Lorentz Report-Chart Characterization in EAS: Non-Primitive Simultaneity and Relational Accommodation Foundations Paper F3

This paper is archived as a speculative research work. Entanglement–Algebraic Spacetime (EAS) does not take spacetime, a Lorentz metric, inertial frames, physical time, or physical simultaneity as primitive scalar-field structure. Foundations Paper F1 fixes instead a formal scalar-field ontology and a strict ontology–report–interface firewall. Foundations Paper F2 adds contextual same-path same-phase SOO recurrence and recurrence–accommodation synchrony: for a selected relational-path abstraction, phase 0 is the path-facing recurrence role, and every realized nontrivial phase-0 repeat is synchronized one-for-one with one path accommodation. F2 also supplies the exact canonical free photon-like K=4 recurrence control, which repeats at every successive path-facing phase occurrence. This paper asks a narrower question than earlier EAS Lorentz treatments: what Lorentz structure follows once those F1/F2 records are placed in a separately declared homogeneous report-chart architecture? For a completed trace, T_ raw counts completed rank–3 cycles and N_ raw counts realized path-facing accommodation events. Because at most one such binary event is recorded per cycle, 0≤ N_ raw≤ T_ raw. Recurrence–accommodation synchrony is not needed for that bare bound; it is needed to make the K=4 free control saturate it, N_ raw=T_ raw. A single global report-axis orientation ∈-1,+1 defines X_ raw^( )= N_ raw. No event-by-event sign choice is permitted. Under equal report calibration, the saturated control is represented by one boundary ray x= t, while global axis reversal supplies the opposite ray in the symmetric report completion. The discrete trace records are not assumed to form a vector space or even an unrestricted additive semigroup. F3 instead forms the integer-generated report group and then its real linear completion V_ rep. On that completed report space, F3 explicitly imposes continuous homogeneous chart equivalence, individual preservation of the two saturation rays, a moving-origin condition, reciprocal chart equivalence, and covariance under global report-axis reversal. Saturation-ray preservation already restricts the admissible linear maps to the conformal Lorentz class. Reciprocity and orientation covariance then fix the conformal scale, yielding t'= (t- x), x'= (x- t), =(1- ^2)^-1/2, and hence preservation of t^2-x^2. The central result is therefore a Lorentz report-chart characterization theorem, not a derivation of Lorentz kinematics from F1/F2 alone. F1/F2 supply the typed recurrence/accommodation data and an exactly saturating free-control class; F3 adds the invariant-boundary chart postulate and the remaining chart symmetries. The completed matrix family is SO^+(1,1), but the paper does not prove that every real boost parameter is realized by an actual EAS trace or chart. It also makes no standalone calibrated empirical prediction. A single-direction 3+1 embedding is stated only conditionally and requires independently supplied three-dimensional report geometry and transverse invariance; a complete SO^+(1,3) interface remains open.