docs(hf): add 33_Z_SPAR_Semantic_Parity/WHITEPAPER.md matching whitepaper standard

33_Z_SPAR_Semantic_Parity/WHITEPAPER.md

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+# Invention Class 33: Z-SPAR (Zymatica Semantic Parity and Repair Protocol)
+
+## Abstract
+Traditional Forward Error Correction (FEC) algorithms operate exclusively over syntactic bits, answering only whether transmitted binary frames survived channel noise. In distributed and heterogeneous generative AI communications—where independent large language models (e.g. SmolLM2, Qwen3.5, Gemma) operate across air-gapped radio mesh networks—a deeper failure mode emerges: **Semantic Model Drift**. Even under bit-perfect RF reception, two heterogeneous LLMs can reconstruct divergent conceptual actions.
+
+**Z-SPAR** introduces finite-field Reed-Solomon error correction over discrete multidimensional semantic coordinates ($\text{GF}(16)$ $\text{RS}(12,8)$) and invariant entity guards. By comparing the re-encoded semantic state against systematic parity symbols, the receiving node computes a **Semantic Syndrome**, locally repairing up to two drifted conceptual axes without natural language prompt retransmission.
+
+---
+
+## Mathematical Formulation
+
+### 1. $\text{GF}(16)$ Field Construction
+Calculated over the field $\mathbb{F}_{2^4}$ modulo the irreducible primitive polynomial:
+$$p(x) = x^4 + x + 1$$
+
+### 2. Systematic $\text{RS}(12,8)$ Semantic Codeword
+Given 8 discrete 4-bit semantic coordinates $S = [D, SD, OP, M, S, P, T, E] \in \mathbb{F}_{16}^8$, four parity symbols $P_0, P_1, P_2, P_3$ are generated via:
+$$P_j = \sum_{i=0}^{7} S_i \cdot \alpha^{(j+1)(i+1)}$$
+where $\alpha = 2$ is the primitive element of $\text{GF}(16)$.
+
+### 3. Semantic Syndrome & Auto-Repair
+The receiver re-encodes its model-reconstructed intent $\hat{S}$ into Language-U coordinates and evaluates syndrome vector:
+$$S_j = P_j \oplus \sum_{i=0}^{7} \hat{S}_i \cdot \alpha^{(j+1)(i+1)}$$
+* If $S_j = 0 \; \forall j$: **Exact Semantic Match** ($0\%$ drift).
+* If $1 \le \text{weight} \le 2$: **Autonomous Local Axis Restoration** (e.g. restoring $OP = \text{CLOSE}$ and $M = \text{MANDATORY}$).
+* If $\text{weight} > 2$: Emits a compact 3-byte **Semantic Repair Chirp** requesting targeted nibble reconstruction.
+
+---
+
+## 3-Layer Integrity Architecture
+1. **Coordinate Parity**: $\text{GF}(16)$ algebraic protection over continuous and discrete manifold axes.
+2. **Invariant Parity**: Hash and bit-level protection over critical entity IDs, numerical parameters ("50 PSI"), and negation flags.
+3. **Trajectory Parity**: Rolling sequence verification across multi-turn agent execution graphs.
+
+
+---
+
+## 📜 License & Upstream Developer Attributions
+
+- **Primary IP & Specification License:** Governed by the **[ZYMATICA COMMERCIAL & NOVEL-HOLDER COVENANT LICENSE (Version 2.0)](https://zymatica.space)** (LicenseRef-Zymatica-Covenant-2.0).
+- **Upstream Open-Source Acknowledgments:** Base neural model architectures, tokenizers, mathematical libraries, and cryptographic primitives derived from or interoperable with third-party open-source projects (including Alibaba Qwen, Google Gemma, Hugging Face Transformers/Tokenizers, Arkworks zkSNARKs, PyTorch, and ONNX Runtime) remain respectfully attributed to their original creators and are governed by their respective upstream licenses (Apache-2.0, MIT, BSD-3) under Section 3 of the Covenant License.