UMCP v2.3.1 · 23 Domains · 746 Theorems · 20,337 Tests

Structure Explorer

Interactive research tool for the GCD kernel K: [0,1]n × Δn → (F, ω, S, C, κ, IC). Fifteen analysis modes across three tiers: core computation, identity verification, and deep structural diagnostics — all running client-side.

The Spine — Every Computation Follows This Path

CONTRACT
freeze → CANON
5 words → CLOSURES
thresholds → LEDGER
reconcile → STANCE
verdict

Omnia per spinam transeunt — Everything passes through the spine

15 Analysis Tools — Click to Jump

Core Computation
◉ Kernel Compute
Trace vector → 6 invariants + regime + radar chart
 〰 Sensitivity Sweep
Vary one channel 0→1, chart all 6 outputs
 ◧ Phase Diagram
2D heatmap of regime landscape across two channels
Verification & Seam
≡ Identity Lab
Verify F+ω=1, IC≤F, IC=exp(κ) + S+κ curve
 ⊢ Seam Budget
Full debit/credit breakdown + Γ(ω) chart
 ✓ Orientation Proofs
Live computation of all 10 structural receipts
Cross-Domain Analysis
⊕ Composition
Compose two systems — F arithmetic, IC geometric
 ▦ Batch Compare
Multi-domain side-by-side comparison table
 τ τ_R* Surface
Thermodynamic return heatmap over (ω, C)
Diagnostic Suite — Deep Structural Analysis
⊞ Extended IDs
10 identity checks
 ∂ Perturbation
Channel sensitivity
 θ Fisher Geometry
Flat manifold, f(θ)
 ⊡ Rank Analysis
DOF classification
 ⊞ Domain Compare
Pairwise matrix
 ≋ Multi-Sweep
All-channel overlay

Domain Presets — Pre-Loaded Systems

Click any preset to load it into the active tool below. Each button shows the regime color and fidelity.

Core Kernels
Standard Model
Astrophysics & Cosmology
Atomic & Nuclear
Neuroscience & Biology
Quantum Mechanics
Thermodynamics
Materials Science
Semiotics & Computing
Finance & Other
Corner Probes & Fixed Points

Quick Reference — The Six Invariants

F Fidelity
Σ wᵢcᵢ — what survives
fidelitas
ω Drift
1 − F — what is lost
derivatio
S Entropy
Bernoulli field uncertainty
entropia
C Curvature
stddev(cᵢ)/0.5 — coupling
curvatura
κ Log-integrity
Σ wᵢ ln(cᵢ) — logarithmic sensitivity
log-integritas
IC Integrity
exp(κ) — multiplicative coherence
integritas composita
■ Stable: ω < 0.038, F > 0.90, S < 0.15, C < 0.14 (12.5% of manifold)
■ Watch: 0.038 ≤ ω < 0.30 (24.4%)
■ Collapse: ω ≥ 0.30 (63.1%)
Tier 1 — Core Computation

What to look for

Custom
Σw = 1.000
Tier 2 — Cross-Domain Analysis

Advanced Research Tools

Composition algebra, cross-domain batch analysis, thermodynamic surfaces, and live orientation proofs.

System A

System B

Tier 3 — Deep Diagnostics

Diagnostic Suite

Deep structural analysis tools — identity networks, perturbation sensitivity, Fisher geometry, rank classification, and cross-domain comparison

Mathematical Reference

Three Algebraic Identities (always true by construction):

  • F + ω = 1 — Duality identity (complementum perfectum)
  • IC ≤ F — Integrity bound (solvability condition for trace recovery)
  • IC = exp(κ) — Log-integrity relation

One Statistical Constraint:

  • S ≈ f(F, C) — Entropy is asymptotically determined by (F, C) via CLT

Effective Degrees of Freedom:

  • 6 kernel outputs → 3 independent DOF (F, κ, C)
  • Rank-1: homogeneous (1 DOF) ⊂ Rank-2: binary (2 DOF) ⊂ Rank-3: general (3 DOF)

Frozen Parameters (seam-derived):

  • ε = 10⁻⁸ guard band · p = 3 (Cardano root of x³+x−1=0)
  • α = 1.0 coupling · tol = 0.005 seam width
  • c* = 0.7822 self-dual · c_trap = 0.3177 drift trap

All computation runs client-side — no data leaves your browser.

Collapsus generativus est; solum quod redit, reale est.