What question did this study set out to answer?

The aim is to derive the abundance of dark matter using the Ahmadov Constraint Theory through mathematical frameworks.

April 4, 2026Open Access

Dark Matter Abundance from Ahmadov Constraint Theory (ACT): Topological and Geometric Derivations

Key Points

The aim is to derive the abundance of dark matter using the Ahmadov Constraint Theory through mathematical frameworks.
Utilized topological and geometric mathematical approaches to derive predictions.
Method I involved calculating the Euler characteristic and electroweak doublet count.
Method II used dimensional compression from geodesic circles to derive the abundance.
Both methods validated against Planck 2018 measurements.
Predicted dark matter abundance of 84.21% from topological method and 85.04% from geometric method.
Results aligned closely with Planck 2018 measurement of 84.38% ± 1%.
No direct detection of dark matter expected, with zero free parameters considered throughout.

Abstract

The Ahmadov Constraint Theory (ACT) derives dark matter abundance as 84-85% from the single axiom that constraint exists in physical systems (Aut(U) ⊊ Sym(U)). Two independent mathematical methods yield predictions agreeing with Planck 2018 measurement (84.38% ± 1%) within observational error. Method I (Topological): Euler characteristic χ(Spin(8)/G₂) = 32 and electroweak doublet count 6 = rank(G₂) × τ yield 32/38 = 84.21%. Method II (Geometric): Dimensional compression (21-π)/21 from geodesic circle on S⁶ ≅ G₂/SU(3) at fundamental G₂ angle 30° yields 85.04%. Methods converge via sin⁵(30°) = 1/32. Physical mechanism derives from standard mathematical physics: cohomology theory establishes topological modes possess energy-momentum without gauge coupling, Noether's theorem yields stress-energy tensor, equipartition theorem distributes early-universe energy by mode count. Predicts null direct detection (σ = 0 exactly) as geometric necessity, not adjustable property. Zero free parameters throughout. All results traced to constraint axiom forcing octonions (Hurwitz) and G₂ automorphism group (Cartan). Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/

Dark Matter Abundance from Ahmadov Constraint Theory (ACT): Topological and Geometric Derivations

Key Points

Abstract

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