This paper is archived as a speculative research work. This paper rewrites the EAS scalar-field axiom system around point-to-associate second-order ordering (SOO). The earlier point-to-self comparison Phiₑll - Phi₄₋₋-₁ is demoted to the identity-association special case. The primary scalar-field comparison is instead PiAₑll = Phiₑll - Aₓ₇₄ₓ₀䂰₋₋ Phi₄₋₋-₁, where Aₓ₇₄ₓ₀䂰₋₋ is the active association operator selected by the global rank-3 phase thetaₑll in 0, 1, 2. This makes rank-3 association records active in scalar-value ordering without treating them as spatial directions, geometric tensor components, or propagating channels. The paper separates three notions that must not be conflated. Rank-3 phase is global, discrete, and presentation-level. Pointwise handedness, where defined, is local cyclic orientation/facing relative to the global phase order. Continuous phase appears only later, as report-wave phase in stable recurrent wave sectors. Thus the phase relevant to Noether-facing structure is not the EAS rank-3 phase and is not imported from QFT. It arises from stable recurrent pattern waves generated by the association-indexed cyclic return map F₂ₘ₂, ₀ = F₂, ₀ o F₁, ₀ o F₀, ₀. A recurrent pattern wave is defined as a stable elliptic block of this cyclic return map. On such a block, the return action has rotation form, or equivalently complex eigenvalues e^ (+/- i omegaⱼ). This permits a report-wave coordinate zⱼ = Aⱼ e^ (i alphaⱼ), where alphaⱼ in R / 2piZ is a continuous report-level phase. Continuous symmetries of stable wave-coordinate sectors then supply the scalar-field location of Noether-facing conservation. In particular, when Z₍+₁ = Dₒmega Zₙ and a continuous wave-sector generator Xi commutes with Dₒmega, the report J^waveXi (n) = Z is conserved under full cyclic return. The result is conditional and report-level. It does not derive QFT, Maxwell's equations, the Dirac equation, canonical anticommutation relations, empirical charge, or a primitive electromagnetic field. It identifies the scalar-field mathematical location where recurrent pattern waves, continuous report phases, Noether-facing conserved reports, and later gauge-facing comparison structures can arise without making rank-3 phase local and without importing spacetime or QFT phase into scalar-field ontology.
0009-0008-0231-7067 Labhard (Thu,) studied this question.