verify_entropy.py

Download verify_entropy.py

What the script does

For every matrix and operator defined in the paper it builds the graph geometry of the cube \(Q_3\) and the prism \(Q_4\) with NetworkX (networkx.hypercube_graph), applies the paper's stated rule to form each operator, and diffs the result entrywise against the value printed in the manuscript. It then recomputes every derived number from those objects and diffs each against the reported value — 88 checks in all.

Objects covered include the cube and prism adjacency and Laplacian \(A_3,A_4,L_0,L_1\), the entanglement matrix \(M_{\mathrm{ent}}\), the disentangler \(D_{8}\), the incidence \(B\), \(I_z\), \(DB\), the composite \(C\), the deformed bond action \(M_{Q_3}\) and its inverse sub-blocks, and the weighted Laplacian \(L_\omega\).

The derived numbers

The residual capacity \(\xi^{*}=1/36\), the \(17/16\) identity, \(g^{2}=17/72\), the counts \(c_I=4\) and \(c_C=2\), the couplings through the full \(M_{Q_3}\) inverse giving \(g_L^{2}=0.253935\) and \(g_Y^{2}=0.226220\), the gravitational constant \(G_N\) (\(0.906033\) bare to \(0.999057\,\ell_P^{2}\)), the descent \(\exp(-1/\xi^{*})=\exp(-36)\), the vacuum expectation value \(v=246.9\) GeV, and the string tension \(\sqrt{\sigma}=422.4\) MeV.

How to run

Requirements: Python 3.8+ with NumPy and NetworkX. Run python3 verify_entropy.py; the final line reads

Scope

The property checks — eigenvalues, ranks, Betti numbers, positive-definiteness — require no answer key. The diff step verifies internal consistency: that the NetworkX geometry with the paper's rules reproduces the matrices in the text, and that those reproduce every derived number. It does not verify that the underlying physics is correct.