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The exponent shifts down by exactly $\\rho(1-R)$ relative to the unconstrained Ar{\\i}kan--Merhav exponent, with each of the $"},"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":"2607.00205","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-30T21:35:56Z","cross_cats_sorted":["cs.GT","math.CO","math.IT","math.PR"],"title_canon_sha256":"e6a60b5ce54d77e6442b8fbea79be31050bc134fc4e8b09bf603800ab061d4b4","abstract_canon_sha256":"ad52c2113341d7ff6713e822da7ac6aa5e3c45d4d253e20ec8733dcae6b2acf8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T00:18:39.004706Z","signature_b64":"7GtjhS6ylvNqe6lPSizXvFue3pMkxil+movpFSzQ7G7abp/eQT/qV5MNBQWZCa4bU9bsvmIgaKQpCDNvOjpuAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c16dbdb6ebdb2f5a6f5cc448c12e1accdcd19a1ef59385085be0b329efc1c10","last_reissued_at":"2026-07-02T00:18:39.004222Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T00:18:39.004222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Guesswork Under Linear Constraints: Exact Exponent for Coset Decoding","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.GT","math.CO","math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Hassan Tavakoli","submitted_at":"2026-06-30T21:35:56Z","abstract_excerpt":"We establish the exact exponential growth rate of the $\\rho$-th moment of the constrained guesswork $G_{\\mathrm{coset}}$ -- the rank of the true noise vector within its syndrome coset of a random binary linear code under i.i.d.\\ Bernoulli$(p)$ noise: \\( \\lim_{n\\to\\infty} \\frac{1}{n}\\log_2\\Eb\\!\\left[G_{\\mathrm{coset}}^{\\rho}\\right] = \\rho\\,h_{\\frac{1}{1+\\rho}}(p)\\;+\\;\\rho(R-1), \\, \\rho>0, \\) where $h_\\alpha(p)$ is the binary R\\'{e}nyi entropy and $R=k/n$ is the code rate. 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