The Emergence of Physical Reality within the Framework of the Projective Dynamic Logo (PDL)

This work develops the Projective Dynamic Logo (PDL), a foundational framework that reconstructs physical reality from purely relational axioms instead of assuming an a priori space–time, fields, or material substance. Reality is modeled as a network of minimal logical closures: finite signed graphs whose edges encode binary agreement/disagreement relations and whose configurations evolve under a coherence‑optimisation principle. Under four axioms (minimal binary pulsation, triangular coherence, minimal completeness, and logical optimisation) the first admissible elementary stationary structure is shown to be a complete signed graph on four vertices and six edges, the (4,6) structure. A specific sign assignment renders all triangles coherent and admits a global pulsation s \leftrightarrow -s that preserves this coherence. This minimal closure is interpreted as a logical stationary regime naturally associated with the electron at rest: its Compton pulsation is re‑read as an internal 2‑cycle, with the reduced Planck constant \hbar quantifying the minimal action per coherence cycle. The proton is modeled as a hierarchical two‑level architecture: three local stationary regimes (valence “cores”) built from superpositions of logical tetrads (with n_u = 24, n_d = 28), embedded in a dense relational sea of order 10^4 dynamical relations and terminating in a finite active surface that couples to an electron‑type (4,6) structure. The integers (24, 28, 930, 10 087, 11 017) arise from the same optimisation functional under explicit combinatorial constraints, yielding a ≈9 % / 91 % split between stationary and dynamical contributions, in qualitative agreement with QCD. Within this framework, several dimensionless constants acquire a unified structural interpretation as ratios of internal coherence. The fine‑structure constant \alpha is read as a surface‑to‑volume coherence fraction; a candidate expression for Boltzmann’s constant k_B is linked to the dynamical fraction of the proton’s relational sea and to a small coherence‑leakage parameter \varepsilon; and an effective gravitational coupling emerges as the metric manifestation of this minimal leakage once hierarchically amplified. The manuscript also sketches a relational reformulation of proper time (as coherence‑cycle counting), gravitation (as variation of coherence cost in an emergent metric) and a speculative cosmological scenario in which Big‑Bang‑like episodes and black‑hole singularities appear as constraint events in a pre‑physical logical field.