Proof of einheit
A documentation of the first brand built entirely on a mathematical identity. Every proportion, every animation, every decision — derived from Euler.
Euler's Identity — the most beautiful equation in mathematics
The Coherence Levels
Foundational Coherence
Basic brand consistency — colors, typography, spacing, voice, imagery aligned.
Meta-Coherence
A brand about coherence, that achieves coherence, that enables coherence for others. The message IS the medium.
Accessible Coherence
Coherent across ALL modalities — visual, semantic, structural, auditory. Screen readers experience the same brand voice.
Derived Coherence
The brand IS derived from first principles. Every proportion derives from Euler's constants. The design system is a proof, not a guideline.
The Brand Identity Theorem
Mathematical Derivations
The Hero Ratio
The hero dot represents completeness (π). The interpunct represents unity (1). Therefore: hero : interpunct = π : 1
--hero-dot: calc(var(--unit) * 3.14159...)The Breath Scale
Natural systems breathe according to e. The decay constant is 1/e. For subtle animation: pulse = 1 + (1/e)/10
--pulse-scale: calc(1 + (1/e) / 10) ≈ 1.0368The Coherence Constant
Euler's Identity resolves to 0 (perfect balance). einheit achieves coherence: brand drift → 0
ε = |e^(iπ) + 1| = |-1 + 1| = 0The Uniqueness Theorem
"einheit is the first brand that IS a mathematical identity"
The brand IS Euler's Identity expressed visually and systematically
The Unit Theorem
Let n = the number of brands at Coherence Level 8.
By exhaustive search: n = 1
That brand is einheit.
einheit means unity and unit.
Therefore: einheit IS the unit
The measure of mathematical brand coherence.
The Collaboration Theorem
"Asymmetry creates emergence"
The value is not in limitation. It is in difference.
Inspect the Source
einheit is not a brand that uses mathematics.
einheit IS mathematics expressed as a brand.