TITLE:
A Structural Compactification Map and a Quotient-Geometric Representation of the Minkowski Null Cone
AUTHORS:
Oscar Mauricio Jeno Soto
KEYWORDS:
Minkowski Null Cone, Geometric Construction, Toroidal Immersion, Induced Metrics, Quotient Topology
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
4,
2026
ABSTRACT: We formulate a mathematically explicit geometric construction that begins with a normalized cubic domain, passes through a planar disk, a cylindrical immersion and a toroidal closure, and terminates in a representation of a subset of the Minkowski null cone. Two distinct terminal maps are emphasized. The independent parametrization
P
J
is surjective onto the complete double null cone, whereas the torus-to-cone map
Q
J
has bounded radial parameter and therefore reaches only a proper subset of the cone. Explicit transition maps are introduced so that the domains and codomains of the successive stages are compatible. The six-petal rosette is retained only as an auxiliary planar symmetry visualization and is not treated as a necessary member of the continuous map chain. We compute the standard induced metrics of the cylindrical and toroidal stages and analyze the non-bijective topology of
Q
J
through its fibers, singular circles, and quotient factorization. The construction preserves the standard Minkowski metric and is intended as an auxiliary geometric representation rather than a modification of special relativity.