Formula Builder
Algebra est cautio, non porta. — The algebra is a warranty, not a gate.
Build arbitrary kernel expressions, bind variables to sliders, evaluate in real time, and sweep over parameter ranges. All standard mathematical functions plus the full kernel vocabulary are available. Computation runs client-side.
How It Works
Variable Bindings
Each kernel invariant (F, ω, S, C, κ, IC) is bound to a slider. Adjust any slider and all expressions re-evaluate immediately. Values are clamped to their natural domains.
Expression Engine
Type any mathematical expression using the kernel symbols. The evaluator supports standard functions (exp, log, sqrt, abs, sin, cos, etc.) and arithmetic operations. Expressions are parsed safely — no arbitrary code execution.
Parameter Sweep
Sweep any variable over a range and visualize how the expression changes. Useful for finding critical points, phase transitions, and regime boundaries where kernel behavior changes qualitatively.
Interactive Formula Builder
Formula Builder
Build and evaluate kernel expressions with live results. Variables are bound to slider values. All standard math functions supported.
Variable Bindings
Expression
Preset Expressions
Sweep: Evaluate Over Range
Example Expressions
F + omega Duality identity — always equals 1 F - IC Heterogeneity gap Δ — always ≥ 0 exp(kappa) - IC Log-integrity residual — should be ~0 IC / F Coherence ratio — 1.0 = homogeneous, low = geometric slaughter S + kappa Entropy-integrity sum — zero at equator (c = ½) omega**3 / (1 - omega + 1e-8) Γ(ω) — drift cost with Cardano exponent p = 3 Variable Reference
| Variable | Symbol | Range | Description |
|---|---|---|---|
| F | F | [0, 1] | Fidelity — what survives collapse |
| omega | ω | [0, 1] | Drift — what is lost (1 − F) |
| S | S | ≥ 0 | Bernoulli field entropy |
| C | C | [0, 1] | Curvature — coupling to DOF |
| kappa | κ | ≤ 0 | Log-integrity |
| IC | IC | (0, 1] | Integrity composite — exp(κ) |
All variables are computed from the trace vector c ∈ [0,1]ⁿ with weights w ∈ Δⁿ.