Spectral AM-Regulator Geometry: An Experimental and Engineering Programme for Detecting Scale-Regulated Structure Across Nuclear, Quantum, Gravitational and Cosmological Systems

This paper proposes an experimentally falsifiable programme for testing whether a scale-dependent spectral geometry can be identified consistently across physical systems that are presently analysed by distinct mathematical and experimental formalisms. The proposed Spectral Regulator Geometry (SRG) is not introduced as a new force, particle, material medium or replacement for established physical law. It is treated as a structural hypothesis arising from the Scale-Regulated Aggregation (SRA) and Additive–Multiplicative (AM-Regulator) programme.[36] Earlier work in this programme formulated regulated accumulation, spectral saturation, geometric projection and cross-domain statistical constraints across mathematical, physical, astronomical and engineering systems.[1][2][3][4][5][6][7][8] The present paper converts that programme into an explicit experimental protocol. The central test is deliberately severe. Observed structures are transformed into coordinate-, graph- and spectral representations; the same data are independently analysed under conventional null models and under the SRA–AM construction; controlled perturbations are introduced; the resulting changes are measured; and the predicted and observed transformations are compared without allowing visual similarity to constitute evidence. The empirical layer is designed around publicly accessible observational, experimental and archival datasets documented in peer-reviewed literature or official collaboration releases, with particular emphasis on DESI, Euclid, Planck, LIGO–Virgo–KAGRA, MeerKAT, uGMRT, AstroSat, CERN collider data, contemporary nuclear-reaction measurements and quantum-computing experiments. The datasets include measurements of cosmological expansion, filament connectivity, pulsar timing, gravitational-wave strain, particle masses, nuclear fragment distributions, quantum logical-error rates and high-resolution radio/optical structure.[9][10][11][12][13][14][15][16][17][18][19][20][21][22][27][28][29] The experimental programme has two complementary components. The first is a passive observational test, in which existing measurements are subjected to the same geometric and spectral analysis. The second is a controlled laboratory/nuclear-physics perturbation test, using existing accelerator, detector and interferometric infrastructure rather than requiring the construction of a new physical observatory. The proposed outcome is not confirmation by resemblance. The decisive criterion is whether a common set of dimensionless structural observables survives independent transformations, resolutions, algorithms, software environments and null-model comparisons. Failure of this criterion would falsify the proposed universal interpretation. The paper therefore constitutes a call to physicists, experimental physicists, nuclear physicists, astronomers, statisticians, quantum engineers and computational scientists: Here is the predicted structure. Here are the transformations. Here are the invariants. Here are the null models. Here are the perturbations. Here are the independent computational environments. Here are the existing observations. Now test the construction without protecting it.