{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2XZMRWOAQK6TRV2OWFJPHJLI2K","short_pith_number":"pith:2XZMRWOA","canonical_record":{"source":{"id":"1709.05236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-09-15T14:41:43Z","cross_cats_sorted":[],"title_canon_sha256":"0bdd41e7145ad2734ec8a3620781132873945d5817be61958d5d2e92212accab","abstract_canon_sha256":"fca7d6f233ac7fab1097230d28e8bf1605e5eaaf452258e2e9c6052e76483f29"},"schema_version":"1.0"},"canonical_sha256":"d5f2c8d9c082bd38d74eb152f3a568d28680db9afabd073f33c253052d676513","source":{"kind":"arxiv","id":"1709.05236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05236","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05236v1","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05236","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"2XZMRWOAQK6T","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2XZMRWOAQK6TRV2O","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2XZMRWOA","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2XZMRWOAQK6TRV2OWFJPHJLI2K","target":"record","payload":{"canonical_record":{"source":{"id":"1709.05236","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-09-15T14:41:43Z","cross_cats_sorted":[],"title_canon_sha256":"0bdd41e7145ad2734ec8a3620781132873945d5817be61958d5d2e92212accab","abstract_canon_sha256":"fca7d6f233ac7fab1097230d28e8bf1605e5eaaf452258e2e9c6052e76483f29"},"schema_version":"1.0"},"canonical_sha256":"d5f2c8d9c082bd38d74eb152f3a568d28680db9afabd073f33c253052d676513","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:06.292156Z","signature_b64":"iDHJTbHrDjbS9u04XQBm6vyyuCggs7HRu3oeyceBGat4UhIXKcBO6OjmD7jhUjO8k6nwTEJokMP1tebPuv3cBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5f2c8d9c082bd38d74eb152f3a568d28680db9afabd073f33c253052d676513","last_reissued_at":"2026-05-18T00:35:06.291459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:06.291459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.05236","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":"2026-05-18T00:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dHthvXqtM3kbMRTWXoc8o2URSmD7jDUBqHkNokerf4bL4fuVZVccqdv92x5A0iiXgzB63eFnZLvFMSOyT8UBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:22:55.204051Z"},"content_sha256":"b4e678ac56acf4264a799118171a218bae1b22fd501f25af2cfac3a5ca756807","schema_version":"1.0","event_id":"sha256:b4e678ac56acf4264a799118171a218bae1b22fd501f25af2cfac3a5ca756807"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2XZMRWOAQK6TRV2OWFJPHJLI2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chebyshev Approximation and Higher Order Derivatives of Lyapunov Functions for Estimating the Domain of Attraction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Dimitra Panagou, Dongkun Han","submitted_at":"2017-09-15T14:41:43Z","abstract_excerpt":"Estimating the Domain of Attraction (DA) of non-polynomial systems is a challenging problem. Taylor expansion is widely adopted for transforming a nonlinear analytic function into a polynomial function, but the performance of Taylor expansion is not always satisfactory. This paper provides solvable ways for estimating the DA via Chebyshev approximation. Firstly, for Chebyshev approximation without the remainder, higher order derivatives of Lyapunov functions are used for estimating the DA, and the largest estimate is obtained by solving a generalized eigenvalue problem. Moreover, for Chebyshev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05236","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":"2026-05-18T00:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uueiUyySNO4BMhxG4aBEeMBU40Jvx1aJazgHmEzy4q31fL1i5nUsWgAB5K6c+a08uTmdn2j+Yes4lmfmu6BaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:22:55.204419Z"},"content_sha256":"f941a17fd126c22664e974934d90f4a1d0968ffc9e3090be80d21a9c69e99de4","schema_version":"1.0","event_id":"sha256:f941a17fd126c22664e974934d90f4a1d0968ffc9e3090be80d21a9c69e99de4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2XZMRWOAQK6TRV2OWFJPHJLI2K/bundle.json","state_url":"https://pith.science/pith/2XZMRWOAQK6TRV2OWFJPHJLI2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2XZMRWOAQK6TRV2OWFJPHJLI2K/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":"2026-07-01T22:22:55Z","links":{"resolver":"https://pith.science/pith/2XZMRWOAQK6TRV2OWFJPHJLI2K","bundle":"https://pith.science/pith/2XZMRWOAQK6TRV2OWFJPHJLI2K/bundle.json","state":"https://pith.science/pith/2XZMRWOAQK6TRV2OWFJPHJLI2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2XZMRWOAQK6TRV2OWFJPHJLI2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2XZMRWOAQK6TRV2OWFJPHJLI2K","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":"fca7d6f233ac7fab1097230d28e8bf1605e5eaaf452258e2e9c6052e76483f29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-09-15T14:41:43Z","title_canon_sha256":"0bdd41e7145ad2734ec8a3620781132873945d5817be61958d5d2e92212accab"},"schema_version":"1.0","source":{"id":"1709.05236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05236","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05236v1","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05236","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"2XZMRWOAQK6T","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2XZMRWOAQK6TRV2O","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2XZMRWOA","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:f941a17fd126c22664e974934d90f4a1d0968ffc9e3090be80d21a9c69e99de4","target":"graph","created_at":"2026-05-18T00:35:06Z","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":"Estimating the Domain of Attraction (DA) of non-polynomial systems is a challenging problem. Taylor expansion is widely adopted for transforming a nonlinear analytic function into a polynomial function, but the performance of Taylor expansion is not always satisfactory. This paper provides solvable ways for estimating the DA via Chebyshev approximation. Firstly, for Chebyshev approximation without the remainder, higher order derivatives of Lyapunov functions are used for estimating the DA, and the largest estimate is obtained by solving a generalized eigenvalue problem. Moreover, for Chebyshev","authors_text":"Dimitra Panagou, Dongkun Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-09-15T14:41:43Z","title":"Chebyshev Approximation and Higher Order Derivatives of Lyapunov Functions for Estimating the Domain of Attraction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05236","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:b4e678ac56acf4264a799118171a218bae1b22fd501f25af2cfac3a5ca756807","target":"record","created_at":"2026-05-18T00:35:06Z","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":"fca7d6f233ac7fab1097230d28e8bf1605e5eaaf452258e2e9c6052e76483f29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-09-15T14:41:43Z","title_canon_sha256":"0bdd41e7145ad2734ec8a3620781132873945d5817be61958d5d2e92212accab"},"schema_version":"1.0","source":{"id":"1709.05236","kind":"arxiv","version":1}},"canonical_sha256":"d5f2c8d9c082bd38d74eb152f3a568d28680db9afabd073f33c253052d676513","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5f2c8d9c082bd38d74eb152f3a568d28680db9afabd073f33c253052d676513","first_computed_at":"2026-05-18T00:35:06.291459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:06.291459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iDHJTbHrDjbS9u04XQBm6vyyuCggs7HRu3oeyceBGat4UhIXKcBO6OjmD7jhUjO8k6nwTEJokMP1tebPuv3cBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:06.292156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4e678ac56acf4264a799118171a218bae1b22fd501f25af2cfac3a5ca756807","sha256:f941a17fd126c22664e974934d90f4a1d0968ffc9e3090be80d21a9c69e99de4"],"state_sha256":"b39a43ccfe4d99fa79cb3f8dd4b378885f7cc23bfbe89eb5ef038a42dd1fa9bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNkhpjgHBJaGW8kToa6y0/6iNiBZKIab/6HiRBvomDfiIeKTo34vTXgbv3zKThRQXJEfW2pr/+azo7L81ZymAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T22:22:55.206340Z","bundle_sha256":"1a33879d1c8780057d076c4aa90379a0e7b722ef13e83e5c187768239b3409ff"}}