Meaning-Based Theory (MBT) Quantum Reconstruction of the Unresolved Problemsin Space 2_3_and 4
Fumiyoshi Tamura
Meaning-Based Theory (MBT) — Quantum Reconstruction of the Unresolved Problems in Space 2, 3, and 4 This paper revisits and reconstructs several unresolved problems remaining in the Space 2, Space 3, and Space 4 developments of Meaning-Based Theory (MBT) from an explicitly quantum-generative perspective. The central principle of this reconstruction is that, when multiple not-yet-established generative possibilities remain compatible with the present MBT structure, they must not be prematurely reduced to a single classical state. The quantum perspective adopted here therefore does not begin by importing the conventional postulates of quantum mechanics. No wave function, probability amplitude, Born rule, or measurement-induced collapse is assumed. Instead, quantum generation is treated as a more fundamental condition in which multiple unresolved generative sequences are retained until MBT's own establishment conditions restrict or distinguish them. Starting from irreversible temporal distinction, the paper examines how temporal differences require positional distinction when the identity of established states is to be preserved. It then reinterprets the three-position mutual Relation structure, Σ, as the maximal established non-Closure structure from which the addition of one new position can lead toward a four-position Closure candidate. From this basis, the paper integrates several previously unresolved issues: the relation between internal change, shared structures, and continuation of Closure generation; the minimal preservation conditions for generative identity; the initiation of Comparison when a new position is established; the continuation of previously established Closures into later present states; and the meaning of generative order length, G. These results are then reorganized into a quantum-generative sequence. For a present state S_n, the theory does not initially assume a unique successor. Instead, it considers a set of not-yet-established generative possibilities, U(S_n) = {X_1, X_2, ..., X_m}, and progressively restricts this set through irreversible temporal consistency, preservation of generative history, positional distinction, Comparison, pairwise Relations, three-position mutual Relations, four-position consistency, and formation of the four-position Relation structure Ω₄. A further quantum-generative layer appears within Ω₄ itself. Even after a four-position structure has been formed, multiple local Relation-action sequences may remain possible. Their noncommutative composition produces four-point Relation interference, represented by cycle-dependent actions Q(Γ). Consequently, neither a candidate position nor a particular local-action sequence is selected in advance. Finite Closure is then treated as the structural condition that restricts these unresolved action sequences toward completed I₄ Closure. To avoid circularity, the general quantum-generative formulation does not take the already known numerical relations Q³ = −I and Q⁶ = I as prior selection assumptions. Instead, finite Closure is imposed at the structural level, while those numerical relations are to be recovered as consequences once the local actions themselves have been derived internally. The resulting framework leads to an MBT quantum-generative next-present-state establishment rule: a future state is not assumed to exist beforehand and then selected. Rather, multiple not-yet-established generative sequences are progressively constrained by the structures already established in MBT, and a next present state emerges only when the required sequence of Comparison, Relation formation, Ω₄ interference, and finite Closure is completed. If more than one candidate continues to satisfy all currently established conditions, MBT does not introduce an additional probabilistic or classical selection rule. Those candidates remain unresolved until subsequent generation provides a structural distinction. This reconstruction also clarifies the relation between quantum generation and the emergence of space. Space is not treated as a pre-existing background in which quantum processes occur. Instead, the generative hierarchy proceeds through irreversible temporal establishment → multiple generative possibilities → positional distinction → Comparison → Relations → three-position mutual Relation Σ → four-position structure → Ω₄ → four-point Relation interference → finite I₄ Closure → completed local space. Thus, quantum generation and spatial generation become parts of a single MBT generative hierarchy. The paper finally identifies the principal unresolved bridge that remains: the derivation of concrete present Relation structures and local actions from differences in the underlying T-state. Establishing this bridge would make it possible to submit individual quantum-generative candidates to explicit Ω₄ interference and finite-Closure calculations without introducing an arbitrary external mapping.
•Sep 29, 2026•0 citations