Optimal Local Decompression: Uniform Finite-View Reduction
A uniform finite-view reduction at the paper's counting-optimal k-bit vertex budget for odd maximum degree 2k-1. Given one total finite-view orientation rule with a sufficient one-bit advice guarantee, one decoder family is chosen before graph order, topology, markers, advice and payload. Every connected graph on Fin n with n>16(k+1) and degree at most 2k-1 admits an encoder recovering every edge bit at either endpoint from a 2^k-symbol vertex alphabet. The same total decoder is local across different connected graphs and arbitrary labelings, with no marker validity or encoded-input premise.…
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