Foundations of Generator Physics II Closure, Mass, and Hierarchical Disclosure From Higgs Intertwiners to Recursive Family Closure

Generator Physics I asks which generator, selector, and carrier structures are available. Generator Physics II asks how those structures close, partially close, and produce hierarchy. Generator Physics III is reserved for closure dynamics: why particular closure depths are dynamically selected. Generator Physics II develops a closure-based organization of mass and hierarchy. The central proposal is not that familiar Dirac, Higgs, flavor, or seesaw mathematics is new, but that a common structural language becomes visible when these systems are read in terms of preserving sectors, reciprocal bridges, closure rank, weak singular directions, and directional novelty. Mass is treated first as a matrix-closure problem: relativistic propagation generators require an anticommuting closure operator, and gauge covariance promotes that closure to an intertwiner between inequivalent chiral representation spaces. The Higgs field provides the canonical Standard Model realization of that covariant bridge. The framework then generalizes from complete Dirac closure to Partial Closure. For a block decomposition V=V_A⊕V_B, a reciprocal bridge Z leaves a closure defect Δ_cl=a+b−2 rank Z, with an unavoidable minimum |a−b| when the sector dimensions are unequal. Near rank-deficient systems replace exact zero modes by weak singular directions. In three-family space this gives a natural weak-line/active-plane geometry in which line-plane mixing appears at first order while induced weak mass appears at second order. The construction is stress-tested against two published SO(10) flavor benchmarks of Saad and Susič. Their symmetric H and F tensors and antisymmetric G tensor independently identify an approximate common weak family line. The amplified antisymmetric channel can dominate orientation without creating the near-rank-two closure volume, leading to a kernel-gated determinant identity. The Type-I seesaw is then decomposed into weighted rank-one closure directions whose determinant factorizes into sequential novelty contributions. A strong common-carrier hypothesis is falsified by the invariant generalized spectrum of FH⁻¹; a weaker common-access hypothesis survives and motivates Recursive Closure. The resulting architecture separates access geometry, relative closure depth, and final directional novelty, while explicitly withholding a dynamical derivation of the numerical closure depths.