{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LPJSW7V33IV3LX7X6STXGYBWSI","short_pith_number":"pith:LPJSW7V3","canonical_record":{"source":{"id":"1603.05499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T14:15:44Z","cross_cats_sorted":[],"title_canon_sha256":"b1e44e338ad49b139e129ba6f58d424f41e45962a58be3200e56c3837bf1fbcb","abstract_canon_sha256":"774cddc8d725af1b3e08f9752dc4b57b0c1ca9b3b31980aa42978492b8e70e48"},"schema_version":"1.0"},"canonical_sha256":"5bd32b7ebbda2bb5dff7f4a77360369238e3608c6ec468722bec8d1eeb84764f","source":{"kind":"arxiv","id":"1603.05499","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05499","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05499v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05499","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"LPJSW7V33IV3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LPJSW7V33IV3LX7X","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LPJSW7V3","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LPJSW7V33IV3LX7X6STXGYBWSI","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T14:15:44Z","cross_cats_sorted":[],"title_canon_sha256":"b1e44e338ad49b139e129ba6f58d424f41e45962a58be3200e56c3837bf1fbcb","abstract_canon_sha256":"774cddc8d725af1b3e08f9752dc4b57b0c1ca9b3b31980aa42978492b8e70e48"},"schema_version":"1.0"},"canonical_sha256":"5bd32b7ebbda2bb5dff7f4a77360369238e3608c6ec468722bec8d1eeb84764f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:56.186655Z","signature_b64":"M0M+wusPcabdPEd/VEFdVFSgb6P/pGMiR5f0ERLIlgjGt10JXLqzxr3NzvFUFWHxS2hgrvw1qAnX19O3+YXqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bd32b7ebbda2bb5dff7f4a77360369238e3608c6ec468722bec8d1eeb84764f","last_reissued_at":"2026-05-18T01:18:56.186138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:56.186138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05499","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":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJU51VhSnyVDXPdOY90Ee5qEX1O793gNAwpAM7wRkzDxccKkdeXAUTZArdjpf9OusUVRBft6qzCxq24DZclPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:27:33.307069Z"},"content_sha256":"87e7d8d2c42907b54acd65e3d65f3931678ace8dda313e455225ccacf729eb26","schema_version":"1.0","event_id":"sha256:87e7d8d2c42907b54acd65e3d65f3931678ace8dda313e455225ccacf729eb26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LPJSW7V33IV3LX7X6STXGYBWSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integral control on nonlinear spaces: two extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alain Sarlette, Zhifei Zhang, Zhihao Ling","submitted_at":"2016-03-17T14:15:44Z","abstract_excerpt":"This paper applies the recently developed framework for integral control on nonlinear spaces to two non-standard cases. First, we show that the property of perfect target stabilization in presence of actuation bias holds also if this bias is state dependent. This might not be surprising, but for practical purposes it provides an easy way to robustly cancel nonlinear dynamics of the uncontrolled plant. We specifically illustrate this for robust stabilization of a pendulum at arbitrary angle, a problem posed as non-trivial by some colleagues. Second, as previous work has been restricted to syste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05499","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":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QZwU/FJPrNU//cF2nbKjbevUwVwA1P0lpRv2nSH9Bz+kQLiZLU+lyD1R3NvvHBQZ9S39xuEVu6dkkcyo9xSqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:27:33.307514Z"},"content_sha256":"c0806b40c2575d9119d577e1c3efb00ce22d9bd8cb1d07b1dff8353e9696855c","schema_version":"1.0","event_id":"sha256:c0806b40c2575d9119d577e1c3efb00ce22d9bd8cb1d07b1dff8353e9696855c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LPJSW7V33IV3LX7X6STXGYBWSI/bundle.json","state_url":"https://pith.science/pith/LPJSW7V33IV3LX7X6STXGYBWSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LPJSW7V33IV3LX7X6STXGYBWSI/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":"2026-05-31T14:27:33Z","links":{"resolver":"https://pith.science/pith/LPJSW7V33IV3LX7X6STXGYBWSI","bundle":"https://pith.science/pith/LPJSW7V33IV3LX7X6STXGYBWSI/bundle.json","state":"https://pith.science/pith/LPJSW7V33IV3LX7X6STXGYBWSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LPJSW7V33IV3LX7X6STXGYBWSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LPJSW7V33IV3LX7X6STXGYBWSI","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":"774cddc8d725af1b3e08f9752dc4b57b0c1ca9b3b31980aa42978492b8e70e48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T14:15:44Z","title_canon_sha256":"b1e44e338ad49b139e129ba6f58d424f41e45962a58be3200e56c3837bf1fbcb"},"schema_version":"1.0","source":{"id":"1603.05499","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05499","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05499v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05499","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"LPJSW7V33IV3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LPJSW7V33IV3LX7X","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LPJSW7V3","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:c0806b40c2575d9119d577e1c3efb00ce22d9bd8cb1d07b1dff8353e9696855c","target":"graph","created_at":"2026-05-18T01:18:56Z","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":"This paper applies the recently developed framework for integral control on nonlinear spaces to two non-standard cases. First, we show that the property of perfect target stabilization in presence of actuation bias holds also if this bias is state dependent. This might not be surprising, but for practical purposes it provides an easy way to robustly cancel nonlinear dynamics of the uncontrolled plant. We specifically illustrate this for robust stabilization of a pendulum at arbitrary angle, a problem posed as non-trivial by some colleagues. Second, as previous work has been restricted to syste","authors_text":"Alain Sarlette, Zhifei Zhang, Zhihao Ling","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T14:15:44Z","title":"Integral control on nonlinear spaces: two extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05499","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":"sha256:87e7d8d2c42907b54acd65e3d65f3931678ace8dda313e455225ccacf729eb26","target":"record","created_at":"2026-05-18T01:18:56Z","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":"774cddc8d725af1b3e08f9752dc4b57b0c1ca9b3b31980aa42978492b8e70e48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-17T14:15:44Z","title_canon_sha256":"b1e44e338ad49b139e129ba6f58d424f41e45962a58be3200e56c3837bf1fbcb"},"schema_version":"1.0","source":{"id":"1603.05499","kind":"arxiv","version":1}},"canonical_sha256":"5bd32b7ebbda2bb5dff7f4a77360369238e3608c6ec468722bec8d1eeb84764f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bd32b7ebbda2bb5dff7f4a77360369238e3608c6ec468722bec8d1eeb84764f","first_computed_at":"2026-05-18T01:18:56.186138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:56.186138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M0M+wusPcabdPEd/VEFdVFSgb6P/pGMiR5f0ERLIlgjGt10JXLqzxr3NzvFUFWHxS2hgrvw1qAnX19O3+YXqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:56.186655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05499","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87e7d8d2c42907b54acd65e3d65f3931678ace8dda313e455225ccacf729eb26","sha256:c0806b40c2575d9119d577e1c3efb00ce22d9bd8cb1d07b1dff8353e9696855c"],"state_sha256":"cea2ad2d50ea216f4d1d5b8b0d7edd4d003def780bd9f344850a75a17332a488"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g8CNIjUAdTFea0GSySA5F22mgvTKtdWDuoailohke3UHCvfBWuEhK/89yKQBvzUpPw8P31XecRM2UNjjY84pCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:27:33.310917Z","bundle_sha256":"1568cf82241202d87a771243dd728234c6e5d8520e3a229291ed50108ff2090e"}}