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We show that the error amplification is governed by certain algebraic curves $S_{F,i},$ in the parameter space of signals $F$, alon"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.01482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-05T21:25:01Z","cross_cats_sorted":[],"title_canon_sha256":"6f086f1a15b18bcf7d821eb8a48443a6a0416a9a5a77f34e77058d8f2af907f6","abstract_canon_sha256":"b3e02cb18e43157d5066e29daed0288153ee10cf49a61fc6ba6c8f302cf81469"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:16.719391Z","signature_b64":"5es/BQn4gNubPUAb84nvoWnX0VJ7oV6qEjYY8XRym/SnEeyTC8sZsrda5whnrLxkYZm3ZV/pNhc6eOQ285eiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38c7b81e963b0faf7bba8f1ed1fb6d1320b24193c3976e5452b17214940e8634","last_reissued_at":"2026-05-18T00:53:16.718939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:16.718939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Accuracy of reconstruction of spike-trains with two near-colliding nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrey Akinshin, Gil Goldman, Vladimir Golubyatnikov, Yosef Yomdin","submitted_at":"2017-01-05T21:25:01Z","abstract_excerpt":"We consider a signal reconstruction problem for signals $F$ of the form $ F(x)=\\sum_{j=1}^{d}a_{j}\\delta\\left(x-x_{j}\\right),$ from their moments $m_k(F)=\\int x^kF(x)dx.$ We assume $m_k(F)$ to be known for $k=0,1,\\ldots,N,$ with an absolute error not exceeding $\\epsilon > 0$.\n  We study the \"geometry of error amplification\" in reconstruction of $F$ from $m_k(F),$ in situations where two neighboring nodes $x_i$ and $x_{i+1}$ near-collide, i.e $x_{i+1}-x_i=h \\ll 1$. 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