The ASH Model
Adinkra-Stabilized Hypercube — an exploratory finite-mathematics and computational-ontology framework built on a 9-dimensional binary state space: 512 binary states (the vertices of F₂⁹, the 9-cube Q9), of which 256 are parity-valid.
A Verified Finite-Mathematical Core
Built from binary mathematics, a doubly-even error-correcting code, and Adinkra (supersymmetry) graph theory.
9D Hypercube
512 binary states — the vertices of the 9-cube F₂⁹, each a 9-bit string. Of these, exactly 256 are parity-valid, satisfying the integrity relation x9 = x1 ⊕ … ⊕ x8.
XOR Transformations
Agents are translated by XOR with the 16 doubly-even [9,4,4] codewords, preserving integrity and keeping each agent within a 16-state code orbit; broader spread across the hypercube requires added noise.
Error Correction
Error correction is a property of an explicit radius-1 nearest-codeword decoder, not of the simulations: 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 Markov simulations apply noise and code XORs but never decode.
Five Interpretive Postulates
Adopted 2025-12-23 as research hypotheses that supply conceptual vocabulary — relation, compressibility, persistence, erasure cost, self-reference. They are interpretive postulates, not empirically established laws of cosmology, consciousness, identity, or survival.
Relational Existence
An element is treated as relationally present only in relation to another.
Compressibility
Real patterns compress below their raw description — a definitional criterion, not a computable test.
Persistence
Entities persist when they change little across declared scales.
Erasure Cost
Erasing information carries a thermodynamic cost (the Landauer bound), used as a constrained analogy.
Self-Reference
Proposes self-modeling as an operational criterion for consciousness; whether it is necessary or sufficient is an open question.
Computational Results
Key results from the committed default run — 1,000 agents × 250 ticks, noise p=0.01, seed 20260624 — and the seeded ablation suite, on the 512-vertex hypercube.
Controlled-Noise Baseline
Under controlled symmetric bit-flip noise the state occupancy converges to uniform, whose Hamming-weight marginal is exactly Binomial(9, ½) (mean 4.5, variance 2.25) — a generic finite-hypercube baseline that non-ASH controls also reproduce, not an ASH-specific result. With XOR transforms and no noise the dynamics stay confined to a 16-state code orbit (weights {0,4,8}) and do not converge (TV ≈ 0.73 from the binomial).
Controlled Mixing
Seeded Markov runs at low noise (p=0.01–0.02) relax toward the uniform baseline; the committed default run reaches TV = 0.032 from Binomial(9, ½). These are controlled, deterministic computations, not a demonstration of error correction — and there is no “6% noise threshold” (the kernel mixes to uniform for any 0<p<1).
Branch Structure
The branch layer is a specified deterministic depth-4 ternary tree (121 nodes, 81 leaves, 16 codeword messages), rendered with an L-system — a versioned engineering construction, not a quantum-measurement, decoherence, or Many-Worlds process. The repository does not establish that its branching realizes quantum measurement.
Explore the Mathematics
Formal proofs, simulation code, and academic references.
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.