{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:F4XWDP6ZAOACIROFE3XZCJQ4DO","short_pith_number":"pith:F4XWDP6Z","canonical_record":{"source":{"id":"math-ph/9807014","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1998-07-13T07:25:21Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"2e1fea29465ee68478f04068e149b0ea84bd3ed0a8fea55d2a0cf3403f511f23","abstract_canon_sha256":"ff67ea05502583b142aad75f361c3964326fd1946a9651c2d38c5d68e56d3d54"},"schema_version":"1.0"},"canonical_sha256":"2f2f61bfd903802445c526ef91261c1bb0c7c7befa532af49c866bd625095dbf","source":{"kind":"arxiv","id":"math-ph/9807014","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9807014","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9807014v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9807014","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"F4XWDP6ZAOAC","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"F4XWDP6ZAOACIROF","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"F4XWDP6Z","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:F4XWDP6ZAOACIROFE3XZCJQ4DO","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/9807014","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1998-07-13T07:25:21Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"2e1fea29465ee68478f04068e149b0ea84bd3ed0a8fea55d2a0cf3403f511f23","abstract_canon_sha256":"ff67ea05502583b142aad75f361c3964326fd1946a9651c2d38c5d68e56d3d54"},"schema_version":"1.0"},"canonical_sha256":"2f2f61bfd903802445c526ef91261c1bb0c7c7befa532af49c866bd625095dbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:30.764074Z","signature_b64":"1MCIAeVZ4YvSa22myaJGXdY+GgR5En3stLGj1Rb9+alMXmFbNYLyNeoRcbuqCBSGVR/mTYzuemZ5V5ph0AZcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f2f61bfd903802445c526ef91261c1bb0c7c7befa532af49c866bd625095dbf","last_reissued_at":"2026-05-18T01:38:30.763679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:30.763679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/9807014","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":"2026-05-18T01:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CiSmus4nqf86ehjn2AvQunqN0UEhb+E7FbtNmr7oWCZz7OqxGGVViKgsfaiE1A8ly6MDN0H4Ud6aBVWZVm9hCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:53:23.284081Z"},"content_sha256":"c0aa476ebf6ed3a4013f2916c1f8c3ddb259bd91c87d61c5ffef56c537032a6c","schema_version":"1.0","event_id":"sha256:c0aa476ebf6ed3a4013f2916c1f8c3ddb259bd91c87d61c5ffef56c537032a6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:F4XWDP6ZAOACIROFE3XZCJQ4DO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonholonomic Constraints in Time-Dependent Mechanics","license":"","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"G.Giachetta, G.Sardanashvily, L.Mangiarotti","submitted_at":"1998-07-13T07:25:21Z","abstract_excerpt":"The constraint reaction force of ideal nonholonomic constraints in time-dependent mechanics on a configuration bundle $Q\\to R$ is obtained. Using the vertical extension of Hamiltonian formalism to the vertical tangent bundle $VQ$ of $Q\\to R$, the Hamiltonian of a nonholonomic constrained system is constructed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9807014","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":"2026-05-18T01:38:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G98IuhsK2L/GhM7pzb7vMwPSAAk0CmOJFG6FEEyPY+87WrgmI9RlQYmZgGa+OstwQ38w2XDWhjzAFuhp5D+nDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:53:23.284464Z"},"content_sha256":"a31b2d5bb670bca950ae78d5b9235f67c039b439e5f9cb2b5bf2eacca5db69c3","schema_version":"1.0","event_id":"sha256:a31b2d5bb670bca950ae78d5b9235f67c039b439e5f9cb2b5bf2eacca5db69c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F4XWDP6ZAOACIROFE3XZCJQ4DO/bundle.json","state_url":"https://pith.science/pith/F4XWDP6ZAOACIROFE3XZCJQ4DO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F4XWDP6ZAOACIROFE3XZCJQ4DO/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":"2026-06-10T23:53:23Z","links":{"resolver":"https://pith.science/pith/F4XWDP6ZAOACIROFE3XZCJQ4DO","bundle":"https://pith.science/pith/F4XWDP6ZAOACIROFE3XZCJQ4DO/bundle.json","state":"https://pith.science/pith/F4XWDP6ZAOACIROFE3XZCJQ4DO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F4XWDP6ZAOACIROFE3XZCJQ4DO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:F4XWDP6ZAOACIROFE3XZCJQ4DO","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":"ff67ea05502583b142aad75f361c3964326fd1946a9651c2d38c5d68e56d3d54","cross_cats_sorted":["math.DG","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1998-07-13T07:25:21Z","title_canon_sha256":"2e1fea29465ee68478f04068e149b0ea84bd3ed0a8fea55d2a0cf3403f511f23"},"schema_version":"1.0","source":{"id":"math-ph/9807014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9807014","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9807014v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9807014","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"F4XWDP6ZAOAC","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"F4XWDP6ZAOACIROF","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"F4XWDP6Z","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:a31b2d5bb670bca950ae78d5b9235f67c039b439e5f9cb2b5bf2eacca5db69c3","target":"graph","created_at":"2026-05-18T01:38:30Z","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":"The constraint reaction force of ideal nonholonomic constraints in time-dependent mechanics on a configuration bundle $Q\\to R$ is obtained. Using the vertical extension of Hamiltonian formalism to the vertical tangent bundle $VQ$ of $Q\\to R$, the Hamiltonian of a nonholonomic constrained system is constructed.","authors_text":"G.Giachetta, G.Sardanashvily, L.Mangiarotti","cross_cats":["math.DG","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"1998-07-13T07:25:21Z","title":"Nonholonomic Constraints in Time-Dependent Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9807014","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:c0aa476ebf6ed3a4013f2916c1f8c3ddb259bd91c87d61c5ffef56c537032a6c","target":"record","created_at":"2026-05-18T01:38:30Z","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":"ff67ea05502583b142aad75f361c3964326fd1946a9651c2d38c5d68e56d3d54","cross_cats_sorted":["math.DG","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1998-07-13T07:25:21Z","title_canon_sha256":"2e1fea29465ee68478f04068e149b0ea84bd3ed0a8fea55d2a0cf3403f511f23"},"schema_version":"1.0","source":{"id":"math-ph/9807014","kind":"arxiv","version":1}},"canonical_sha256":"2f2f61bfd903802445c526ef91261c1bb0c7c7befa532af49c866bd625095dbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f2f61bfd903802445c526ef91261c1bb0c7c7befa532af49c866bd625095dbf","first_computed_at":"2026-05-18T01:38:30.763679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:30.763679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1MCIAeVZ4YvSa22myaJGXdY+GgR5En3stLGj1Rb9+alMXmFbNYLyNeoRcbuqCBSGVR/mTYzuemZ5V5ph0AZcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:30.764074Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/9807014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0aa476ebf6ed3a4013f2916c1f8c3ddb259bd91c87d61c5ffef56c537032a6c","sha256:a31b2d5bb670bca950ae78d5b9235f67c039b439e5f9cb2b5bf2eacca5db69c3"],"state_sha256":"c057e877a3b416385914dd852c7b735d44f6e61fdc6ab720dcc1e3126f760377"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ob/fWR6bdnpSY4WODKmWkVJd9STuX3guaVTSpwfPLSbC4RIKVvTXY25y8g0mQl/RA3BbpLJmOzs3P+mCxy+ADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:53:23.286943Z","bundle_sha256":"ca6a57dec778f5218aa0694aa1fc5422926726373b10493dca1ec0142e784c22"}}