verify_het_sg.py

Download verify_het_sg.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 — 242 checks in all.

Objects covered include the cube and prism adjacency and Laplacian A₃,A₄,L₀,L₁, the entanglement matrix M_ent, the disentangler D₈, 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_ω.

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 the bare \(g_{L}^{2}=0.253173\) and \(g_{Y}^{2}=0.229006\) and the bond-action \(g_{L}^{2}=0.255268\) and \(g_{Y}^{2}=0.227406\), the gravitational constant G_N (0.906033 bare to 0.999057 ℓ_P²), the descent \(\exp(-1/\xi^{*})=\exp(-36)\), the vacuum expectation value v=246.9 GeV, the string tension \(\sqrt{\sigma}=422.4\) MeV, and the scalar glueball mass \(m_{0^{++}}=1732.34\) MeV.

How to run

Requirements: Python 3.8+ with NumPy and NetworkX. Run python3 verify_het_sg.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.