Open Research Index

Distance-Shell Tomography: Geometric Certificates for Fault-Tolerant Sensing, Moment Compression, and Hypercube Equalization

Lennart Rudolph

Palomar Registrypalomar/PALOMAR-2026-10-04-000001Oct 4, 2026math.COscore 0

Substantive Lean development for labelled distance-shell observations of anonymous integer populations. The focused 14-statement interface covers six result groups. Square grids have an exact four-corner interval-cut characterization of recovery of all populations of mass at most two after one erased report, an equivalent distance-sum compression contract, and exact corner-constrained optimum ceil(3(n+1)/2) for every n at least 3. For every positive q, the actual-distance equalizer cardinality of Q_(4q) lies between 2^(4q-1)+2q-1 and 2^(4q-1)+2q; explicit prefixes also give the infinite…

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