Purpose
The Geometry Garden is an interactive exploration space for mathematical structures, logical frameworks, and computational geometry — the tools underlying the Presignal research program. Topology, prime distributions, adelic geometry, and the Asymptotic Foundry all live here.
Asymptotic Foundry
The Asymptotic Foundry is the mathematical engine of Presignal Inc. — applying subtractive inversion to foundational problems. The Riemann Hypothesis construction proof framework (
DOI: 10.5281/zenodo.20263839) and Möbius Signal Conservation principle both emerged from this methodology.
Honeycomb Lattice — A2 Root Geometry
This very page is an instance of the geometry it studies. The hexagonal tessellation follows the A2 root lattice — the densest 2D packing — with all dimensions derived from Φ and all timing from the Schumann resonance (7.83 Hz). Geometry as interface.
Subtractive Methodology Applied to Math
Standard approaches add complexity. The Presignal approach subtracts noise — removing systemic variable exclusion to expose the underlying geometric signal. Applied to the Riemann Hypothesis, this means working with the prime distribution as a geometric object rather than an analytic one.
Golden Ratio — Φ
Φ = (1 + √5) / 2 = 1.6180339887…
Governs all spatial proportions in the Honeycomb Manifold architecture. Fibonacci sequence convergence ratio. Appears in logarithmic spirals governing natural signal propagation and the GPDM earth light emission geometry.
Schumann Resonance — 7.83 Hz
f₁ = 7.83 Hz → T = 0.12771 s
Earth-ionosphere cavity resonance frequency. Used as the base timing constant for all interface transitions and counter updates. Cross-referenced with GPDM earth lights correlation work and anomaly dashboard event timing.
Riemann Zeta Function — ζ(s)
ζ(s) = Σ(n=1→∞) n⁻ˢ = Π(p prime) (1 - p⁻ˢ)⁻¹
The Riemann Hypothesis conjectures all non-trivial zeros lie on the critical line Re(s) = 1/2. The Presignal construction approach frames this geometrically via the Asymptotic Foundry.
See preprint →
A2 Root Lattice — Honeycomb Tessellation
√3/2 · size = row offset
The A2 root lattice is the densest packing of circles in 2D. The honeycomb hex grid on this page is an A2 lattice instantiation — each cell offset by (hex_w + gap) × 0.5 per row. Basis vectors at 60° angle, consistent with the Schumann b-constant in logarithmic spirals.