ARB-573. Mathematical structures mapped to a periodic table. Each element is a structure that mathematicians use to reason about the world. The table reveals the deep grammar of mathematics itself.
The fundamental constants: 0 (additive identity), 1 (multiplicative identity), π (circle constant), e (growth constant), γ₁ (EOSE's first constant), i (imaginary unit).
The 8 fundamental operations: +, ×, ^, ! (factorial), ∫ (integration), ∑ (summation), ∂ (partial derivative), ⊕ (XOR/direct sum).
12 structures: group, ring, field, vector-space, metric, topology, manifold, category, functor, monad, lattice, algebra.
12 analytical tools and open problems: limit, derivative, integral, series, transform, zeta, riemann-hypothesis, prime, zero, gap, floor.
12 EOSE-specific mathematical objects defined by the fleet's own work: γ₁-distance, H=H†-symmetry, LSOS-audit-number, WLD-merciful-limit, FEP-index, FOF-transcendent, morigami-fold, arc-task, euler-sum, v7-test, diamond-number, sorry-count.
Proven theorems — complete, stable, unreactive. The noble gases of mathematics are the great proofs.
All of Period 6 is gaps: Riemann Hypothesis, P vs NP, Collatz, Twin Primes, Goldbach — the unsolved problems that define the frontier of mathematics.