Riemann Engine
A specialized mathematical instrument designed to visually stress-test the Riemann Hypothesis through an Oracle-Observer architecture.
Riemann Engine
A specialised mathematical instrument designed to visually stress-test the Riemann Hypothesis (RH) under discrete scale-gauge transformations. It functions as an Analytic Interferometer, detecting structural instabilities in the Riemann Zeta function's analytic continuation.
Core Capabilities
| Compute | Visualise | Experiment |
|---|---|---|
| High-precision zeta function computation at 50 decimal places via Python/mpmath Oracle. | Interactive real-time visualisation of complex-plane transformations and zero distributions. | Seven distinct experiments probing the structure and invariance of the critical line. |
Architecture: Oracle-Observer Pattern
The system enforces a strict separation of concerns to ensure computational integrity:
The Oracle (Python/mpmath)
Computes integrals, summations, and zeros at 50 decimal places of precision. Pure mathematics — no rendering, no approximation, no shortcuts.
The Observer (Next.js/Recharts)
Pure visualisation with a Zero Math Policy — no computation in the frontend. The Observer renders what the Oracle computes, maintaining a clean separation between calculation and display.
Experiments
EXP-01: Equivariance (Scale Invariance)
Tests whether the zeta function maintains structural properties under scale transformations. Looks for invariance in zero distribution across dilation parameters.
EXP-02: Centrifuge (Rogue Zero)
Searches for structural anomalies — zeros that deviate from the critical line under specific transformations. The centrifuge applies rotational probes to the zero distribution.
EXP-03: Falsification (Beta=Pi)
Systematic falsification attempt using β = π as a probe parameter. Tests the critical strip for instability under transcendental scaling.
EXP-04: Translation vs Dilation
Compares the behaviour of the zeta function under horizontal translation versus vertical dilation in the complex plane.
EXP-05: Zero Correspondence (Lattice Hypothesis)
Investigates lattice-like structure in the zero distribution — testing whether zeros exhibit periodic or quasi-periodic patterns.
EXP-06: Critical Line Drift
Monitors the position of zeros relative to the critical line (Re(s) = 1/2) under progressive transformation to detect systematic drift.
EXP-07: Centrifuge Fix
Refined centrifuge experiment with corrected rotational parameters and enhanced precision.
Zeta Transform Explorer
A standalone visualisation module rendering the conformal mapping of the zeta function with high-precision (50 dps). Multiple τ-lenses allow different views of the input and output planes, revealing the geometric structure of the analytic continuation.
Related Solutions
- Demonstrate Ideas — Interactive mathematical visualisations
- Present Research — Number theory research publication
Related Use Cases
- For Education — Number theory education through interactive visualisation
- For Media — Mathematical research publishing
- For Software — Computational mathematics tooling