📐 REACT-STATE-BASIS

Behavioral State Analysis for React

It observes how state variables change over time to identify strong correlations that indicate architectural redundancy.

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TL;DR: React-State-Basis watches your state like a mathematician: every useState, useReducer, and even useEffect-driven update becomes a tracked signal that turns into a time-series vector. When two signals move identically over time, they’re collinear (redundant) - and Basis instantly flags it with location, math details, and a copy-paste refactor to derived state.

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React-State-Basis is a real-time architectural auditing engine that treats a React application as a dynamic system of discrete-time vectors. Instead of static linting, which only analyzes syntax, Basis monitors the State Space Topology of your application to detect mathematical redundancy (collinearity) and synchronization anti-patterns in real-time.

Inspired by the work of Sheldon Axler ("Linear Algebra Done Right"), Basis aims to enforce a mathematically optimal "Source of Truth" by ensuring your application state forms a Basis.

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📦 Installation

npm i react-state-basis

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🧠 The Philosophy: State as a Vector Space

In a perfectly architected application, every state variable should represent a unique dimension of information.

Mathematically, your state variables ${v_1, v_2, \dots, v_n}$ should form a Basis for your application’s state space $V$. A Basis must be linearly independent. If two variables update in perfect synchronization, they are collinear (linearly dependent). This creates:

1. Redundant Renders: Multiple cycles for a single logical change.
2. State Desynchronization: High risk of "impossible states" (e.g., user exists but isLoggedIn is false).
3. Architectural Entropy: High cognitive load in tracing data causality.

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🚀 See It In Action

💡 Detecting Causal Links & Double Renders

The Problem: Manually syncing fahrenheit via useEffect creates a "Double Render Cycle" (React renders once for Celsius, then again for Fahrenheit).

The Basis Solution: Basis identifies this sequential dependency in real-time. It flags the Causal Link and provides a copy-paste refactor to move from expensive state synchronization to a pure Mathematical Projection (useMemo).

🕸️ Identifying Boolean Entanglement

The Problem: Using multiple boolean flags (isLoading, isSuccess, hasData) often leads to "impossible states" and redundant updates.

The Basis Discovery: Even though these are separate variables, Basis monitors their transition vectors and detects they are perfectly synchronized.

The Insight: It flags a Dimension Collapse, alerting you that 3 independent state variables are actually spanning only 1 dimension of information. It suggests consolidating them into a single state machine or a status string.

🛑 Circuit Breaker (Infinite Loop Protection)

The Trap: A recursive useEffect that triggers an infinite state oscillation, a common mistake that usually freezes the browser’s main thread.

The Intervention: Basis acts as a real-time stability monitor. If it detects a high-frequency state oscillation (e.g., 25 updates within 500ms), it automatically activates the Circuit Breaker.

The Result: The engine forcefully halts the update chain before the browser locks up. It provides a critical diagnostic report with the exact location of the loop, allowing you to fix the bug without having to kill the browser process.

🌐 Cross-Context Dependency Audit

The Scenario: Modern apps often split state into multiple providers (e.g., AuthContext and ThemeContext). While architecturally decoupled, they are often manually synchronized in logic (e.g., switching to "dark theme" every time a user logs in).

The Global Discovery: Basis performs a Global State Space Audit. It doesn’t care where your state lives in the component tree; it only cares about the temporal signals.

The Insight: By initiating a "Global Sync," Basis identifies that user and theme are moving in perfect synchronization. It exposes hidden coupling between disparate parts of your architecture.

The Benefit: This helps architects identify states that should potentially be merged or derived from a single source of truth, even when they are physically separated across different providers.

📊 System Health & Structural Audit

System Rank & Efficiency: Basis performs a global audit of your state space to calculate its Mathematical Rank—the actual number of independent information dimensions. An efficiency of 40% (Rank: 4/10) warns you that 60% of your state is mathematically redundant.

Redundancy Clusters: Instead of a raw matrix, Basis automatically groups "entangled" variables into Redundancy Clusters. Whether they are booleans in a single component or states across different contexts, Basis identifies them as a single, collapsed dimension if they move in perfect sync.

Cross-Context Discovery: The report exposes hidden dependencies across your entire tree (e.g., identifying that theme in one context is perfectly correlated with user in another).

Architectural KPI: Use the Efficiency Score as a real-time health metric. Your goal is to reach 100% Efficiency, where every state variable in your application is linearly independent and serves as a true "Source of Truth."

Try the full interactive demo here: /example

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How react-state-basis is different from existing tools

There are many great tools for React state management and debugging. Basis doesn’t try to replace them - it solves a very specific pain point that most of them don’t address directly: detecting behavioral redundancy at runtime (when two or more states always change together, even if they contain different values).

Here’s a quick comparison:

Tool / Approach	Static analysis	Runtime behavior tracking	Detects temporal synchronization	Gives refactor suggestions	Overhead in production	Focus on mathematical independence
ESLint + plugins (no-redundant-state, etc.)	✅	❌	❌	Partial (rules only)	None	❌
React DevTools	❌	Partial (component tree)	❌	No	Low	❌
Why Did You Render	❌	✅ (render tracking)	Partial (render causes)	No	Removable	❌
Redux/Zustand DevTools	❌	✅ (store changes)	❌ (only store level)	No	Removable	❌
react-state-basis (Basis)	Partial (Babel)	✅	✅ (tick-based sync detection)	✅ (copy-paste useMemo)	Zero (change imports)	✅ (inspired by linear algebra)

Basis shines when:

• You have manual state syncing (setA → setB in effects/onClick/etc.)
• Multiple booleans or flags that are always updated together
• You want to know which state is the true "source of truth" without guessing
• You want runtime insights that linters can’t see (because they don’t run the code)

It is not trying to be a full state manager, linter replacement, or performance profiler. It is a specialized diagnostic tool for one very common anti-pattern - and it tries to do that one thing really well.

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🚀 Setup & Integration

To enable the mathematical monitoring of your application, follow these two steps:

1. Initialize the Basis Monitor

Wrap your application root (e.g., main.tsx or App.tsx) with the BasisProvider. Setting debug={true} enables the real-time diagnostic dashboard and the visual system status monitor.

import { BasisProvider } from 'react-state-basis';

export default function Root() {
return (
<BasisProvider debug={true}>
<App />
</BasisProvider>
);
}

2. Use Drop-in Replacement Imports

Replace your standard React hook imports with react-state-basis. This allows the engine to instrument your state updates without changing your component logic.

Standard Named Imports (Recommended):

// ❌ Change this:
// import { useState, useEffect } from 'react';

// ✅ To this:
import { useState, useEffect, useMemo, useContext } from 'react-state-basis';

function MyComponent() {
const [data, setData] = useState([]); // Automatically vectorized and tracked
}

Namespace Imports: Basis also supports namespace imports if you prefer to keep your hooks grouped:

import * as Basis from 'react-state-basis';

function MyComponent() {
const [count, setCount] = Basis.useState(0); // Also tracked automatically
}

3. The Babel plugin

The Babel plugin is optional but highly recommended. Without it, state variables will be tracked as anonymous_state, making it difficult to identify specific redundancies in large applications. You can also manually provide a label as the last argument to any hook if you prefer not to use Babel.

If you choose not to use the Babel plugin, you can still get specific labels by passing a string as the last argument:

const [count, setCount] = useState(0, "MyComponent -> count");

To get the most out of Basis, you should enable the Babel plugin. This automatically injects the filename and variable name into your hooks so you don’t have to label them manually.

If you are using Vite, add the following to your vite.config.ts:

// vite.config.ts
import { defineConfig } from 'vite'
import react from '@vitejs/plugin-react'

export default defineConfig({
plugins: [
react({
babel: {
// Automatically labels useState, useMemo, etc.
// for richer diagnostics in the console.
plugins: [['react-state-basis/plugin']]
}
})
]
})

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🕵️‍♂️ Technical Architecture

React-State-Basis utilizes a three-tier instrumentation pipeline to audit your system:

1. The Compiler Layer (Babel AST)

A build-time plugin performs static analysis, injecting the filename and variable name directly into the runtime calls. This transforms an anonymous execution graph into a structured state map.

2. The Runtime Layer (Signal Mapping)

Every state transition is intercepted. Basis groups updates occurring within a 16ms window into a single "System Tick." Each state variable is mapped to a vector in $\mathbb{R}^{50}$.

• 1 = State transition occurred in this tick.
• 0 = State remained stagnant.

React-State-Basis does not compare state values. It analyzes the timing and synchronization of updates, treating each state variable as a discrete activation signal over time.

3. The Analysis Layer (The Heuristic)

In pure Linear Algebra, proving linear independence for $N$ variables requires solving the system $a_1v_1 + \dots + a_nv_n = 0$. Using algorithms like Gaussian elimination or SVD to determine the Rank of the state matrix has a computational complexity of $O(N^3)$. Running this in a browser runtime for every state update would be prohibitively expensive.

To maintain real-time performance, React-State-Basis uses Cosine Similarity as a high-speed heuristic ($O(D)$, where $D$ is the vector dimension) to detect pairwise collinearity:

$$ \text{similarity} = \cos(\theta) = \frac{\mathbf{A} \cdot \mathbf{B}}{\Vert \mathbf{A} \Vert \Vert \mathbf{B} \Vert} $$

If $\cos(\theta) \approx 1.00$, the vectors are collinear (linearly dependent), and the engine triggers a redundancy alert.

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📝 Real-World Demonstration: The Auth Anti-Pattern

Developers often manually sync related states, creating a redundant dimension in the Basis:

❌ Redundant Basis (State Bloat)

const [user, setUser] = useState(null);
const [isLogged, setIsLogged] = useState(false);

const onLogin = (userData) => {
setUser(userData);
setIsLogged(true); // ⚠️ BASIS ALERT: Always updated in sync with 'user'
};

Engine Analysis: The Engine calculates that user and isLogged are perfectly synchronized. It warns you that you are using two dimensions to describe a 1D problem.

✅ Independent Basis (Optimal Design)

Basis suggests a Projection-transforming a basis vector into a derived value.

const [user, setUser] = useState(null);
const isLogged = useMemo(() => !!user, [user]); // Mathematically clean

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🖥️ Diagnostic Dashboard

Basis provides high-end diagnostic feedback directly in your browser console:

• 📍 Location Tracking: Identifies exact files and variable names causing redundancy.
• 🛠️ Refactor Snippets: Provides dark-themed code blocks you can copy-paste to fix your state architecture.
• 📊 Health Matrix: Call printBasisReport() to see your Efficiency Score and the full Correlation Matrix of your application.

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✨ Key Features

• 🕵️‍♂️ Content-Agnostic: Identifies logical links through temporal synchronization, not data types.
• 🛡️ Circuit Breaker: Halts high-frequency state oscillations (Infinite Loops) to protect the browser thread.
• 💡 Causal Detective: Tracks causality chains from useEffect to useState to identify cascading renders.
• 🔄 Zero Lock-in: Simply point your imports back to 'react' in production. Basis is a Development-time verification infrastructure.

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🎓 Mathematical Inspiration

📜 The Basis Theorem

According to Axler (Linear Algebra Done Right, Definition 2.27):

A basis of $V$ is a list of vectors in $V$ that is linearly independent and spans $V$.

To satisfy this theorem in the context of application state:

1. Linear Independence: No state variable in the list can be expressed as a linear combination of the others. If a state $v_n$ can be derived from ${v_1, \dots, v_{n-1}}$, the list is linearly dependent and contains redundancy.
2. Spanning the Space: The list of state variables must contain enough information to represent every possible configuration of the user interface.

React-State-Basis ensures that your state list is a true Basis by identifying and flagging vectors that fail the test of linear independence.

"Linear algebra is the study of linear maps on finite-dimensional vector spaces."

• Sheldon Axler

React-State-Basis bridges the gap between abstract algebra and UI engineering. By ensuring your application state forms an independent, non-redundant basis, it helps you build software that is inherently more stable, efficient, and easier to reason about.

📜 Implementation of the Linear Dependency Lemma

According to Axler (Lemma 2.21), in a linearly dependent list of vectors, there exists an index $j$ such that $v_j$ is in the span of the preceding vectors ($v_1, \dots, v_{j-1}$).

React-State-Basis implements this sequential logic to audit your state:

1. The Ordered List: Every state variable is treated as an element in an ordered list $(v_1, v_2, \dots, v_n)$ based on its registration order in the application.
2. Sequential Discovery: As time progresses, the engine monitors the list. It doesn’t just look for "similar" vectors; it looks for vectors that fail to add a new dimension to the subspace generated by the vectors that came before them.
3. Identifying the Redundant Element: If $v_{isLogged}$ is perfectly correlated with $v_{user}$, the engine identifies that $v_{isLogged} \in \text{span}(v_{user})$. Since $v_{user}$ preceded it, $v_{isLogged}$ is mathematically the redundant element.
4. Basis Reduction: Following the lemma’s second conclusion, the engine advises removing $v_j$, proving that the "information span" of your app remains identical while the complexity of the Basis decreases.

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⚠️ Design Constraints & Heuristics

React-State-Basis uses probabilistic, time-windowed heuristics to approximate linear dependence. As with any runtime analysis:

• Rarely-updated states may appear correlated by chance
• High-frequency UI interactions may trigger conservative warnings
• Results are advisory, not prescriptive

React-State-Basis is designed to surface architectural questions, not enforce correctness.

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❓ Frequently Asked Questions

Is React-State-Basis a replacement for React DevTools or linters?

No.

React-State-Basis complements existing tools. Linters analyze code structure, and React DevTools show component behavior. React-State-Basis analyzes state relationships over time-something neither tool is designed to detect.

It answers questions like:

• “Why do these two states always change together?”
• “Which state is the true source of truth?”
• “Am I manually synchronizing derived data?”

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Does this change React behavior or execution order?

No.

React-State-Basis does not modify React’s scheduling, rendering, or reconciliation. It observes state updates at runtime and logs diagnostics during development.

Removing React-State-Basis restores your application to standard React behavior with no residual effects.

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Is this safe to use in production?

React-State-Basis is designed for development-time analysis.

While it is technically safe to run in production, it:

• adds runtime overhead
• logs diagnostic output
• performs continuous analysis

For production builds, simply switch your imports back to 'react'.

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How accurate is the redundancy detection?

React-State-Basis uses time-windowed behavioral analysis, not formal proofs.

This means:

• Strong, consistent correlations are highly reliable indicators of redundancy
• Rare or coincidental correlations may trigger conservative warnings

All results are advisory and should be interpreted as architectural signals, not errors.

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Can this detect all redundant state?

No-and that’s intentional.

React-State-Basis detects behavioral redundancy, not semantic equivalence. Two states may contain the same data but update independently, which is architecturally valid.

React-State-Basis only flags redundancy when two states behave as a single information dimension over time.

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Why not just use selectors or derived state manually?

You should-and React-State-Basis encourages that.

The challenge is finding where derived state should exist in large or evolving codebases. React-State-Basis helps identify:

• state that should be derived
• state that is unintentionally synchronized
• state that adds no new information

It surfaces opportunities for refactoring, not rules you must follow.

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Does this work with Redux, Zustand, or other state managers?

React-State-Basis currently instruments React hooks directly.

However, the underlying model is store-agnostic. Any system with:

• discrete state updates
• identifiable update points
• consistent labeling

could theoretically be analyzed using the same approach.

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What about performance?

React-State-Basis is optimized for real-time use in development.

Key design choices:

• Fixed-size sliding windows
• O(D) similarity checks
• Batched analysis every N ticks

For typical applications, overhead is negligible. For extremely high-frequency updates (e.g., animations), React-State-Basis may emit conservative warnings.

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Is this “formal verification”?

No.

React-State-Basis performs runtime architectural auditing, not formal mathematical verification. It applies concepts from linear algebra to observe and analyze behavior, not to prove correctness.

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Who is this tool for?

React-State-Basis is best suited for:

• Medium to large React applications
• Codebases with complex state interactions
• Engineers debugging synchronization bugs
• Teams prioritizing architectural clarity

It may be unnecessary for small or short-lived projects.

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Why linear algebra?

Because state redundancy is linear dependence.

If two state variables always change together, they span the same dimension of information. Linear algebra provides a precise language-and useful tools-for detecting and reasoning about that relationship.

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Will this ever produce false positives?

Yes.

React-State-Basis favors visibility over silence. When in doubt, it surfaces potential issues so developers can make informed decisions.

Think of it as an architectural smoke detector-not a fire marshal.

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🗺️ Roadmap & Future Improvements (v0.2.0+)

React-State-Basis is a solo-developed diagnostic infrastructure. I am currently working on the following features to enhance the "Zero-Friction" developer experience:

1. ⚡ Hybrid Production Strategy

I am moving towards a "Set and Forget" model to eliminate manual import management:

• Production Pass-through: A production-mode toggle that bypasses the auditing logic and maps directly to React core hooks with zero overhead.
• Tree-Shaking Optimization: Ensuring the Linear Algebra engine and Circuit Breaker logic are physically excluded from production bundles via conditional exports.

2. 🛠️ CLI "Clean-Exit" Utility

For engineers who prefer a purist approach or want to remove the dependency after a refactor phase:

• Automated Codemod: I plan to release npx rsb-clean, a utility to automatically revert all react-state-basis imports back to standard react imports across your entire project.
• One-Command Cleanup: Ensures a zero-overhead production build without manual searching and replacing.

3. 📉 Dependency Topology Visualizer

I want to transform the "Audit Report" from console logs into a visual map:

• Redundancy Clusters: A 2D canvas showing "entangled" states as physical clusters.
• Vector Distance Mapping: A visual representation of how close your state variables are to being collinear.

4. 🧪 CI/CD Integration

• Test-Health Reporting: Integration with Vitest/Jest to automatically fail builds if a "Dimension Collapse" or "Infinite Loop" is detected during automated test runs.
• Architectural KPI tracking: Monitoring your System Efficiency Score over time as the codebase grows.

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📬 Get Involved

If you have an idea for a mathematical heuristic or a DX improvement, feel free to open an issue or a PR.

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Developed by LP For engineers who treat software as applied mathematics. 🚀📐