# What

> Independent research on transformer internals and the mathematical structures they implicitly compute on.

*by John Zachary Fitch*

## Typed Embeddings

Tokens don't just relate pairwise. Language has clauses with structure of their own, and the embedding space should know it — that's an algebra question, not a feature-engineering one. Active work.

## The Harmonic Maass Form Framework

Different teams build different transformers — Mistral, Qwen, Pythia — and they converge on the same internal shape. The framework is one way of saying *why*: what they're all approximating belongs to a specific kind of mathematical object. Structural predictions hold cross-model.

## Shadow-Line Helical Transformer (Transformer²)

Softmax is *soft* — it never actually chooses, it just biases the average. The architecture replaces it with hard structure that still moves: two interlinked helices in a curved space, where the geometry says where you are without forcing a choice.

## Published

**Inherit All of Nothing — Parts 1 and 2.** Eight months of Codex security analysis.

**Who Steers the User.** A 24-hour research project; presented at Dev Day office hours.