Topaas // Topology-as-a-Service · est. MMXXVI

Laplace ENGINE

The spectral graph engine for legacy code. We compute the topology of large software systems and hand the structure to the AI agents that will rebuild them.

ℒ { codebase } ⟶ Lv = λv ⟶ agent-ready spectrum

Transmit Read the shape

Domain: Spectral graph theory · Riemannian topology · LLM systems
Substrate: Legacy codebases · 10⁶+ LOC
State: Stealth · onboarding partners

ℒtopology as a service· spectral decomposition of legacy systems· ∂simplicial complex of intent· fundamental group of the codebase· π₁Calabi-Yau of computation· ℒtopology as a service· spectral decomposition of legacy systems· ∂simplicial complex of intent· fundamental group of the codebase· π₁Calabi-Yau of computation·

01 The Shape of Code

Coding agents see tokens.
Engineers see files.
A codebase is a manifold.

Functions, modules, and data flows form a high-dimensional simplicial complex with measurable topology — homology, fundamental group, spectrum. Most of what makes legacy systems hard is invariant under refactoring. We compute the invariants.

Ingest

Raw code · symbols · runtime traces · commit history

C = ⋃_i f_i

Lift to a graph

Build the dependency complex G = (V, E) and weight edges by behavioural coupling.

G ↪ K(C)

Compute the Laplacian

Diagonalise L = D − A. The spectrum encodes clusters, bottlenecks, and the true seams of the system.

L v_k = λ_k v_k

Hand to the agent

Structured intelligence — components, intent, behavioural commitments, risk surfaces — at a scale no context window can hold.

spec(L) → 𝒜

02 Field Operators

Three invariants we hold quietly, for now.

manifold Scale

Built for codebases that exceed any single context window by orders of magnitude. Where agents go blind, the engine sees a smooth manifold.

spectrum Structure

We extract the spectrum of the Laplacian — clusters, connectivity, bottlenecks, components. The unit of work becomes the eigenmode, not the line.

homotopy Continuity

Software deforms over time. We track the system up to homotopy — keeping the topology coherent as code, intent, and behaviour drift.

The same operator — Laplace's — runs through signal processing, graph theory, Riemannian geometry, and quantum mechanics. We brought it to legacy software.

03 Transmit

Quiet, not closed.

Investors, prospective design partners, engineers who think about software as a topological object — write to us.