{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PFF4OOPHNUBPNRJJGODDAKYKEV","short_pith_number":"pith:PFF4OOPH","schema_version":"1.0","canonical_sha256":"794bc739e76d02f6c5293386302b0a25424841088a49b458adc44c484f20f31d","source":{"kind":"arxiv","id":"1505.06391","version":3},"attestation_state":"computed","paper":{"title":"Classical Mechanics in Hilbert Space: Path Integral Formulation, and a Quantum Correction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"James Shee","submitted_at":"2015-05-24T01:48:52Z","abstract_excerpt":"While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory, which recasts classical mechanics in terms of a Hilbert space wherein the Liouville operator acts as the generator of motion, we derive a path integral representation of the classical propagator and suggest an efficient numerical implementation using fast fourier transform techniques. We then include a first quantum correction to derive a revealing expression f"},"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":"1505.06391","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2015-05-24T01:48:52Z","cross_cats_sorted":[],"title_canon_sha256":"43c006b22ccad02aa6a987d63ee1a1e11ddc9c13a57f169a39063594424f709b","abstract_canon_sha256":"b8ff8986454c59d4bec73174135368dbef42a5d5da8a121a13f26144f46689e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:35.550707Z","signature_b64":"scDcxp/e+ENy7dk8wXE99cg3s96j//jTuySRnYGEjBIqDlvR8L3DTJbyWS6oa4Fr8jlAHsoDqEYmn2IanyDQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"794bc739e76d02f6c5293386302b0a25424841088a49b458adc44c484f20f31d","last_reissued_at":"2026-05-18T00:59:35.550077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:35.550077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classical Mechanics in Hilbert Space: Path Integral Formulation, and a Quantum Correction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"James Shee","submitted_at":"2015-05-24T01:48:52Z","abstract_excerpt":"While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory, which recasts classical mechanics in terms of a Hilbert space wherein the Liouville operator acts as the generator of motion, we derive a path integral representation of the classical propagator and suggest an efficient numerical implementation using fast fourier transform techniques. We then include a first quantum correction to derive a revealing expression f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06391","kind":"arxiv","version":3},"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":"1505.06391","created_at":"2026-05-18T00:59:35.550186+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06391v3","created_at":"2026-05-18T00:59:35.550186+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06391","created_at":"2026-05-18T00:59:35.550186+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFF4OOPHNUBP","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFF4OOPHNUBPNRJJ","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFF4OOPH","created_at":"2026-05-18T12:29:37.295048+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/PFF4OOPHNUBPNRJJGODDAKYKEV","json":"https://pith.science/pith/PFF4OOPHNUBPNRJJGODDAKYKEV.json","graph_json":"https://pith.science/api/pith-number/PFF4OOPHNUBPNRJJGODDAKYKEV/graph.json","events_json":"https://pith.science/api/pith-number/PFF4OOPHNUBPNRJJGODDAKYKEV/events.json","paper":"https://pith.science/paper/PFF4OOPH"},"agent_actions":{"view_html":"https://pith.science/pith/PFF4OOPHNUBPNRJJGODDAKYKEV","download_json":"https://pith.science/pith/PFF4OOPHNUBPNRJJGODDAKYKEV.json","view_paper":"https://pith.science/paper/PFF4OOPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06391&json=true","fetch_graph":"https://pith.science/api/pith-number/PFF4OOPHNUBPNRJJGODDAKYKEV/graph.json","fetch_events":"https://pith.science/api/pith-number/PFF4OOPHNUBPNRJJGODDAKYKEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFF4OOPHNUBPNRJJGODDAKYKEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFF4OOPHNUBPNRJJGODDAKYKEV/action/storage_attestation","attest_author":"https://pith.science/pith/PFF4OOPHNUBPNRJJGODDAKYKEV/action/author_attestation","sign_citation":"https://pith.science/pith/PFF4OOPHNUBPNRJJGODDAKYKEV/action/citation_signature","submit_replication":"https://pith.science/pith/PFF4OOPHNUBPNRJJGODDAKYKEV/action/replication_record"}},"created_at":"2026-05-18T00:59:35.550186+00:00","updated_at":"2026-05-18T00:59:35.550186+00:00"}