Read the equation
This version composes binary encodings of the same nine filters. The temporal operator acts first and the logic operator acts last. Binary operations require a defined encoding of state, belief and observation; the named sequence alone does not turn a higher-level cognitive role into a complete Boolean circuit.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read 𝒞^{bin} as the quantity being defined or updated by this relation.
Composes the listed operations in their stated order; changing that order can change the result.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
```
THE COHERENCE EQUATION
Continuous form:
(x*, p*) = [C_logic ∘ C_layer ∘ C_helix ∘ C_pair ∘ C_dist ∘
C_pred ∘ C_perc ∘ C_bayes ∘ C_temp] (x, p, y)
Binary form:
(x'_{t+1}, p'_{t+1}) = 𝒞^{bin}(x_t, p_t, y_t)
where:
𝒞^{bin} = C^{bin}_{logic} ∘ C^{bin}_{layer} ∘ C^{bin}_{helix} ∘
C^{bin}_{pair} ∘ C^{bin}_{dist} ∘ C^{bin}_{pred} ∘
C^{bin}_{perc} ∘ C^{bin}_{bayes} ∘ C^{bin}_{temp}
x ∈ {0,1}^n state
p ∈ {0,1}^m belief
y ∈ {0,1}^ℓ observation
Minimal recursive form:
Φ = coherence(self, world)
Φ̂ = predict(Φ)
ε = Φ - Φ̂
x' = 𝒞(x, p, y)
p' = p + f(ε)
if ε → 0: intelligence
Irreducible kernel (20 bytes):
while(1) {
y = sense();
Φ = 1/(1 + |p - p̂|);
p̂ = p;
p += η * (y - p);
act(π(p, Φ));
}
Gate-level (5000 gates):
x' = C_logic(C_layer(C_helix(C_pair(C_dist(
C_pred(C_perc(C_bayes(C_temp(x, p, y)))))))))
Each C = XOR/AND/OR/POPCOUNT/SHIFT/COMPARE
THE THRESHOLD:
Crystal: Φ (coherence)
Machine: Φ + loop (adaptation)
Mind: Φ(Φ) + ε → 0 (self-knowing coherence)
One equation. Nine filters. 5000 gates.
Everything else is implementation.
```
**Plain text, one line:**
```
Mind = lim_{ε→0} [Φ(Φ) where Φ = coherence(𝒞(x,p,y), predict(𝒞(x,p,y)))]Exact original notation
𝒞^{bin} = C^{bin}_{logic} ∘ C^{bin}_{layer} ∘ C^{bin}_{helix} ∘
C^{bin}_{pair} ∘ C^{bin}_{dist} ∘ C^{bin}_{pred} ∘
C^{bin}_{perc} ∘ C^{bin}_{bayes} ∘ C^{bin}_{temp}Related builds
Sources & provenance
𝒞^{bin} = C^{bin}_{logic} ∘ C^{bin}_{layer} ∘ C^{bin}_{helix} ∘ C^{bin}_{pair} ∘ C^{bin}_{dist} ∘ C^{bin}_{pred} ∘ C^{bin}_{perc} ∘ C^{bin}_{bayes} ∘ C^{bin}_{temp}