{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7FWIMWV3Q5SVGB2Z5UJYTWY5RD","short_pith_number":"pith:7FWIMWV3","schema_version":"1.0","canonical_sha256":"f96c865abb8765530759ed1389db1d88c8297754a408556d8998a2afaceee28f","source":{"kind":"arxiv","id":"2607.01024","version":1},"attestation_state":"computed","paper":{"title":"Madelung hydrodynamics and Poisson geometry of wave functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG"],"primary_cat":"math.DG","authors_text":"Boris Khesin, Klas Modin","submitted_at":"2026-07-01T14:57:09Z","abstract_excerpt":"We describe the Poisson geometry of the Madelung transform between quantum mechanics and hydrodynamics for generic wave functions. We prove that for arbitrary oriented manifolds this transform, being regarded as a momentum map, naturally defines prequantum bundles for coadjoint orbits of semidirect extensions of diffeomorphism groups. Furthermore, we show that the Madelung framework provides a natural infinite-dimensional version of the convexity results for Hamiltonian torus actions, thus giving a partial answer to Atiyah's question.\n  In particular, for wave functions without zeros our resul"},"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":"2607.01024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-01T14:57:09Z","cross_cats_sorted":["math-ph","math.MP","math.SG"],"title_canon_sha256":"de607fae1c0dbb9636c7e9be2fc6eff970e50eae9841b89b4dfec63ee0298b97","abstract_canon_sha256":"fbf5a768bf3b263bb6c6f7dfcfe1b2dad22e91e7ae7fa77c1befffe86b846033"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:26.289289Z","signature_b64":"0W8IzijGvdtSaSCcRLIlzcLrLS/N/TdOTbrCkRkhvul4SAitFc6er/u8YnU1c0+6JwSiHk6zPPpVkribvxVrAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f96c865abb8765530759ed1389db1d88c8297754a408556d8998a2afaceee28f","last_reissued_at":"2026-07-02T01:18:26.288890Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:26.288890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Madelung hydrodynamics and Poisson geometry of wave functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG"],"primary_cat":"math.DG","authors_text":"Boris Khesin, Klas Modin","submitted_at":"2026-07-01T14:57:09Z","abstract_excerpt":"We describe the Poisson geometry of the Madelung transform between quantum mechanics and hydrodynamics for generic wave functions. We prove that for arbitrary oriented manifolds this transform, being regarded as a momentum map, naturally defines prequantum bundles for coadjoint orbits of semidirect extensions of diffeomorphism groups. Furthermore, we show that the Madelung framework provides a natural infinite-dimensional version of the convexity results for Hamiltonian torus actions, thus giving a partial answer to Atiyah's question.\n  In particular, for wave functions without zeros our resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01024","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/2607.01024/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.01024","created_at":"2026-07-02T01:18:26.288950+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.01024v1","created_at":"2026-07-02T01:18:26.288950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01024","created_at":"2026-07-02T01:18:26.288950+00:00"},{"alias_kind":"pith_short_12","alias_value":"7FWIMWV3Q5SV","created_at":"2026-07-02T01:18:26.288950+00:00"},{"alias_kind":"pith_short_16","alias_value":"7FWIMWV3Q5SVGB2Z","created_at":"2026-07-02T01:18:26.288950+00:00"},{"alias_kind":"pith_short_8","alias_value":"7FWIMWV3","created_at":"2026-07-02T01:18:26.288950+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/7FWIMWV3Q5SVGB2Z5UJYTWY5RD","json":"https://pith.science/pith/7FWIMWV3Q5SVGB2Z5UJYTWY5RD.json","graph_json":"https://pith.science/api/pith-number/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/graph.json","events_json":"https://pith.science/api/pith-number/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/events.json","paper":"https://pith.science/paper/7FWIMWV3"},"agent_actions":{"view_html":"https://pith.science/pith/7FWIMWV3Q5SVGB2Z5UJYTWY5RD","download_json":"https://pith.science/pith/7FWIMWV3Q5SVGB2Z5UJYTWY5RD.json","view_paper":"https://pith.science/paper/7FWIMWV3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.01024&json=true","fetch_graph":"https://pith.science/api/pith-number/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/graph.json","fetch_events":"https://pith.science/api/pith-number/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/action/storage_attestation","attest_author":"https://pith.science/pith/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/action/author_attestation","sign_citation":"https://pith.science/pith/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/action/citation_signature","submit_replication":"https://pith.science/pith/7FWIMWV3Q5SVGB2Z5UJYTWY5RD/action/replication_record"}},"created_at":"2026-07-02T01:18:26.288950+00:00","updated_at":"2026-07-02T01:18:26.288950+00:00"}