Precision Verifier

Probatio per reditum — test by return.

The kernel's three algebraic identities hold to machine precision for every valid trace vector. This tool lets you verify that claim directly — generate random traces, enter custom channels, explore structural presets, audit seam budgets, and compose subsystems. All computation runs client-side.

The Three Algebraic Identities

These are not approximations or statistical claims. They are exact algebraic consequences of the kernel definition. Any trace vector that violates them indicates an implementation error, not a theoretical exception.

F + ω = 1
Duality Identity

Fidelity and drift are complementary — every unit of signal preserved is a unit not lost. Residual: exactly 0.0 across all traces.

complementum perfectum
IC ≤ F
Integrity Bound

Multiplicative coherence cannot exceed arithmetic mean. The solvability condition: c₁,₂ = F ± √(F² − IC²) requires IC ≤ F for real solutions.

limbus integritatis
IC = exp(κ)
Log-Integrity Relation

The multiplicative coherence is exactly the exponential of the log-integrity. Links additive (κ) and multiplicative (IC) measures of coherence.

integritas composita

Interactive Verifier

Bulk Identity Verification

Generate random trace vectors and verify all three algebraic identities (F + ω = 1, IC ≤ F, IC = exp(κ)) to machine precision.

Click "Run Verification" to begin.
Conformance Key — What Each Gate Requires
STABLE Regime (all four must hold)
  • ω < 0.038 — Drift below 3.8%. Reduce channel losses to decrease ω.
  • F > 0.90 — Fidelity above 90%. Raise low channels toward 1.0.
  • S < 0.15 — Bernoulli entropy below 0.15. Move channels away from 0.5 (toward 0 or 1).
  • C < 0.14 — Curvature below 0.14. Reduce spread between channels (make them more uniform).
WATCH Regime

0.038 ≤ ω < 0.30 — or any Stable gate not met. System is operational but drifting.

COLLAPSE Regime

ω ≥ 0.30 — Drift exceeds 30%. Significant channel degradation.

CRITICAL Overlay

IC < 0.30 — Multiplicative coherence is dangerously low. At least one channel is near ε. Raise the weakest channel to restore IC.

How to Restore Conformance
  1. Identify the weakest channel — the one closest to 0. This is the IC killer (geometric slaughter).
  2. Raise the weakest channel first — raising a channel from 0.01 to 0.30 has more impact than raising one from 0.80 to 0.95.
  3. Reduce channel spread — if C is too high, make channels more uniform.
  4. Check regime gates in order: ω first (is drift OK?), then F, S, C. The first failing gate tells you where to act.
  5. IC ≤ F is structural — you cannot increase IC past F. To raise IC, you must also raise F (the arithmetic mean).
Three Algebraic Identities (Always True)
  • F + ω = 1 — Duality identity. Exact to 0.0e+00. If this fails, the computation is wrong.
  • IC ≤ F — Integrity bound. The solvability condition. If IC > F, a channel was misclamped.
  • IC = exp(κ) — Log-integrity relation. Links multiplicative and additive coherence.

Five Verification Modes

1. Random Trials

Generate thousands of random trace vectors and verify all three identities across every one. Configure channel count and trial count. Reports max residual and pass/fail statistics.

2. Manual Trace

Enter channel values directly and see per-gate conformance in real time. Includes conformance guidance — the tool shows exactly which invariant failed and what would need to change.

3. Preset Explorer

Six structural presets (equator, near-zero, near-one, mixed, dead-channel, all-ones) plus 32 cross-domain entities. Click any preset to verify identities with known-good data.

4. Seam Budget

Interactive seam accounting: compute Γ(ω), D_C (curvature debit), and Δκ (budget balance). Verify that the conservation budget Δκ = R·τ_R − (D_ω + D_C) closes within tolerance.

5. Composition

Compose two independent traces and verify the composition algebra: IC composes geometrically (IC₁₂ = √(IC₁·IC₂)), F composes arithmetically (F₁₂ = (F₁+F₂)/2).

Why Five Modes?

Each mode tests a different aspect of kernel correctness: algebraic identity, input sensitivity, domain specificity, seam closure, and compositional consistency. Together they cover the full verification surface.

Verification Methodology

Precision Standard

  • • Machine epsilon: ~2.22 × 10⁻¹⁶ (IEEE 754 double precision)
  • • Guard band: ε = 10⁻⁸ (frozen — prevents pole at ω = 1)
  • • Seam tolerance: tol = 0.005 (frozen — width where IC ≤ F holds at 100%)
  • • F + ω = 1: exact to 0.0e+00 residual (not approximate — exactly zero)
  • • IC = exp(κ): residual < 10⁻¹⁶

What the Verifier Proves

  • • The browser's JavaScript engine reproduces the same identities as the Python test suite
  • • The frozen parameters (ε, p, α, tol) produce the same kernel outputs across implementations
  • • The three identities hold universally — no trace vector can violate them
  • • Composition algebra (geometric IC, arithmetic F) is exact
  • • This is the Cognitive Equalizer in action: same data + same contract = same verdict
Non agens mensurat, sed structura. — Not the agent measures, but the structure.
Numeri sunt intellectus. — The numbers are the understanding.