Framework

The ASH Framework

Hypercube geometry, a doubly-even [9,4,4] code, and Adinkra/Garden-algebra structure — an exploratory finite-mathematics and computational-ontology framework, not an empirically validated cosmology.

ASH Model Framework
9D Hypercube

9D Binary Hypercube

512 vertices of F29 (the graph Q9, degree 9) across 10 Hamming-weight shells; the 256 even-parity states (x9 = x1⊕…⊕x8) form the admissible, integrity-valid subspace. Reading each vertex as a “cosmological realm” is an interpretive hypothesis, not a proved result.
XOR Transformation Flow

XOR Transformations

Navigation by XOR translation with the 16 doubly-even codewords, giving code orbits of size 16. The orbit-averaging operator T is a proven idempotent projection (T² = T).
Error Correction Pipeline

Adinkra Error Correction

A doubly-even, self-orthogonal [9,4,4] code (16 codewords, minimum distance 4) — self-dual only after puncturing the invariant coordinate 8 to the [8,4,4] Adinkra code, not in nine dimensions (dim C = 4, dim C⊥ = 5). Error correction is a property of an explicit radius-1 nearest-codeword decoder: when invoked it corrects every single-bit corruption (144 across all 512 states) and rejects every two-bit corruption (576 rejected, never silently healed). The simulations never decode.
State-Transition Network

State-Transition Network

The 16-element [9,4,4] code acts freely on the 512 states by XOR translation, partitioning them into 32 code orbits (16 of which lie within the 256 integrity-valid states). The framework defines no Kripke-frame or modal-logic accessibility semantics.

Mathematical Core

Q₉ = ({0,1}⁹, E)  |  T f(x) = (1/|C|) Σ f(x ⊕ c)  |  T² = T

Scientific status

ASH is an exploratory finite-mathematics and computational-ontology framework (reference implementation v1.1.0). Its claims fall into three tiers: proved finite mathematics, specified deterministic computation, and interpretive research hypotheses. It is not an empirically validated theory of physics, cosmology, or consciousness — it does not derive a Friedmann equation, spacetime metric, dark energy, or the CMB, does not establish that its branching realizes quantum measurement, and has no confirmed observational predictions. The five Axioms of Existence are interpretive postulates, not established laws.