-05-18T03:40:02Z","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":"In this paper, we give the general solution of the functional equation $$\\big\\{\\|f(x)+f(y)\\|,\\|f(x)-f(y)\\|\\big\\}=\\big\\{\\|x+y\\|,\\|x-y\\|\\big\\}\\qquad(x,y\\in X)$$ where $f:X\\to Y$ and $X,Y$ are inner product spaces. Related equations are also considered. Our main tool is a real version of Wigner's unitary--antiunitary theorem.","authors_text":"Gyula Maksa, Zsolt P\\'ales","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-19T21:37:49Z","title":"Wigner's theorem revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4600","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:b9cf5c6ac0e88b8c1a5c1296bb6bc00bf34c56e32ac8b56dfff0546fad7e1845","target":"record","created_at":"2026-05-18T03:40:02Z","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":"a101daf5e29a080bef556d4aa4bf3736afc1b38fcfd4e7898c499faae1cf47e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-19T21:37:49Z","title_canon_sha256":"647de0a362d7dc10b493a86436a1b569c727922f076b03b4c6e3b7dfa4e25cfd"},"schema_version":"1.0","source":{"id":"1211.4600","kind":"arxiv","version":1}},"canonical_sha256":"c96bed789db659ddaa23bb0788db58573f18bca0f06ebb6e1cfb19c57f267c83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c96bed789db659ddaa23bb0788db58573f18bca0f06ebb6e1cfb19c57f267c83","first_computed_at":"2026-05-18T03:40:02.544947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:02.544947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SKsz8MViJMMixoCU/g0FTISDw9aFORoYL5QUn1zWFjHgbz1+RoKBKQgaKeUYJVuyj7qrSGQxvSgLbKxRAU9SAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:02.545448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9cf5c6ac0e88b8c1a5c1296bb6bc00bf34c56e32ac8b56dfff0546fad7e1845","sha256:630e26e3dccb084c9c4fb3054d2ccfa1df244d298516d4e04b05295981074224"],"state_sha256":"83b7f5fd6d45ca31371944816f8259f6741a4738e9cb44062c64e5ab6defd10a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JWriRChIgDRdcOGXJ5NaJ35rPwralmUs1bPSuyHUedVxLZ+SWRlqM0Z1RyaxeCVSBRLAGYsA3dRu8xfqjRA3BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T23:48:13.649044Z","bundle_sha256":"8947df4de1387c26f44dd28fe9034a7556ab14d5ddc582efa4337df9d47d3508"}}