The G¹⁶ Federation: a golden-ratio, 16-dimensional dynamical-systems substrate for artificial cognition
SEFERIM is a clean-room, zero-dependency reference implementation of ThatAIGuyCore — a unified mathematical framework that treats cognition as the evolution of a 16-dimensional meta-state under sixteen coupled "cognitive families," all governed by the golden ratio φ. It is a substrate: a small, fully-deterministic engine for golden-ratio dynamical systems, holographic memory, and federated multi-agent coherence.
📖 Full interactive documentation, live demos, and the complete mathematical reference: thataiguy.org/core
This repository implements all 69 documented equations of the ThatAIGuyCore v1.0.0 specification verbatim — every function in src/seferim-core.js cites the spec section (§) it implements, and test/run.js verifies the math (including the canonical FNV‑1a test vectors).
npm install seferim-coreOr load it straight in the browser as an ES module (no build step):
<script type="module">
import { MetaState, DNAMemory } from "https://cdn.jsdelivr.net/npm/seferim-core/src/seferim-core.js";
</script>import { MetaState, DNAMemory, NeuralBrain, PHI } from "seferim-core";
// 1. A single-stack cognitive core: 16 families + golden normalization.
const mind = new MetaState({ init: new Array(16).fill(0.1) });
const out = mind.step({ dx_norm: 0.3, ed_error: 0.1, utility: 0.6, stability: 0.8 });
console.log(out.state, "Ω =", out.omega); // 16-D meta-state + objective (free-energy-style)
// 2. Holographic memory — knowledge smeared across 16 golden bases.
const mem = new DNAMemory();
mem.learn("rhythm").learn("groove").learn("pocket");
console.log(mem.queryNorm("groove")); // correlation recall in [0,1]
// 3. An 88-agent neural brain (dna_v9 dynamics).
const brain = new NeuralBrain();
for (let i = 0; i < 100; i++) brain.step(0.6);
console.log(brain.consciousness(), brain.synchrony());npm test # 42 assertions: constants, FNV-1a vectors, every family, all engines| # | System | What it does |
|---|---|---|
| 1 | Fundamental constants | φ, δ (DNA increment), τ |
| 2 | Golden basis | ψ_k(x) = sin(2πφ^k x) + cos(2πφ^k x), normalization, spiral angles |
| 3 | The 16 families | continuous/discrete dynamics, reaction-diffusion, optimization, Bayesian, learning, mutual-information, rate-distortion, consensus, swarm, field accumulator, free-energy, compression, memory-trace (Zecher), policy, global coherence (Kehillah) |
| 4 | Meta-state core | weighted family application → φ-correction (inertial blend) → stability gating → golden normalization |
| 5 | Objective Ω | Surprise + Uncertainty − Value + Penalty (a free-energy-style functional) |
| 6 | DNA holographic memory | golden-basis encode/recall + cosine coherence |
| 7 | Gate5000 | 5,000-gate XOR binary substrate driven by two quasi-periodic phases |
| 8 | Neural brain (dna_v9) | 88 agents with velocity, drive, gating, potential, coupling → consciousness & synchrony |
| 9 | Consciousness engine | 174 core + 200 supplemental equations → a 374-D binding field |
| 10 | Lattice engine | 16 strands, golden rotation kernels, Hebbian plasticity |
| 11 | Federation cross-talk | coupled consciousness signals across agents (decay + coherence-weighted coupling) |
| 12–13 | Activations & hashing | softsign, sigmoid, clamp; FNV-1a |
The framework synthesizes established theory — the Free Energy Principle (Friston), information theory (Shannon; Cover & Thomas), holographic / vector-symbolic memory, Hebbian plasticity, swarm consensus (Vicsek / Cucker–Smale), and golden-ratio harmonics. Full citations are in docs/FOUNDATIONS.md.
We document the lineage precisely rather than overclaim. In particular:
- δ = 0.013618 is an empirical quasi-periodic phase increment — not 1/φ³ (which is ≈ 0.236).
- The memory system is a golden-ratio frequency-domain Vector Symbolic Architecture, inspired by — not a literal implementation of — Plate's circular-convolution Holographic Reduced Representations.
- The mutual-information (Family 6) and rate-distortion (Family 7) updates are information-theory-inspired one-step rules, not exact estimators/solvers.
docs/MATHEMATICS.md— the complete 69-equation reference (the spec this code implements).docs/FOUNDATIONS.md— cited mathematical foundations for every component.
SEFERIM / ThatAIGuyCore is the cognitive-substrate research of Joseph W. Anady (ThatAIGuy.org). Interactive docs + live demos at thataiguy.org/core.
SEFERIM / ThatAIGuyCore is the original work of Joseph W. Anady (ORCID 0009-0008-8625-949X). Authorship and priority are established by a permanent, timestamped public record:
- Archived & dated (DOI): 10.5281/zenodo.20564321
- Public commit history: this repository
- ORCID: 0009-0008-8625-949X
Use is welcome under the MIT License, which requires retaining the copyright notice (see LICENSE and NOTICE). Derivative works must preserve this attribution and must not present SEFERIM / ThatAIGuyCore, or this framework, as their own original creation. Forks must be renamed and must credit this origin and DOI.
Anady, J. W. (2026). SEFERIM / ThatAIGuyCore: A Golden-Ratio, 16-Dimensional Dynamical-Systems Framework for Artificial Cognition (v1.0.0). Zenodo. https://doi.org/10.5281/zenodo.20564321
- DOI: 10.5281/zenodo.20564321
- OSF project: https://osf.io/8e9ks/
- ORCID: 0009-0008-8625-949X
MIT © 2026 Joseph W. Anady / ThatAIGuy.org