Type a zero, an integer, a height, a point σ+it, or a curve over Fp. Press =. The dictionary is every representation the instruments have built for that object; the board is what each RH-equivalent statement says about it, each row labeled by what it is. The dial is the Bergen Disc; the tower is the live Hankel test; the windows are Paper 14's A(m). Ten thousand zeros, everything recomputed in your browser and self-checked against the committed Python twin.
Every row above is computed for this input, exactly. RH is the statement that every EQUIVALENT row holds for every input. That quantifier — “every” — is the one key this calculator does not carry; it is the door, and every RH-equivalent parks it somewhere (the Infinity-Relocation Catalog, IMM Paper 22). FREE rows hold for any mirror-symmetric zero set and detect nothing; EQUIVALENT rows are theorems of the form “RH ⟺ …”, and they can fail — the traitor and the displaced-zero presets show them failing; MEASURED rows are descriptive; DISPROVEN rows are the strong forms history killed; PROVEN WORLD is the one place the door is open.
Nothing on this page proves or disproves the Riemann Hypothesis. It computes finite instances of equivalent statements and displays each at its grade. Zero ordinates: Odlyzko's table, first 10,000 of 100,000 (9 decimals). Sieve cap 2·10⁶ for the counting functions; 3,445,000 for Paper 14's prime term. ζ(s) by Euler–Maclaurin (12 Bernoulli terms), log Γ by Lanczos; both verified against mpmath in the twin. Eigenvalues by cyclic Jacobi, whose relative accuracy on a positive matrix is bounded by κ(D−½HD−½)·ε (Demmel–Veselić 1992) — that bound is the certification floor printed next to every λmin. Citations flagged as from memory in the twin's comments: Lagarias 1999, Robin 1984, Hasse 1933, Schoenfeld 1976, Bays–Hudson 2000, Rubinstein–Sarnak 1994, Barnet-Lamb–Geraghty–Harris–Taylor 2011, Demmel–Veselić 1992. The traitor zero is a certified zero of the Davenport–Heilbronn function (winding number 1, 2026-09-11) — a function with a functional equation and real coefficients but no Euler product.
Twin: receipts/rh_calculator_twin.py writes the embedded reference values; receipts/check_page_math.js runs this same self-check under Node. Click the self-check line for the per-item list.