A Torus-Node Model for Emergent Spacetime, Gravity, and Gauge Structure: D4 Moves, Level-3 Commensurability, the S4 Ordered-History Algebra, and a Poisson-Source Interface

We construct a model in which low-energy \( 3+1 \)-dimensional spacetime, gravity, gauge fields and chiral matter all arise from flat two-torus node data through a single conditional chain. The construction combines a declared finite completion of bounded geometry with \( D_4 \) spatial moves, a level-three cusp action, determinant-two Hecke correspondences and an \( S_4 \) ordered-history algebra, and leads from the node data to four-dimensional kinematics, the metric, gauge and matter blocks, and a low-energy effective action. Each premise and each source-to-continuum condition is stated separately; deriving the finite completion from an unrestricted Poisson torus source remains open. The \( D_4 \) lattice model selects four dimensions and one oriented temporal direction; with the stated Osterwalder--Schrader reconstruction assumptions, this gives Lorentz signature \( (-,+,+,+) \). The ordered-history commutant supplies the finite gauge factors, which reduce after the cutoff-scale central \( U(1) \) combinations are removed to \( SU(3)_c× SU(2)_L× U(1)_Y \). The resulting chiral module has quantised charges and cancels the local gauge, mixed gauge--gravitational and global \( SU(2) \) anomalies; the choice of three generations is vacuum data. The canonical finite model yields a conditional Einstein--Hilbert term, while the induced finite action supplies the gauge-kinetic and matter structures under their stated assumptions. In the static limit the sector actions give Newton's and Coulomb's laws, the short-range weak force with its Fermi coupling, and the asymptotically free force between quarks at short distances. For the Wilson action, confinement follows from the decay of the vortex free energy, which a renormalisation flow through the intermediate couplings would supply; the mass gap is open in the same range of couplings. An observationally constrained specialisation uses measured couplings and declared matching, threshold and overlap inputs. Its matching equations admit exact gauge-coupling solutions and, with the stated heavy-state threshold, give the conditional bound \( m_t173.0 \)--\( 173.9 \) GeV. These are input-dependent outputs, not parameter-free predictions of the canonical finite model. Photon masslessness for the integer Wilson action, the non-perturbative electroweak gap, the physical \( SU(3) \) Yang--Mills gap and reflection positivity of the unrestricted Poisson source remain open, as does the source-to-continuum identification itself.