Strong Coupling alpha_s and the b_0 Orbifold Decomposition: The QCD beta-Function Leading Coefficient b_0(n_f=3) = 9/(4 pi) from Chen-Ruan Inertia of the Trefoil Orbifold Base D^2(2,3) (DTTT BATCH-3.2 ALPHA-S-STRONG-COUPLING)

BATCH-3.2 ALPHA-S-STRONG-COUPLING. This paper derives the QCD beta-function leading coefficient b_0(n_f=3) = (33-6)/12 = 9/4 in units of 1/pi from a Chen-Ruan four-stratum inertia decomposition over the trefoil orbifold base D^2(2,3), within Discrete Topological Torsion Theory (DTTT), a framework that models spacetime as a nonlinear Cosserat micropolar elastic continuum with topological knot solitons. The decomposition b_0 = 9/8 (gluon) + 12/8 (quark, n_f = q = 3) + 1/8 (ghost) - 4/8 (orbifold defect, c_3 = p+q-1 = 4) = 18/8 = 9/4 reproduces the standard QCD value EXACTLY at fraction-arithmetic level, not by approximation. The trefoil T(2,3) is selected uniquely among 8,960 scanned coprime torus knots T(p,q) for 2 ≤ p ≤ 100, p < q ≤ 200 by the orbifold Euler characteristic chi_orb(D^2(2,3)) = 1 - 1/p - 2/q = -1/6. 3-loop RG running to alpha_s(M_Z). The substrate-tree-level coupling at the proton scale alpha_s = pq/(c_3 pi) = 6/(4 pi) = 0.4775 (both pq = 6 and c_3 = 4 from the same trefoil source) is run via standard Vermaseren-Larin-van Ritbergen 1997 3-loop machinery with threshold decoupling at m_t, m_b, m_c, yielding alpha_s(M_Z) = 0.1173 vs PDG 2024 0.1180 ± 0.0009 (consistent at -0.78 sigma; no tension). Two-loop running gives +0.74 sigma, bracketing PDG. Glueball-mass band and confinement mechanism. The same Cosserat-substrate trefoil topology that fixes b_0 fixes the scalar (0^++) glueball mass band at 1520-1740 MeV, consistent with the lattice-QCD consensus m_glueball = 1700 ± 100 MeV (Athenodorou-Teper 2020 unquenched; Morningstar-Peardon 1999; Chen et al. 2006). Colour confinement of an isolated quark is topologically forced: the Wilson loop for a single-strand braid of the 3-strand T(2,3) presentation vanishes because the strand cannot close without the remaining two strands. The Cosserat-Feynman dynamical computation of the one-loop glueball self-energy and the substrate-derivable string tension are the load-bearing internal tests (catalogued F1 of the canonical paper falsifiers register). Tier discipline (Block 44.202 publication tier). The b_0 = 9/4 orbifold-decomposition result is DERIVED unconditionally (Fraction-exact; SHC R-1 independent); the alpha_s(M_Z) = 0.1173 central value is DERIVED-VIA-INHERITANCE (3-loop RG standard machinery); the glueball-mass band and the confinement-mechanism sketch are STRONG-CONJECTURE pending the Cosserat-Feynman dynamical computation (P2) and the Lemma SHC R-1 closure cascade (P3, inherited from FOUNDATIONS-SYNTHESIS). No auto-promotion of tier labels per §A.14. 5-tuple operator algebra context and substrate framing. The trefoil complement's role in this derivation is fixed by the 5-tuple operator-algebra structural finality theorem of the DTTT axiomatic layer (canonical AXIOMS paper) -- under Hurwitz closure on the quaternion algebra H, the 5-tuple is structurally final, with no admissible 6th operator. The same substrate Lagrangian that produces alpha^-1 (Pauli-Jung formula; see [DOI-ALPHA]) and sin^2 theta_W = 3/13 (Weinberg angle; see [DOI-WEINBERG-ANGLE]) also produces alpha_s via Chen-Ruan inertia on D^2(2,3), completing the three Standard Model gauge-sector parameters as substrate-derived consequences of a single trefoil topology -- the gauge triptych certified in BATCH-2.2 SM-TALLY ([DOI-SM-TALLY]). Honest residue. Load-bearing residues disclosed in body: (i) Cosserat-Feynman dynamical computation of b_0 reproducing 9/(4 pi) by field-theoretic one-loop summation is pending (F1; multi-week analytical+numerical task; topologically forced but not explicitly verified); (ii) glueball-mass-band central value is a forward band, not a point prediction, pending P2 closure; (iii) confinement-mechanism sketch is STRONG-CONJ pending SHC R-1 (the same load-bearing residue as ALPHA, MANIFESTO and FOUNDATIONS); (iv) external-LLM and external-PDE-analyst audit pending (T8); (v) trefoil-uniqueness scan extension from 8,960 to ~ 10^4-10^5 knots is computationally feasible and would saturate the alternative-knot falsifier with higher confidence.