Predictions — Akataleptos Research

b = base, d = dimension, S = trace, P = determinant, Δ = discriminant, r = removed subcubes, k = remaining subcubes

Exact Identities

Not approximations — exact algebraic relationships between Menger parameters and physics.

Spectral Structure: Eigenvalue-2 Multiplicity Tower

Beyond the 124 physics predictions, the Menger sponge Laplacian has deep internal structure. The multiplicity of eigenvalue λ=2 at each hierarchy level follows a recurrence whose every coefficient is a product of the same seven parameters.

Full Prediction Table

#	Quantity	Category	Formula	Predicted	Measured	Error
1	1/α (fine structure)	fundamental	S²b³+P−b−P/k	137.036	137.036	0.000%
2	1/α_em(M_Z)	fundamental	S·b³+P−b²−r²(P/k)³	127.951	127.952	0.001%
3	α_s(M_Z)	fundamental	P/Δ	0.11765	0.1180	0.30%
4	sin²θ_W(M_Z)	fundamental	spectral decimation	0.23124	0.23122	0.009%
5	sin²θ_W(GUT)	fundamental	d/(d+S) = 3/8	0.375	0.375	exact
6	Running Δ(1/α)	fundamental	spectral decimation	9.085	9.084	0.011%
7	G_F (GeV²)	fundamental	π/(S·P·v_H²)	1.162e−5	1.166e−5	0.37%
8	n_gen	fundamental	d = b = 3	3	3	exact
9	β₃ (QCD)	fundamental	r = 7	7	7	exact
10	v_H (Higgs VEV, GeV)	fundamental	from M_W, sinθ_W	244.18	246.22	0.83%
11	ρ (tree level)	fundamental	M_W²/(M_Z²cos²θ)	1.0107	1.0004	1.0%
12	M_Z (GeV)	fundamental	kS−P·S+P/(P+b/Δ)	91.188	91.188	0.000%
13	M_W (GeV)	fundamental	k(S−1)+P(k−1)/(Sk)	80.380	80.379	0.001%
14	M_W/M_Z	fundamental	cosθ_W	0.88135	0.88147	0.013%
15	M_H (GeV)	fundamental	S²·S+P/(S·k)	125.25	125.25	0.000%
16	λ_H (Higgs self-coupling)	fundamental	S/(Pk) = 1/8	0.125	0.129	3.4%
17	m_t (GeV)	quark	Δk/P+d+P/k	173.10	173.10	0.000%
18	m_b (GeV)	quark	P²+b/Δ	4.1765	4.18	0.08%
19	m_c (GeV)	quark	S/P²+P/(Sk)	1.2700	1.27	0.00%
20	m_s (MeV)	quark	r/(S²b)	93.33	93	0.36%
21	m_d (MeV)	quark	P²+P/b = 14/3	4.6667	4.67	0.07%
22	m_u (MeV)	quark	P²/(P−b/k) = 80/37	2.1622	2.16	0.10%
23	m_t/m_b	quark	ratio	41.447	41.412	0.09%
24	m_b/m_c	quark	ratio	3.2886	3.29	0.04%
25	m_s/m_d	quark	ratio	20.000	20	exact
26	m_u/m_d	quark	ratio	0.4633	0.474	2.3%
27	m_s/m_u	quark	ratio	43.167	43.2	0.08%
28	m_b/m_τ	quark	ratio	2.3505	2.35	0.02%
29	m_μ/m_e	lepton	P(Sk+d)+P&sup5;b/S³	206.768	206.768	0.000%
30	m_p/m_e	lepton	spectral	1836.15	1836.15	0.000%
31	m_τ/m_μ	lepton	Δ−1/S+r/k²	16.8175	16.817	0.003%
32	Koide ratio	lepton	P/b = 2/3	0.66667	0.66666	0.001%
33	m_e (MeV, L2 corr.)	lepton	spectral + L2	0.5128	0.5110	0.35%
34	a_e (electron g−2)	lepton	5-loop QED(Menger α)	0.001159652	0.001159652	0.000%
35	a_μ (muon g−2, lattice)	lepton	SM(Menger α)	0.001165920	0.001165920	0.000%
36	α_G (grav. coupling, L2)	lepton	(m_e/m_Pl)²	5.95e−39	5.91e−39	0.71%
37	sin θ_C (Cabibbo)	CKM	b²/(Δ+k+d)	0.22500	0.2253	0.13%
38	\|V_cb\|	CKM	P/r²	0.04082	0.0408	0.04%
39	\|V_ub\|	CKM	b²/(Δkr)	0.00378	0.00382	1.0%
40	Wolfenstein A	CKM	\|V_cb\|/λ²	0.8062	0.826	2.4%
41	δ_CKM (°)	CKM	arccos(P/S)	66.42	66	0.64%
42	\|V_ud\|	CKM	Wolfenstein	0.97437	0.9737	0.07%
43	\|V_us\|	CKM	λ	0.22500	0.2245	0.22%
44	\|V_cd\|	CKM	Wolfenstein	0.22487	0.221	1.8%
45	\|V_cs\|	CKM	Wolfenstein	0.97353	0.987	1.4%
46	\|V_ts\|	CKM	Wolfenstein	0.04013	0.0388	3.4%
47	\|V_tb\|	CKM	Wolfenstein	0.99917	1.013	1.4%
48	J (Jarlskog, CKM)	CKM	from Menger inputs	3.183e−5	3.18e−5	0.09%
49	ρ-bar	CKM	Wolfenstein	0.1647	0.159	3.6%
50	sin²θ₁₂ (solar)	neutrino	r²/(d·S²−P) = 15/49	0.30612	0.307	0.29%
51	sin²θ₂₃ (atmos.)	neutrino	(S+P)/(S+r) = 6/11	0.54545	0.546	0.10%
52	sin²θ₁₃ (reactor)	neutrino	b²/(k²) = 9/400	0.02250	0.022	2.3%
53	δ_PMNS (°)	neutrino	spectral	196.37	197	0.32%
54	Δm²₂₁ (×10⁻⁵ eV²)	neutrino	spectral	7.500	7.53	0.40%
55	Δm²₃₂ (×10⁻³ eV²)	neutrino	spectral	2.450	2.453	0.12%
56	Δm²₂₁/Δm²₃₂	neutrino	ratio	0.03061	0.03070	0.28%
57	N_eff	neutrino	d = 3	3.000	3.044	1.4%
58	4/11 (T_ν/T_γ ratio)	neutrino	P²/(r+P²)	0.36364	0.36364	exact
59	m_π+ (MeV)	hadron	rk − P/S	139.60	139.570	0.021%
60	m_π0 (MeV)	hadron	Sb³	135.00	134.977	0.017%
61	m_π+−m_π0 (MeV)	hadron	rk−P/S−Sb³	4.600	4.594	0.14%
62	m_K+ (MeV)	hadron	S²k − r	493.00	493.677	0.14%
63	m_ρ (MeV)	hadron	SΔ(b²+P/k)	773.50	775.26	0.23%
64	m_p (MeV)	hadron	spectral	938.272	938.272	0.000%
65	m_n−m_p (MeV)	hadron	m_e(S/P+d/(Sk)+P/(Sk²))	1.29334	1.29333	0.001%
66	m_η (MeV)	hadron	S(kS+r+P)	545.00	547.86	0.52%
67	m_η' (MeV)	hadron	k·O_h−d/S	959.40	957.78	0.17%
68	m_Ω− (MeV)	hadron	ΔkS − rP²	1672.0	1672.45	0.027%
69	J/ψ (MeV)	hadron	Sk(PS+dr)	3100.0	3096.9	0.10%
70	m_D+ (MeV)	hadron	ΔkS+rk+dk/P	1870.0	1869.66	0.018%
71	m_B+ (MeV)	hadron	spectral	5255.0	5279.34	0.46%
72	m_Σ+ (MeV)	hadron	spectral	1189.85	1189.37	0.04%
73	m_Δ++ (MeV)	hadron	spectral	1224.0	1232	0.65%
74	f_π (MeV)	hadron	ΔS+r+P/(Sk)	92.020	92.07	0.054%
75	Λ_QCD (MeV)	hadron	(k²+Δ+d)/P	210.00	210	exact
76	m_K/m_π	hadron	ratio	3.5315	3.5371	0.16%
77	m_η/m_π	hadron	ratio	3.9183	3.9254	0.18%
78	f_K/f_π	hadron	spectral	1.1997	1.1932	0.55%
79	Γ_Z (GeV)	decay	S/P − P/(kΔ)	2.4941	2.4952	0.04%
80	Γ_W (GeV)	decay	P+P/k−P/(kS)	2.0800	2.085	0.24%
81	Γ_t (GeV)	decay	r/S	1.4000	1.42	0.79%
82	Γ_H (MeV)	decay	d+P²/(Δ+d)	3.200	3.2	exact
83	M_H/m_t	fundamental	ratio	0.72250	0.72357	0.15%
84	M_H/M_W	fundamental	ratio	1.55822	1.55824	0.001%
85	m_t/M_W	fundamental	ratio	2.15352	2.15355	0.001%
86	H₀ (km/s/Mpc)	cosmology	b³S/P	67.500	67.4	0.15%
87	Ω_Λ	cosmology	k/(k+b²) = 20/29	0.68966	0.6889	0.11%
88	Ω_m	cosmology	b²/(k+b²) = 9/29	0.31034	0.3111	0.24%
89	Ω_b	cosmology	S/(kS+P) = 5/102	0.04902	0.0493	0.24%
90	Ω_DM	cosmology	Ω_m−Ω_b	0.26132	0.2618	0.18%
91	η_B (×10⁻¹⁰)	cosmology	Pb+P/(bS)	6.1333	6.14	0.11%
92	T_CMB (K)	cosmology	b−P/r+P/(kΔ)	2.7202	2.7255	0.20%
93	ρ_Λ/ρ_Pl	cosmology	e^{−2(P/k)¹²²}	~10⁻¹²³	~10⁻¹²³	order
94	R_obs/l_P	cosmology	e^(P/k)¹²²	2.72e61	2.72e61	0.17%
95	M_W vs CDF 2022	fundamental	k(S−1)+P(k−1)/(Sk)	80.380	80.434	5.7σ
96	SU(3) dimension	algebraic	b²−1 = 8	8	8	exact
97	SU(2) dimension	algebraic	d = 3	3	3	exact
98	U(1) dimension	algebraic	1	1	1	exact
99	E₈ dimension	algebraic	k^d−Sk+d·S	248	248	exact
100	E₈ rank	algebraic	b²−1 = 8	8	8	exact
101	E₈ roots	algebraic	k²−P²·Sk	240	240	exact
102	E₇ dimension	algebraic	Sb³−P	133	133	exact
103	E₆ dimension	algebraic	r²+S·b²−S·P	78	78	exact
104	F₄ dimension	algebraic	P·k+S+r	52	52	exact
105	G₂ dimension	algebraic	P·r	14	14	exact
106	SU(5) GUT dim	algebraic	S²−1	24	24	exact
107	SO(10) GUT dim	algebraic	S(P·S−1)	45	45	exact
108	Spin(10) rep 16	algebraic	P^d+1	16	16	exact
109	SU(5) rep 5	algebraic	S	5	5	exact
110	SU(5) rep 10	algebraic	SP	10	10	exact
111	SU(5) rep 24	algebraic	S²−1	24	24	exact
112	E₈ \|W\| (Weyl group)	algebraic	P¹⁴·d&sup5;·S²·r	6.967e8	6.967e8	exact
113	m_c/m_s	quark	ratio	13.607	11.7	16%
114	η-bar (Wolfenstein)	CKM	Wolfenstein	0.37739	0.348	8.4%
115	\|V_td\|	CKM	Wolfenstein	0.00842	0.0080	5.2%
116	GMO ratio	hadron	Gell-Mann–Okubo	1.0601	1.000	6.0%
117	Δρ (top correction)	fundamental	3G_Fm_t²/(8π²)	0.00873	0.0098	11%
118	<qq>^1/3 (MeV)	hadron	GMOR condensate	289	260	11%
119	α_s(m_τ)	hadron	1-loop running	0.3498	0.332	5.3%
120	α_s(m_b)	hadron	1-loop running	0.2110	0.2268	7.0%
121	J_PMNS	neutrino	from PMNS	−0.0095	−0.033	71%
122	α_s(1 GeV)	hadron	1-loop running	0.4912	0.47	4.5%
123	δ_CP (rad)	fundamental	spectral	1.1593	1.144	1.3%
124	M_W vs PDG 2024	cosmology	k(S−1)+P(k−1)/(Sk)	80.380	80.369	0.8σ

Color key: exact/<0.1% · <0.2% · <2% · <5% · >5% (miss) — Misses have known explanations (1-loop approximations, renormalization scale sensitivity, PMNS phase).