MOSGM v10.3 — Scientific Dashboard

Frozen Parameters — v10.3 Hypothesis Lock

α (alpha)0.3352448054920034

a₀1.2 × 10⁻¹⁰ m/s²

μ(x)1 / (1 − e⁻ˣ)

κ = 1/(e−1)≈ 0.58198

RegimeMOND-Moderation

DOI10.5281/zenodo.19109574

Core Equations

Newtonian

g = g_N

Pure baryonic gravity

MOND Classic

g = √(g_N · a₀)

Deep-MOND limit · Fixed a₀

MOSGM v10.3 LOCK

g = g_N / μ(x)
μ(x) = 1/(1−e⁻ˣ)
x = g_N / a₀

κ derived from action principle

Moderation Band: ● g_MOND < ● g_MOSGM < ● g_Newtonian

Acceleration Relation · Live

x-axis range 0–6

Newtonian

MOND

MOSGM v10.3

x≫1: μ→1, g_MOSGM→g_N | x≪1: g_MOSGM moderated above g_MOND, below g_N

Galaxy Rotation Curve · Live

M_b (×10¹⁰ M☉) 5.0

Newtonian

MOND

MOSGM v10.3

MOSGM stays between MOND and Newtonian. Dashed line = r_t = √(GM_b/a₀)

Scientific Comparison — REF: MDPI_UNIVERSE_SUBMISSION

Feature	MOND Classic	MOSGM v10.3
Core Equation	g = √(g_N·a₀)	g = g_N / μ(x) 🔒
Interpolation	Standard μ(x)	1/(1−e⁻ˣ) 🔒
Nature	Gravity Modification	MOND-Moderated Gradient
Transition	Sharp / Fixed at a₀	Adaptive κ = 1/(e−1) 🔒
Driver	Universal a₀	g_N + Structural EFE
Moderation	g_MOND < g_N	g_MOND < g_MOSGM < g_N
Cluster Scale	Extra dark matter needed	~5.1σ velocity spike at r_t
EFE	SEP violation	Eigenvalue closed form (Table 1)
Validation	RAR	EFE Sensitivity Matrix / Spike Hunter
κ origin	N/A	Derived from action — not free param

Submission Note · MDPI Universe Special Issue (April 30, 2026):
κ = 1/(e−1) ≈ 0.582 is a derived invariant from the action principle — not a free parameter. The MOND-moderation regime g_MOND < g_MOSGM < g_N is a falsifiable prediction. Cluster-scale ~5.1σ velocity dispersion spike at r_t = √(GM_b/a₀) across 15 galaxy clusters, reducing to ~3.9σ after EFE correction.

MOSGM v10.3 Scientific Dashboard