## 1 Reference Systems--Relativistic Positioning vs. Localizing Systems  
As demonstrated in previous works [1; 2; 3], the physical justification of the 'projective geometry of spacetime, and thus the validity of the 'projective theory of relativity' [4; 5; 6], is completely deduced from peculiar characteristics of the physical observables that are expressed in relativistic localizing protocols of spacetime events. These protocols are explicitly implemented in the so-called'relativistic localizing systems' (RLS) [1; 2; 3] that are extensions of the so-called'relativistic positioning systems' (RPS) [7; 8; 9; 10; 11; 12; 13; 14]. The latter have been designed to correct the current, first generation, non-relativistic positioning systems such as the GPS, Galileo, Glonass, Beidou, or IRNSS. These new, second generation, relativistic positioning systems not only answer the question of possible technological improvements to current positioning systems but also very fundamental questions in spacetime physics. For example, in special or general relativity, particular protocols have historically been devised to construct physical observables associated with the position in space at a given time relative to a reference frame. But all are based, in particular, on a convention of simultaneity [15] that is not inherently relativistic because, as it is well known, simultaneity is relative to one frame and only one. Relativistic positioning systems solve this difficulty by freeing themselves from the need to define a notion of simultaneity in one way or another. Then, moreover, relativistic observables are obtained from RLSs without, in particular,the use of any geometric symmetry criteria and can then be applied to, for example, the determination of a genuine relativistic quantum field theory. Only constraints resulting from causal axiomatics are really necessary and better still, it is not even necessary to make hypotheses about the geometric, differential nature and even about the existence or not of these spacetime characteristics. The latter are the results of the relativistic localizing protocol, detailed in the present section, which ultimately only involves causal orders of information exchanges [16]. To put it succinctly, these are processes of _code geometrization_. Besides, it should also be noted that the 'projective theory of relativity' is not a particular string theory. String theories all have a pseudo-Riemannian, base spacetime manifold whose geometry follows the axiomatics of Euclidean geometry. In the present case of the projective theory of relativity, the pseudo-Riemannian spacetime manifold follows the axiomatics of projective geometry. It is therefore a geometric theory with a radically different basic axiomatics and, moreover, it is not a string theory upon such projective geometry. Also, we ought to indicate that there are alternative theories to the projective theory of relativity, in particular, the so-called Fantappie-Arcidiacono one developed by [PERSON], [PERSON], and [PERSON] [17; 18; 19; 20; 21]. But then, the question is to know what other manifestations of the projective geometry of spacetime could appear, and in particular in astrophysics. Two results have previously been obtained on this subject [22]: A foliation of spacetime with a structure similar to those of black holes, and fits of galactic rotational velocity curves. These results are presented briefly in Sections 2-4 but their difficult interpretations are discussed in Section 5 in greater depth and in a new way both from a mathematical point of view and from the point of view of physical implications and meanings. In order to give some details about these RLSs, we recall briefly in this introductory section some definitions and principles of how reference systems, RPSs, and RLSs strongly differ and work, and why RPSs are relativistic unlike current positioning systems such as the GPS.