{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:W77KHWK5JSAFEIGOBY4FR73RHQ","short_pith_number":"pith:W77KHWK5","canonical_record":{"source":{"id":"math/0702687","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2007-02-23T10:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"3c4a71e4d17a24b341562559b36c2d54fc442de5594a6d21c45326674df5fb24","abstract_canon_sha256":"81afd51498af330da2a7e363a4cb37cf6ff571ce5d8bf446982b728fa091f65d"},"schema_version":"1.0"},"canonical_sha256":"b7fea3d95d4c805220ce0e3858ff713c2ccf3ec2836f36866f1e7272463c5ea9","source":{"kind":"arxiv","id":"math/0702687","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702687","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702687v1","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702687","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"W77KHWK5JSAF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"W77KHWK5JSAFEIGO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"W77KHWK5","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:W77KHWK5JSAFEIGOBY4FR73RHQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0702687","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2007-02-23T10:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"3c4a71e4d17a24b341562559b36c2d54fc442de5594a6d21c45326674df5fb24","abstract_canon_sha256":"81afd51498af330da2a7e363a4cb37cf6ff571ce5d8bf446982b728fa091f65d"},"schema_version":"1.0"},"canonical_sha256":"b7fea3d95d4c805220ce0e3858ff713c2ccf3ec2836f36866f1e7272463c5ea9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:15.383920Z","signature_b64":"+41JmrXbXZ1OXhjsH3Pz7dYSql2kF0XWvxDc7dsii+o15kIpbpsmAhXWLuzmjHAWwLMPB2fGLWdTTE0bNPZKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7fea3d95d4c805220ce0e3858ff713c2ccf3ec2836f36866f1e7272463c5ea9","last_reissued_at":"2026-05-18T01:09:15.383275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:15.383275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0702687","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":"2026-05-18T01:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yGqFa1gpdQNbVjNr5x+46LtRrV+qwvyvcnAzwSKb9CoV0rTwQoJzsUBXOrdL8Zzql4o0DB0Fwc2BfEdjGvbLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:28:40.072406Z"},"content_sha256":"83d7d5b2ed8075baf209e7d19e4efe55dc53cb887956b5ea93dafaf0de5b30e3","schema_version":"1.0","event_id":"sha256:83d7d5b2ed8075baf209e7d19e4efe55dc53cb887956b5ea93dafaf0de5b30e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:W77KHWK5JSAFEIGOBY4FR73RHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases","license":"","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antoine Chaillet, Antonio Lor\\'ia (LSS), Iecn), Mario Sigalotti (INRIA Lorraine / IECN / MMAS, Yacine Chitour (LSS)","submitted_at":"2007-02-23T10:28:37Z","abstract_excerpt":"Consider the controlled system $dx/dt = Ax + \\alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\\alpha(t)$ takes values in $[0,1]$ and is persistently exciting, i.e., there exist two positive constants $\\mu,T$ such that, for every $t\\geq 0$, $\\int_t^{t+T}\\alpha(s)ds\\geq \\mu$. In particular, when $\\alpha(t)$ becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback $u=Kx$, with $K$ only depending on $(A,B)$ and possibly on $\\mu,T$, which globally asymptotically stab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702687","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":"2026-05-18T01:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KhttY4a/ePjKOx/1nvbmYS7L5ZtDeRpJNm2FpUynGsteFddVdwPU+PJzmwqdwnGF30Vcgb/HVTU0f4pIoJ1zCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:28:40.073122Z"},"content_sha256":"1e6fdf0bd5c4dd85f550a0558dc019b026c3eeb92350fa4b789ba213b0e811a0","schema_version":"1.0","event_id":"sha256:1e6fdf0bd5c4dd85f550a0558dc019b026c3eeb92350fa4b789ba213b0e811a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W77KHWK5JSAFEIGOBY4FR73RHQ/bundle.json","state_url":"https://pith.science/pith/W77KHWK5JSAFEIGOBY4FR73RHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W77KHWK5JSAFEIGOBY4FR73RHQ/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":"2026-06-08T19:28:40Z","links":{"resolver":"https://pith.science/pith/W77KHWK5JSAFEIGOBY4FR73RHQ","bundle":"https://pith.science/pith/W77KHWK5JSAFEIGOBY4FR73RHQ/bundle.json","state":"https://pith.science/pith/W77KHWK5JSAFEIGOBY4FR73RHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W77KHWK5JSAFEIGOBY4FR73RHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:W77KHWK5JSAFEIGOBY4FR73RHQ","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":"81afd51498af330da2a7e363a4cb37cf6ff571ce5d8bf446982b728fa091f65d","cross_cats_sorted":[],"license":"","primary_cat":"math.OC","submitted_at":"2007-02-23T10:28:37Z","title_canon_sha256":"3c4a71e4d17a24b341562559b36c2d54fc442de5594a6d21c45326674df5fb24"},"schema_version":"1.0","source":{"id":"math/0702687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702687","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702687v1","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702687","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"W77KHWK5JSAF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"W77KHWK5JSAFEIGO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"W77KHWK5","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:1e6fdf0bd5c4dd85f550a0558dc019b026c3eeb92350fa4b789ba213b0e811a0","target":"graph","created_at":"2026-05-18T01:09:15Z","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":"Consider the controlled system $dx/dt = Ax + \\alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\\alpha(t)$ takes values in $[0,1]$ and is persistently exciting, i.e., there exist two positive constants $\\mu,T$ such that, for every $t\\geq 0$, $\\int_t^{t+T}\\alpha(s)ds\\geq \\mu$. In particular, when $\\alpha(t)$ becomes zero the system dynamics switches to an uncontrollable system. In this paper, we address the following question: is it possible to find a linear time-invariant state-feedback $u=Kx$, with $K$ only depending on $(A,B)$ and possibly on $\\mu,T$, which globally asymptotically stab","authors_text":"Antoine Chaillet, Antonio Lor\\'ia (LSS), Iecn), Mario Sigalotti (INRIA Lorraine / IECN / MMAS, Yacine Chitour (LSS)","cross_cats":[],"headline":"","license":"","primary_cat":"math.OC","submitted_at":"2007-02-23T10:28:37Z","title":"Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702687","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":"sha256:83d7d5b2ed8075baf209e7d19e4efe55dc53cb887956b5ea93dafaf0de5b30e3","target":"record","created_at":"2026-05-18T01:09:15Z","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":"81afd51498af330da2a7e363a4cb37cf6ff571ce5d8bf446982b728fa091f65d","cross_cats_sorted":[],"license":"","primary_cat":"math.OC","submitted_at":"2007-02-23T10:28:37Z","title_canon_sha256":"3c4a71e4d17a24b341562559b36c2d54fc442de5594a6d21c45326674df5fb24"},"schema_version":"1.0","source":{"id":"math/0702687","kind":"arxiv","version":1}},"canonical_sha256":"b7fea3d95d4c805220ce0e3858ff713c2ccf3ec2836f36866f1e7272463c5ea9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7fea3d95d4c805220ce0e3858ff713c2ccf3ec2836f36866f1e7272463c5ea9","first_computed_at":"2026-05-18T01:09:15.383275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:15.383275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+41JmrXbXZ1OXhjsH3Pz7dYSql2kF0XWvxDc7dsii+o15kIpbpsmAhXWLuzmjHAWwLMPB2fGLWdTTE0bNPZKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:15.383920Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83d7d5b2ed8075baf209e7d19e4efe55dc53cb887956b5ea93dafaf0de5b30e3","sha256:1e6fdf0bd5c4dd85f550a0558dc019b026c3eeb92350fa4b789ba213b0e811a0"],"state_sha256":"81877a928750c35da9007400e8c6591f03f273a699de1e0b4fd50905efc51f23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jBjh4+ljxkSY938dX3LpVihVVburQI7zoNIta3NF2zeTG1l+oO2cwbS0guKi5oScJe9834dKfLhFQHGD+vUICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:28:40.077004Z","bundle_sha256":"61757c7574215dce9b8f6c373c39cc8043cd6abfb12051e23a7783ce8434c323"}}