{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:56DPYZDWZMVBMJOPEQYVOUZHBY","short_pith_number":"pith:56DPYZDW","canonical_record":{"source":{"id":"2604.04455","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-04-06T06:03:18Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"70509737d70b766a1105745f123fe7a62c569311b8dd7984be0811aea89ab806","abstract_canon_sha256":"0daef31014b2ef8b7140b71a01f3fb404f3dfe362c47f2bd6f89ba1ec4fb11b3"},"schema_version":"1.0"},"canonical_sha256":"ef86fc6476cb2a1625cf24315753270e17d4b6249b305e8428f4e091e2bf6b92","source":{"kind":"arxiv","id":"2604.04455","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.04455","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2604.04455v2","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.04455","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"56DPYZDWZMVB","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"56DPYZDWZMVBMJOP","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"56DPYZDW","created_at":"2026-05-21T01:04:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:56DPYZDWZMVBMJOPEQYVOUZHBY","target":"record","payload":{"canonical_record":{"source":{"id":"2604.04455","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-04-06T06:03:18Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"70509737d70b766a1105745f123fe7a62c569311b8dd7984be0811aea89ab806","abstract_canon_sha256":"0daef31014b2ef8b7140b71a01f3fb404f3dfe362c47f2bd6f89ba1ec4fb11b3"},"schema_version":"1.0"},"canonical_sha256":"ef86fc6476cb2a1625cf24315753270e17d4b6249b305e8428f4e091e2bf6b92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:25.371039Z","signature_b64":"Krk/JF29RNuzNyTn9Rmbbh7dVHJ425jIpJD1zBc6Q/duh9be8bd9FyUsGeKyEvkzt3A3fpqc7wX0oiellRkXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef86fc6476cb2a1625cf24315753270e17d4b6249b305e8428f4e091e2bf6b92","last_reissued_at":"2026-05-21T01:04:25.370193Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:25.370193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.04455","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":"2026-05-21T01:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rWziEZiNKLiuy2KEl4HY2IdsPe+mfq0YtlJtTRL3RDghnzQ0xMy1nhuxF74rAZjip4KFV6KLLd+fvEsHds94AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:56:18.586205Z"},"content_sha256":"54ff2e482fb61b7c8142017f83d9076961e42777c09d468aa13cb8bf58010ea8","schema_version":"1.0","event_id":"sha256:54ff2e482fb61b7c8142017f83d9076961e42777c09d468aa13cb8bf58010ea8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:56DPYZDWZMVBMJOPEQYVOUZHBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Region of Attraction Estimation for Linear Quadratic Regulator, Linear and Robust Model Predictive Control on a Two-Wheeled Inverted Pendulum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A Lyapunov-derived invariant set combined with Monte Carlo sampling estimates the region of attraction for three controllers on a two-wheeled inverted pendulum.","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Alvaro Detailleur, Dalim Wahby, Guillaume Ducard, Lorenzo Fici, Matthieu Barreau","submitted_at":"2026-04-06T06:03:18Z","abstract_excerpt":"Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which the closed-loop system converges to the equilibrium. The RoA of nonlinear and constrained systems is generally nonconvex and analytically intractable, requiring numerical or approximate estimation methods. This work investigates the estimation of the RoA for a TWIP stabilized under three model-based control strategies: saturated linear quadratic regulator (LQR), linear model predictive control (MPC), and constraint t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The proposed methodology combines analytical guarantees with data-driven estimation, providing both a formally certified inner bound and an empirical characterization of the RoA, offering a practical way to evaluate controller performance without relying solely on conservative analytical bounds or purely empirical simulation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the chosen Lyapunov function yields a valid invariant set for the closed-loop nonlinear system and that Monte Carlo sampling adequately captures the true boundary of the RoA beyond the certified inner set.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A Lyapunov invariant set supplies a certified inner RoA bound for TWIP controllers, augmented by Monte Carlo sampling for a fuller empirical characterization.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Lyapunov-derived invariant set combined with Monte Carlo sampling estimates the region of attraction for three controllers on a two-wheeled inverted pendulum.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"736afbac82cb82ec52394eef024cad4030d954c7fe722c1174379e98000b0e5a"},"source":{"id":"2604.04455","kind":"arxiv","version":2},"verdict":{"id":"3aef6fd4-4c61-4962-931a-b39a5708f10d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T20:18:04.880353Z","strongest_claim":"The proposed methodology combines analytical guarantees with data-driven estimation, providing both a formally certified inner bound and an empirical characterization of the RoA, offering a practical way to evaluate controller performance without relying solely on conservative analytical bounds or purely empirical simulation.","one_line_summary":"A Lyapunov invariant set supplies a certified inner RoA bound for TWIP controllers, augmented by Monte Carlo sampling for a fuller empirical characterization.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the chosen Lyapunov function yields a valid invariant set for the closed-loop nonlinear system and that Monte Carlo sampling adequately captures the true boundary of the RoA beyond the certified inner set.","pith_extraction_headline":"A Lyapunov-derived invariant set combined with Monte Carlo sampling estimates the region of attraction for three controllers on a two-wheeled inverted pendulum."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.04455/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":2,"snapshot_sha256":"5eafbb9e5b48ccfd82dfbec16dcb48dcba03ecaab5f21a2251d7b67e2bf3713f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"3aef6fd4-4c61-4962-931a-b39a5708f10d"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pHa5bZ8QGA91XM3GtdLhfO3mX0jiVsS1mRYNfpIKVkSZQgI8dYX4i2AOGqDfcB/q9cuSCNyiiQGjr/lLVvZCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:56:18.587164Z"},"content_sha256":"40cfccaf79a49afa0b6c70d6154c6b780f861a158d67400c417ac8f75d4f0655","schema_version":"1.0","event_id":"sha256:40cfccaf79a49afa0b6c70d6154c6b780f861a158d67400c417ac8f75d4f0655"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/56DPYZDWZMVBMJOPEQYVOUZHBY/bundle.json","state_url":"https://pith.science/pith/56DPYZDWZMVBMJOPEQYVOUZHBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/56DPYZDWZMVBMJOPEQYVOUZHBY/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":"2026-05-27T17:56:18Z","links":{"resolver":"https://pith.science/pith/56DPYZDWZMVBMJOPEQYVOUZHBY","bundle":"https://pith.science/pith/56DPYZDWZMVBMJOPEQYVOUZHBY/bundle.json","state":"https://pith.science/pith/56DPYZDWZMVBMJOPEQYVOUZHBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/56DPYZDWZMVBMJOPEQYVOUZHBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:56DPYZDWZMVBMJOPEQYVOUZHBY","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":"0daef31014b2ef8b7140b71a01f3fb404f3dfe362c47f2bd6f89ba1ec4fb11b3","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-04-06T06:03:18Z","title_canon_sha256":"70509737d70b766a1105745f123fe7a62c569311b8dd7984be0811aea89ab806"},"schema_version":"1.0","source":{"id":"2604.04455","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.04455","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2604.04455v2","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.04455","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"56DPYZDWZMVB","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"56DPYZDWZMVBMJOP","created_at":"2026-05-21T01:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"56DPYZDW","created_at":"2026-05-21T01:04:25Z"}],"graph_snapshots":[{"event_id":"sha256:40cfccaf79a49afa0b6c70d6154c6b780f861a158d67400c417ac8f75d4f0655","target":"graph","created_at":"2026-05-21T01:04:25Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The proposed methodology combines analytical guarantees with data-driven estimation, providing both a formally certified inner bound and an empirical characterization of the RoA, offering a practical way to evaluate controller performance without relying solely on conservative analytical bounds or purely empirical simulation."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the chosen Lyapunov function yields a valid invariant set for the closed-loop nonlinear system and that Monte Carlo sampling adequately captures the true boundary of the RoA beyond the certified inner set."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A Lyapunov invariant set supplies a certified inner RoA bound for TWIP controllers, augmented by Monte Carlo sampling for a fuller empirical characterization."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A Lyapunov-derived invariant set combined with Monte Carlo sampling estimates the region of attraction for three controllers on a two-wheeled inverted pendulum."}],"snapshot_sha256":"736afbac82cb82ec52394eef024cad4030d954c7fe722c1174379e98000b0e5a"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5eafbb9e5b48ccfd82dfbec16dcb48dcba03ecaab5f21a2251d7b67e2bf3713f"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.04455/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which the closed-loop system converges to the equilibrium. The RoA of nonlinear and constrained systems is generally nonconvex and analytically intractable, requiring numerical or approximate estimation methods. This work investigates the estimation of the RoA for a TWIP stabilized under three model-based control strategies: saturated linear quadratic regulator (LQR), linear model predictive control (MPC), and constraint t","authors_text":"Alvaro Detailleur, Dalim Wahby, Guillaume Ducard, Lorenzo Fici, Matthieu Barreau","cross_cats":["cs.SY"],"headline":"A Lyapunov-derived invariant set combined with Monte Carlo sampling estimates the region of attraction for three controllers on a two-wheeled inverted pendulum.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-04-06T06:03:18Z","title":"Region of Attraction Estimation for Linear Quadratic Regulator, Linear and Robust Model Predictive Control on a Two-Wheeled Inverted Pendulum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.04455","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T20:18:04.880353Z","id":"3aef6fd4-4c61-4962-931a-b39a5708f10d","model_set":{"reader":"grok-4.3"},"one_line_summary":"A Lyapunov invariant set supplies a certified inner RoA bound for TWIP controllers, augmented by Monte Carlo sampling for a fuller empirical characterization.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A Lyapunov-derived invariant set combined with Monte Carlo sampling estimates the region of attraction for three controllers on a two-wheeled inverted pendulum.","strongest_claim":"The proposed methodology combines analytical guarantees with data-driven estimation, providing both a formally certified inner bound and an empirical characterization of the RoA, offering a practical way to evaluate controller performance without relying solely on conservative analytical bounds or purely empirical simulation.","weakest_assumption":"That the chosen Lyapunov function yields a valid invariant set for the closed-loop nonlinear system and that Monte Carlo sampling adequately captures the true boundary of the RoA beyond the certified inner set."}},"verdict_id":"3aef6fd4-4c61-4962-931a-b39a5708f10d"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:54ff2e482fb61b7c8142017f83d9076961e42777c09d468aa13cb8bf58010ea8","target":"record","created_at":"2026-05-21T01:04:25Z","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":"0daef31014b2ef8b7140b71a01f3fb404f3dfe362c47f2bd6f89ba1ec4fb11b3","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2026-04-06T06:03:18Z","title_canon_sha256":"70509737d70b766a1105745f123fe7a62c569311b8dd7984be0811aea89ab806"},"schema_version":"1.0","source":{"id":"2604.04455","kind":"arxiv","version":2}},"canonical_sha256":"ef86fc6476cb2a1625cf24315753270e17d4b6249b305e8428f4e091e2bf6b92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef86fc6476cb2a1625cf24315753270e17d4b6249b305e8428f4e091e2bf6b92","first_computed_at":"2026-05-21T01:04:25.370193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:25.370193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Krk/JF29RNuzNyTn9Rmbbh7dVHJ425jIpJD1zBc6Q/duh9be8bd9FyUsGeKyEvkzt3A3fpqc7wX0oiellRkXDQ==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:25.371039Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.04455","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54ff2e482fb61b7c8142017f83d9076961e42777c09d468aa13cb8bf58010ea8","sha256:40cfccaf79a49afa0b6c70d6154c6b780f861a158d67400c417ac8f75d4f0655"],"state_sha256":"a9388f2f0e91c85344e68040a88c95a0964ac2e628dcef4c28f39b6a8995eeee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PVTSI4qz4pDqbvdJXXekmGPrapmMZTv7ys4a8zT5CTqW4wtXjRAOXVqnzcTrHjxrjhZjCxjwHdGJdmMQ8v7Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:56:18.591086Z","bundle_sha256":"429ba2e22b312bb68ede7e29b84dd1fb9dd4ea0932c28301281a4216e949e504"}}