Software

A place for reproducible scripts, data, and computational artifacts. Kept deliberately plain: the goal is clarity and longevity.

Spectral experiments

We compute the bottom spectrum of $L_1^{\uparrow}(T)$ and $L_1(T)$ for small graphs and track how eigenvalues evolve under triangle additions. This helps identify monotonicity failures, saturation points, and candidate extremizers.

Why computation matters here

practical reality

Closed-form spectra are rare outside highly symmetric families. Computation provides (i) conjecture discovery, (ii) counterexample discovery, and (iii) sanity checks for proofs.

Minimal code snippet

import numpy as np
from scipy.linalg import eigvalsh

def lambda_min_pos(A, eps=1e-10):
    ev = eigvalsh(A)
    for x in ev:
        if x > eps:
            return float(x)
    return 0.0

Suggested repo layout

code/
  spectra/
  homology/
data/
  examples.json
notes/
  experiments.md

Links (edit)

Sage/Jupyter: ...
GitHub: ...
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