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Conditioned on a transcript $E$, the post-Step 7 coordinate state on $(\\mathbb{Z}_M)^n$ is supported on an affine grid line $\\{\\, j\\Delta + v^{\\ast}(E) + M_2 k \\bmod M : j \\in \\mathbb{Z},\\ k \\in \\mathcal{K} \\,\\}$, with $\\Delta = 2D^2 b$, $M = 2M_2 = 2D^2 Q$, and $Q$ odd. The amplitudes include a quadratic Karst-wave chirp $\\exp(-2\\pi i j^2 / Q)$ and an unknown run-dependent offset $v^{\\ast}(E)$. We show that Chen's Steps 8-9 can be replaced by a s"},"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":"2509.12341","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-09-15T18:10:28Z","cross_cats_sorted":["cs.CL","cs.CR"],"title_canon_sha256":"fb2ca6c8cad7a9ef4725c52dab205433da3eb9131262d8fbb24f4ae78f77ba52","abstract_canon_sha256":"bcfb4e009354f5846dfe840cfc84e7914cba0827797c13b49118bac10ed5996c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:17.542405Z","signature_b64":"Y6EquNitrYuSzOpEqfgm/hQNqfI0w6QxHnIF+w/QRWVaQVg0LkxbjXFECpOX1ZknsP2ERMIebVTOlQyabpJPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15cf21bdfb8430be819160c3967e5a18788b788f54a4bda3dabe6971e5d88107","last_reissued_at":"2026-05-17T23:39:17.541703Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:17.541703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact Coset Sampling for Quantum Lattice Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CL","cs.CR"],"primary_cat":"quant-ph","authors_text":"Yifan Zhang","submitted_at":"2025-09-15T18:10:28Z","abstract_excerpt":"We revisit the post-processing phase of Chen's Karst-wave quantum lattice algorithm (Chen, 2024) in the Learning with Errors (LWE) parameter regime. Conditioned on a transcript $E$, the post-Step 7 coordinate state on $(\\mathbb{Z}_M)^n$ is supported on an affine grid line $\\{\\, j\\Delta + v^{\\ast}(E) + M_2 k \\bmod M : j \\in \\mathbb{Z},\\ k \\in \\mathcal{K} \\,\\}$, with $\\Delta = 2D^2 b$, $M = 2M_2 = 2D^2 Q$, and $Q$ odd. The amplitudes include a quadratic Karst-wave chirp $\\exp(-2\\pi i j^2 / Q)$ and an unknown run-dependent offset $v^{\\ast}(E)$. 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