{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MQCJQTTYAVJ5YYICEXE75RLHBW","short_pith_number":"pith:MQCJQTTY","canonical_record":{"source":{"id":"1106.1211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-06-06T22:39:42Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4de87384ce2e4bde2597a4731fa9ebff9af95e219671212b91bad5796ba39d1c","abstract_canon_sha256":"3301239dc1200ca403432154100872e53c037486f995123b1a8d962b4320f6dd"},"schema_version":"1.0"},"canonical_sha256":"6404984e780553dc610225c9fec5670d81599da8e88ed2dcb44358a640303547","source":{"kind":"arxiv","id":"1106.1211","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1211","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1211v2","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1211","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"MQCJQTTYAVJ5","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MQCJQTTYAVJ5YYIC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MQCJQTTY","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MQCJQTTYAVJ5YYICEXE75RLHBW","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-06-06T22:39:42Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4de87384ce2e4bde2597a4731fa9ebff9af95e219671212b91bad5796ba39d1c","abstract_canon_sha256":"3301239dc1200ca403432154100872e53c037486f995123b1a8d962b4320f6dd"},"schema_version":"1.0"},"canonical_sha256":"6404984e780553dc610225c9fec5670d81599da8e88ed2dcb44358a640303547","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:23.972367Z","signature_b64":"JhHOFvHJ4gLvBTAumBbkI7BvB31y7G7zJhLkaw5d8g/e3vmBr4Y9D6VM41mIiLduOxoGwtVtx+CMbbc+G4PMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6404984e780553dc610225c9fec5670d81599da8e88ed2dcb44358a640303547","last_reissued_at":"2026-05-18T03:38:23.971810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:23.971810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1211","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":"2026-05-18T03:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qzm/1hbNFVWnbiept9AbPFJJM9SCsKNE6My4Gbycpx4i9/1yI97K08CwyhH3+smQEuswVrL0mF7PlSAzPI5ACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:58:11.718944Z"},"content_sha256":"9b11b69ae5c4822695dde4d26c9c52c2eb2fceae86f54065f475067d8c73c840","schema_version":"1.0","event_id":"sha256:9b11b69ae5c4822695dde4d26c9c52c2eb2fceae86f54065f475067d8c73c840"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MQCJQTTYAVJ5YYICEXE75RLHBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of fractional-order linear time-invariant system with noncommensurate orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"YangQuan Chen, Yi-Sheng Zhong, Zhuang Jiao","submitted_at":"2011-06-06T22:39:42Z","abstract_excerpt":"Bounded-input bounded-output stability conditions for fractional-order linear time-invariant (LTI) system with multiple noncommensurate orders have been established in this paper. The orders become noncommensurate orders when they do not have a common divisor. Sufficient and necessary conditions of stability for this kind of fractional-order LTI system with multiple noncommensurate orders. Based on the numerical inverse Laplace transform technique, time-domain responses for a fractional-order system with double noncommensurate orders are presented to illustrate the obtained stability results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1211","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":"2026-05-18T03:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"maQxvT1HczuAAv/21Ht52f3VHD5WfhfDeX7IZ/6wniEAbSmSZkjwNO5sV/VNWZNiRbhfJg2r9+2BOiI8VrmUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:58:11.719300Z"},"content_sha256":"83472254be3447ae32e0f09d5a61cc51a3a5ba14c3c7901190d36c4880d01255","schema_version":"1.0","event_id":"sha256:83472254be3447ae32e0f09d5a61cc51a3a5ba14c3c7901190d36c4880d01255"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MQCJQTTYAVJ5YYICEXE75RLHBW/bundle.json","state_url":"https://pith.science/pith/MQCJQTTYAVJ5YYICEXE75RLHBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MQCJQTTYAVJ5YYICEXE75RLHBW/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":"2026-06-21T22:58:11Z","links":{"resolver":"https://pith.science/pith/MQCJQTTYAVJ5YYICEXE75RLHBW","bundle":"https://pith.science/pith/MQCJQTTYAVJ5YYICEXE75RLHBW/bundle.json","state":"https://pith.science/pith/MQCJQTTYAVJ5YYICEXE75RLHBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MQCJQTTYAVJ5YYICEXE75RLHBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MQCJQTTYAVJ5YYICEXE75RLHBW","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":"3301239dc1200ca403432154100872e53c037486f995123b1a8d962b4320f6dd","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-06-06T22:39:42Z","title_canon_sha256":"4de87384ce2e4bde2597a4731fa9ebff9af95e219671212b91bad5796ba39d1c"},"schema_version":"1.0","source":{"id":"1106.1211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1211","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1211v2","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1211","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"MQCJQTTYAVJ5","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MQCJQTTYAVJ5YYIC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MQCJQTTY","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:83472254be3447ae32e0f09d5a61cc51a3a5ba14c3c7901190d36c4880d01255","target":"graph","created_at":"2026-05-18T03:38:23Z","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":"Bounded-input bounded-output stability conditions for fractional-order linear time-invariant (LTI) system with multiple noncommensurate orders have been established in this paper. The orders become noncommensurate orders when they do not have a common divisor. Sufficient and necessary conditions of stability for this kind of fractional-order LTI system with multiple noncommensurate orders. Based on the numerical inverse Laplace transform technique, time-domain responses for a fractional-order system with double noncommensurate orders are presented to illustrate the obtained stability results.","authors_text":"YangQuan Chen, Yi-Sheng Zhong, Zhuang Jiao","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-06-06T22:39:42Z","title":"Stability of fractional-order linear time-invariant system with noncommensurate orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1211","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":"sha256:9b11b69ae5c4822695dde4d26c9c52c2eb2fceae86f54065f475067d8c73c840","target":"record","created_at":"2026-05-18T03:38:23Z","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":"3301239dc1200ca403432154100872e53c037486f995123b1a8d962b4320f6dd","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2011-06-06T22:39:42Z","title_canon_sha256":"4de87384ce2e4bde2597a4731fa9ebff9af95e219671212b91bad5796ba39d1c"},"schema_version":"1.0","source":{"id":"1106.1211","kind":"arxiv","version":2}},"canonical_sha256":"6404984e780553dc610225c9fec5670d81599da8e88ed2dcb44358a640303547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6404984e780553dc610225c9fec5670d81599da8e88ed2dcb44358a640303547","first_computed_at":"2026-05-18T03:38:23.971810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:23.971810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JhHOFvHJ4gLvBTAumBbkI7BvB31y7G7zJhLkaw5d8g/e3vmBr4Y9D6VM41mIiLduOxoGwtVtx+CMbbc+G4PMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:23.972367Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b11b69ae5c4822695dde4d26c9c52c2eb2fceae86f54065f475067d8c73c840","sha256:83472254be3447ae32e0f09d5a61cc51a3a5ba14c3c7901190d36c4880d01255"],"state_sha256":"73000f4dd5a5bd4a01d8963bfe13fe6000f877e4b7e0d52bc8efc34177244e09"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7IEDyFIWM3Li8vh2B1hAs6lFDnhmFJxiRWCVrQI4gJ8TpG3cihN77qdA5m+GPhoEECpNr3c1ME3Ik6x+HqsdCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:58:11.721356Z","bundle_sha256":"f415088bca249685f4c7f1ae41ee7b5766e2650a2fdb4650faa5dc62245c6e35"}}