Comment by JonScott79

Jon here. I built Pythos (https://pythos.lanzar.me) because existing EdTech tools usually fall into one of two traps:

LLM tutors hallucinate calculations or dump full homework solutions: They can't do exact symbolic algebra reliably, and they spoon-feed answers instead of actually teaching students how to think through the derivation. Interactive physics sandboxes (like PhET) are silent: You can drag a slider or watch a pendulum swing, but when you get confused by the underlying equations, the simulation can't talk to you, diagnose your misconceptions, or walk you through the math. Pythos is an open, 100% free educational platform that merges deterministic computer algebra, real-time interactive physics simulations, and Socratic guidance. No paywalls, no logins required, and zero student fees.

Here is the complete architectural and functional breakdown of what’s under the hood:

1. Dual-Engine Mathematical Ground Truth (Zero Hallucinations) Instead of trusting an LLM’s stochastic text generator for calculations, Pythos uses a multi-tier deterministic verification bridge:

SymPy Computer Algebra System (CAS): An authoritative backend symbolic math engine that computes exact derivatives, integrals, limits, differential equations, and algebraic equivalence. Client-Side Math.js & Deterministic Router: Intercepts calculations, unit conversions, and known STEM queries, resolving them deterministically in < 2ms without burning unnecessary LLM tokens. Claim-Verification & Withholding Gateway: Every mathematical claim generated by the conversational model is parsed into formal symbolic assertions and verified against the CAS before being displayed. If a step contradicts mathematical truth, Pythos withholds the error and Socratic-guides the student. 2. The PhET-Style Simulation Lab (17 Interactive Instruments) Accessible right from the top toolbar ([ Sim Lab ]), students can launch full-stage, slider-controlled interactive simulations that update in real time with high-contrast, responsive canvas rendering:

Mechanics & Dynamics (10 Models): Classical Projectile Motion: Parabolic ballistics under uniform gravity, apex tracking, ground range, flight time, and launch/apex velocity vectors. Newton's Second Law & Inclined Plane: $F_{\text{net}} = ma$ on adjustable inclines with mass, applied force, gravity, and kinetic friction coefficients. Conservation of Mechanical Energy: Trading gravitational potential energy ($mgh$) for kinetic energy ($\frac{1}{2}mv^2$) with real-time bar graphs. 1D Momentum & Collisions: Elastic and inelastic particle collisions with momentum and kinetic energy conservation tracking. Hooke's Law & Oscillations: Restoring spring forces ($F = -kx$), frequency, and elastic potential energy ($U = \frac{1}{2}kx^2$). Simple Harmonic Pendulum: Period calculations with Borda large-angle corrections ($T \approx 2\pi\sqrt{L/g}$), restoring torque ($\tau = -mgL\sin\theta$), and energy distribution. Wave Mechanics & Propagation: Continuous harmonic waves examining amplitude, frequency, phase, wave speed ($v = f\lambda$), and wavelength. Geometric Optics & Snell's Law: Planar boundary refraction ($n_1\sin\theta_1 = n_2\sin\theta_2$), media refractive index presets (Air, Water, Glass, Diamond), angle arcs, and automatic Total Internal Reflection (TIR) detection. Archimedes' Buoyancy & Upthrust: Hydrostatic displacement ($F_b = \rho_f V g$), dynamic waterline calculations, material densities (Wood, Ice, Steel, Gold), and net force vector equilibrium. Direct-Current Circuits & Ohm's Law: $V = IR$ with adjustable electromotive force, resistance, and current flow animations. Mathematics & Geometry (6 Models): Right Triangle Inspector: Interactive Pythagorean geometry ($a^2 + b^2 = c^2$), trigonometric ratios ($\sin, \cos, \tan$), and dynamic angle calculations. Unit Circle Trigonometry: Continuous angle rotation ($\theta$) mapping sine and cosine projections onto the Cartesian coordinate plane in radians and degrees. Differential Calculus & Tangent Lines: Secant lines converging to instantaneous derivatives ($f'(x)$) with zoomable slope tangents. Circle & Sector Geometry: Radius, circumference, area, arc length ($s = r\theta$), and sector area calculations. Normal Distribution & Gaussian Curve: Standard deviation ($\sigma$), mean ($\mu$), and empirical probability density shading ($68-95-99.7%$ rule). Exponential Growth & Decay: Compound growth modeling $N(t) = N_0 e^{kt}$ with doubling times and half-life projections. Chemistry & Thermodynamics (1 Model): Ideal Gas Laws: Kinetic molecular container modeling pressure, volume, temperature, and moles ($PV = nRT$). 3. The "Ask Pythos" Socratic Bridge Inside any active simulation, students can adjust sliders, observe an unexpected physical phenomenon (e.g. Total Internal Reflection or a floating block), and click Ask Pythos .

This seamlessly passes the active state parameters directly into the conversation. Rather than answering for them, Pythos uses a "Give the Student the Next Step" loop:

Guides learners one cognitive step at a time. Validates student derivations. Catches misconceptions early with targeted hints rather than endless trivia. 4. Built-in STEM Utilities 2D Function Grapher: Canvas-based continuous plotting for scalar curves with pan/zoom and coordinate readouts. CAS / Scientific Calculator: Built-in keypad with exact root and fraction parsing. Multimodal Vision Input: Students can drag-and-drop or snap phone photos of math worksheets; an OCR normalizer extracts and cleans up fractions, matrices, and expressions for tutoring. Direct Feedback & Tool Requesting: Students can click the Report button on any message to request new simulations or report bugs directly to our engineering team without support-ticket red tape. Tech Stack: Frontend: Vanilla JavaScript + HTML5 Canvas (zero heavy frontend frameworks, instant load times, clean dark/light classical aesthetic, fully accessible). Backend Gateway: Node.js / Express deployed on Railway. CAS & Verification: Python SymPy + Math.js. Inference Pipeline: Hybrid local/remote LLM orchestration (Ollama + Groq/Llama-3 reasoning) with strict deterministic fast-paths. The web app is live at https://pythos.lanzar.me.

I’d love for teachers, students, and engineers to try it out, poke holes in the physics models, and let me know what tools or simulations you'd like to see added next!