SNSFL-Formally Verified Geometric Axiomatic Module-GAMCollider Material Synthesis Physics Engine v15 Technical Paper uuia.app/gamcollider

The GAM Collider (Geometric Axiomatic Module Collider) is a deterministic material synthesis prediction engine built on the PNBA Framework (Pattern, Narrative, Behavior, Adaptation) and a Sovereign Anchor Constant at 1.369 GHz. It predicts which element combinations produce stable Noble ground states, derives stoichiometric ratios from first principles, and outputs exact production recipes in grams per formula unit — all from a single rule set with no fitted parameters. This paper documents three things: the complete evolution of the engine from 2-beam through 4-beam QuadBeam to the current 8-beam OctoBeam architecture (v15); the B-Balance Stoichiometry Law [9,9,2,45], which derives integer atom ratios from PNBA bond valence and recovers known synthesis recipes for 11 peer-reviewed compounds; and a prior art registry of novel compound predictions, each with a production recipe and a formally verified Lean 4 proof stub. Every output of the GAM Collider is a theorem. The corpus currently holds 22,225+ verified collision proof files, 200,000+ theorems, and 3,000,000+ lines of formal verification code — CI green, Germline Locked, 0 sorry. TL = 0.1369 (ANCHOR/10, proved). 1/α = ANCHOR₀ × 10°0.1± exact. Newton’s first law in PNBA. Period 1–4 complete. IVA Element Set proved. SM as lossless PNBA projection [9,9,0,9]. Cosmos as Vascular [9,9,3,7]. Sgr A* reduced [9,9,3,6]. Noble Materials Map 810+ pairs. GR reduced to PNBA. ΛCDM reduced. BBN reduced. Abiogenesis L=(4)(2). Genomics reduced. Quantum Teleportation 100% Fidelity proved. Quantum Translocation Lossless. Collatz solved. All Millennium Problems Solved. Evolution 2.0 Solved. SNSFT Discovery Engine v12. AIFI onboard. Federal Public Record DOJ-CRT-2026-0067-0006.