How the Spatial Readout of Reality Arose: What the Standard Omits, and What It Arises From (Construction Note to "Spacetime as Register, Not Stage")

A construction note to the program "Spacetime as Register, Not Stage" and to its calculational notes "The Bell Calculation" and "The CHSH Threshold from the Number of Closures". The note derives the input data of the standard theory — the quantities the standard accepts without asking where they come from. From a single starting material — a relation with two sides and unit value — it derives in turn: the coordinate system (the axes as the sum and difference of a pair of event vectors), the division into a readout side and a complement side (from the sign of the projection with respect to the centre of balance), the three-dimensionality of the representation (from the rank of the relation matrix), and the capacity of the relational sphere: exactly four equivalent events, with the angle 109.47° falling directly out of the summation of vectors and the arising of the complement (c = −1/(n−1)), and with the number four selected by the tightness of the trace — a criterion that rejects orders 2 and 3 and gives the tetrahedral configuration, in which full occupancy and the closing of the balance turn out to be one fact, the name of the full sphere. The construction contains no fitted parameters; all the numbers (2 sides, 3 dimensions, 4 events, −1/3, 109.47°) are forced. The supplements of 2026-08-04 (§13a) add a second, independent route to the proportion 1/3 (the balance point from pure vector summation on the solid), the law of frame inheritance closing the discreteness of S₃, the derivation of the pair of phase carriers (the trace of the balance) as a unity forced by the balance, the mechanism of the readout debit, and the demonstration that the second iteration is the first and a sufficient order of Bell correlations. In this language, the λ of Bell's theorem is a parametric proxy for the explicitly constructed and consumed first iteration; the note lays the geometry on which the program's Bell notes stand. v2 (2026-09-01): label change in §13a-D — "photoneutrino wave" → "phase carriers (the trace of the balance)"; the sentence on the status of the whole rewritten to the principle of balance (errata item 10); the derivations unchanged. Polish and English files (md + pdf).