{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IIU5KMQ6L2CSJOVYGISQI7U5ZY","short_pith_number":"pith:IIU5KMQ6","canonical_record":{"source":{"id":"1806.05003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-13T13:01:45Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"650da3c92046cfe91fe3dc4c46c44a0adeafac9f79c4cb6b5d92e9ef97a1b996","abstract_canon_sha256":"abc59e8639bd421218b433809cb52921319bfc992980fc8b04a0ce08c6e75652"},"schema_version":"1.0"},"canonical_sha256":"4229d5321e5e8524bab83225047e9dce03e5c530f665867990a083994d7a9441","source":{"kind":"arxiv","id":"1806.05003","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05003","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05003v1","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05003","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"IIU5KMQ6L2CS","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_16","alias_value":"IIU5KMQ6L2CSJOVY","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_8","alias_value":"IIU5KMQ6","created_at":"2026-07-05T02:00:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IIU5KMQ6L2CSJOVYGISQI7U5ZY","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-13T13:01:45Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"650da3c92046cfe91fe3dc4c46c44a0adeafac9f79c4cb6b5d92e9ef97a1b996","abstract_canon_sha256":"abc59e8639bd421218b433809cb52921319bfc992980fc8b04a0ce08c6e75652"},"schema_version":"1.0"},"canonical_sha256":"4229d5321e5e8524bab83225047e9dce03e5c530f665867990a083994d7a9441","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:00:40.942111Z","signature_b64":"7R5LR0VhumRLq/NvOHUyxCNO+lwJDkXCs7XeXHU/tSyKwhDzMLOJZ4chgyPZl/gYzilinItZw3NIf21ZIfevDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4229d5321e5e8524bab83225047e9dce03e5c530f665867990a083994d7a9441","last_reissued_at":"2026-07-05T02:00:40.941680Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:00:40.941680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05003","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":"2026-07-05T02:00:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HgO+wE7FkpSfJNkEge9EvTEGnwfInS4p2XLRzjVDtytYarmasDYaBBq3d6UtTtRCmmuFDafxLf06Z6IxnfrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:03:07.081480Z"},"content_sha256":"fc4a45646e19a48bae77525702f2b8e9a996a0bf0f16a1442541caf72cffa07a","schema_version":"1.0","event_id":"sha256:fc4a45646e19a48bae77525702f2b8e9a996a0bf0f16a1442541caf72cffa07a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IIU5KMQ6L2CSJOVYGISQI7U5ZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poissonization of Three Dimensional Nonholonomic Dynamics with the Method of Extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Naoki Sato","submitted_at":"2018-06-13T13:01:45Z","abstract_excerpt":"In this study we develop a systematic procedure to construct a Poisson operator that describes the dynamics of a three dimensional nonholonomic system. Instead of reducing by symmetry the antisymmetric operator that links the energy gradient to the velocity on the tangent bundle, the system is embedded in a larger space. Here, the extended antisymmetric operator, which preserves the original equations of motion, satisfies the Jacobi identity in a conformal fashion. Thus, a Poisson operator can be obtained by a further time reparametrization. Such Poissonization does not rely on the specific fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05003","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/1806.05003/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:00:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XaS3R8ZJlKt3anZA2sDHCDw8dnxp16I4SV7wAWlonO1U72Ki7bVDrWB/WnOMgs065Oc8JKU+/H5rv/zVY7NDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:03:07.082234Z"},"content_sha256":"2f7cf52cac548d04c59aaf063f2f53c802714b5171b33c3c1d05ba655e672177","schema_version":"1.0","event_id":"sha256:2f7cf52cac548d04c59aaf063f2f53c802714b5171b33c3c1d05ba655e672177"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IIU5KMQ6L2CSJOVYGISQI7U5ZY/bundle.json","state_url":"https://pith.science/pith/IIU5KMQ6L2CSJOVYGISQI7U5ZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IIU5KMQ6L2CSJOVYGISQI7U5ZY/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":"2026-08-16T20:03:07Z","links":{"resolver":"https://pith.science/pith/IIU5KMQ6L2CSJOVYGISQI7U5ZY","bundle":"https://pith.science/pith/IIU5KMQ6L2CSJOVYGISQI7U5ZY/bundle.json","state":"https://pith.science/pith/IIU5KMQ6L2CSJOVYGISQI7U5ZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IIU5KMQ6L2CSJOVYGISQI7U5ZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IIU5KMQ6L2CSJOVYGISQI7U5ZY","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":"abc59e8639bd421218b433809cb52921319bfc992980fc8b04a0ce08c6e75652","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-13T13:01:45Z","title_canon_sha256":"650da3c92046cfe91fe3dc4c46c44a0adeafac9f79c4cb6b5d92e9ef97a1b996"},"schema_version":"1.0","source":{"id":"1806.05003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05003","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05003v1","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05003","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"IIU5KMQ6L2CS","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_16","alias_value":"IIU5KMQ6L2CSJOVY","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_8","alias_value":"IIU5KMQ6","created_at":"2026-07-05T02:00:40Z"}],"graph_snapshots":[{"event_id":"sha256:2f7cf52cac548d04c59aaf063f2f53c802714b5171b33c3c1d05ba655e672177","target":"graph","created_at":"2026-07-05T02:00:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1806.05003/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this study we develop a systematic procedure to construct a Poisson operator that describes the dynamics of a three dimensional nonholonomic system. Instead of reducing by symmetry the antisymmetric operator that links the energy gradient to the velocity on the tangent bundle, the system is embedded in a larger space. Here, the extended antisymmetric operator, which preserves the original equations of motion, satisfies the Jacobi identity in a conformal fashion. Thus, a Poisson operator can be obtained by a further time reparametrization. Such Poissonization does not rely on the specific fo","authors_text":"Naoki Sato","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-13T13:01:45Z","title":"Poissonization of Three Dimensional Nonholonomic Dynamics with the Method of Extension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05003","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:fc4a45646e19a48bae77525702f2b8e9a996a0bf0f16a1442541caf72cffa07a","target":"record","created_at":"2026-07-05T02:00:40Z","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":"abc59e8639bd421218b433809cb52921319bfc992980fc8b04a0ce08c6e75652","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-13T13:01:45Z","title_canon_sha256":"650da3c92046cfe91fe3dc4c46c44a0adeafac9f79c4cb6b5d92e9ef97a1b996"},"schema_version":"1.0","source":{"id":"1806.05003","kind":"arxiv","version":1}},"canonical_sha256":"4229d5321e5e8524bab83225047e9dce03e5c530f665867990a083994d7a9441","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4229d5321e5e8524bab83225047e9dce03e5c530f665867990a083994d7a9441","first_computed_at":"2026-07-05T02:00:40.941680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:00:40.941680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7R5LR0VhumRLq/NvOHUyxCNO+lwJDkXCs7XeXHU/tSyKwhDzMLOJZ4chgyPZl/gYzilinItZw3NIf21ZIfevDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:00:40.942111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc4a45646e19a48bae77525702f2b8e9a996a0bf0f16a1442541caf72cffa07a","sha256:2f7cf52cac548d04c59aaf063f2f53c802714b5171b33c3c1d05ba655e672177"],"state_sha256":"9b54a012105b1cf12fc04daf4d3992309586f095fed5e0a32802b07685af36a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZeosAYq7buO+T4FiNbDBOY+cVXQ5QV7cD87v3WJ1Bgmx7YojJhYFlVP0nmbQR04R6Hqctoi9Tsokf75acWE0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T20:03:07.101147Z","bundle_sha256":"070c8d5dc2332e8b3645c1ffd775f46db93bb5c00403c7bb57c216909e7022d6"}}