This paper is archived as a speculative research work. This paper documents a finite diagnostic modeling program for EAS scalar fields grounded in a non-geometric axiom framework of scalar points, scalar presentations, rank-3 association records, global phase-specific exposure, point-to-associate SOO admissibility, cyclic return, and automorphic recurrence. The purpose is model-facing: to show how scalar-field recurrent patterns can be investigated without imposing downstream physical structures such as particles, supports, matter, mass, charge, energy, force, waves, or spacetime geometry as ontology. The central case study asks what scalar-field conditions must be satisfied before a recurrent report may be treated as mass-bearing-like at a later interface. The investigation shows that raw recurrence, recurrence-density magnitude, common-mode SOO, proxy closure, and single canonical realization are insufficient. Robust threshold candidates require corrected unit-modulus recurrence diagnostics, baseline-subtracted recurrence-density accounting, compatible and strong compensation, direct cyclic-return rest-floor crossing, primitive phase-specific update survival, and explicit scalar-point realization robustness. The resulting minimal threshold rule is a finite model-facing admissibility stack, not an empirical derivation of particle masses. Its speculative implication is that rest-mass-facing behavior may correspond, at an interface level, to a closure-established recurrence-density burden retained by compensated, primitive-stable, realization-robust recurrent structure. The paper therefore presents the mass-bearing-like investigation primarily as a demonstration of how the scalar-field model is disciplined and improved by admissibility-driven computation.
Michael Labhard (Fri,) studied this question.