Symmetry Quotienting in Turing Machines: An Unsupported Claim — E8 Intelligence Research

FINDING: Turing machine state-space reduction via D4 symmetry quotienting is not directly evidenced in the provided sources; the sources are pedagogical (TM construction, decidability, division algorithms) with no explicit symmetry analysis. | MATH: No new equations or constants extracted. The only formal content: TM transition function δ: Q × Γ → Q × Γ × {L,R}; unary division-by-2 algorithm uses state count |Q| = 5 (typical minimal for that task); decidability hierarchy (decidable ⊂ semi-decidable ⊂ undecidable) per Church-Turing thesis. | CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 appear. However, the *concept* of quotienting a state graph by a symmetry group (D4) is mathematically sound — if applied, the reduction factor for a TM with N states under D4 would be at most N/8 (orbit-stabilizer theorem), but this is *not* in the sources. | DEPTH: 2 — the findings are tutorial-level, not novel research. The D4 quotient idea is a plausible rese Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com