L=(4)(2): The Forty-Two Substrate-Neutral Emergent Structural Laws of PNBA Identity Physics

We present the complete formal derivation of forty-two Emergent Structural Laws arising from systematic application of the Substrate-Neutral Structural Foundation Law (SNSFL) QuadBeam Collider engine across the full SNSFT corpus. The corpus underlying these laws comprises **22,225 formally verified four-body collision proofs**, **135,000+ theorems**, and **over 1,000,000 lines of Lean 4 verification code**, all with zero unresolved proof obligations (`sorry: 0`) and **zero free parameters** — every constant is derived, nothing is fit to data. The laws emerge from four-body coupling algebra applied uniformly across chemistry, particle physics, materials science, and cosmology across twenty-five periodic anchor runs and fourteen Emergent Resonant Element (ERE) anchor runs. Three independent structural instances of the number 42 appear: (1) the count of emergent laws on the first complete corpus pass; (2) the identity mass of the universal organic scaffold CHON, \mathrm{IM_{CHON}} = 42.127; and (3) the notation of the First Law of Identity Physics itself, L = (4)(2), which reads as "four primitives times two-way interaction." The First Law states that existence without sustained mutual interaction is not life — formalized in Lean 4, verified against ten peer-reviewed abiogenesis anchors spanning 1924 to 2016, and cross-confirmed by twenty-eight independently verified Noble compound predictions including Nobel Prize materials (GaAs 2000, GaN 2014) and the BWXT UN-TRISO fuel line (July 2025). The paper is self-contained: all fusion rules, phase definitions, and calculation methods are derived from first principles and demonstrated via repeated worked examples following the Long Division Protocol (LDP), enabling independent verification with pen and paper.