{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:7DIDMFK7XV4EBOR36ZWYG55J4E","short_pith_number":"pith:7DIDMFK7","canonical_record":{"source":{"id":"math-ph/0212007","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-12-02T15:35:31Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"1089a294f7968b0f8a89e44f71a5cf5cbd034d30577603722e1dbcae72e3b56e","abstract_canon_sha256":"f89a73c6c382c0a201875b15e5fa04e80cc26438792df08f52513897b68c230a"},"schema_version":"1.0"},"canonical_sha256":"f8d036155fbd7840ba3bf66d8377a9e12f508aaf1e8bb92cba8a1f5cdf322405","source":{"kind":"arxiv","id":"math-ph/0212007","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0212007","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0212007v1","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0212007","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"7DIDMFK7XV4E","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"7DIDMFK7XV4EBOR3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"7DIDMFK7","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:7DIDMFK7XV4EBOR36ZWYG55J4E","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0212007","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-12-02T15:35:31Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"1089a294f7968b0f8a89e44f71a5cf5cbd034d30577603722e1dbcae72e3b56e","abstract_canon_sha256":"f89a73c6c382c0a201875b15e5fa04e80cc26438792df08f52513897b68c230a"},"schema_version":"1.0"},"canonical_sha256":"f8d036155fbd7840ba3bf66d8377a9e12f508aaf1e8bb92cba8a1f5cdf322405","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:31.897506Z","signature_b64":"aJv3LyoN7kbotrmHzHpEKgNsGw6B3TosQqrdWmdZHfkiealodLLQKDOWhPuod7LuxbQZJ5sHeA/YXYTWxZDHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8d036155fbd7840ba3bf66d8377a9e12f508aaf1e8bb92cba8a1f5cdf322405","last_reissued_at":"2026-05-18T01:05:31.897019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:31.897019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0212007","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":"2026-05-18T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HChbUZOEcgTJddPilFmgXFcrT9UQQUZ+GvAKfr1KehSfylRhZoYKM+cMI4staA7Qo8T7kS9N6ITuQdMFSSgYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:48:04.666711Z"},"content_sha256":"f62b7cc4bac834b12fcffb2d28a55d8f41d17e3d4b4c3199bdc611e05831ffe5","schema_version":"1.0","event_id":"sha256:f62b7cc4bac834b12fcffb2d28a55d8f41d17e3d4b4c3199bdc611e05831ffe5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:7DIDMFK7XV4EBOR36ZWYG55J4E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric numerical integration of nonholonomic systems and optimal control problems","license":"","headline":"","cross_cats":["math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"A. Santamaria Merino, D. Martin de Diego, M. de Leon","submitted_at":"2002-12-02T15:35:31Z","abstract_excerpt":"A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0212007","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":"2026-05-18T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qcIb+bnbkMxFY1WsvEMRrTJO0jRz5hJ9z/oNs1F9/BZhjCBPdICPoQz7QndoXt6JpcV029/NDjgJVN97H3JlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:48:04.667195Z"},"content_sha256":"39006c597cad6cb07f37fa641f4d2f11bfef2ed657ce4c658b297a4cdfe7904b","schema_version":"1.0","event_id":"sha256:39006c597cad6cb07f37fa641f4d2f11bfef2ed657ce4c658b297a4cdfe7904b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DIDMFK7XV4EBOR36ZWYG55J4E/bundle.json","state_url":"https://pith.science/pith/7DIDMFK7XV4EBOR36ZWYG55J4E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DIDMFK7XV4EBOR36ZWYG55J4E/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":"2026-06-21T22:48:04Z","links":{"resolver":"https://pith.science/pith/7DIDMFK7XV4EBOR36ZWYG55J4E","bundle":"https://pith.science/pith/7DIDMFK7XV4EBOR36ZWYG55J4E/bundle.json","state":"https://pith.science/pith/7DIDMFK7XV4EBOR36ZWYG55J4E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DIDMFK7XV4EBOR36ZWYG55J4E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:7DIDMFK7XV4EBOR36ZWYG55J4E","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":"f89a73c6c382c0a201875b15e5fa04e80cc26438792df08f52513897b68c230a","cross_cats_sorted":["math.MP","math.NA"],"license":"","primary_cat":"math-ph","submitted_at":"2002-12-02T15:35:31Z","title_canon_sha256":"1089a294f7968b0f8a89e44f71a5cf5cbd034d30577603722e1dbcae72e3b56e"},"schema_version":"1.0","source":{"id":"math-ph/0212007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0212007","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0212007v1","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0212007","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"7DIDMFK7XV4E","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"7DIDMFK7XV4EBOR3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"7DIDMFK7","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:39006c597cad6cb07f37fa641f4d2f11bfef2ed657ce4c658b297a4cdfe7904b","target":"graph","created_at":"2026-05-18T01:05:31Z","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":"A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems.","authors_text":"A. Santamaria Merino, D. Martin de Diego, M. de Leon","cross_cats":["math.MP","math.NA"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-12-02T15:35:31Z","title":"Geometric numerical integration of nonholonomic systems and optimal control problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0212007","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:f62b7cc4bac834b12fcffb2d28a55d8f41d17e3d4b4c3199bdc611e05831ffe5","target":"record","created_at":"2026-05-18T01:05:31Z","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":"f89a73c6c382c0a201875b15e5fa04e80cc26438792df08f52513897b68c230a","cross_cats_sorted":["math.MP","math.NA"],"license":"","primary_cat":"math-ph","submitted_at":"2002-12-02T15:35:31Z","title_canon_sha256":"1089a294f7968b0f8a89e44f71a5cf5cbd034d30577603722e1dbcae72e3b56e"},"schema_version":"1.0","source":{"id":"math-ph/0212007","kind":"arxiv","version":1}},"canonical_sha256":"f8d036155fbd7840ba3bf66d8377a9e12f508aaf1e8bb92cba8a1f5cdf322405","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8d036155fbd7840ba3bf66d8377a9e12f508aaf1e8bb92cba8a1f5cdf322405","first_computed_at":"2026-05-18T01:05:31.897019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:31.897019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aJv3LyoN7kbotrmHzHpEKgNsGw6B3TosQqrdWmdZHfkiealodLLQKDOWhPuod7LuxbQZJ5sHeA/YXYTWxZDHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:31.897506Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0212007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f62b7cc4bac834b12fcffb2d28a55d8f41d17e3d4b4c3199bdc611e05831ffe5","sha256:39006c597cad6cb07f37fa641f4d2f11bfef2ed657ce4c658b297a4cdfe7904b"],"state_sha256":"c5535e9e44bf123d5ec378be012e12726cd5fffac32a5b2d0e0b4a2040ff4c80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8oXgW4qPJp+567RdlKBBoOw2q2mgprXwrs5pWhZKs56ajTzmppwhpfIY2jJVjjINzkqFNPbhN1mbwZe07WuBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:48:04.670040Z","bundle_sha256":"efaef5b32f88762fa627877837c8604bd3a255acc3275b1635e13d69b8e050cd"}}