This paper derives physical reality from the three axioms of Operatiology (Japanese: 操作原論) —non-commutativity (A1), Πd-saturation (A2), and redundancy exclusion (A4) —via the unique minimal algebra M3 (C) with Cartan generator H = diag (1, 1, −2), with zero free parameters. The structural necessity operator Nec (S) = Dist (S) ∩ Clos (S) ∩ Irr (S) identifies the electron and proton as the unique necessary elements of physical reality. Physical constants α, µ, π, e, γE, αG, and αs are derived as structural projections of M3 (C) without empirical input. The Translatability criterion classifies classical mechanics, electromagnetism, the Standard Model, and quantum structure into Translatable components and Untranslatable frameworks. Field theory fails to constitute a Tier-2 derivation: continuous spacetime is excluded by A4. Bell inequality violations follow from A1 alone, constituting a structural proof of the non-essentiality of wave mechanics. The measurement problem dissolves as a Tier-3 pseudo-problem. Cosmology has no well-formed Tier-2 formulation. The falsifiability trilogy confirms that Tier-3 internal consistency cannot reach Tier-2 structural necessity. The appended Python code derives α⁻¹, αG, and αs exclusively from the M3 (C) spectrum 1, 1, −2 with no empirical input; the numerical outputs constitute an independent verification of the zero-parameter claim. import mathfrom mpmath import mp, mpf, pi, sqrt mp. dps = 50 # === M3 (C) spectrum 1, 1, -2 ===h = mpf (1), mpf (1), mpf (-2) e1 = sum (h) e2 = h0*h1 + h0*h2 + h1*h2e3 = h0*h1*h2d = sqrt (mpf (3) /2) g = mpf (1) /2D = (d - 1) *d*gch2 = (e1**2 - 2*e2) /2ch3 = (e1**3 - 3*e1*e2 + 3*e3) /6N2 = mpf (10) /4N3 = mpf (7) /2C2 = sqrt (ch2/N2) *gf3 = abs (ch3) /N3term0 = 6*pi/Dterm1 = C2*Dterm2 = f3*D**6invₛ = term0 + term1 + term2 # === Structural invariant 1: exponent n=3 ===n = 3df = math. sqrt (3/2) exp_ = n * (2*n + 1) pref = math. sqrt (n* (n+1) / (2*n+1) ) C3 = df**2 - df / (2 * math. sqrt (n) ) corr = 1 - C3 * (1/float (invₛ) ) **2inv1 = (1/float (invₛ) ) **exp_ * pref * corr # === Structural invariant 2: cyclotomic P1, P3, P6 ===P1 = 2P3 = 13P6 = 7main = P6 * (2*P3 - n) / (2 * math. pi * n) corrₛ = P1 / n**3inv2ᵢnv = main - corrₛinv2 = 1 / inv2ᵢnv print ("=== Structural scalar from M3 (C) spectrum ===") print (f"invₛ: invₛ") print ("=== Structural invariant 1 ===") print (f"Derived: inv1: . 5e") print ("=== Structural invariant 2 ===") print (f"inv2^-1: inv2ᵢnv: . 6f") print (f"Derived: inv2: . 6f")
T.O. (Sun,) studied this question.