**NOTICE**

**Modular Assembly of High-Performance Logical Blocks from the Lorentzian Causal Diamond - Verification Suite**

This software implements and verifies the exact algebraic scaling, distance certifications, and geometric constructions presented in the paper:
> Yannick Schmitt. (2026). Modular Assembly of High-Performance Logical Blocks from the Lorentzian Causal Diamond: Pareto-Optimal Finite-Block Codes, Asymmetric Distance Families, and an E8 Structural Obstruction. Zenodo. https://doi.org/10.5281/zenodo.19484043

The verification suite generates the novel Augmented-Seed code families and implements the exact Integer Linear Program (ILP) distance oracle. Key highlights of the implementation include:

| Component / Code | Parameters | Highlights |
| :--- | :--- | :--- |
| **Augmented F₆** | [[112, 4, (6, 6)]] | Pareto-optimal finite block; best FOM at N~100 ($kd^2/N \approx 1.29$) |
| **Augmented Z-Bias** | [[176, 32, (3, 6)]] | Asymmetric distance profile tailored for Z-biased noise hardware |
| **Augmented Self-HGP** | [[208, 16, 6]] | Distance $d=6$ proven algebraically via Tillich–Zémor |
| **D4 HGP (Corrected)** | [[193, 25, (4, 6)]] | Retracts earlier sampled $d \ge 67$; exact distances proven via ILP |
| **ILP Distance Oracle** | Exact Certification | Solves GF(2) logical weights via integer slack variables in <100ms |
| **E₈ Obstruction** | [[28, 0]] Code | Proves puncturing is structurally blocked by 7-disconnected-4-cycles |

If you use this code, the exact ILP distance optimization algorithm, or the generated CSS matrices in your research, please cite the paper mentioned above.