{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:D4XQQXGSJWHHEEW2YK44CLUTYY","short_pith_number":"pith:D4XQQXGS","canonical_record":{"source":{"id":"1304.2086","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-08T01:53:06Z","cross_cats_sorted":["hep-th","math.MP","physics.class-ph"],"title_canon_sha256":"a14a0b1a66a90007c2926d548b21457480f5a8878daf31fcef80010f3be2f5ca","abstract_canon_sha256":"ac1c1afd740a53be4e4e713fb7b396aed9a6d2a98018874380b7f90c40bdf9e8"},"schema_version":"1.0"},"canonical_sha256":"1f2f085cd24d8e7212dac2b9c12e93c6034ae102231c4d2557866f5a3dd1c061","source":{"kind":"arxiv","id":"1304.2086","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2086","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2086v3","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2086","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"D4XQQXGSJWHH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D4XQQXGSJWHHEEW2","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D4XQQXGS","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:D4XQQXGSJWHHEEW2YK44CLUTYY","target":"record","payload":{"canonical_record":{"source":{"id":"1304.2086","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-08T01:53:06Z","cross_cats_sorted":["hep-th","math.MP","physics.class-ph"],"title_canon_sha256":"a14a0b1a66a90007c2926d548b21457480f5a8878daf31fcef80010f3be2f5ca","abstract_canon_sha256":"ac1c1afd740a53be4e4e713fb7b396aed9a6d2a98018874380b7f90c40bdf9e8"},"schema_version":"1.0"},"canonical_sha256":"1f2f085cd24d8e7212dac2b9c12e93c6034ae102231c4d2557866f5a3dd1c061","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:33.773996Z","signature_b64":"7Sb54b3tGQdLC/2w8SfjN5zx97x/1sNktJOdIg0K6Gyz5UoRoK4Td+MsrRI2os34czlztskfW4aJysrfoYXcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f2f085cd24d8e7212dac2b9c12e93c6034ae102231c4d2557866f5a3dd1c061","last_reissued_at":"2026-05-18T03:13:33.773435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:33.773435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.2086","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/e3FRtgkpwkmBsx+4I6d9ay1lDbYGJ5zRMA6HkyU96FvJK0fflHa/fi5X9BlY81RNZtv2MZR8W44mfVQJxgICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:55:50.886029Z"},"content_sha256":"40807050866cec19713572ecd08a11581b36f12c9c8a50b9ac1428867a56d48e","schema_version":"1.0","event_id":"sha256:40807050866cec19713572ecd08a11581b36f12c9c8a50b9ac1428867a56d48e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:D4XQQXGSJWHHEEW2YK44CLUTYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hidden Nambu mechanics - A variant formulation of Hamiltonian systems -","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Atsushi Horikoshi, Yoshiharu Kawamura","submitted_at":"2013-04-08T01:53:06Z","abstract_excerpt":"We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extended dynamics whose master equation is the Nambu equation or its generalization. Partition functions associated with the extended dynamics in many degrees of freedom systems are given. Our formulation can also be applied to Hamiltonian systems with first class constraints."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2086","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KcmwK7zRh2Hih34wkqTJzzRvn/ipZyBnQVuUFuJvje+nbuUo7AkzS43+s4u1nC/LO/hwLE3canNG9rBCfagkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:55:50.886517Z"},"content_sha256":"6e736836d8527c1d835d45e91c95c47251255240b76b77dfb593a3f245bb58f0","schema_version":"1.0","event_id":"sha256:6e736836d8527c1d835d45e91c95c47251255240b76b77dfb593a3f245bb58f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4XQQXGSJWHHEEW2YK44CLUTYY/bundle.json","state_url":"https://pith.science/pith/D4XQQXGSJWHHEEW2YK44CLUTYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4XQQXGSJWHHEEW2YK44CLUTYY/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":"2026-06-08T14:55:50Z","links":{"resolver":"https://pith.science/pith/D4XQQXGSJWHHEEW2YK44CLUTYY","bundle":"https://pith.science/pith/D4XQQXGSJWHHEEW2YK44CLUTYY/bundle.json","state":"https://pith.science/pith/D4XQQXGSJWHHEEW2YK44CLUTYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4XQQXGSJWHHEEW2YK44CLUTYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D4XQQXGSJWHHEEW2YK44CLUTYY","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":"ac1c1afd740a53be4e4e713fb7b396aed9a6d2a98018874380b7f90c40bdf9e8","cross_cats_sorted":["hep-th","math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-08T01:53:06Z","title_canon_sha256":"a14a0b1a66a90007c2926d548b21457480f5a8878daf31fcef80010f3be2f5ca"},"schema_version":"1.0","source":{"id":"1304.2086","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2086","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2086v3","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2086","created_at":"2026-05-18T03:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"D4XQQXGSJWHH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D4XQQXGSJWHHEEW2","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D4XQQXGS","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:6e736836d8527c1d835d45e91c95c47251255240b76b77dfb593a3f245bb58f0","target":"graph","created_at":"2026-05-18T03:13:33Z","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":"We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extended dynamics whose master equation is the Nambu equation or its generalization. Partition functions associated with the extended dynamics in many degrees of freedom systems are given. Our formulation can also be applied to Hamiltonian systems with first class constraints.","authors_text":"Atsushi Horikoshi, Yoshiharu Kawamura","cross_cats":["hep-th","math.MP","physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-08T01:53:06Z","title":"Hidden Nambu mechanics - A variant formulation of Hamiltonian systems -"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2086","kind":"arxiv","version":3},"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":"sha256:40807050866cec19713572ecd08a11581b36f12c9c8a50b9ac1428867a56d48e","target":"record","created_at":"2026-05-18T03:13:33Z","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":"ac1c1afd740a53be4e4e713fb7b396aed9a6d2a98018874380b7f90c40bdf9e8","cross_cats_sorted":["hep-th","math.MP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-08T01:53:06Z","title_canon_sha256":"a14a0b1a66a90007c2926d548b21457480f5a8878daf31fcef80010f3be2f5ca"},"schema_version":"1.0","source":{"id":"1304.2086","kind":"arxiv","version":3}},"canonical_sha256":"1f2f085cd24d8e7212dac2b9c12e93c6034ae102231c4d2557866f5a3dd1c061","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f2f085cd24d8e7212dac2b9c12e93c6034ae102231c4d2557866f5a3dd1c061","first_computed_at":"2026-05-18T03:13:33.773435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:33.773435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Sb54b3tGQdLC/2w8SfjN5zx97x/1sNktJOdIg0K6Gyz5UoRoK4Td+MsrRI2os34czlztskfW4aJysrfoYXcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:33.773996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2086","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40807050866cec19713572ecd08a11581b36f12c9c8a50b9ac1428867a56d48e","sha256:6e736836d8527c1d835d45e91c95c47251255240b76b77dfb593a3f245bb58f0"],"state_sha256":"358e6b9495a48407741b71cad91823c20bf2586103941bfadb30103c6f935138"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80/z1B34KhBBP8tphJnk7bF7VYlvNilaVBSeNrNT4R8aqICvjOI4G1iizhiJ3A0W9IRbcAJ5DxQ2MSSaa0VPAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:55:50.888926Z","bundle_sha256":"e9b499e09b2882163036af517f44596659b1fb922a6486ed1e7fb3c7907ee6d3"}}