Structure Explorer
Interactive research tool for the GCD kernel K: [0,1]n × Δn → (F, ω, S, C, κ, IC). Five analysis modes let you compute invariants, sweep channels for sensitivity, map regime landscapes, verify identities, and explore seam budgets.
Quick Reference — The Six Invariants
What to look for
Sweep Configuration
Phase Diagram Configuration
Seam Budget Parameters
Kernel Radar — 6 Invariants
Sensitivity Sweep
Phase Diagram — Regime Landscape
Tier-1 Identity Verification
Bernoulli Field: S(c), κ(c), and f = S + κ
S + κ = 0 exactly at c = ½ (equator). f(θ) = 2cos²θ·ln(tan θ) verified < 10⁻¹⁶.
Seam Budget — Debit/Credit Ledger
Γ(ω) — Drift Cost Function
Γ(ω) = ω³/(1−ω+ε). Pole at ω=1; first weld at c ≈ 0.318 where Γ drops below 1.
Structural Reading
Advanced Research Tools
Composition algebra, cross-domain batch analysis, thermodynamic surfaces, and live orientation proofs.
System A
System B
Comparison & Composition
| Invariant | System A | System B | Composed | Rule |
|---|
Dual Radar — A vs B vs Composed
Composition Law Verification
Select Entities for Comparison
Cross-Domain Comparison
| Entity | Domain | F | ω | IC | Δ | S | C | Regime | Rank | IDs |
|---|
Multi-Entity Radar Overlay
Regime Distribution
τ_R* Thermodynamic Return Favorability
τ_R* = (1 − ω) / (Γ(ω) + α·C + ε) — higher values = more favorable return conditions. The surface over (ω, C) plane reveals the thermodynamic landscape.
Fixed Points on the τ_R* Surface
Live Orientation Receipts
These 10 receipts are the compressed derivation chains from scripts/orientation.py. Each receipt constrains classification — they are computed live in your browser to machine precision.
Proof Summary
Fixed Point Analysis — Three Special Points
Regime Partition (Monte Carlo, n=10K)
Mathematical Notes
Three algebraic identities (always true): F + ω = 1, IC ≤ F, IC = exp(κ).
One statistical constraint: S ≈ f(F, C) — entropy is asymptotically determined by fidelity and curvature.
Three effective DOF: 6 kernel outputs reduce to 3 independent dimensions (F, κ, C).
Frozen parameters: ε = 10⁻⁸, p = 3 (Cardano root), α = 1.0, tol = 0.005 — seam-derived, not chosen.
All computation runs client-side — no data leaves your browser.