{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:LNV5IVSQPR47FPXKKRK5BM3WUD","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":"85180243d1337abdee951ac8c998faa4bb50c2782eb4fd697ad0a819d2e52abc","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-01-26T19:20:11Z","title_canon_sha256":"41a1642ed79b326fb06fc4cdf84031b15ac24da881f0c4c9756ae946da70c350"},"schema_version":"1.0","source":{"id":"quant-ph/0401160","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0401160","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0401160v2","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0401160","created_at":"2026-05-18T01:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"LNV5IVSQPR47","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"LNV5IVSQPR47FPXK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"LNV5IVSQ","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:46597b181f394f6e981081e135c899b8680b61d0ac67c9d3aca30a1b91dd5571","target":"graph","created_at":"2026-05-18T01:37:58Z","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":"$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations affect $p$-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of $p$-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state","authors_text":"Alastair Brodlie","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-01-26T19:20:11Z","title":"Non-Linear Canonical Transformations in Classical and Quantum Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0401160","kind":"arxiv","version":2},"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:d57fce3f60856096b5d3bf6c6a0cc182c64d4806002098efe34ed2c5f12ec42e","target":"record","created_at":"2026-05-18T01:37:58Z","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":"85180243d1337abdee951ac8c998faa4bb50c2782eb4fd697ad0a819d2e52abc","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-01-26T19:20:11Z","title_canon_sha256":"41a1642ed79b326fb06fc4cdf84031b15ac24da881f0c4c9756ae946da70c350"},"schema_version":"1.0","source":{"id":"quant-ph/0401160","kind":"arxiv","version":2}},"canonical_sha256":"5b6bd456507c79f2beea5455d0b376a0ca7c64267d71c3e495f402996b3b98a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b6bd456507c79f2beea5455d0b376a0ca7c64267d71c3e495f402996b3b98a3","first_computed_at":"2026-05-18T01:37:58.746587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:58.746587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gfkUg8wEoEUdKr1wYCo7L97fFUuQMWB7z/JumkJSQLaDf78wL+3ORhupQwiAuEntKGQr+Yk2xCdbPlyAz8G3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:58.747125Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0401160","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d57fce3f60856096b5d3bf6c6a0cc182c64d4806002098efe34ed2c5f12ec42e","sha256:46597b181f394f6e981081e135c899b8680b61d0ac67c9d3aca30a1b91dd5571"],"state_sha256":"37cfaa0586cf2d02e1c0458bce75714fdf40cacc8aaf1745749b6f0f5a656c7e"}