The Compositional Rational Dynamics (CRD) framework identifies a structured algebraic lattice in the mass spectrum of the Standard Model particles. The framework defines a six-prime basis P₆ = {2, 3, 5, 7, 11, 13} and calls an integer "CRD-smooth" if all its prime factors lie in P₆. It then tests whether ratios of known particle masses are well approximated by ratios of CRD-smooth integers.
Within the current analysis, the strongest result is this: the masses of 64 Standard Model particles can be derived from a single reference mass (the top quark) via a 63-edge minimum spanning tree with RMS error 0.0127% and maximum error 0.025%, with all 63 non-reference predicted masses inside their PDG uncertainties, using only CRD-smooth fractions as edges. The spanning tree supports 2,188 exact composing triangles (mass-ratio closure ≤ 0.0001%), of which 1,701 (68.2%) are algebraically independent of the spanning tree. Two overdetermination metrics should be distinguished: the constraint-to-basis ratio (1,701 independent constraints / 63 spanning-tree degrees of freedom ≈ 27×) and the redundancy ratio (1,701 independent / 487 tree-dependent ≈ 3.5×); see §2.5. The count of exact composing triangles exceeds the expectation from log-uniform random masses by Z = 5.5 standard deviations. Five motifs (EWSB³=11³, Hi³=13³, Color³=3³, Color⁷=3⁷, Hi²=13²) function as algebraic generators of this lattice; three others (3773, EM¹¹, Color⁶) appear as mixed or local approximants.
From the CRD lattice, a constrained dark-matter model is derived: a dark proton of mass m_DP = 5×m_p = 4.69 GeV communicating with the Standard Model via a massive B-L gauge boson of mass m_ZBL = (5/7)×m_p = 670 MeV and coupling g_BL = α_EM^(5/2) = 4.55×10⁻⁶. This model predicts σ_SI = 1.6×10⁻⁴⁹ cm² (within the projected DARWIN/XLZD sensitivity) and a dark-matter relic abundance Ω_DM/Ω_b = 27/5 (0.83% from Planck 2018), with ΔN_eff ≈ 0.
Five rare-decay branching ratios are predicted as interaction-structure consequences of CRD mass compatibility; none is currently measured.
An important correction (COR-011) affects the dark-sector claim: the original Darkness=Peripherality theorem — which assigned dark-sector status to the dark proton via its low bridge count B(DP)=2 — is retracted. Full enumeration gives B(DP)=10–14 at the canonical threshold, and no single bridge-count threshold cleanly separates dark from SM particles. The dark proton remains motivated on three independent surviving axes: the exact algebraic ratio m_DP=5m_p, the cosmological match Ω_DM/Ω_b=27/5, and the unique portal-prime consistency with experimental bounds and DARWIN testability.
The framework is internally validated but has not been externally reproduced. Its primary weakness is the absence of a physical derivation explaining why the SM mass spectrum should satisfy prime-smoothness conditions. The next phase will test the framework against external null models, experimental measurements, and formal mathematical consistency requirements.
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