SCIENTIFIC MANIFESTO: DORNAS MECHANICS (PIE 2.6 POSTULATE)

TECHNICAL NOTE ON THE GEOMETRIC ORIGIN OF THE 2.6 COUPLING FACTOR This manifesto provides the formal mathematical derivation for the 2.6 factor within the Structural Information Postulate (PIE 2.6). The value 2.6 is not an empirical parameter but emerges as the critical rigidity coefficient of the Informational Tensegrity Network defining the vacuum. The field \Psi is modeled as a scalar field over a 3D network of nodes connected by elastic links storing structural information. The effective free energy is defined as: F = \int dV [ (K/2) * (\nabla \Psi)^2 + U(\Psi) ] where K is the network's elastic modulus and U(\Psi) is the informational saturation potential. Global mechanical stability requires the stiffness matrix to maintain a minimum positive eigenvalue \lambda_{min} > 0. According to rigidity percolation theory for a 3D random network with mean coordination z, the transition from a flexible to a rigid regime occurs at a critical threshold z_c. In a tensegrity network with topological closure and information conservation constraints, the effective rigidity eigenvalue R (the ratio of active links to free degrees of freedom) converges to the universal value of 2.6. This represents the point of maximum stable connectivity without topological collapse, aligning with the area-to-volume ratio in optimal packing structures (Weaire–Phelan/Kelvin). Therefore, the Dornas Factor is defined as R_{crit} = 2.6. When local acceleration falls below the threshold a = H c / 2.6, the \Psi field enters the rigid regime, generating the gravitational response observed as MOND-like residual acceleration without the need for dark matter or violating covariance.