GCE: Computation Engine for the BCCF Framework

GCE is the computational implementation of the Binary Complementary Computational Framework (BCCF), which derives fundamental physics from a single axiom (0≠0) and the topology of the complete graph K4, with zero free parameters. The engine implements a 10-level derivation cascade: - Level 0–2: Axiom → oscillation (π) → four face products (ε=1/π²) - Level 3: K4 graph structure → fine structure constant α (0.0002% error) - Level 4: Mass scales, CKM/PMNS matrices, CMB acoustic peaks, cosmological parameters - Level 5: 200+ hadron mass ratios, QCD β-functions to four loops, Born rule (C=1/18) - Level 6: Running couplings, Hubble constant, dark energy fraction Ω_Λ = (π−1)/π - Level 7: 118 ionisation energies, 320 bond dissociation energies, crystal structure predictions - Level 8: Decay rates (α, β, fission), phase transitions, catalysis thresholds - Level 9: Genetic code integers (64, 20, 3), black hole entropy Convergence state (V7): 1069 cells, 736 with experimental measurements. 70 exact identities. 681 sub-1% (92.5%). 733 sub-5% (99.6%). 569 tests passing. Includes: - Full derivation chain (level0.py–level9.py) runnable from source - Unified query API with forward prediction and reverse cascade search - 269 per-bond K4 structural expressions - Prediction database generator producing 1547 testable predictions across 8 categories - Compound discovery engine with 38 home-laboratory synthesis protocols - Equipment ROI analysis and inventory tracking All numerical outputs are K4 expressions. No fitted parameters, no adjustable constants, no empirical inputs beyond the axiom.