Lorentz Structure as Relational Report Symmetry in EAS: From Scalar-Field Recurrence to a Conditional Lorentz Report-Chart Characterization

Abstract

This paper is archived as a speculative research work. Entanglement-Algebraic Spacetime (EAS) does not begin with a spacetime manifold, primitive physical time, a Lorentz metric, inertial frames, or a global observer-independent scalar state. Its scalar-field ontology is strictly relational and binary, with rank–3 phase organization and minimum-count relational paths. This paper asks what Lorentz structure can mean in such an ontology and identifies a precise downstream construction. For one selected relational-path context, the second-order ordering framework supplies phase-specific recurrence and recurrence–accommodation synchrony. The free photon-like has a unique path-facing Phase-0 role with exact K_0=4 recurrence cadence. F3 constructs two discrete report quantities: the number T_ raw of completed rank–3 cycles and the number N_ raw of realized path-facing accommodation events. Binary phase typing gives 0≤ N_ raw≤ T_ raw , while the free K_0=4 control plus synchrony gives exact saturation N_ raw=T_ raw . After a single global report-axis orientation and equal calibration, the report therefore satisfies |x|≤ t , with symmetric saturation rays x=± t . Raw traces are not assumed to form a vector space. They are explicitly completed first to an integer-generated additive group and then to a real two-dimensional report space V_ rep . On this completed space, F3 considers continuous additive homogeneous charts, a moving-origin parameter , reciprocity, global report-axis orientation covariance, and, decisively, individual preservation of the two saturation rays. Boundary preservation first selects the conformal Lorentz class; the moving-origin condition fixes the mixing ratio; reciprocity and orientation covariance fix the conformal normalization. The unique identity-connected transformation is the standard SO^+(1,1) Lorentz boost and preserves t^2-x^2 . An explicit Galilean countermodel shows that relationality, non-primitive simultaneity, reciprocity, and moving-origin behavior do not select Lorentz structure without saturation-boundary invariance. The resulting Minkowski form is therefore not a primitive scalar-field metric but the invariant quadratic form of a completed recurrence/accommodation report. Physical null and timelike interpretations require additional provenance-preserving geometry gates. Conditionally, the photon path-facing relationship may acquire a Lorentz-null representative, while three independently reconstructed exterior relationships of a coherent bounded support span a spatial three-plane whose Lorentz-orthogonal complement is timelike and supplies a rest direction. The core result is a conditional Lorentz report-chart characterization, not a derivation of Lorentz kinematics from F1/F2 alone, not a proof that every real boost is physically realized, and not yet a standalone empirical Lorentz test.