{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:LLWUTTLBP2BD4STM3BGI2WXQYT","short_pith_number":"pith:LLWUTTLB","schema_version":"1.0","canonical_sha256":"5aed49cd617e823e4a6cd84c8d5af0c4fc7f3c8adebf8015b148d46dcdd79067","source":{"kind":"arxiv","id":"hep-th/0407161","version":1},"attestation_state":"computed","paper":{"title":"A Quantum is a Complex Structure on Classical Phase Space","license":"","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"J.M. Isidro","submitted_at":"2004-07-19T08:38:39Z","abstract_excerpt":"Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase space. Under an observer we understand, as in general relativity, a local coordinate chart. While classical mechanics can be formulated using a symplectic structure on classical phase space, quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold are often not unique. This arti"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-th/0407161","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-07-19T08:38:39Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"989308dba6de513da8e73901fca48ae3f4d8355cfe8c75ab2d7ade83b0ae0c25","abstract_canon_sha256":"ab7d93f2361182f751c3994ffb89c4c55b4d6dee6d8527bce1709f5e6099362a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:46.175608Z","signature_b64":"GVW9GFgNRI54wKqP4QPZfigQgq+PM5BRIFmhSQ/x0s14aTyGY08orlU+laat3SZ/DUGFnPx3TXyx3/Qdqg/3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5aed49cd617e823e4a6cd84c8d5af0c4fc7f3c8adebf8015b148d46dcdd79067","last_reissued_at":"2026-05-18T01:38:46.175142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:46.175142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Quantum is a Complex Structure on Classical Phase Space","license":"","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"J.M. Isidro","submitted_at":"2004-07-19T08:38:39Z","abstract_excerpt":"Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase space. Under an observer we understand, as in general relativity, a local coordinate chart. While classical mechanics can be formulated using a symplectic structure on classical phase space, quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold are often not unique. This arti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0407161","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0407161","created_at":"2026-05-18T01:38:46.175223+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0407161v1","created_at":"2026-05-18T01:38:46.175223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0407161","created_at":"2026-05-18T01:38:46.175223+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLWUTTLBP2BD","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLWUTTLBP2BD4STM","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLWUTTLB","created_at":"2026-05-18T12:25:52.687210+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT","json":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT.json","graph_json":"https://pith.science/api/pith-number/LLWUTTLBP2BD4STM3BGI2WXQYT/graph.json","events_json":"https://pith.science/api/pith-number/LLWUTTLBP2BD4STM3BGI2WXQYT/events.json","paper":"https://pith.science/paper/LLWUTTLB"},"agent_actions":{"view_html":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT","download_json":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT.json","view_paper":"https://pith.science/paper/LLWUTTLB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0407161&json=true","fetch_graph":"https://pith.science/api/pith-number/LLWUTTLBP2BD4STM3BGI2WXQYT/graph.json","fetch_events":"https://pith.science/api/pith-number/LLWUTTLBP2BD4STM3BGI2WXQYT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT/action/storage_attestation","attest_author":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT/action/author_attestation","sign_citation":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT/action/citation_signature","submit_replication":"https://pith.science/pith/LLWUTTLBP2BD4STM3BGI2WXQYT/action/replication_record"}},"created_at":"2026-05-18T01:38:46.175223+00:00","updated_at":"2026-05-18T01:38:46.175223+00:00"}