{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4XHYDFK723GZKSIC7GX2NYUSRK","short_pith_number":"pith:4XHYDFK7","canonical_record":{"source":{"id":"1207.7357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-07-29T15:43:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c0f9c65fa168f4a4f7fa0e96617a1060064c8c44d314b3c6e0f6d2d92b0112da","abstract_canon_sha256":"70f6fc357b26af773f106061df97f03e00bad0ee4e27d2dcf8d85fe1e6a8cbde"},"schema_version":"1.0"},"canonical_sha256":"e5cf81955fd6cd954902f9afa6e2928aba6bffe1c16022b66a0120bfd726b9f2","source":{"kind":"arxiv","id":"1207.7357","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.7357","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1207.7357v2","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.7357","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"4XHYDFK723GZ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4XHYDFK723GZKSIC","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4XHYDFK7","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4XHYDFK723GZKSIC7GX2NYUSRK","target":"record","payload":{"canonical_record":{"source":{"id":"1207.7357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-07-29T15:43:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c0f9c65fa168f4a4f7fa0e96617a1060064c8c44d314b3c6e0f6d2d92b0112da","abstract_canon_sha256":"70f6fc357b26af773f106061df97f03e00bad0ee4e27d2dcf8d85fe1e6a8cbde"},"schema_version":"1.0"},"canonical_sha256":"e5cf81955fd6cd954902f9afa6e2928aba6bffe1c16022b66a0120bfd726b9f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:58.441939Z","signature_b64":"ai5Q/sXDGE+H+bKlqEWhbqTwgWM50MwJeKzp7GmWxmkqnW62fBTYQa7Gp3ngUWS/+S/ONZN8szq/356IEFGEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5cf81955fd6cd954902f9afa6e2928aba6bffe1c16022b66a0120bfd726b9f2","last_reissued_at":"2026-05-18T03:48:58.440332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:58.440332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.7357","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":"2026-05-18T03:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wL8wgQG77J+VRiIoAfjmUh3hjXLpCohs2OZEPBoaaEPTMkLp1UobS3mk9m6VP7vMMvGOpWrKXPoxgsD1qeLOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:11:50.364748Z"},"content_sha256":"c82819b555e7cd7e17f755096c9fb3fb781cd818d57d5532e994da80d42797c9","schema_version":"1.0","event_id":"sha256:c82819b555e7cd7e17f755096c9fb3fb781cd818d57d5532e994da80d42797c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4XHYDFK723GZKSIC7GX2NYUSRK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reconstruction mechanism with self-growing equations for hyper, improper and proper fractional chaotic systems through a novel non-Lyapunov approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.CD","authors_text":"Fei Gao, Feng-Xia Fei, Ilangko Balasingham, Qian Xu, Yan-Fang Deng, Yi-Bo Qi","submitted_at":"2012-07-29T15:43:57Z","abstract_excerpt":"Identification of the unknown parameters and orders of fractional chaotic systems is of vital significance in controlling and synchronization of fractional-order chaotic systems. However there exist basic hypotheses in traditional estimation methods, that is, the parameters and fractional orders are partially known or the known data series coincide with definite forms of fractional chaotic differential equations except some uncertain parameters and fractional orders. What should I do when these hypotheses do not exist?\n  In this paper, a non-Lyapunov novel approach with a novel united mathemat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7357","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":"2026-05-18T03:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doWGiIXyID4NgYq+y0m79qiTQ237tzwh9nQYgi3HiqElC/yTzFtat4UiG7NBy3tg7Ve+r1RcyhMlVUJTK8ByDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:11:50.365096Z"},"content_sha256":"ac4b1464760da43bca2dfdda122e91c54ff77107d0d76ada89f2d5ff54ff19e8","schema_version":"1.0","event_id":"sha256:ac4b1464760da43bca2dfdda122e91c54ff77107d0d76ada89f2d5ff54ff19e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XHYDFK723GZKSIC7GX2NYUSRK/bundle.json","state_url":"https://pith.science/pith/4XHYDFK723GZKSIC7GX2NYUSRK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XHYDFK723GZKSIC7GX2NYUSRK/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":"2026-06-02T14:11:50Z","links":{"resolver":"https://pith.science/pith/4XHYDFK723GZKSIC7GX2NYUSRK","bundle":"https://pith.science/pith/4XHYDFK723GZKSIC7GX2NYUSRK/bundle.json","state":"https://pith.science/pith/4XHYDFK723GZKSIC7GX2NYUSRK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XHYDFK723GZKSIC7GX2NYUSRK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4XHYDFK723GZKSIC7GX2NYUSRK","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":"70f6fc357b26af773f106061df97f03e00bad0ee4e27d2dcf8d85fe1e6a8cbde","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-07-29T15:43:57Z","title_canon_sha256":"c0f9c65fa168f4a4f7fa0e96617a1060064c8c44d314b3c6e0f6d2d92b0112da"},"schema_version":"1.0","source":{"id":"1207.7357","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.7357","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1207.7357v2","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.7357","created_at":"2026-05-18T03:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"4XHYDFK723GZ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4XHYDFK723GZKSIC","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4XHYDFK7","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:ac4b1464760da43bca2dfdda122e91c54ff77107d0d76ada89f2d5ff54ff19e8","target":"graph","created_at":"2026-05-18T03:48:58Z","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":"Identification of the unknown parameters and orders of fractional chaotic systems is of vital significance in controlling and synchronization of fractional-order chaotic systems. However there exist basic hypotheses in traditional estimation methods, that is, the parameters and fractional orders are partially known or the known data series coincide with definite forms of fractional chaotic differential equations except some uncertain parameters and fractional orders. What should I do when these hypotheses do not exist?\n  In this paper, a non-Lyapunov novel approach with a novel united mathemat","authors_text":"Fei Gao, Feng-Xia Fei, Ilangko Balasingham, Qian Xu, Yan-Fang Deng, Yi-Bo Qi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-07-29T15:43:57Z","title":"Reconstruction mechanism with self-growing equations for hyper, improper and proper fractional chaotic systems through a novel non-Lyapunov approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7357","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:c82819b555e7cd7e17f755096c9fb3fb781cd818d57d5532e994da80d42797c9","target":"record","created_at":"2026-05-18T03:48:58Z","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":"70f6fc357b26af773f106061df97f03e00bad0ee4e27d2dcf8d85fe1e6a8cbde","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-07-29T15:43:57Z","title_canon_sha256":"c0f9c65fa168f4a4f7fa0e96617a1060064c8c44d314b3c6e0f6d2d92b0112da"},"schema_version":"1.0","source":{"id":"1207.7357","kind":"arxiv","version":2}},"canonical_sha256":"e5cf81955fd6cd954902f9afa6e2928aba6bffe1c16022b66a0120bfd726b9f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5cf81955fd6cd954902f9afa6e2928aba6bffe1c16022b66a0120bfd726b9f2","first_computed_at":"2026-05-18T03:48:58.440332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:58.440332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ai5Q/sXDGE+H+bKlqEWhbqTwgWM50MwJeKzp7GmWxmkqnW62fBTYQa7Gp3ngUWS/+S/ONZN8szq/356IEFGEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:58.441939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.7357","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c82819b555e7cd7e17f755096c9fb3fb781cd818d57d5532e994da80d42797c9","sha256:ac4b1464760da43bca2dfdda122e91c54ff77107d0d76ada89f2d5ff54ff19e8"],"state_sha256":"c0f6ad5d8616e44ae70386742db0340bbb09f0a22b78433c4547626a5447a657"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LsTgGpyPvhgwPgXQQttoLNDpz6IcfuzCs7sa8ghNBuLo7yQtG4e+8m/Kb7y4KmqOxq7Gbm/cLHSVFBzljy0lBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:11:50.367311Z","bundle_sha256":"fda60bb927f9989c62fda92f061c5e1f4a89e305fd60529da1f9b784d78a55cb"}}