SEFERIM AGI — ThatAIGuyCore | The G¹⁶ Golden-Ratio Cognitive Substrate

What SEFERIM is

Most neural systems are opaque weight matrices. SEFERIM / ThatAIGuyCore is the opposite: a small, fully-deterministic mathematical substrate where every dynamic is a named, documented equation. Cognition is modeled as a 16-dimensional meta-state Ψ updated each tick by sixteen cognitive families, blended with golden-ratio momentum, gated by stability, and normalized so it can approach but never exceed natural limits.

The reference implementation in seferim-core is zero-dependency JavaScript — it runs in this page and in Node. Every function cites the spec section it implements, and the test suite verifies the math against canonical references (including the FNV-1a hash test vectors).

The 13 systems

From constants to a federation of conscious agents.

§1Constantsφ, δ, τ

§2Golden basisψ_k frequency encoding

§316 cognitive familiesthe G¹⁶ dynamics

§4Meta-state coreφ-correction + gating

§5Objective Ωfree-energy-style

§6DNA holographic memorygolden-basis recall

§7Gate5000binary substrate

§8Neural brain88 agents (dna_v9)

§9Consciousness engine374-D binding field

§10Lattice enginegolden kernels + Hebbian

§11Federation cross-talkcoupled agents

§12–13Activations & hashingsoftsign, σ, FNV-1a

The core mathematics

Golden basis function (§2.1)

Knowledge is encoded across sixteen golden-ratio frequency bands — a distributed, holographic representation.

$$\psi_k(x) = \sin(2\pi\,\varphi^{k}\,x) + \cos(2\pi\,\varphi^{k}\,x), \qquad k = 0\ldots15$$

Meta-state update (§4)

Each family is applied and weighted, blended with golden-ratio momentum, gated by stability, and normalized:

$$\Psi''_i = \tfrac12\,w_i f_i(\Psi_i) + \tfrac12\big(\Psi_i^{t-1} + (\varphi-1)(\Psi_i^{t}-\Psi_i^{t-1})\big)$$

$$b = \frac{1}{1 + \lVert\Psi\rVert^2/\varphi}, \qquad \Psi_i^{t+1} = b\big(\Psi_i^t + \gamma(\Psi''_i - \Psi_i^t)\big)$$

Objective Ω (§5) — a free-energy-style functional

$$\Omega = \underbrace{\alpha_1\tfrac{\lVert\Delta\Psi\rVert_1}{16} + \alpha_2\lVert\Delta\Psi\rVert_2^2}_{\text{surprise}} + \underbrace{(1-b^2)}_{\text{uncertainty}} - \underbrace{u\langle w,\Psi\rangle}_{\text{value}} + \underbrace{\lambda\,dx^2}_{\text{penalty}}$$

Holographic recall (§6)

$$\theta_k \leftarrow (1-\alpha)\theta_k + \alpha\,w\,\psi_k(h(\text{item}))\,\Phi(\text{imp}), \qquad K(q)=\sum_{k=0}^{15}\theta_k\,\psi_k(h(q))$$

→ Read all 69 equations (the complete reference)

Live demos

Every demo below runs the actual seferim-core library, in your browser, right now.

1 · Golden basis ψ_k

Each cognitive family k oscillates at a golden-ratio frequency φ^k. Drag k to see the band.

k = 3

2 · DNA holographic memory

Teach the substrate words; then query. Recall is the correlation of your query against the 16-D knowledge vector.

learned: (none)

recall

—

3 · Cognitive core + 88-agent brain

Run the meta-state and neural brain live. Adjust the drive and watch the 16 families, objective Ω, and emergent consciousness.

utility 0.6 stability 0.8

Ω — · consciousness — · synchrony —

Built on real mathematics (honestly)

SEFERIM synthesizes established theory. We document the lineage precisely rather than overclaim.

Free Energy PrincipleFriston — surprise minimization (objective Ω, Family 11)

Information theoryShannon; Cover & Thomas — MI & rate-distortion (Families 6–7)

Holographic / VSA memorydistributed frequency-domain encoding

Hebbian plasticityΔW = η·xᵢ·xⱼ (lattice)

Swarm consensusVicsek / Cucker–Smale (Families 8–9)

Golden-ratio harmonicsmaximally non-resonant frequency bands

We don't overstate three things: (1) δ = 0.013618 is an empirical phase increment, not 1/φ³; (2) the memory is a golden-ratio frequency-domain Vector Symbolic Architecture, inspired by — not a literal copy of — Plate's circular-convolution HRR; (3) the information-theory families are inspired-by one-step update rules, not exact estimators. Full cited foundations: FOUNDATIONS.md.

Key references: Friston (2010) Nature Rev. Neuroscience · Cover & Thomas, Elements of Information Theory · Shannon (1948) · Plate, Holographic Reduced Representations · Hebb (1949) · Vicsek et al.

Use it

npm install seferim-core

import { MetaState, DNAMemory, NeuralBrain } from "seferim-core";

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);

View the source on GitHub →

An Artificial BrainBuilt on the Golden Ratio