The Theory of the Three Angles: a co-emergent metaphysics of Consciousness, Love, and Form, and its categorical formalization

This paper presents the Integral System (Sistema Integral), a metaphysical framework positing three co-emergent fundamental dimensions —Consciousness, Love (relationality), and Form— derived from a single minimal phenomenon, the Mother Paradox (the act of distinction that all experience already presupposes).1 Unlike the dominant monopolar frameworks —materialism, which reduces all three to Form, and idealism, which reduces them to Consciousness— the System holds the three angles to be co-equal and not derivable from one another. The paper offers a self-contained presentation of the framework's foundations and of its two-layered formalization. The first layer, combinatorial and elementary, derives as theorems the structure of the catalogue: the six angle pathologies as 23−2, the four topological modes as a pushout, the fifteen structural pathologies, the fifteen sectorial Zero Distances as C(6,2), and the orthogonal movement Eros/Agape as an adjunction colim ⊣ Δ with its two canonical natural transformations. The second, more recent layer models each angle within a single cartesian closed category: Form as an invariant (the limit of a symmetry, on an ontological reading of Noether's theorem), Love as a relational profile (the Yoneda lemma), and Consciousness as the fixed point of a self-representation (Lawvere's theorem). From this second layer follows the central result: each angle, taken as the sole reality, is undermined by the structure of its own central concept, so that co-emergence ceases to be a postulate and becomes a consequence —conditioned on a few explicitly falsifiable interpretive bridges. The framework incorporates an in-principle limit (the ceiling of formalization): the indexical first person is located as the residue that no external objectification captures, in correspondence with the converse of Lawvere's theorem. The paper discusses the relation to contemporary mathematical consciousness science —in particular Tsuchiya and Saigo's Yoneda-for-qualia programme and the categorical formalization of Integrated Information Theory— and argues that the System's distinctive contribution is the combination of three co-equal angles, a derived co-emergence, and a ceiling treated as confirmation rather than failure. A scrupulous demarcation between theorem, interpretive bridge, and conjecture is maintained throughout.