An Investigation into the Lepton Mass Hierarchy Problem in Entanglement--Algebraic Spacetime

This paper is archived as a speculative research work. This paper develops a fixed synthetic numerical and structural environment for investigating the charged-lepton mass hierarchy problem in the Entanglement–Algebraic Spacetime (EAS) framework. Rather than postulating three family masses or three independent family coefficients, the paper reformulates the hierarchy problem as the problem of determining whether distinct plateau motifs, subjected to one fixed forcing class and read through a slot-plane-first interface map, leave distinct irreducible residual organizations capable of supporting a common detector-facing mass law. A staged law search on an anchor family consisting of the electron seed, the muon hierarchy anchor M2, and the tau minimal template shows that coarse additive and globally compressed laws are insufficient. Progressively refined sector and boundary laws localize the dominant hierarchy-bearing structure to compound boundary return geometry, and the strongest current synthetic discriminator is the routing state of the boundary return junction. A detector-facing calibration bridge then shows that a pure power readout fails on the tau anchor, whereas a routing-state corrected bridge yields a common three-family anchor fit and preserves off-anchor family-band membership on the tested nearby-family and alternate tau-like motif sets. The result is not yet a final first-principles derivation of the empirical charged-lepton masses, but a reusable fixed synthetic environment in which the lepton hierarchy can be investigated structurally, numerically, and detector-facingly under common conditions.