Origins: Pliny, the Go Board, and the Swarm

This page keeps the founding framing of Gaius. It is history and design intent, not the current architecture; for what runs today start at the Introduction. Where a capability below is still live, the page that owns it is linked; where it is retired, it says so.

Gaius was named after Gaius Plinius Secundus (Pliny the Elder), whose Naturalis Historia catalogued the natural world across 37 books. The first product was a terminal interface for navigating high-dimensional embedding spaces: it computed persistent homology and Ollivier–Ricci curvature on the original embeddings, projected the results onto a discrete 19×19 lattice via UMAP, and rendered topological and geometric features as interactive overlays.

The founding capabilities

1. Lattice projection — UMAP (cosine metric, k=15 neighbours, min_dist=0.1) maps embedding vectors to continuous 2D coordinates, quantised to a 19×19 integer lattice by rounding and clipping to [0, 18]. Two 9×9 orthographic mini-grids follow the cursor: an Embed view of the local cosine-similarity neighbourhood and an Iso view rendering scalar fields (curvature, total persistence, complexity) as elevation maps via inverse-distance-weighted interpolation (power=2). Live in the TUI (The Grid Metaphor, Embeddings); the vectors are ColBERT-Zero agg vectors, 128-d.

2. Persistent homology (H₀–H₂) — Ripser computes a Vietoris–Rips filtration over the cosine distance matrix of the original embeddings, producing barcodes for dimensions 0 through 2; intervals with persistence > 0.1 are marked significant (a heuristic threshold, no stability analysis). Live (Persistent Homology).

3. Ollivier–Ricci curvature — discrete Ricci curvature on a k-nearest-neighbour graph (k=15, cosine) with the OTD method, α=0.5; per-node curvature is the mean of incident edge curvatures; curvature, gradient and divergence fields project to the Iso mini-grid. Live (Grammar Engine).

4. Multi-agent exploration — seven agents (Leader, Risk, Optimizer, Planner, Critic, Executor, Adversary) navigated the lattice with role-specific positioning: Leader sought cluster centroids, Risk sat at semantic boundaries, Adversary sampled uniformly. Training used the RASE framework, where constraints compose declaratively (AllOf/AnyOf/Not) and a ground-truth oracle produces verifiable rewards. RASE is live (RASE Metamodel); the swarm and its 768-d latent working memory are on the retirement list — they predate ColBERT-Zero and the cognition cycle.

5. Modal interface — vim-style navigation (hjkl, slash commands, overlay toggles) over the lattice and the gRPC service graph. Live (The TUI).

The founding pipeline

Embed → Project → Filtration → Curvature → Exploration → Rendering. Embed, Project, Filtration, Curvature and Rendering (LuxCore) are current; Exploration by the swarm is not. The lattice was conceived as both a visualisation surface and a discrete approximation of the data manifold, and that reading still holds for the TUI.

What changed

The peer described in the Introduction grew around this core: a thinking lane and a cognition cycle instead of a swarm; ColBERT-Zero instead of the 2025 single-vector embedders; the Signals lattice (Airflow clock, YuniKorn admission, Metaflow flows, the shared warehouse) instead of an in-engine scheduler running everything in one process. “37 services in one daemon” was the 2025 shape; today the engine coordinates and yields execution.