A Topological Invariant from Generation Symmetry in the Critical Bias of Viro Patchwork on Four-Dimensional Reflexive Polytopes — Computational Data and Source Code

This deposit contains the complete computational data, source code, paper manuscript, and figures supporting the investigation of the critical bias for the Viro patchwork phase transition on four-dimensional reflexive polytopes from the Kreuzer-Skarke database. PRINCIPAL FINDINGS: A high-resolution computational study has been performed across thirteen reflexive polytopes spanning the lattice point range N = 201 to N = 680. Three principal results have been established: (1) A power-law scaling of the empirical critical bias: pc (N) = (2. 497 ± 0. 05) × N^ (-1. 021 ± 0. 01) with coefficient of determination R² = 0. 9975. (2) The dimensionless invariant pc × N has been demonstrated to remain constant across the polytope ensemble, with measured value: ⟨pc × N⟩ = 2. 1902 ± 0. 0111 (3) A coincidence has been identified between the empirical invariant and the group-theoretic constant 2 ln|Z₃| = ln 9 = 2. 197225, with statistical separation of 0. 633σ. The proposed identification connects the topological percolation threshold of patchwork complexes to the cyclic subgroup of the binary icosahedral group I* governing the generation structure in M-theory compactifications on G₂-holonomy manifolds. CONTENTS OF THE ARCHIVE: — data/pcₚarallelᵥ4ᵣesults. json: Complete numerical results for all thirteen polytopes, including (h11, h21) Hodge numbers, lattice point counts N, three threshold-crossing bias estimators, maximum observed component counts, and complete bias-resolved profiles at 396 bias values per polytope (5, 148 measurements per polytope). — data/pcᵥ4. log: Complete execution log with wall-clock timings for each polytope (total runtime: 17, 184 seconds on 12 cores). — code/pcₚarallelᵥ4. py: Main computational pipeline implementing polytope retrieval via CYTools, fine regular star triangulation, sign assignment, depth-first connected component enumeration, and parallel Monte Carlo estimation across 12 cores. — code/latticediagnostic. py: Diagnostic script verifying the CYTools lattice convention employed (lattice="N" with subsequent. dual () application). — code/figgeneration. py: Python/matplotlib script reproducing the three figures of the paper. — figures/: Three publication-quality PDF figures (scaling law, dimensionless invariant, and bias-resolved profiles). — paper/main. tex and references. bib: Complete LaTeX source of the manuscript with 119 bibliographic references. COMPUTATIONAL DETAILS: Each Monte Carlo experiment has employed T = 2, 000 independent trials at fine bias resolution Δp = 10^ (-4). The cumulative computational effort has comprised 1. 03 × 10⁷ single-trial component enumerations across the complete dataset. The pseudorandom number generation has employed the PCG64 algorithm seeded deterministically, ensuring complete reproducibility to machine precision. REPRODUCING THE RESULTS: The complete pipeline can be reproduced by: 1. Installing CYTools (https: //cy. tools) 2. Running: python3 code/pcₚarallelᵥ4. py3. Total runtime: approximately 4. 8 hours on 12 cores4. Comparing the resulting JSON file against data/pcₚarallelᵥ4ᵣesults. json CONNECTION TO PRIOR WORK: This investigation has built upon the systematic study of Viro patchwork complexes on four-dimensional reflexive polytopes documented in: — Radwan (2026), "Phase transition in connected components of Viro patchwork complexes for four-dimensional reflexive polytopes", DOI: 10. 5281/zenodo. 19588698— Radwan (2026), "Systematic survey of G₂ Betti numbers from Joyce-Karigiannis construction on the Kreuzer-Skarke database", DOI: 10. 5281/zenodo. 19582178— Radwan (2026), "Ab initio derivation of the compactification volume modulus K₀ from the binary icosahedral group I*", DOI: 10. 5281/zenodo. 19603730 The thirteen polytopes employed have been drawn from the unique candidate Calabi-Yau threefold CY₃ (13, 433) yielding the QGU Betti numbers (b₂, b₃) = (27, 451) plus twelve additional polytopes spanning the relevant lattice point range. LICENSE: This work has been released under the Creative Commons Attribution-NoDerivatives 4. 0 International License (CC BY-ND 4. 0). Citation of the original work is required for any use of the data or code. CONTACT: For questions regarding the data, code, or scientific content: Dr. Moustafa Amin RadwanSuez Canal University, Ismailia 41522, EgyptEmail: mosₐmin@edu. suez. edu. eg