U: The Unified Settlement and the Definition of Value — The Sole Boson Proposition, the Tiling Origins of Force Properties, Closed-Form Heuristic Parameter Settlement, and the Zhangyu Standard

We complete the third pillar of the N.E.A. (Network EmergentArchitecture) framework: the unified settlement of physical constantsand the formal definition of universal value. We establish the SoleBoson Proposition—the photon is the unique fundamental carrier ofpropagating interaction in the universe. The gauge groups of the fourpropagating forces—U(1) electromagnetic, spin-2 gravity, SU(2) weak,and SU(3) strong—are identified through Force-Body Duality. The fifthforce, the Platonic contact repulsion, is a non-propagating contactterm treated in F. The W/Z bosons, gluons, and the graviton arereinterpreted as topological excitation modes or protocol headers ofthe photonic pulse on various geometric carriers. The macroscopic differences between the forces—range, strength,confinement versus liberation—are not properties of distinctfundamental bosons but consequences of whether the geometric carriertiles 3D space. The photon's operation on the successfully tilingC8 cube produces gravity—long-range and vanishingly weak because itsrent is diluted across the infinite translational symmetry of thecubic lattice. Its operation on the non-tiling K4 tetrahedronproduces the Strong Force—short-range and enormously strong becauseits entire cycle-space rent is trapped within the isolated simplex.Mass is failed space. The four propagating fundamental interactions are described by asingle four-equation framework: a bandwidth-deficit field equation, auniversal metric, a bandwidth–field relation, and a force lawnormalised by tiling dilution factors. The Platonic force is acontact term outside this propagating sector. The dilution factor andsource density of each force are fixed by the tiling fate of itsgeometric carrier. The core constants of the Standard Model are settled ashigh-precision numerical correspondences of three topological genes:spatial dimension d = 3, electromagnetic steady-state rentU_EM = 0.4π, and weak activation rent U_weak = 10√3. The Zhang-YuIdentity, α⁻¹ = 25√3π + 1 ≈ 137.035, matches the measuredfine-structure constant to within 0.0008%. The weak mixing angle atM_Z is sin²θ_W = 1/(1+π) − Δ/(4π) ≈ 0.23079, matching the measuredvalue to 0.18%. This weak activation rent defines a total logicaladdressing capacity of N_max = exp(10√3) ≈ 3.32 × 10⁷ nodes—anear-25-bit machine whose finite capacity provides the common originfor the fermion generation limit, CP violation, and couplingsaturation. We distinguish clearly between anchored parameters,whose values are fixed by matching to measured constants, andderived quantities, whose values follow from topologicalexpressions. A three-tier parameter ledger is presented: pure predictions withno experimental anchors, conditional predictions using a smallnumber of anchors, and openly identified candidates. Knowndeviations are reported together with successes. A sharedtopological inventory is presented, demonstrating that the sameprojection operators—the K4 edge count 6, the K12 edge count 66,the geometric residue R = 1/(1+π), and the cascade impedance √6—recur across physically unrelated sectors. The scale problem isresolved through decoupling of hadronic physics from the latticespacing and power-law suppression of cubic anisotropy. We formally define the Zhangyu (ZY) as the universal unit oftopological value. One Zhangyu is the minimal bandwidth required tomaintain a single logical node in causally coherent existence,anchored to the electron's topological rent U_EM = 0.4π. The ZY-SIconversion is currently an empirical calibration:1 ZY ≈ 0.4066 MeV. From this volume onward, all subsequentquantitative audits are denominated in ZY.