The Spectral Computing Programme: Open Problems, Conjectures, and New Directions

This document synthesises the current state of the Spectral Computing Programme across its six major threads — the Spectral Sieve, the Arithmetic Cylinder, the Information-Scaling Manifold, the Unified Constants Programme, the robotics and applied engineering validation work, and the neuroscience/diagnostic application — for the specific purpose of identifying what remains genuinely open, what stands as conjecture rather than proof, and where new, untested connections between threads may be worth pursuing. It is a map, not a new derivation: every status claim below reflects work already completed and documented across the programme’s existing papers, sorted honestly by epistemic status rather than restated as settled.