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 -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 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 nᵤ = 24, nd = 28), embedded in a dense relational sea of order 10⁴ 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 is read as a surface‑to‑volume coherence fraction; a candidate expression for Boltzmann’s constant kB is linked to the dynamical fraction of the proton’s relational sea and to a small coherence‑leakage parameter ; 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.
Cédric Laubscher (Mon,) studied this question.