The zeros of the zeta function seen through triangles: a geometric and experimental reading of the Weil form

We translate several known constructions on the zeros of ζ into an elementary geometry.Each prime p is a triangle of height log p, each power pkis a stack of k triangles, and eachnatural number acts as a clock of speed log n. With these pieces we write the Riemann–Siegelapproximation, the truncated Weil form and three operators from earlier work by the author.With five stacks and 90 digits of precision, the minimal-energy state of the Weil formreproduces the first eight zeros with error below 2 · 10−13, and the first twelve agree tosix decimals. Small alterations of the primes break positivity, and the same constructionapplied to the Davenport–Heilbronn function yields a stable negative minimal value. Noneof this proves the Riemann Hypothesis: all results are numerical or reformulations,and the passage to the limit remains open. The code reproduces every table and figure.