Structural Trinity Conjecture in Registration Theory

Abstract

Registration Theory treats the primitive “Trinity” not as three already separated substances called space, time, and energy, but as a single symmetric relational condition from which distinguishable physical roles would have to emerge through registration. For canonical ACRF-4, the permutation representation on the four registration variables decomposes exactly as R⁴ = span{1} ⊕ H4, with dim span{1} = 1 and dim H4 = 3. These results motivate the Structural Trinity Conjecture: the invariant scalar is a candidate precursor of a time-facing current-actuality role, the rank-three zero-mean sector is a candidate precursor of a space-facing relational-differentiation role, and the registration update is a candidate precursor of an energy-facing consequential-transformation role. No identification with physical time, three-space, or energy is claimed here; those remain separate reconstruction problems.

Relation to other papers

• Superseded by Structural Trinity Conjecture (v2.0)