Observable Uncertainty in Deterministic Systems: code and data
Description
This dataset accompanies the paper "Observable Uncertainty in Deterministic Systems: Structure, Information Allocation, and the Power of Coupling" (Vicenzo P DeMaar, 2026). The paper studies how a deterministic transformation discloses hidden initial-state information to an observer over time: how long each output stays uncertain, when information becomes observable, and which parts of the state can never be observed. For binary linear systems it proves exact laws for this disclosure and determines the minimum number of operations needed to make it optimal, comparing coupled and independent word updates. The code reproduces every computation in the paper with exact arithmetic, including: – the two-layer observability law and the gcd tiling criterion for rotations; – the classification of all 3,969 rotation-offset pairs of a two-shear update on a 128-bit state; – the separation between coupled updates, which are optimal with two operations, and independent updates, which can never be optimal using rotations alone; – exact minimum operation counts for every bandwidth, including odd bandwidths; – observability profiles for selected bit readouts of the xoroshiro128++ and xoroshiro128** state transitions. A single command runs 46 regression tests and regenerates the 7 reference result files, comparing them byte for byte.
Files
Steps to reproduce
Unzip and open a terminal in the folder. Run: python3 -B -S reproduce.py README.md lists which section of the paper each file verifies.