0. Architecture Overview
CSE‑v1 is a closed sensorimotor loop with four coupled layers, all evaluated every tick by the
worker thread (never on the render thread):
- J‑Space — micro recurrent dynamics (N = 8 units)
- GWT — global workspace with a broadcast hub (M = 10 modules)
- HOT — higher-order re-representation + gate
- IIT / Φ — integration measured by minimum-information-bipartition search
- H‑Space — macro order parameters and downward constraint
The Φ computation here is a linear‑Gaussian proxy for integrated information,
not the full IIT 4.0 cause–effect structure. It is fully deterministic and computable, but it
measures integration of a linearised response covariance rather than of a cause–effect repertoire.
1. J‑Space (micro level)
State vector x(t) ∈ [0,1]^N, N = 8. Update rule:
x_i(t+1) = clip₀₁[ 0.5
+ Σ_j W_ij · (2x_j(t) − 1)
+ g_u · (2u_i(t) − 1)
+ g_f · κ_eff · (2m_i(t) − 1)
+ η ]
with g_u = 0.45, g_f = 1.1, and η a zero-mean uniform noise term scaled by the novelty slider.
W is a ring lattice (nearest-neighbour weight 1.0, next-nearest 0.35) plus 18% sparse
long-range connections, rescaled so max_i Σ_j |W_ij| = 0.5 — this keeps the spectral
radius below 1 and the fixed point stable.
- Input vector dim — N.
- Local activation (x̄) —
mean(x).
- Effective feedback (κ_eff) —
κ · h(t).
2. Global Workspace (GWT)
M = 10 modules; index 9 is the broadcast hub. Each tick performs 3 Jacobi relaxation sweeps:
drive_i = clip₀₁( 0.5 + Σ_j P_ij (2x_j − 1) ) for i ≠ hub
g_i ← clip₀₁( drive_i + 0.45 · g_hub − 0.30 )
g_hub ← clip₀₁( 1.05 · mean(g_modules) + 0.15 )
The hub-to-module term implements ignition: once the hub is active it amplifies every
module, which further raises the hub — a positive feedback loop bounded by the clipping.
- Broadcast efficiency — share of total activation held by the
recruited coalition
{i : g_i > mean(g)}.
- Signal distribution —
H(g) / log₂ M, the normalized
Shannon entropy of the activation profile.
3. HOT — Higher‑Order Thought
A meta-representation m is formed by gating a copy of the first-order micro state
through the workspace broadcast:
h(t) = clip₀₁( (g_hub(t) − 0.50) / 0.50 ) [HOT gate]
m_i(t) = 0.5 + h(t) · (x_i(t) − 0.5) [meta state]
The gate reports active when h > 0.25. Because ∂m_i/∂x_i = h,
the HOT loop contributes an extra self-coupling term to the effective Jacobian (see §4), which is
how higher-order representation feeds back into integration.
4. IIT — Integrated Information Φ
Effective Jacobian. Linearising the micro update and folding in the HOT self-coupling:
a_i = 1 if 0.02 < x_i < 0.98 else 0.15 [saturation mask]
J_ij = 2 · W_ij · a_i
J_ii += 2 · g_f · κ_eff · h · a_i
Response covariance. Under a linear-Gaussian approximation the stationary
response covariance is
Σ = (I − J)⁻¹ (I − J)⁻ᵀ + εI , ε = 1e-6
Bipartition mutual information. For a bipartition (A, B) of the N units:
MI(A;B) = ½ · log₂( det Σ_A · det Σ_B / det Σ )
All determinants are computed as log-determinants via Cholesky factorisation for numerical
stability. With unit 0 pinned to side A there are exactly 2^(N−1) − 1 = 127
bipartitions.
Φ is the minimum over the minimum information bipartition (MIB):
Φ_raw = min over 127 bipartitions of MI(A;B) [bits]
Φ̂ = 1 − exp( −Φ_raw / 2 ) [normalized, 0..1]
- Φ̂ (gauge) — the normalized MIB value; the raw bit value is shown beneath it.
- Mean partition MI — the mean of MI over all 127 bipartitions, normalized the same way.
- Partition threshold —
Φ̂ > Φ_thr.
- Causal density —
mean_{i≠j} |J_ij|.
- Heatmap — the |J_eff| matrix itself, row → column.
5. H‑Space (macro level)
The macro state is characterised by order parameters derived from Σ and the closed loop:
PR = (tr Σ)² / ‖Σ‖_F² [participation ratio, ∈ [1, N]]
V = clip₀₁( (PR − 1) / (N − 1) ) [macro spatial volume]
C = κ_eff [downward constraint weight]
σ_Φ = std( Φ̂ over last 24 ticks )
S = 1 / (1 + 12 · σ_Φ) [stability index]
Stability label: low if S < 0.45, medium if S < 0.75, high otherwise.
An emergent seed is declared formed on a tick when both
Φ̂ > Φ_thr (integration passes) and h > 0.25 (a higher-order
representation exists). The seed is visualised as the pulsing icosahedron; the green arc is the
downward-constraint feedback path into J‑Space.
6. Exports
Export JSON writes { meta, samples } where meta contains the
engine version, timestamp, live slider parameters and a model description, and samples is the
full per-tick record buffer.
Export CSV writes the same samples as a flat table with a header row:
t, u_mean, x_mean, phi_raw, phi_norm, phi_mean, gwt_eff, gwt_dist, hot_gate, hot_active,
kappa_eff, h_volume, h_constraint, h_stability, seed.
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