As the final paper of the series, this paper constructs the minimal system in which two composites coexist — the twin minimal space model — and examines how much of the behavior that looks quantum mechanical is derived as a reading of hierarchy interfaces in a discrete relational model that assumes neither amplitudes nor continuous time. External face of the stable species: The handles (hairs) by which a composite is observed from outside divide into three ledgers: the face fundamental wave ν0 = 1/ (2√s) (the dominant line of the self-container spectrum), the parent-record line νobs = |k|, and the energy-like norm R' = √s. The exact identity ν0R' = 1/2 (the zero point) links the first two, and R' never appears as a line — it is readable from outside as the spacing 1/R' of the odd comb (the particle-level realization of the record theorem). The external face is a minimal-uncertainty quasi-rectangular wave packet that carries a built-in odd comb of spacing 1/R' and is localized within an extent 2R' (half-width × fundamental wave = 1/2). Construction of the twin system: The initial value Ω0² = 2ν1² = 18 is an even label and, by the classification theorem (Paper 5), cannot exist as a single state — being born as a pair is forced by parity (the first event requires no dynamics). The allowed lattice separations of the twins (each s = 9) are quantized to |Δ|² ∈ 2, …, 20, and |Δ|² ≡ 1 (mod 4) is entirely forbidden. The relational classes (21 under B4 × swap) are completely separated once the branch (cos/sin) channels are read in addition to the fringe intensity data (intensity-only fringe data degenerates to 18 kinds as ordered data, and to 11 kinds under the operationally available unordered reading) — the scale marks of space are born as chord sets of equal-frequency shells. The exact form of measurement: Inspecting the two conditions for measurement (affecting the system; detecting the change), the detection of change requires knowledge of the prior state and regresses infinitely; in this model, however, the record of the prior state is absent by censorship, and the λ ledger is append-only (the monotonic increase theorem, Paper 6), so the regress is structurally cut. Measurement = an append to the record (absence → presence) ; "collapse" is the appearance of a record, and its irreversibility reduces to the same single bit as the arrow of time. Computing the first decay of the twins explicitly, the appearance of the reference wave (s = 1) promotes the information class of the record from interferometric to holographic — the measuring apparatus is generated by the event itself. We also show that the final-state statistics depend on the choice of measure (one-shot equal weight over configurations 60/61 versus sequential conditional counting 396/403) — measure bifurcation, with an exact difference of +0. 00098. Layer resolution of entanglement: The self-spectrum of a single fragment lies on all-components-even vectors and is therefore identically invisible in the logical-wave (odd) sector — only counts and relations can be read (the relational-only readout theorem). The decay of one twin instantaneously rewrites the branching statistics of the other (total variation 0. 774), but this shift does not depend on the twin separation at all, and the influence does not propagate through the space of the child layer — instantaneity is not a speed but a mismatch of levels. Since order and attribution do not exist in the final record, operational no-signalling follows. An entangled pair, being an even label, cannot become a single particle at the layer above (parity protection). The same map applies to two-path interference of a single wave packet. Vertex deficits and the two hidden axes: An exhaustive inspection of the record continuity rule across an event (that the parent's identity line persists in the cross spectrum of the daughter system) derives, as the persistence condition, a conservation law of position vectors v5 ± v3 = ±v9 (a momentum analogue), which holds for parents in the (2, 1, 0, 0) orbit but fails for parents in the (1, 1, 1, 1) orbit by exactly one unit (one axis / one quantum). Furthermore, in the bookkeeping of the excitation degree ε = (−1) Σ|k| there exists a second one-bit deficit independent of this one (specific orbits at s = 7, 9). The visible four-axis ledgers demand two invisible directions — R on the curvature side and Q on the bare-parity side — and intermediate displacements along the invisible directions, being unrecorded, are permitted (the licensing principle for virtual displacements). This licence virtually unlocks two-body splittings that are forbidden in the visible ledgers, and decomposes every decay into sequences of cubic vertices (multiple paths to the same final state). Finally, we organize the correspondence between the obtained structure and standard theory as a transport principle (a theorem is transported whenever the counterparts of its premises are verified), and state explicitly the candidate answers this model gives to questions that remain postulates on the standard-theory side (the measurement problem, the location of the cut, the problem of time, dimensionality, the measure), together with falsifiability (gravitationally mediated entanglement experiments, etc. ). Bilingual edition (Japanese and English): Markdown, LaTeX, and PDF for each language, plus four figures (PNG). v0. 3 (2026-06-12): Corrects Sec. 3. 2 and the abstract: the twin pairs decompose into 21 relational classes under B4 × swap (not 18) ; intensity-only fringe data degenerates to 18 kinds (ordered) / 11 kinds (unordered, operational), and complete separation is recovered by the branch-channel readout. All other results are unchanged.
Noriaki Kihara (Sun,) studied this question.