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We give a verifiable data-level certificate under which it does not. Hyperbolicity of the reduced state--costate transition matrix, together with scaled stable--unstable boundary transversality, yields an endpoint-corrected Green inverse with horizon-independent constants and weighted contractions transfer this inverse to the nonlinear problem, so the original Pontryagin endpoint rows $x_0=x_{\\rm in}$ and $p_T=r_x(x_T,y)$ carry a unique local stationary branch whose first-order expansion and Lipschitz constants are uniform in the horizon. Consequently the finite-horizon feedback map is horizon-uniformly Lipschitz, first-order expandable, and satisfies an exact shrinking-horizon consistency identity. Symplectic and Riccati criteria certify the hypotheses from matrix da","title":"Horizon-Uniform Sensitivity Certificates for Finite-Horizon Pontryagin Systems","url":"https://arxiv.org/abs/2606.17762","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.17762v2 Announce Type: replace-cross \nAbstract: Finite-horizon optimal-control computations repeatedly solve two-point Pontryagin boundary value problems whose conditioning can deteriorate as the horizon grows. We give a verifiable data-level certificate under which it does not. Hyperbolicity of the reduced state--costate transition matrix, together with scaled stable--unstable boundary transversality, yields an endpoint-corrected Green inverse with horizon-independent constants and weighted contractions transfer this inverse to the nonlinear problem, so the original Pontryagin endpoint rows $x_0=x_{\\rm in}$ and $p_T=r_x(x_T,y)$ carry a unique local stationary branch whose first-order expansion and Lipschitz constants are uniform in the horizon. Consequently the finite-horizon feedback map is horizon-uniformly Lipschitz, first-order expandable, and satisfies an exact shrinking-horizon consistency identity. Symplectic and Riccati criteria certify the hypotheses from matrix da","title":"Horizon-Uniform Sensitivity Certificates for Finite-Horizon Pontryagin Systems","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-03T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.17762"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:83fae27df51c54b98a2d7cb2d0d7f58efe88b2ebe404030a2c7bed5e050191edbe318fdb8fb185007fd1a07e151248d44919ca2bf69515aa56dfcc9391b5db04","signer":"crovia.substrate","subject":{"observed_at":"2026-07-03T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.17762"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"1e0fb1317e63ca70f79357f331f625af2a6d469e615f74576abd1b3ee5067188","leaf_index":275670,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"3fc1404d0cc1235d45e160701534128b5a70c050b59070c288552a92a20e5cab","side":"right"},{"sibling":"ca57e0ab9614ff6fdd271497fa19b3537b3c2bf7ae1dc4111a921f42bdaf02aa","side":"left"},{"sibling":"a1b8079444f9efdc7ad93dbc17ca07a403a89e17b6f9f8bef27478191c563deb","side":"left"},{"sibling":"ec2154c3580e5c23533328c96913b6a914ffd186e24d48404492979052cb8614","side":"right"},{"sibling":"40b3783ff1e71d3ebb17984aaa4e13e65bd1e0f6fd9ad4e7b7dfdc4848e2a397","side":"left"},{"sibling":"d3634fa5229dabfd18f6b2c431c82a9824e42092f16e4d5ca24f7ff63b3f123e","side":"right"},{"sibling":"01f6ff086bf4ba57ce8ef2e69a75991694c44d99ba581de7d218b24d698e7b27","side":"left"},{"sibling":"afd7390845185d24208014fda1eda02563e823c07b9f4ce03d1011344ff5e6f8","side":"left"},{"sibling":"da9343635b180d3ddf07636b2a7814fcbf809adc1979958fa092ef6d16ef0db5","side":"right"},{"sibling":"1685b068d9bba0447845c97429c2a9ba728526abe2dc9d9522fed7b13d6620e4","side":"right"},{"sibling":"cf1e47b22a12b71fda307cbe1b98bc247fa4226ac8691ca8d99e6cc72a905b34","side":"left"},{"sibling":"4dbd8247ba08a5432c7d6540711da9acb2f59e6189865aa8552dee37f69286a9","side":"right"},{"sibling":"41cd1885dc3fcb51e49eeb887d6d22ec2cfa58df0e4f8d7c7dddf3a1b0ce8249","side":"left"},{"sibling":"8a09562f6b247c1c3cd1fea36cb3b8f1cf5c575479dd514573856a380a964bf5","side":"left"},{"sibling":"723981908169653ca6d835aa9b8381a8c7ad3e3e3830d0792bc32032cda615ee","side":"right"},{"sibling":"c0594fa1ee81d5f019cccc7b5e51af603c6d7e43995498c451012060c7d06165","side":"right"},{"sibling":"4de6a2fb22efbb50c84dc62abeb0f2cbc8c663a9540aeba9e758ebfdfe3e86dd","side":"right"},{"sibling":"fdbb3519f8dc411a4043dfb5abdbfea5441e130326183ac2247c42584033f152","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":275799,"merkle_root":"2581d0d6e5fa345cdf2e8ab3b191ace76d6b14189901ab0e4c2291ca1d1ae1e6","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260703T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-03T05:38:09Z","sig_algorithm":"ed25519","signature":"e44a386a5ae00c0e7fc67b1179bb9060bf0fefc006e454fec70e27668182ff497d1e2faf0c3b22de0917beefb7c80e880dae925a3f67e1b16aa0eb44bf947407","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_1d71124023350378600136bbea072bfe95f4c47f896d69081490640556e9f6d3"}}