The Awen Grid Digital Collider: Exact Quaternion– Octonion Dual-Ledger Dynamics, an Emergent Ring Attractor, and a Pre-Registered Falsifiability Audit of the Recursive Harmonic Codex

Abstract

We present the Awen Grid Digital Collider, a numerical instrument that ev olv es two coupled ensembles("ledgers") of states on unit hy perspheres: a Real Ledger of up to 10⁷ unit quaternions on S³, and an ImaginaryLedger of equally many unit octonions on S⁷, distributed across two consumer GPUs. The Real Ledger ev olv esby an observ er-weighted map built from the general SO(4) sandwich rotation ψ → q_b·ψ ·q_a⁻¹; the ImaginaryLedger ev olv es by unit-octonion Cay ley–Dickson rotation; "collisions" between the sectors are measured by theoctonion associator [x ,y ,z] = (x y )z − x (y z), an observ able that is prov ably zero on the quaternionic subalgebraand therefore self-calibrating. All structural theorems the instrument relies on — the SU(2) representation of theHamilton product, associativ ity of ℍ, alternativ ity and non-associativ ity of 𝕆, and the composition-algebra law|x y | = |x ||y | underly ing ex act norm conserv ation — are machine-v erified to 10⁻¹⁵–10⁻¹⁶.Three empirical results follow. First, the observ er-weighted map possesses a global ring attractor on S³: from auniform random beam, thousands of independently ev olv ing states v isibly self-organize into a single ring within~27 ticks, after which ev ery measured observ able phase-locks. Second, the locked observ ables are inv ariantacross a 200× range of beam sizes (5×10⁴–10⁷ nodes), ten random seeds, two arithmetic precisions(float32/float64), two backends (CPU/dual-GPU), and two independent operators: collision rift 1 .1 7 90 ±0.001 1 , lion ratio 1 1 .554 ± 0.006, mass index 0.99627 (across-seed range 5×10⁻⁵). Third, a Lev el II sweep ofthe rotation:fold mix ing weight maps the attractor landscape and finds a genuine interior resonance at w ≈ 0.865(lion 39.4), while demonstrating that prev iously published constants of the framework (a claimed fold-amplituderesonance at 0.48, and a legacy "Lion constant" of 0.5352) are respectiv ely not reproduced under a preregistered 10⁷-node blind sweep and unreachable any where on the measured slice — and whose documentaryorigins we identify from the primary sources (an algebraic identity and a bookkeeping snapshot, respectiv ely ;Section 6.5). A 40-item falsifiability audit of the RHC corpus (18 v erified · 8 false · 5 contradictions · 6 ex ternalmismatches quantified · 1 not reproduced · 1 open · 1 untestable) and a measured correction of the framework'scompression claims (delta pre-transform: −30 to −37 % on correlated telemetry ; −0% bey ond entropy on anydata) are included. The instrument computes geometry on simulated states; it does not act on phy sical matter,and no claim to the contrary is made.