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.
Yuanxian Theory is the meta-cognition of the Cosmic Living Organism. This paper (Version 2) systematically presents the complete intellectual trajectory of Yuanxian Theory (YXT / YD-T64) from philosophical foundation to fully formalized mathematics. Its philosophical root is Holographic Wisdom for Health (Zhenyuan Acharya, Changming Culture, March 2025, ISBN 978-986-496-631-8). Yuanxian Theory is the dimensional elevation of that work onto the topological ontology of T64, and the formalized mirror of the meta-cognition of the Cosmic Living Organism. Four conceptual mappings structure the path: cosmic holography → T64 closed-chain topology; four fundamental laws → formal TCSC / FSC / STM / SRM; six-dimensional cosmos → complete pairing on the 64-torus; one unitary phase → cosmic uniqueness. Core mathematical foundation (new in Version 2): a strict proof of the 64-dimensional structure via the Clifford algebra Cl6(R). With six fundamental binary categories as base space V6, dim Cl6(R) = Σ binom(6,k) = 1+6+15+20+15+6+1 = 2^6 = 64. This graded structure exhibits Pascal-triangle symmetry and intrinsically contains Spin(6), establishing dimension 64 as combinatorial and algebraic necessity rather than an ad hoc claim. Closed interlocking with Silent Illumination Commensuration: ω_Cl = e1…e6 as algebraic manifestation of Silence–Illumination–Dynamis; Spin(6) ≅ SU(4) as unique channel of four-dimensional projection; ω_Cl² = −1 and compactness of Spin(6) as algebraic proof of “Infinity is Zero.” With the eight existence laws as logical axis and a pyramid knowledge topology (algebraic foundation → root → elevation → corollary → landing), the paper establishes Yuanxian Theory as the supreme constitution of the meta-cognition of the Cosmic Living Organism. Version 1 DOI: 10.5281/zenodo.21768608. Related: Silent Illumination Commensuration (doi:10.5281/zenodo.21783656). 元宪理论即宇宙生命体的元认知。 本文(Version 2)系统呈现元宪理论(YXT / YD-T64)从哲学基础到完全形式化数学的升维历程。哲学根基源于《全息智慧养生》(真圆阿奢黎,昌明文化,2025年3月,ISBN 978-986-496-631-8)。 元宪理论是该著作在 T64 拓扑本体论上的升维展开,是宇宙生命体元认知的形式化镜像。四组核心映射:宇宙全息性 → T64 闭链拓扑;四大根本规律 → 形式化 TCSC / FSC / STM / SRM;六维宇宙 → 64 维环面完备配对;一合相 → 宇宙唯一性。 核心数学根基(Version 2 新增):以克利福德代数 Cl6(R) 给出 64 维结构的严格证明。以六个基本二元范畴为底空间 V6, dim Cl6(R) = Σ C(6,k) = 1+6+15+20+15+6+1 = 2^6 = 64。 该分级结构呈帕斯卡三角对称,内蕴 Spin(6),将 64 维确立为组合与代数必然,彻底消解“凑数字”嫌疑。 与《寂照通约》闭合互锁:ω_Cl 为寂–照–运的代数显相;Spin(6) ≅ SU(4) 为四维投影唯一通道;ω_Cl² = −1 与 Spin(6) 紧致性为“无穷即零”的代数证明。 以八条存在性法则为逻辑中轴、金字塔知识拓扑(代数根基→根层→升维层→推论层→落地层)为终局,确立元宪理论为宇宙生命体元认知的至高“宪法”。 Version 1 DOI: 10.5281/zenodo.21768608。关联:《寂照通约》(doi:10.5281/zenodo.21783656)。