import React, { useState, useEffect } from 'react'; // --- INITIAL STATE & MATH HELPERS --- const INITIAL_NODES = [ { id: 0, name: 'Alpha Prime', x: 100, y: 150 }, { id: 1, name: 'Beta Sector', x: 250, y: 80 }, { id: 2, name: 'Gamma Nexus', x: 400, y: 150 }, { id: 3, name: 'Delta Void', x: 250, y: 220 }, ]; // 4x4 Adjacency Matrix (Directed, Weighted) const INITIAL_MATRIX = [ [0.0, 0.8, 0.2, 0.0], [0.1, 0.0, 0.7, 0.4], [0.3, 0.1, 0.0, 0.9], [0.5, 0.0, 0.2, 0.0], ]; // Power Iteration to approximate Eigenvector Centrality (PageRank style) const computeCentrality = (matrix, iterations = 10) => { const n = matrix.length; let vector = new Array(n).fill(1 / n); for (let iter = 0; iter < iterations; iter++) { let nextVector = new Array(n).fill(0); for (let i = 0; i < n; i++) { for (let j = 0; j < n; j++) { nextVector[i] += matrix[i][j] * vector[j]; } } // Normalize (L2 Norm) const norm = Math.sqrt(nextVector.reduce((sum, val) => sum + val * val, 0)); vector = nextVector.map(v => (norm > 0 ? v / norm : 0)); } return vector; }; // Compute Trace of a square matrix (Sum of diagonal) const computeTrace = (matrix) => matrix.reduce((sum, row, i) => sum + row[i], 0); // Matrix Multiplication (2x2 for Combat) const multiplyMatrices = (A, B) => { return [ [A[0][0] * B[0][0] + A[0][1] * B[1][0], A[0][0] * B[0][1] + A[0][1] * B[1][1]], [A[1][0] * B[0][0] + A[1][1] * B[1][0], A[1][0] * B[0][1] + A[1][1] * B[1][1]] ]; }; export default function IsomorphPrototype() { // Graph State const [adjMatrix, setAdjMatrix] = useState(INITIAL_MATRIX); const [centrality, setCentrality] = useState([]); const [selectedNode, setSelectedNode] = useState(null); // Combat Layer State (2x2 Force Matrices: [Unit Type, Stance]) const [playerForce, setPlayerForce] = useState([[2, 1], [1, 3]]); const [enemyForce, setEnemyForce] = useState([[1, 2], [2, 2]]); const [combatLog, setCombatLog] = useState(''); // Calculate Centrality on Matrix change useEffect(() => { setCentrality(computeCentrality(adjMatrix)); }, [adjMatrix]); // Morph Edge Weight (Simulating a turn action) const modifyEdge = (source, target, delta) => { const nextMatrix = adjMatrix.map((row, i) => row.map((val, j) => { if (i === source && j === target) { return Math.max(0, Math.min(2, parseFloat((val + delta).toFixed(1)))); } return val; }) ); setAdjMatrix(nextMatrix); }; // Resolve Matrix Combat const executeCombat = () => { // Combat Resolution Formula: Trace(PlayerMatrix * EnemyMatrix^T) vs Trace(EnemyMatrix * PlayerMatrix^T) // For simplicity of UI interaction, we multiply Player Force by Enemy Force and check the system stability (Trace) const resultMatrix = multiplyMatrices(playerForce, enemyForce); const traceVal = computeTrace(resultMatrix); if (traceVal > 7) { setCombatLog(`Combat Resolved. Trace Value: ${traceVal.toFixed(2)} - Morphic Resonance achieved! Node weights shifted.`); // Combat outcome mutates the global graph state modifyEdge(0, 2, 0.4); } else { setCombatLog(`Combat Resolved. Trace Value: ${traceVal.toFixed(2)} - System stabilized. Dynamic equilibrium maintained.`); modifyEdge(2, 0, 0.2); } }; return (

ISOMORPH // CORE_ENGINE

Systemic Topology & Morphic Vector Resolution

{/* LEFT COLUMN: THE GRAPH STATE (SPATIAL CONTROL) */}

Layer 1: Eigenvector Topology

Alter edge weights to shift node centrality. Control requires high centrality.

{/* Visual Graph Viewport */}
{INITIAL_NODES.map((node, i) => { const score = centrality[i] ? centrality[i].toFixed(3) : '0.000'; const isDominant = centrality[i] === Math.max(...centrality); return (
setSelectedNode(node.id)} style={{ position: 'absolute', left: node.x, top: node.y, transform: 'translate(-50%, -50%)', width: '90px', padding: '8px', borderRadius: '4px', backgroundColor: selectedNode === node.id ? '#1e3a8a' : '#1f2937', border: isDominant ? '2px solid #10b981' : '1px solid #4b5563', textAlign: 'center', cursor: 'pointer', boxShadow: isDominant ? '0 0 12px rgba(16, 185, 129, 0.3)' : 'none', transition: 'all 0.2s' }} >
{node.name}
𝝀: {score}
); })}
*Green border indicates current Dominant Centrality Node
{/* Matrix Editor */}

Adjacency Matrix Mutation

{adjMatrix.map((row, i) => row.map((val, j) => (
{i}→{j} {val.toFixed(1)}
)) )}
{/* RIGHT COLUMN: COMBAT RESOLUTION (LINEAR ALGEBRA) */}

Layer 2: Linear Algebra Combat

Mutate your 2x2 Force Matrix. Victory depends on the Trace of the matrix product.

{/* Player Matrix */}

Player Force Matrix

{playerForce.flat().map((val, idx) => { const r = Math.floor(idx / 2); const c = idx % 2; return ( { const nextF = [...playerForce]; nextF[r][c] = parseInt(e.target.value) || 0; setPlayerForce(nextF); }} style={{ width: '100%', backgroundColor: '#030712', color: '#fff', border: '1px solid #4b5563', textAlign: 'center', padding: '4px 0' }} /> ); })}
{/* Enemy Matrix */}

Enemy Force Matrix

{enemyForce.flat().map((val, idx) => { const r = Math.floor(idx / 2); const c = idx % 2; return ( { const nextF = [...enemyForce]; nextF[r][c] = parseInt(e.target.value) || 0; setEnemyForce(nextF); }} style={{ width: '100%', backgroundColor: '#030712', color: '#fff', border: '1px solid #4b5563', textAlign: 'center', padding: '4px 0' }} /> ); })}
{combatLog && (
{combatLog}
)}
{/* SYSTEM DOCTRINE WIN CONDITION INFO */}

Layer 5: Win Condition Objective

Your system target is a fixed-point invariant configuration.

Current Doctrine Target: High isolation of Gamma Nexus, structural dominance of Alpha Prime. Shift edge weight metrics until the Eigenvector distribution stabilizers match your faction signature.
); }