{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:NFC6FYSO2JH7OVIZ6AB6U24S5Y","short_pith_number":"pith:NFC6FYSO","canonical_record":{"source":{"id":"math/0509705","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2005-09-29T20:11:44Z","cross_cats_sorted":[],"title_canon_sha256":"769ad8c4d2f25310483e5a97784c90e9333e687e4709daab5775437a038750c3","abstract_canon_sha256":"7475236defd8ab1a5fef354143ba61d89431a114b8dec49ceb69a699ac7b892e"},"schema_version":"1.0"},"canonical_sha256":"6945e2e24ed24ff75519f003ea6b92ee1e8e16b71c0f468a1dd95b12d99404fb","source":{"kind":"arxiv","id":"math/0509705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509705","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509705v1","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509705","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"NFC6FYSO2JH7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NFC6FYSO2JH7OVIZ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NFC6FYSO","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:NFC6FYSO2JH7OVIZ6AB6U24S5Y","target":"record","payload":{"canonical_record":{"source":{"id":"math/0509705","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2005-09-29T20:11:44Z","cross_cats_sorted":[],"title_canon_sha256":"769ad8c4d2f25310483e5a97784c90e9333e687e4709daab5775437a038750c3","abstract_canon_sha256":"7475236defd8ab1a5fef354143ba61d89431a114b8dec49ceb69a699ac7b892e"},"schema_version":"1.0"},"canonical_sha256":"6945e2e24ed24ff75519f003ea6b92ee1e8e16b71c0f468a1dd95b12d99404fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:38.458628Z","signature_b64":"PzOqTz17e0DW+3E4rWRo8+DoHVCHV9QbEciW26zxRFCRitECg2f5LaImJ6y9qdXxjiKqEEiNUB0KdiZOu0W3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6945e2e24ed24ff75519f003ea6b92ee1e8e16b71c0f468a1dd95b12d99404fb","last_reissued_at":"2026-05-18T02:35:38.458147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:38.458147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0509705","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":"2026-05-18T02:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rzz29RTpAqh+CFwaliOxL/8q0qViu9GEz0HLd9ZTYUAt4qSWJojgyCM/lGyZbdlWGkcGepidNYF6p0hsV5ytDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:12:10.307590Z"},"content_sha256":"5e3c8040dbbe91351ffc3354de7951f02580bdbebaa34f1e6d19e22067802c96","schema_version":"1.0","event_id":"sha256:5e3c8040dbbe91351ffc3354de7951f02580bdbebaa34f1e6d19e22067802c96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:NFC6FYSO2JH7OVIZ6AB6U24S5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on Overshoot Estimation in Pole Placements","license":"","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"D. Cheng, L. Guo, Y. Lin, Y. Wang","submitted_at":"2005-09-29T20:11:44Z","abstract_excerpt":"In this note we show that for any given controllable pair (A,B) and any c> 1, a gain matrix K can be chosen so that the transition matrix of the system x' = (A+BK)x decays at the exponential rate exp(-ct) and the overshoot of the transition matrix can be bounded by Mc^L for some M and L that are independent of the choice of c."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509705","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":"2026-05-18T02:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6436R+gL4UwfxsOIFdoPddhIArp6HSN6+OA8To2sIftuQNtQvsFOkm2YGFxEuMdgvkUTvtGBh4LVVhxwD4DaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:12:10.308097Z"},"content_sha256":"c3b828e89f10a5394468163d2d1cdc502574856fd8bcd21fdba408c75e2f79bd","schema_version":"1.0","event_id":"sha256:c3b828e89f10a5394468163d2d1cdc502574856fd8bcd21fdba408c75e2f79bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFC6FYSO2JH7OVIZ6AB6U24S5Y/bundle.json","state_url":"https://pith.science/pith/NFC6FYSO2JH7OVIZ6AB6U24S5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFC6FYSO2JH7OVIZ6AB6U24S5Y/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":"2026-06-08T06:12:10Z","links":{"resolver":"https://pith.science/pith/NFC6FYSO2JH7OVIZ6AB6U24S5Y","bundle":"https://pith.science/pith/NFC6FYSO2JH7OVIZ6AB6U24S5Y/bundle.json","state":"https://pith.science/pith/NFC6FYSO2JH7OVIZ6AB6U24S5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFC6FYSO2JH7OVIZ6AB6U24S5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:NFC6FYSO2JH7OVIZ6AB6U24S5Y","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":"7475236defd8ab1a5fef354143ba61d89431a114b8dec49ceb69a699ac7b892e","cross_cats_sorted":[],"license":"","primary_cat":"math.OC","submitted_at":"2005-09-29T20:11:44Z","title_canon_sha256":"769ad8c4d2f25310483e5a97784c90e9333e687e4709daab5775437a038750c3"},"schema_version":"1.0","source":{"id":"math/0509705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509705","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509705v1","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509705","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"NFC6FYSO2JH7","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NFC6FYSO2JH7OVIZ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NFC6FYSO","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:c3b828e89f10a5394468163d2d1cdc502574856fd8bcd21fdba408c75e2f79bd","target":"graph","created_at":"2026-05-18T02:35:38Z","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":"In this note we show that for any given controllable pair (A,B) and any c> 1, a gain matrix K can be chosen so that the transition matrix of the system x' = (A+BK)x decays at the exponential rate exp(-ct) and the overshoot of the transition matrix can be bounded by Mc^L for some M and L that are independent of the choice of c.","authors_text":"D. Cheng, L. Guo, Y. Lin, Y. Wang","cross_cats":[],"headline":"","license":"","primary_cat":"math.OC","submitted_at":"2005-09-29T20:11:44Z","title":"A Note on Overshoot Estimation in Pole Placements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509705","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":"sha256:5e3c8040dbbe91351ffc3354de7951f02580bdbebaa34f1e6d19e22067802c96","target":"record","created_at":"2026-05-18T02:35:38Z","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":"7475236defd8ab1a5fef354143ba61d89431a114b8dec49ceb69a699ac7b892e","cross_cats_sorted":[],"license":"","primary_cat":"math.OC","submitted_at":"2005-09-29T20:11:44Z","title_canon_sha256":"769ad8c4d2f25310483e5a97784c90e9333e687e4709daab5775437a038750c3"},"schema_version":"1.0","source":{"id":"math/0509705","kind":"arxiv","version":1}},"canonical_sha256":"6945e2e24ed24ff75519f003ea6b92ee1e8e16b71c0f468a1dd95b12d99404fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6945e2e24ed24ff75519f003ea6b92ee1e8e16b71c0f468a1dd95b12d99404fb","first_computed_at":"2026-05-18T02:35:38.458147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:38.458147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PzOqTz17e0DW+3E4rWRo8+DoHVCHV9QbEciW26zxRFCRitECg2f5LaImJ6y9qdXxjiKqEEiNUB0KdiZOu0W3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:38.458628Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0509705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e3c8040dbbe91351ffc3354de7951f02580bdbebaa34f1e6d19e22067802c96","sha256:c3b828e89f10a5394468163d2d1cdc502574856fd8bcd21fdba408c75e2f79bd"],"state_sha256":"413401ef03df3cc41dd9bc46e6f43673bc3de3635a227c5a4e838d52c3b54f62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lFLt0S8RMN5BoZ7zS8z+Q+h8DgLqdOeFz0RuRG7iYy6PnIai+ZFA+yfi0u2JMWGAhqma3WLswVtfD7TWr2M3Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T06:12:10.311935Z","bundle_sha256":"40c19ea7d54880b0d0918034fa65f3b00affb880420b9b9bda9b5add243e6913"}}