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Petar Liovic
Petar Liovic

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Mathematical Audit of Excalidraw: Finding "Logic Echoes" via Linear Algebra

#architecture #computerscience #react #tooling

The Signal is Getting Stronger

When I released the first version of react-state-basis, the goal was theoretical: could we model React hooks as temporal signals to detect architectural debt?

Since then, the project has hit #1 on r/reactjs and gained validation from senior engineers at companies like Calendly and Snowpact. But for v0.3.1, I wanted to move from "Theory" to "Forensics." I wanted to run the auditor against one of the most high-performance engines in the React ecosystem: Excalidraw.

The "Invisibility" Milestone (v0.3.1)

The biggest barrier to architectural telemetry is the "Import Tax." No one wants to change their source code to run an audit.

As of v0.3.1, Basis is now a "Ghost" in the machine. Using a custom Babel AST transformer and a Vite Proxy, it auto-instruments standard React imports at build-time.

  1. Semantic Extraction: It reads your source code to label hooks automatically (e.g., count, user).
  2. Zero Code Changes: You keep your import { useState } from 'react' exactly as is.
  3. Isomorphism: The proxy maintains 100% type congruence, ensuring the IDE and compiler see a "perfect body double" of React.

Case Study: Auditing Excalidraw

Excalidraw is a 114,000-star project and a masterpiece of performance engineering. It handles massive amounts of high-frequency state transitions. It was the perfect "Laboratory" for the R⁵⁰ vector model.

The Audit Results:

1. Dimension Collapse in the Theme Engine

The Basis HUD immediately flagged a perfect collinearity (1.0 similarity) between appTheme and editorTheme in the core theme-handle hook.

  • The Math: These two vectors were pulsing in identical coordinates in the 50-dimensional space.
  • The Debt: One variable was a redundant mirror of the other, kept in sync via an imperative effect.

2. Sequential Sync Leaks (Causal Loops)

The telemetry matrix detected multiple "Blue Box" violations. These represent directed edges in the component's causal topology where an effect "pushes" data back into state after the render pass.

  • The Cost: In a high-performance canvas, these sequential updates force unnecessary double-reconciliation cycles, adding avoidable overhead to every theme toggle and window focus event.

Excalidraw

Closing the Loop: The Refactor

An auditor's job isn't just to find problems; it's to provide the Basis for a Solution.

I submitted a Pull Request to Excalidraw (which was recently noticed and reposted by @vjeux on x.com platform, one of the most important people in the Frontend industry) to refactor this logic.

  • The Fix: We removed the redundant state and moved to a Pure Projection using useSyncExternalStore and useMemo.
  • The Win: Theme transitions now resolve in a single Atomic Render Pass, restoring the linear independence of the component's basis.

What’s Next: v0.4.0 and Linear Maps

We are now moving from Vector Spaces to Linear Operator Theory.

To handle browser-thread jitter (1ms delays), we are investigating Signal Conditioning via linear maps. By applying a temporal convolution (smoothing) and a difference operator (velocity) to our R⁵⁰ basis, we can move from "Bit-Matching" to Scientific Signal Processing.

Formalize Your Basis

Basis is open-source and ready for zero-config integration. If you want to see the "heartbeat" of your own architecture and find where your logic is redundant, give it a run.

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