{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:IEIOLKV3ENK4HIYWKXFQGM7OLP","short_pith_number":"pith:IEIOLKV3","canonical_record":{"source":{"id":"2506.07632","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-09T10:58:13Z","cross_cats_sorted":[],"title_canon_sha256":"40110ee1bfee5ffe2b3e12570a41903bf1353e502917ca6a88c0ffff21d71115","abstract_canon_sha256":"fb0b8bb2e9c9e5f085671324de0295a8c7f73b3748157b561dbae59b3395ab0c"},"schema_version":"1.0"},"canonical_sha256":"4110e5aabb2355c3a31655cb0333ee5bf651b74113fbef1750bc8c9b50c5162c","source":{"kind":"arxiv","id":"2506.07632","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07632","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07632v1","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07632","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"IEIOLKV3ENK4","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"pith_short_16","alias_value":"IEIOLKV3ENK4HIYW","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"pith_short_8","alias_value":"IEIOLKV3","created_at":"2026-07-05T11:18:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:IEIOLKV3ENK4HIYWKXFQGM7OLP","target":"record","payload":{"canonical_record":{"source":{"id":"2506.07632","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-09T10:58:13Z","cross_cats_sorted":[],"title_canon_sha256":"40110ee1bfee5ffe2b3e12570a41903bf1353e502917ca6a88c0ffff21d71115","abstract_canon_sha256":"fb0b8bb2e9c9e5f085671324de0295a8c7f73b3748157b561dbae59b3395ab0c"},"schema_version":"1.0"},"canonical_sha256":"4110e5aabb2355c3a31655cb0333ee5bf651b74113fbef1750bc8c9b50c5162c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:30.623056Z","signature_b64":"ihx9pe6Hf/Wg76L0IC/DklC0LqY1nGd3S3KGhdK3soMilurSVKas4fFFnd9/vShH9GW+wgKkhc+vh1Fyu1UCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4110e5aabb2355c3a31655cb0333ee5bf651b74113fbef1750bc8c9b50c5162c","last_reissued_at":"2026-07-05T11:18:30.622471Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:30.622471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.07632","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":"2026-07-05T11:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvT3fe1LJCpO7z022N9qTcg2oUp/1pNGf44ZNcbC7TWrmLVRMr2OhiPm2ik5cTQGly87Emw57EOZxadEeviyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:57:10.418079Z"},"content_sha256":"6c62f568654077ca379377f9c654aefe730737aa0b47f024b3951443e8d25953","schema_version":"1.0","event_id":"sha256:6c62f568654077ca379377f9c654aefe730737aa0b47f024b3951443e8d25953"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:IEIOLKV3ENK4HIYWKXFQGM7OLP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on Real Quantum Mechanics in a Kahler Space","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Igor Volovich, Irina Aref'eva","submitted_at":"2025-06-09T10:58:13Z","abstract_excerpt":"The necessity of complex numbers in quantum mechanics has long been debated. This paper develops a real Kahler space formulation of quantum mechanics [19], asserting equivalence to the standard complex Hilbert space framework. By mapping the complex Hilbert space ${\\mathbb C}^n$ to a real Kahler space $K ^{2n}$, i.e. ${\\mathbb R}^{2n}$ equipped with a metric, a symplectic structure and an automorphism, we establish a correspondence between Hermitian operators in ${\\mathbb C}^n$ and real operators in $K^{2n}$. While the isomorphism appears straightforward some subtleties emerge: (i) the overcou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07632","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.07632/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9So+6+GzR6BadAf2JAcLwL3p63osm/QHA2pG5Zx++Z0HLBR7yfyEZaJFlxh8DFzoMsct+Ol422N2YUW8iwAYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:57:10.418675Z"},"content_sha256":"d1733ca56d3ed19536c503ec2bf82715ac2ed676a2732182f186b64687b40e59","schema_version":"1.0","event_id":"sha256:d1733ca56d3ed19536c503ec2bf82715ac2ed676a2732182f186b64687b40e59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEIOLKV3ENK4HIYWKXFQGM7OLP/bundle.json","state_url":"https://pith.science/pith/IEIOLKV3ENK4HIYWKXFQGM7OLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEIOLKV3ENK4HIYWKXFQGM7OLP/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":"2026-08-04T07:57:10Z","links":{"resolver":"https://pith.science/pith/IEIOLKV3ENK4HIYWKXFQGM7OLP","bundle":"https://pith.science/pith/IEIOLKV3ENK4HIYWKXFQGM7OLP/bundle.json","state":"https://pith.science/pith/IEIOLKV3ENK4HIYWKXFQGM7OLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEIOLKV3ENK4HIYWKXFQGM7OLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IEIOLKV3ENK4HIYWKXFQGM7OLP","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":"fb0b8bb2e9c9e5f085671324de0295a8c7f73b3748157b561dbae59b3395ab0c","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-09T10:58:13Z","title_canon_sha256":"40110ee1bfee5ffe2b3e12570a41903bf1353e502917ca6a88c0ffff21d71115"},"schema_version":"1.0","source":{"id":"2506.07632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07632","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07632v1","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07632","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"IEIOLKV3ENK4","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"pith_short_16","alias_value":"IEIOLKV3ENK4HIYW","created_at":"2026-07-05T11:18:30Z"},{"alias_kind":"pith_short_8","alias_value":"IEIOLKV3","created_at":"2026-07-05T11:18:30Z"}],"graph_snapshots":[{"event_id":"sha256:d1733ca56d3ed19536c503ec2bf82715ac2ed676a2732182f186b64687b40e59","target":"graph","created_at":"2026-07-05T11:18:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.07632/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The necessity of complex numbers in quantum mechanics has long been debated. This paper develops a real Kahler space formulation of quantum mechanics [19], asserting equivalence to the standard complex Hilbert space framework. By mapping the complex Hilbert space ${\\mathbb C}^n$ to a real Kahler space $K ^{2n}$, i.e. ${\\mathbb R}^{2n}$ equipped with a metric, a symplectic structure and an automorphism, we establish a correspondence between Hermitian operators in ${\\mathbb C}^n$ and real operators in $K^{2n}$. While the isomorphism appears straightforward some subtleties emerge: (i) the overcou","authors_text":"Igor Volovich, Irina Aref'eva","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-09T10:58:13Z","title":"Notes on Real Quantum Mechanics in a Kahler Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07632","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":"sha256:6c62f568654077ca379377f9c654aefe730737aa0b47f024b3951443e8d25953","target":"record","created_at":"2026-07-05T11:18:30Z","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":"fb0b8bb2e9c9e5f085671324de0295a8c7f73b3748157b561dbae59b3395ab0c","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-09T10:58:13Z","title_canon_sha256":"40110ee1bfee5ffe2b3e12570a41903bf1353e502917ca6a88c0ffff21d71115"},"schema_version":"1.0","source":{"id":"2506.07632","kind":"arxiv","version":1}},"canonical_sha256":"4110e5aabb2355c3a31655cb0333ee5bf651b74113fbef1750bc8c9b50c5162c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4110e5aabb2355c3a31655cb0333ee5bf651b74113fbef1750bc8c9b50c5162c","first_computed_at":"2026-07-05T11:18:30.622471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:30.622471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ihx9pe6Hf/Wg76L0IC/DklC0LqY1nGd3S3KGhdK3soMilurSVKas4fFFnd9/vShH9GW+wgKkhc+vh1Fyu1UCCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:30.623056Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c62f568654077ca379377f9c654aefe730737aa0b47f024b3951443e8d25953","sha256:d1733ca56d3ed19536c503ec2bf82715ac2ed676a2732182f186b64687b40e59"],"state_sha256":"310c8caf567ce14f46af4503a8ecee222fc8a63ff6d36bb1d2a535d3d06c2079"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YSHygu3ik/fYaOu8+pnqXcClul4uOS4KV3LKo8nOkpWJeCi06HVB6HjETdqROZQLPAEQPMYQ3u49PACyehGcDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T07:57:10.424992Z","bundle_sha256":"0151a759a460d863b3610e677ae62a724756b57baafb48afd00d6ef5e6c36b7c"}}