Staging specs, codebases, and dedicated whitepapers

GENESIS_FORMAT_WHITEPAPER.md

@@ -2,6 +2,11 @@
 ## A Standard for Low-Rank SVD and Spectral Projection Weights Registry
 ### Watermark: `ip zymatica.space | astronautshe.com | devsone.com`
 
+<p align="center">
+  <img src="Logo.jpg" width="45%" />
+  <img src="language_u_logo.jpg" width="45%" />
+</p>
+
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 ## 1. Abstract
@@ -17,25 +22,25 @@ This document defines the layout specifications, mathematical transformations, a
 ## 2. Mathematical Specifications & Core Mechanics
 
 ### 2.1 Low-Rank SVD Matrix Factorization
-For any target projection matrix $W \in \mathbb{R}^{M 	imes N}$, the `.genesis` encoder performs truncated Singular Value Decomposition:
+For any target projection matrix $W \in \mathbb{R}^{M \times N}$, the `.genesis` encoder performs truncated Singular Value Decomposition:
 
-$$W pprox U \Sigma V^T$$
+$$W \approx U \Sigma V^T$$
 
 The top $R$ singular components are kept, scaling them to construct the active factors:
-$$\mathbf{U}_{	ext{active}} = U_{:, :R} \sqrt{\Sigma_{:R}}$$
-$$\mathbf{V}_{	ext{active}} = V_{:, :R} \sqrt{\Sigma_{:R}}$$
+$$\mathbf{U}_{\text{active}} = U_{:, :R} \sqrt{\Sigma_{:R}}$$
+$$\mathbf{V}_{\text{active}} = V_{:, :R} \sqrt{\Sigma_{:R}}$$
 
 These factors are quantized into 8-bit integer vectors ($U_q, V_q$) and scaled:
-$$U_q = 	ext{quantize}(U_{	ext{active}}, s_u)$$
-$$V_q = 	ext{quantize}(V_{	ext{active}}, s_v)$$
+$$\mathbf{U}_q = \text{quantize}(\mathbf{U}_{\text{active}}, s_u)$$
+$$\mathbf{V}_q = \text{quantize}(\mathbf{V}_{\text{active}}, s_v)$$
 
 During receiver-side inference, the original weight matrix is reconstructed JIT:
-$$\hat{W} = (U_q \cdot s_u) 	imes (V_q \cdot s_v)^T$$
+$$\hat{W} = (U_q \cdot s_u) \times (V_q \cdot s_v)^T$$
 
 ### 2.2 Spectral DCT-II Truncation
 To aggressively reduce parameter sizes for Level 4 and Level 6 representations, the `.genesis` compiler applies a 2D Discrete Cosine Transform over the factorized arrays, preserving only the top-16 low-frequency coefficients:
 
-$$D(i, j) = lpha_i eta_j \sum_{m=0}^{M-1} \sum_{n=0}^{N-1} f(m, n) \cos rac{\pi (2m+1)i}{2M} \cos rac{\pi (2n+1)j}{2N}$$
+$$D(i, j) = \alpha_i \beta_j \sum_{m=0}^{M-1} \sum_{n=0}^{N-1} f(m, n) \cos \frac{\pi (2m+1)i}{2M} \cos \frac{\pi (2n+1)j}{2N}$$
 
 High-frequency spectral coefficients are pruned, and the remaining values are packed using vectorized bit-arrangements.
 
@@ -67,3 +72,6 @@ To ensure zero degradation in representation fidelity, the codebase includes ver
 
 ## 5. Licensing & Copyright
 © 2026 Zymatica.space / Devs One. All rights reserved. Registered under proprietary Genesis Specification protocols.
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