Report Structures over Native EAS SOO: Recurrent Pattern Waves and Lorentz Report Charts

Abstract

This paper is archived as a speculative research work. This paper revises the downstream SOO report stack to conform to the certified EAS SOO v0.3.1 recurrence–accommodation rule. Native SOO is not a passive adjacent-presentation difference and its recurrence is not defined by a three-phase cyclic return operator. At each global rank–3 phase, the completed SOO realization is a deterministic bijection of the immutable scalar-point set whose nontrivial elementary actions are exact full scalar-value transpositions. For one relational path and one phase at a time, the recurrence channel obeys d_{n+1} - 2d_n + d_{n-1} = -K_n d_n, 0 <= K_n <= 4, with no cross-path or cross-phase recurrence coupling. The contextual scalar stiffness K controls recurrence span and never a fractional exchange. For a selected relational path, phase 0 is the path-facing phase. Every realized nontrivial repeat of that same-path phase-0 recurrence is synchronized one-for-one with exactly one atomic accommodation of the same path, |Delta L| = 1. Phases 1 and 2 retain their own full-exchange recurrences but do not generate accommodation of that path. No independent scheduler, cadence variable, or angle accumulator is introduced. The report theory developed here is therefore phase-resolved. For constant K, the second-order recurrence is represented by a determinant-one two-dimensional report map. The interval 0 < K < 4 gives elliptic rotation blocks with cos(omega) = 1 - K/2, while K = 0 and K = 4 are the steady and maximal alternating endpoints. The canonical free photon-like record gives the exact K = 4 positive control, and the K = 1 witness gives an exact antireturn after three same-phase intervals while retaining complete scalar exchange at every active event. A separate Lorentz-facing report branch counts realized phase-0 recurrence–accommodation events. Under declared calibration, additivity, branch preservation, reciprocity, and reciprocal scale parity, the resulting real report coordinates carry the proper branch-preserving reciprocal 1+1 Lorentz boost. These coordinates remain downstream interface structures and are not primitive spacetime coordinates. The complete native functional deriving contextual K from the complete SF/SOO relationship record remains open. That open first arrow is kept strictly separate from the certified rule K -> same-phase recurrence -> repeat -> one atomic path accommodation.