Quantum Copy-Time Geometry: Standard-Model Gauge Algebra, Family Structure, and a Parameter-Free BCC Photon Signature

Quantum Information Copy Time (QICT) is formulated as a receiver-based operator construction in which finite spectral geometry, reversible body-centered-cubic dynamics, compact gauge transport, Riesz–Kato state selection, and matrix-valued spectral reconstruction form a single derivation chain. Within the declared primitive receiver class, orientation visibility fixes a three-state endpoint carrier; its irreducible Weyl pair enforces three-family multiplicity; the visible finite algebra is \(\mathbb C\oplus\mathbb H\oplus M_3(\mathbb C)\); and anomaly compatibility selects the hypercharge ray \((1,4,-2,-3,-6,0,3)\) in the normalization \(q_Y=6Y\). A frozen compact-gauge update, a selected spectral subspace, and the six-source moments \(C_n^{(6)}=V^\dagger U^nV\) generate a positive matrix spectral measure and a regulator-resolved observable map. At \(L=24\), the charged \(SU(2)\) sector is encoded by 13 sparse matrix-product-state cores containing \(2\,804\,819\) nonzero coefficients with maximum observed bond dimension \(594\,652\); the four incident charged plaquettes occupy 128 disjoint sparse shards with support \(77\,036\). The rank-six common contraction contains \(21\,136\) links, \(18\,252\) plaquettes, \(261\,346\) connected \(SU(2)\) recoupling pairs, and a \(3925\)-node \(C_{10}\) graph. Exact color factorization in the charged-lepton relative operator sharpens the propagated representation bound from \(3.85779742077\times10^{-8}\) to \(1.83128545829\times10^{-8}\). The selected finite Kato calculation has dimension \(122\,677\) and gap \(14.4258464463\), while the matrix-free Riesz evaluation reaches projector and density errors of \(1.44\times10^{-17}\) and \(1.57\times10^{-16}\). Fermion masses arise from sector-specific spectral objects generated by the same microscopic dynamics. Dimensionless charged mass coordinates are singular values of the residue-normalized left–right Feshbach block; quark masses are the scalar chirality-changing coefficients of the renormalized color-resolved inverse propagator in a declared short-distance scheme and scale; and the neutral \(6\times6\) complex-symmetric Nambu kernel yields Takagi masses and neutrino observables. The reduced charged-lepton construction produces the parameter-free scale-free mass coordinates \((m_e:m_\mu:m_\tau)_{\mathrm{red}}=1:206.731294355038:3477.03865395274,\ Q_K=0.666671416005203.\) The mass and mixing observables are generated by one common interacting operator hierarchy. Residue-normalized isolated poles and lower charged spectral-support edges determine the physical two-point mass coordinates, while the matched charged-current three-point function on the same regulator net determines CKM and PMNS. The converged spectrum fixes all dimensionless mass ratios, and the single metrological coordinate \(\tau_*\) completes the dimensional map to absolute masses. Finite quark and neutral Takagi coordinates provide regulator-resolved spectral anchors whose common-net limits define the corresponding continuum observables. The construction also yields exact finite-regulator invariants: receiver timing \(1{:}3{:}5\) within the integer structure \((1,3,5,14,21,126)\tau_*\) and a parameter-free normalized BCC photon signature whose quadratic fingerprint has high-symmetry ratio \(9{:}21{:}25\), spherical mean \(31/160\), variance \(1/525\), and a fixed quartic directional map; its anisotropic amplitude exhibits the predicted \(a^2\) suppression, providing a quantitative approach to the Poincaré-covariant continuum limit. The formal closure is organized as ten theorems with explicit hypothesis classes. Universal quantum principles define the admissible finite-geometry category; source-visible receiver data select \(\mathbb C\oplus\mathbb H\oplus M_3(\mathbb C)\) within that class; source completeness plus the primitive endpoint Weyl system fixes \(N_g=3\); and strict CAR functoriality fixes the matter lift. Along a renormalized path the reconstruction defect obeys \(\|D(a)\|_1\le C_D(a\mu_*)^{p}\) with \(p=\min\{2,\omega_*\}\), where \(\omega_*\) is the least irrelevant interacting RG exponent on the selected trajectory and the auxiliary regulators follow the stated cofinal schedules. The overlap-kernel gap, Kato branch-selection gap and physical sector thresholds are treated as distinct spectral quantities; gauge-invariant observables are defined before gauge fixing, with maximal-tree representatives furnishing the auxiliary gauge-fixed comparison functions. The reconstructed continuum anomaly-free gauge theory inherits perturbative renormalizability from the established 't Hooft–Veltman gauge-theory theorems, while the microscopic RG map fixes the renormalized trajectory. The \(L=24\) rank-six data supply the exact precontraction and numerical backends for finite-regulator validation, together with the common-net operator contract that defines the interacting \(G_2/G_3\) mass and mixing construction.