{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GSMZGPD652UHTS3ZOPQMZPQESN","short_pith_number":"pith:GSMZGPD6","canonical_record":{"source":{"id":"1011.3724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-16T15:17:16Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ef0d477f1cba2a6f4110686a393f73ae8f36710562533fa9b46b53b8ae2aea7e","abstract_canon_sha256":"951703bd19f5ae7ed171dfb6cbef1e4dc029ef7f5f3744c1358ad702ea7b6a14"},"schema_version":"1.0"},"canonical_sha256":"3499933c7eeea879cb7973e0ccbe04936a4cb925a6d536ee6b04c17c587ff728","source":{"kind":"arxiv","id":"1011.3724","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3724","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3724v2","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3724","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"GSMZGPD652UH","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GSMZGPD652UHTS3Z","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GSMZGPD6","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GSMZGPD652UHTS3ZOPQMZPQESN","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-16T15:17:16Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ef0d477f1cba2a6f4110686a393f73ae8f36710562533fa9b46b53b8ae2aea7e","abstract_canon_sha256":"951703bd19f5ae7ed171dfb6cbef1e4dc029ef7f5f3744c1358ad702ea7b6a14"},"schema_version":"1.0"},"canonical_sha256":"3499933c7eeea879cb7973e0ccbe04936a4cb925a6d536ee6b04c17c587ff728","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:12.951578Z","signature_b64":"ky8O6oJ4S1wDC4/6qSTrdkrxZn66C5LVswFz8JKmG6DEDZjnQYFVstm0uuG2kIEUJteeOTcKUS0X1tqtQtwXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3499933c7eeea879cb7973e0ccbe04936a4cb925a6d536ee6b04c17c587ff728","last_reissued_at":"2026-05-18T04:25:12.950869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:12.950869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3724","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IwjEBQG5fWptGcuj06kJJkB4odDpdALVy5QHP7ZBHCwZu8ITv5DnN0TXHvtoLk+dR+OoIJaOjXQ7yUPDZ9F2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:15:25.262160Z"},"content_sha256":"ac843a160fbdf847e378b60c8bfd58ce3b4d9b30487525b7105f3bad6bd41ac6","schema_version":"1.0","event_id":"sha256:ac843a160fbdf847e378b60c8bfd58ce3b4d9b30487525b7105f3bad6bd41ac6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GSMZGPD652UHTS3ZOPQMZPQESN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete dynamics in implicit form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"D. Iglesias, D. Martin de Diego, E. Padron, J.C. Marrero","submitted_at":"2010-11-16T15:17:16Z","abstract_excerpt":"A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie groupoid $G$ may be described in terms of Lagrangian implicit difference equations of the corresponding cotangent groupoid $T^*G$. Other situations include finite difference methods for time-dependent linear differential-algebraic equations and discrete nonholonomic Lagrangian systems, as particular examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3724","kind":"arxiv","version":2},"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":"2026-05-18T04:25:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/gIfMGjhrSOZVQSbO64WQIv7jD7P0Ro7Qzd+xP2/TlPxGPWQfOcV2UT7sf7Ug7HSEt9xuIG+aIWtAcwqsQEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:15:25.262743Z"},"content_sha256":"3dc98ac3f07100b67fefb4922245f53b461d7084a89fa4eecb61594bb885f026","schema_version":"1.0","event_id":"sha256:3dc98ac3f07100b67fefb4922245f53b461d7084a89fa4eecb61594bb885f026"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSMZGPD652UHTS3ZOPQMZPQESN/bundle.json","state_url":"https://pith.science/pith/GSMZGPD652UHTS3ZOPQMZPQESN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSMZGPD652UHTS3ZOPQMZPQESN/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":"2026-06-02T14:15:25Z","links":{"resolver":"https://pith.science/pith/GSMZGPD652UHTS3ZOPQMZPQESN","bundle":"https://pith.science/pith/GSMZGPD652UHTS3ZOPQMZPQESN/bundle.json","state":"https://pith.science/pith/GSMZGPD652UHTS3ZOPQMZPQESN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSMZGPD652UHTS3ZOPQMZPQESN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GSMZGPD652UHTS3ZOPQMZPQESN","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":"951703bd19f5ae7ed171dfb6cbef1e4dc029ef7f5f3744c1358ad702ea7b6a14","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-16T15:17:16Z","title_canon_sha256":"ef0d477f1cba2a6f4110686a393f73ae8f36710562533fa9b46b53b8ae2aea7e"},"schema_version":"1.0","source":{"id":"1011.3724","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3724","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3724v2","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3724","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"GSMZGPD652UH","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GSMZGPD652UHTS3Z","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GSMZGPD6","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:3dc98ac3f07100b67fefb4922245f53b461d7084a89fa4eecb61594bb885f026","target":"graph","created_at":"2026-05-18T04:25:12Z","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 notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie groupoid $G$ may be described in terms of Lagrangian implicit difference equations of the corresponding cotangent groupoid $T^*G$. Other situations include finite difference methods for time-dependent linear differential-algebraic equations and discrete nonholonomic Lagrangian systems, as particular examples.","authors_text":"D. Iglesias, D. Martin de Diego, E. Padron, J.C. Marrero","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-16T15:17:16Z","title":"Discrete dynamics in implicit form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3724","kind":"arxiv","version":2},"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:ac843a160fbdf847e378b60c8bfd58ce3b4d9b30487525b7105f3bad6bd41ac6","target":"record","created_at":"2026-05-18T04:25:12Z","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":"951703bd19f5ae7ed171dfb6cbef1e4dc029ef7f5f3744c1358ad702ea7b6a14","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-16T15:17:16Z","title_canon_sha256":"ef0d477f1cba2a6f4110686a393f73ae8f36710562533fa9b46b53b8ae2aea7e"},"schema_version":"1.0","source":{"id":"1011.3724","kind":"arxiv","version":2}},"canonical_sha256":"3499933c7eeea879cb7973e0ccbe04936a4cb925a6d536ee6b04c17c587ff728","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3499933c7eeea879cb7973e0ccbe04936a4cb925a6d536ee6b04c17c587ff728","first_computed_at":"2026-05-18T04:25:12.950869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:12.950869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ky8O6oJ4S1wDC4/6qSTrdkrxZn66C5LVswFz8JKmG6DEDZjnQYFVstm0uuG2kIEUJteeOTcKUS0X1tqtQtwXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:12.951578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3724","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac843a160fbdf847e378b60c8bfd58ce3b4d9b30487525b7105f3bad6bd41ac6","sha256:3dc98ac3f07100b67fefb4922245f53b461d7084a89fa4eecb61594bb885f026"],"state_sha256":"15b1c0b4dc6ae63af379981491e62d1d5122b4cda1c883a6aedbe998326085f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4/p1bx3y8a2zLbYMuJuTr3F1Jy6vFkTB84WH0F6N3WNAp5jtgnlvcM5wk0OkUXRHuc9um6TXdS7CHFCljgiDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:15:25.265453Z","bundle_sha256":"aec36f3c1fd46c192af4cc7f8c71d004299ff856e207ba1cdf8c8abdcfa260aa"}}