{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CIIZ5MOO4BE6GG55LLXX5DG5CP","short_pith_number":"pith:CIIZ5MOO","canonical_record":{"source":{"id":"1611.09029","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T09:08:13Z","cross_cats_sorted":["hep-th","math.MP","math.OA","math.RT","quant-ph"],"title_canon_sha256":"322234d9dd4f60fb8c910be5606e19e23f7ab3607176e16be23eb1a26c182280","abstract_canon_sha256":"945e1717d4ff2d3ba49452079d7213b483bd260fc064a199fc37682a1a4cd2ff"},"schema_version":"1.0"},"canonical_sha256":"12119eb1cee049e31bbd5aef7e8cdd13dfa26c0d246d8c1cbd6e4846e1dc9cd0","source":{"kind":"arxiv","id":"1611.09029","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09029","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09029v4","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09029","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"CIIZ5MOO4BE6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CIIZ5MOO4BE6GG55","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CIIZ5MOO","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CIIZ5MOO4BE6GG55LLXX5DG5CP","target":"record","payload":{"canonical_record":{"source":{"id":"1611.09029","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T09:08:13Z","cross_cats_sorted":["hep-th","math.MP","math.OA","math.RT","quant-ph"],"title_canon_sha256":"322234d9dd4f60fb8c910be5606e19e23f7ab3607176e16be23eb1a26c182280","abstract_canon_sha256":"945e1717d4ff2d3ba49452079d7213b483bd260fc064a199fc37682a1a4cd2ff"},"schema_version":"1.0"},"canonical_sha256":"12119eb1cee049e31bbd5aef7e8cdd13dfa26c0d246d8c1cbd6e4846e1dc9cd0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:23.704332Z","signature_b64":"FkiMY2r6pugTNCp9Ah5HkbAWE29ow1fSVn9s2uS4Epujjcjyv4fG/7uLSttV5tNmyoCsGHOsmUnvQZ9tQPi+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12119eb1cee049e31bbd5aef7e8cdd13dfa26c0d246d8c1cbd6e4846e1dc9cd0","last_reissued_at":"2026-05-18T00:42:23.703829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:23.703829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.09029","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"256+2BDGsejAESarktKxqsj3KjplqW0hUJp5r8OpDJi4C46+ixj95fW09Y44HjnjtBBpB3ajwWVncjzrQmOuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:08:20.687242Z"},"content_sha256":"aa402a671550f69119099a11f9527ed8daa111f50b9d34ff5de3ec6cba86c705","schema_version":"1.0","event_id":"sha256:aa402a671550f69119099a11f9527ed8daa111f50b9d34ff5de3ec6cba86c705"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CIIZ5MOO4BE6GG55LLXX5DG5CP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincar\\'e symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.OA","math.RT","quant-ph"],"primary_cat":"math-ph","authors_text":"Marco Oppio (Trento U.), Valter Moretti","submitted_at":"2016-11-28T09:08:13Z","abstract_excerpt":"As established by Sol\\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\\\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this issue from another viewpoint, we argue that there is a fundamental reason why elementary quantum systems are not described in real Hilbert spaces: their symmetry group. We consider an elementary relativistic system within Wigner's approach defined as a locally-faithful irreducible continuous unitary representation of the Poincar\\'e group in a real Hilbert s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09029","kind":"arxiv","version":4},"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":"2026-05-18T00:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vsAhwZdbs3nVn5HJp4neCdsPdjz+zXjsrufMrBO6mUO6nXV7gu/psKdX4C4Pk5JGF+yKi6De1gUBtTuOCklOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:08:20.687645Z"},"content_sha256":"15089110f896e568e5817c2a32debd4ac87a57b5493d9d433a68c8eff6d05b2c","schema_version":"1.0","event_id":"sha256:15089110f896e568e5817c2a32debd4ac87a57b5493d9d433a68c8eff6d05b2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIIZ5MOO4BE6GG55LLXX5DG5CP/bundle.json","state_url":"https://pith.science/pith/CIIZ5MOO4BE6GG55LLXX5DG5CP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIIZ5MOO4BE6GG55LLXX5DG5CP/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":"2026-06-05T09:08:20Z","links":{"resolver":"https://pith.science/pith/CIIZ5MOO4BE6GG55LLXX5DG5CP","bundle":"https://pith.science/pith/CIIZ5MOO4BE6GG55LLXX5DG5CP/bundle.json","state":"https://pith.science/pith/CIIZ5MOO4BE6GG55LLXX5DG5CP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIIZ5MOO4BE6GG55LLXX5DG5CP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CIIZ5MOO4BE6GG55LLXX5DG5CP","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":"945e1717d4ff2d3ba49452079d7213b483bd260fc064a199fc37682a1a4cd2ff","cross_cats_sorted":["hep-th","math.MP","math.OA","math.RT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T09:08:13Z","title_canon_sha256":"322234d9dd4f60fb8c910be5606e19e23f7ab3607176e16be23eb1a26c182280"},"schema_version":"1.0","source":{"id":"1611.09029","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09029","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09029v4","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09029","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"CIIZ5MOO4BE6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CIIZ5MOO4BE6GG55","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CIIZ5MOO","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:15089110f896e568e5817c2a32debd4ac87a57b5493d9d433a68c8eff6d05b2c","target":"graph","created_at":"2026-05-18T00:42:23Z","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":"As established by Sol\\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\\\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this issue from another viewpoint, we argue that there is a fundamental reason why elementary quantum systems are not described in real Hilbert spaces: their symmetry group. We consider an elementary relativistic system within Wigner's approach defined as a locally-faithful irreducible continuous unitary representation of the Poincar\\'e group in a real Hilbert s","authors_text":"Marco Oppio (Trento U.), Valter Moretti","cross_cats":["hep-th","math.MP","math.OA","math.RT","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T09:08:13Z","title":"Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincar\\'e symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09029","kind":"arxiv","version":4},"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:aa402a671550f69119099a11f9527ed8daa111f50b9d34ff5de3ec6cba86c705","target":"record","created_at":"2026-05-18T00:42:23Z","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":"945e1717d4ff2d3ba49452079d7213b483bd260fc064a199fc37682a1a4cd2ff","cross_cats_sorted":["hep-th","math.MP","math.OA","math.RT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-28T09:08:13Z","title_canon_sha256":"322234d9dd4f60fb8c910be5606e19e23f7ab3607176e16be23eb1a26c182280"},"schema_version":"1.0","source":{"id":"1611.09029","kind":"arxiv","version":4}},"canonical_sha256":"12119eb1cee049e31bbd5aef7e8cdd13dfa26c0d246d8c1cbd6e4846e1dc9cd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12119eb1cee049e31bbd5aef7e8cdd13dfa26c0d246d8c1cbd6e4846e1dc9cd0","first_computed_at":"2026-05-18T00:42:23.703829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:23.703829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FkiMY2r6pugTNCp9Ah5HkbAWE29ow1fSVn9s2uS4Epujjcjyv4fG/7uLSttV5tNmyoCsGHOsmUnvQZ9tQPi+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:23.704332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09029","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa402a671550f69119099a11f9527ed8daa111f50b9d34ff5de3ec6cba86c705","sha256:15089110f896e568e5817c2a32debd4ac87a57b5493d9d433a68c8eff6d05b2c"],"state_sha256":"a87d9ab51fc9f6d1bac63fad0eaceac182f6a0d038d28336a2e8dd1f25c30c98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"81/w0+wUh/OUELjHDBt/yyDWcJ1fTLJ1v0bs/t6hKs+fdTk0+scFS9uX5iIT1q+yvolt/roANrfXX0NzMJ+BBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:08:20.690065Z","bundle_sha256":"274a1a5b137bbf958a90e2b4cbdf7cbb56a2881d9df1ccb7586defa9efe560a9"}}