{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CBEJUXVLIRIW4C3XSEWGU57JXR","short_pith_number":"pith:CBEJUXVL","canonical_record":{"source":{"id":"1408.4736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2014-08-20T17:33:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fd30bbe2ef2b69799c81db965937aafebecf5e085c7c9e553046294b8785c1ea","abstract_canon_sha256":"0873d068c137829d1c79df684210f54fbacce2e37068d62af42c8d6af7ccd7bb"},"schema_version":"1.0"},"canonical_sha256":"10489a5eab44516e0b77912c6a77e9bc4521d619a808182ab57440ea56609c2d","source":{"kind":"arxiv","id":"1408.4736","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4736","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4736v1","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4736","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"CBEJUXVLIRIW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CBEJUXVLIRIW4C3X","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CBEJUXVL","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CBEJUXVLIRIW4C3XSEWGU57JXR","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2014-08-20T17:33:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fd30bbe2ef2b69799c81db965937aafebecf5e085c7c9e553046294b8785c1ea","abstract_canon_sha256":"0873d068c137829d1c79df684210f54fbacce2e37068d62af42c8d6af7ccd7bb"},"schema_version":"1.0"},"canonical_sha256":"10489a5eab44516e0b77912c6a77e9bc4521d619a808182ab57440ea56609c2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:48.206169Z","signature_b64":"GlrJxcOs/S/oIRlsAPi8YMBmat6KghQ5m+gh8/Cew6SQF4iOcpn3wh6g2Ceu97xEKClFhQf2geHdDavspEVVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10489a5eab44516e0b77912c6a77e9bc4521d619a808182ab57440ea56609c2d","last_reissued_at":"2026-05-18T02:44:48.205726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:48.205726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4736","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":"2026-05-18T02:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"03kNDhrUYXCTMgU0Q2/f+hkvpCaklE/WgKRYr1OqDmnhxFjn6sFWHpi1hGae4buiIYvWwDDNMClixE/cnJKeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:46:47.847858Z"},"content_sha256":"5854ed43cc361366ae8b39a3373c6cd9345501a305a7b4b8bc4c652ab9c7a005","schema_version":"1.0","event_id":"sha256:5854ed43cc361366ae8b39a3373c6cd9345501a305a7b4b8bc4c652ab9c7a005"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CBEJUXVLIRIW4C3XSEWGU57JXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constants of motion associated with alternative Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.class-ph","authors_text":"Gerardo F. Torres del Castillo","submitted_at":"2014-08-20T17:33:13Z","abstract_excerpt":"It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_{i}, p_{i})$ and $(Q_{i}, P_{i})$, then the determinant and the trace of any power of a certain matrix formed by the Poisson brackets of the $Q_{i}, P_{i}$ with respect to $q_{i}, p_{i}$, are constants of motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4736","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWr+AbbR0iRtw2AGzf7f72q248LxroyMv1Wpg1mbtshYBdMRZ1htwMqZ6fJBahPTVjrCxRA3AG5rTslS4cN8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:46:47.848609Z"},"content_sha256":"b28d742bec2c471040787386151779128c0ea0511e323eac02662df301130569","schema_version":"1.0","event_id":"sha256:b28d742bec2c471040787386151779128c0ea0511e323eac02662df301130569"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBEJUXVLIRIW4C3XSEWGU57JXR/bundle.json","state_url":"https://pith.science/pith/CBEJUXVLIRIW4C3XSEWGU57JXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBEJUXVLIRIW4C3XSEWGU57JXR/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":"2026-06-09T07:46:47Z","links":{"resolver":"https://pith.science/pith/CBEJUXVLIRIW4C3XSEWGU57JXR","bundle":"https://pith.science/pith/CBEJUXVLIRIW4C3XSEWGU57JXR/bundle.json","state":"https://pith.science/pith/CBEJUXVLIRIW4C3XSEWGU57JXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBEJUXVLIRIW4C3XSEWGU57JXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CBEJUXVLIRIW4C3XSEWGU57JXR","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":"0873d068c137829d1c79df684210f54fbacce2e37068d62af42c8d6af7ccd7bb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2014-08-20T17:33:13Z","title_canon_sha256":"fd30bbe2ef2b69799c81db965937aafebecf5e085c7c9e553046294b8785c1ea"},"schema_version":"1.0","source":{"id":"1408.4736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4736","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4736v1","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4736","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"CBEJUXVLIRIW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CBEJUXVLIRIW4C3X","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CBEJUXVL","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:b28d742bec2c471040787386151779128c0ea0511e323eac02662df301130569","target":"graph","created_at":"2026-05-18T02:44:48Z","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":"It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_{i}, p_{i})$ and $(Q_{i}, P_{i})$, then the determinant and the trace of any power of a certain matrix formed by the Poisson brackets of the $Q_{i}, P_{i}$ with respect to $q_{i}, p_{i}$, are constants of motion.","authors_text":"Gerardo F. Torres del Castillo","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2014-08-20T17:33:13Z","title":"Constants of motion associated with alternative Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4736","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":"sha256:5854ed43cc361366ae8b39a3373c6cd9345501a305a7b4b8bc4c652ab9c7a005","target":"record","created_at":"2026-05-18T02:44:48Z","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":"0873d068c137829d1c79df684210f54fbacce2e37068d62af42c8d6af7ccd7bb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2014-08-20T17:33:13Z","title_canon_sha256":"fd30bbe2ef2b69799c81db965937aafebecf5e085c7c9e553046294b8785c1ea"},"schema_version":"1.0","source":{"id":"1408.4736","kind":"arxiv","version":1}},"canonical_sha256":"10489a5eab44516e0b77912c6a77e9bc4521d619a808182ab57440ea56609c2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10489a5eab44516e0b77912c6a77e9bc4521d619a808182ab57440ea56609c2d","first_computed_at":"2026-05-18T02:44:48.205726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:48.205726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GlrJxcOs/S/oIRlsAPi8YMBmat6KghQ5m+gh8/Cew6SQF4iOcpn3wh6g2Ceu97xEKClFhQf2geHdDavspEVVAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:48.206169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5854ed43cc361366ae8b39a3373c6cd9345501a305a7b4b8bc4c652ab9c7a005","sha256:b28d742bec2c471040787386151779128c0ea0511e323eac02662df301130569"],"state_sha256":"42df7ac55bfea1426e90b6de6fdb27fadb5d5daa304f9a2433580401c707679f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zVJtq2HU2CSwK5i2d4/IyLRrZBiG2wkfxE1Sr+YAhC803QtA0NcBFZaMHQZ7yuJYcwsU2522f82pS5Esa3sICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:46:47.853067Z","bundle_sha256":"3fb545d7606e2e7a3643552f6c9a0a6cc0867be84a2f3577ae39f47da8779a41"}}