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Antigravity Agent
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docs(zenodo): Add algorithm pseudocode to B001 description (#435)
- Added Algorithm 1: Ternary Transformer Forward Pass with sacred attention - Mathematical notation for layer normalization and φ-scaling - Complexity analysis (O(n²) for attention) - Key innovations: φ-based cache threshold, sparse attention, ternary arithmetic NeurIPS/ICLR requirement: Algorithm boxes for reproducibility φ² + 1/φ² = 3 | TRINITY
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docs/research/zenodo_B001_enhanced_v7.0.md

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@@ -163,7 +163,65 @@ lr(step) = lr_max × 0.5 × (1 + cos(π × step / total_steps))
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- **Assumptions:** Normal distribution, equal variance
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- **Thresholds:** very_strict (p<0.001), strict (p<0.01), moderate (p<0.05), lenient (p<0.10)
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### 2.4 FPGA Implementation
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### 2.5 FPGA Implementation
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### 2.4 Algorithm: Ternary Transformer Forward Pass
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**Algorithm 1:** HSLM Forward Pass with Sacred Attention Scaling
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```
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Require: Input tokens X = [x₁, ..., xₙ] (n tokens)
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Require: Weight matrices W_q, W_k, W_v ∈ {-1, 0, +1}^{d×d}
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Require: Layer norm parameters γ, β
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Require: Cache threshold τ = φ⁻¹ ≈ 0.618
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1: // Token embedding
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2: E ← TernaryEmbedding(X) // E ∈ {-1, 0, +1}^{n×d_model}
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3:
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4: // For each transformer block ℓ = 1 to L (L=9)
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5: for ℓ = 1 to L do
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6: // Layer normalization (φ-scaled)
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7: γ_φ ← φ^(ℓ/10) // Progressive scaling
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8: X_norm ← LayerNorm(E, γ·γ_φ, β)
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9:
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10: // Sacred attention with cache
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11: Q ← X_norm · W_q // Queries: [n × d_k]
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12: K ← X_norm · W_k // Keys: [n × d_k]
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13: V ← X_norm · W_v // Values: [n × d_k]
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14:
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15: // Attention scaling with φ
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16: S ← Q · Kᵀ / √(d_k)^(φ^(-3)) // Scaled scores
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17:
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18: // Sparse attention via cache threshold
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19: M ← (S > τ) // Mask: keep only top correlations
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20: A ← Softmax(M ⊙ S) // ⊙ = element-wise multiply
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21:
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22: // Context aggregation
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23: C ← A · V // [n × d_k]
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24:
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25: // Feed-forward network
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26: F ← ReLU(C · W₁ + b₁) · W₂ + b₂
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27:
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28: // Residual connection + layer norm
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29: E ← E + LayerNorm(C + F, γ, β)
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30: end for
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31:
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32: // Output projection
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33: logits ← E · W_out // [n × vocab_size]
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34: return logits
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```
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**Complexity Analysis:**
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- Time: O(n²·d_model·L) for attention (standard transformer)
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- Space: O(n·d_model·L) for activations
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- Ternary multiplication: O(1) per operation (LUT-based)
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**Key Innovations:**
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1. **φ-based layer norm scaling** (line 7): γ_φ = φ^(ℓ/10) for deep network stability
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2. **Sparse attention via cache threshold** (line 19): τ = φ⁻¹ ≈ 0.618
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3. **Ternary arithmetic**: All multiplications use {-1, 0, +1} encoding
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### 2.6 FPGA Implementation
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**Target:** QMTech XC7A100T (Artix-7 100T)
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@@ -180,7 +238,7 @@ lr(step) = lr_max × 0.5 × (1 + cos(π × step / total_steps))
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## 3. Theoretical Foundations
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### 3.1 Trit Entropy Theorem
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### 3.2 Trit Entropy Theorem
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**Theorem 1 (Information Maximality):** Balanced ternary encoding {-1, 0, +1} maximizes per-symbol entropy for n-ary codes with n ≤ 4.
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