From Flatland to Tunnelling: A Falsification Notebook for an Additional-Coordinate Hypothesis

This open research notebook develops a falsification-first route from the Flatland analogy to testable additional-coordinate models in quantum tunnelling. It separates three independent pipelines: predictions derived from one fixed four-spatial-dimensional model, residuals extracted from calibrated measurements without invoking w, and ordinary-physics controls. The primary constitutive hypothesis is S_E=f(w), where S_E is dimensionful Euclidean action and A=S_E/hbar is the dimensionless tunnelling exponent. No linear law is assumed, and the coordinate w is not identified with RMS transverse broadening. Existing controlled calculations establish a coupled-channel effect inside a specified (x,w) Hamiltonian, while matched-broadening stress tests show that center broadening alone does not determine action. Status: open, non-peer-reviewed working paper. The notebook does not report evidence for a fundamental fourth spatial dimension. It provides a pre-registered, no-refit framework for deciding what future observations would count against or in favor of the model. Related control study: https://doi.org/10.5281/zenodo.22071952