Having a mathematical language is only half the battle — you also need a strict enforcer to make sure the AI actually uses it correctly.
The Weaver is a module that parses every output the model generates as a structured Abstract Syntax Tree (AST). It enforces a strict Context-Free Grammar defined in Extended Backus-Naur Form — essentially treating the model's output like source code that must compile.
If the AI slips back into vague, wordy English during a mathematical operation, The Weaver triggers a "Cognitive Segfault" — it immediately halts the output, rewinds the internal state (KV-cache), and heavily penalises the offending token with a massive −100 logit penalty so the AI course-corrects on the very next attempt.
Even with perfect syntax enforcement, numbers in a computer aren't truly perfect. Every floating-point operation introduces a tiny rounding error, and over thousands of recursive steps these errors can snowball. The Continuous Hopfield Network runs a cleanup cycle after every logic step, snapping drifting vectors back toward the nearest clean mathematical state.
The Continuous Hopfield Network minimises:
E = −lse(β, Xᵀξ) + ½ξᵀξ,
where the dictionary matrix X contains only the ~50–100 primitive anchors
(never complex compositions), keeping complexity at O(d·k) per cycle.
FLOP parity insight: 1,000 full reasoning steps with Hopfield
cleanup ≈ 1,000 × 100 × 12,288 ≈ 1.23×10⁹ ops. A single attention
layer's forward pass at N=100K also costs ~1.23×10⁹ ops. So an entire
1,000-step reasoning trace costs the same as one layer of standard
attention on a large context.
The Weaver enforces a Context-Free Grammar (EBNF) via a customised
Python tree-sitter parser. On violation, it rewinds the KV-cache and applies a
−100 logit penalty to the offending BPE token.