Physics = Geometry + E: Geometry of The Observer

A rigorous geometric construction of the observer’s state space is proposed, basedon energy constraints and the act of self-observation. The work is grounded in themethodological principle Physics = Geometry + E, where E denotes the energydimension (or scale) fixed by the measuring observer. It is shown that the conditionof identity between the observer and the observed fixes an invariant angle α, whichacts as a structural coefficient linking local energy to distributed degrees of freedom.The equation of the state cone is derived, its foliation by spherical sections is proved,and an algebraic isomorphism of the obtained quadratic form with the Minkowskimetric is established. The structural similarity is interpreted not as a physical pos-tulate, but as a necessary consequence of geometric constraints combined with theobserver’s choice of the energy scale E.