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    "description": "<p>This repository contains the complete research artifact and computational verification suite for scaling the discrete Lorentzian causal diamond into high-performance Quantum Low-Density Parity-Check (qLDPC) and finite-block codes. By systematically exploring algebraic amplification (Hypergraph Product), geometric tessellation (toric scaling), and lattice enrichment ($E_8$ Lorentzian substrates), this work identifies precise structural obstructions in existing approaches and introduces novel, Pareto-optimal CSS codes tailored for near-term hardware in the $N \\sim 100\\text{--}200$ physical qubit regime.</p>\n<p><strong>Scientific Contributions</strong></p>\n<ol>\n<li><strong>The Augmented-Seed Code Family</strong>: The central discovery that a specific weight-3 row (one of 64 in two $B_4$ symmetry orbits) appended to the primal causal diamond seed raises the classical distance from 4 to 6. This breaks the intrinsic distance ceiling of the basic geometry, unlocking a family of finite-block codes that significantly outperform planar codes (e.g., surface/toric codes) at small block sizes.</li>\n<li><strong>Methodological Warning on Sampling Blindness</strong>: Demonstration that Belief Propagation (BP)-style random sampling fails catastrophically in high-dimensional kernels. Earlier sampled bounds of $d \\ge 67$ for the `[[193, 25]]` code are formally retracted; an exact Integer Linear Program (ILP) oracle is introduced, definitively proving $d = 4$.</li>\n<li><strong>The $E_8$ Structural Obstruction (Theorem 4.5)</strong>: Rigorous proof that the 28-qubit $E_8$ Lorentzian code cannot be punctured to yield a valid quantum code. Its 7-disconnected-4-cycle geometry guarantees $d_Z = 1$ after any single row drop, pointing toward the Euclidean $E_8$ root lattice as the necessary next step.</li>\n<li><strong>Na&iuml;ve CSS Lift Theorem (Theorem 5.3)</strong>: Algebraic proof that setting $H_X = \\ker(H_Z)$ definitionally forces $k=0$, regardless of chain or torus topology, resolving anomalies in earlier geometric scaling attempts.</li>\n</ol>\n<p><strong>Highlighted Code Families</strong><br>The augmented geometric construction yields a frontier of codes optimized for neutral-atom and trapped-ion architectures, including:</p>\n<ul>\n<li><strong>[[112, 4, (6, 6)]]</strong>: Achieves an exceptional figure of merit $kd^2/N \\approx 1.29$, making it a highly efficient logical block for near-term implementation.</li>\n<li><strong>[[176, 32, (3, 6)]</strong>: Features an asymmetric distance profile naturally aligned with the $Z$-biased noise characteristic of superconducting hardware.</li>\n<li><strong>[[208, 16, 6]]</strong>: A self-hypergraph product code with $d=6$ proven algebraically via the Tillich&ndash;Z&eacute;mor theorem.</li>\n</ul>\n<p><strong>Artifact Contents</strong></p>\n<ul>\n<li>Verification Suite (`verification_modular_assembly.py`): A unified, self-contained Python script using `scipy.optimize.milp` that computationally verifies every theorem, constructs all augmented seeds, performs exact distance certifications via ILP in under 100ms per operator, and reproduces the geometric obstructions.</li>\n<li>Manuscript: Complete LaTeX source files and compiled PDF of the paper.</li>\n</ul>\n<div class=\"container\">\n<div class=\"mat-expansion-panel-content-wrapper\">\n<div class=\"mat-expansion-panel-content\">\n<div class=\"mat-expansion-panel-body\">&nbsp;</div>\n</div>\n</div>\n</div>\n<p>&nbsp;</p>",
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    "subjects": [
      {
        "subject": "causal diamond"
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      {
        "subject": "hypergraph product"
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      {
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    "title": "Modular Assembly of High-Performance Logical Blocks from the Lorentzian Causal Diamond: Pareto-Optimal Finite-Block Codes, Asymmetric Distance Families, and an E\u2088 Structural Obstruction"
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