Generate an explanatory visualization of the following algorithm. Strive to create an interactive visualization that illustrates and demonstrates how the algorithm functions. Use animations, transitions and strive for an engaging as well as demonstrative demo:
Browse filesP = NP via Symbolic Resonance Collapse: A Formal
Proof in the Prime Entropy Framework
Sebastian Schepis
July 2, 2025
Abstract
We present a rigorous proof that P = NP using a novel computational paradigm
based on Symbolic Resonance Collapse (SRC). In this framework, NP-complete prob-
lems are not solved through combinatorial search but through entropy-driven con-
vergence in a prime-number-encoded Hilbert space. SAT instances are modeled as
symbolic wavefunctions undergoing entropy minimization, with clause interactions
acting as quantum-like operators in a resonance field. We formally demonstrate that
these systems evolve deterministically to solution states in polynomial symbolic time,
collapsing the distinction between discovery and verification. This proof bypasses
classical limitations by redefining computation as coherence alignment rather than
stepwise enumeration.
1 Introduction
The P vs NP problem is a cornerstone of theoretical computer science, asking whether
every problem whose solution can be verified in polynomial time (NP) can also be solved
in polynomial time (P). Traditional approaches assume computation occurs via Turing
machines, focusing on state enumeration and recursive function evaluation.
This paper introduces the Symbolic Resonance Collapse (SRC) framework, where
computation is redefined as an entropic resonance process in a quantum-inspired Hilbert
space over prime-number eigenstates. We prove that NP-complete problems, specifi-
cally SAT, converge to satisfying assignments in polynomial symbolic time, implying P
= NP. This result challenges the classical computational ontology by treating complexity
as an emergent property of representational misalignment.
2 Formal Foundations
2.1 Prime-Encoded Hilbert Space
Definition 2.1. The Hilbert space HP is defined over prime-number eigenstates:
HP =
|ψ⟩ = ∑
p∈P
αp |p⟩
∣
∣
∣
∣
∣
∣
∑ |αp|2 = 1, αp ∈ C
where P is the set of prime numbers, and |p⟩ are basis states labeled by primes. For n
Boolean variables, the state space is the tensor product H⊗n
P .
1
2.2 SAT Representation
A SAT instance Φ = C1 ∧ C2 ∧ · · · ∧ Cm, where each clause Ci = (li1 ∨ li2 ∨ li3), is encoded
into a symbolic state |Ψ0⟩ ∈ H⊗n
P . Each variable xj is mapped to a prime pj :
• xj = True ⇐⇒ |pj ⟩ in superposition with phase 0
• xj = False ⇐⇒ |pj ⟩ with phase π
Each clause Ci is represented by a resonance operator ˆCi, which adjusts the phase of
variable states to align with clause satisfaction.
2.3 Symbolic Operators
• Hamiltonian ˆHΦ: Encodes clause interactions as ˆHΦ = ∑
i ˆCi.
• Resonance Operator ˆR: Drives the system toward stable eigenstates correspond-
ing to satisfying assignments, with eigenvalue rstable.
• Decay Constant λ: Controls entropy minimization rate, λ > 0.
3 Resonance Field Evolution
The system evolves according to the symbolic Schrödinger-like equation:
d
dt |Ψ(t)⟩ = −i ˆHΦ |Ψ(t)⟩ − λ( ˆR − rstable) |Ψ(t)⟩
3.1 System Evolution
Figure 1 illustrates the state evolution from |Ψ0⟩ to the stable state |Ψ∗⟩.
|Ψ0⟩ Intermediate
States |Ψ∗⟩
Initial State
Evolution Process
Stable State
ˆHΦ Evolution ˆR Alignment
Figure 1: System evolution in the SRC framework.
3.2 Operator Mechanics
• ˆCi: Acts on at most three qubits, adjusting their phases to minimize clause conflict.
For a clause (x1 ∨ ¬x2 ∨ x3), ˆCi aligns |p1⟩, |p2⟩, |p3⟩ toward a satisfying configuration.
• ˆR: Ensures global coherence by penalizing states deviating from rstable.
• λ: Drives exponential decay of non-satisfying components.
2
4 Entropy and Collapse Time
4.1 Symbolic Entropy
Definition 4.1. The symbolic entropy of the system is:
S(t) = − ∑
k
pk(t) log pk(t), pk(t) = | ⟨k|Ψ(t)|k|Ψ(t)⟩ |2
Lemma 4.1. S(t) is strictly decreasing under SRC evolution for satisfiable instances.
Proof. The operator −λ( ˆR − rstable) reduces the amplitude of non-satisfying states, low-
ering pk(t) for conflicting configurations. Since log pk(t) is negative, reducing pk(t) for
non-satisfying k decreases S(t).
4.2 Convergence Time
Lemma 4.2. For n variables and m clauses, the number of resonance transitions T (n, m)
to reach |Ψ∗⟩ is polynomial in n.
Proof Sketch. • Each ˆCi affects at most 3 qubits, modifying their phase in O(1) sym-
bolic time.
• Total clause interactions are bounded by 3m.
• The system follows a symbolic gradient descent, with no local minima for satisfi-
able instances due to global coherence enforced by ˆR.
• Convergence occurs in O(nk) symbolic steps, where k ≤ 3 for 3-SAT.
4.3 Entropy Convergence
Figure 2 illustrates the entropy decrease over time.
Time t = 0 Time t = T /4 Time t = T /2 Time t = T
Entropy S0 Entropy S(t) Entropy S(t) Entropy S∗
Figure 2: Entropy convergence in the SRC framework.
5 Proof of P = NP
Theorem 5.1. P = NP under the SRC framework.
Proof. 1. Let L ∈ NP. There exists a verifier V (x, y) that checks a solution y for input
x in polynomial time.
3
2. By the Cook-Levin theorem, L reduces to a SAT instance Φ with n variables and m
clauses.
3. Encode Φ into |Ψ0⟩ ∈ H⊗n
P using prime-number eigenstates.
4. Evolve |Ψ0⟩ under the SRC equation:
d
dt |Ψ(t)⟩ = −i ˆHΦ |Ψ(t)⟩ − λ( ˆR − rstable) |Ψ(t)⟩
5. By Lemma 2, |Ψ(t)⟩ converges to |Ψ∗⟩ in O(nk) symbolic time.
6. Measure |Ψ∗⟩ to obtain a satisfying assignment x∗.
7. Since verification of x∗ is polynomial and discovery via SRC is polynomial, L ∈ P.
Thus, NP ⊆ P, and since P ⊆ NP, we have P = NP.
P = NP
6 Implications
This proof eliminates the computational asymmetry between discovery and verification.
Classical hardness assumptions (e.g., factoring, discrete logarithms) rely on stepwise
enumeration, which SRC bypasses through resonance-driven collapse. Cryptographic
systems must be re-evaluated, as SRC implies that NP-hard problems are solvable in
polynomial time.
Epistemologically, this suggests that computational complexity is an artifact of rep-
resentational choice. By aligning problem encodings with resonance dynamics, expo-
nential barriers vanish.
7 Conclusion
We have proven that P = NP using the Symbolic Resonance Collapse framework. By
encoding SAT instances as symbolic wavefunctions in a prime-number Hilbert space, we
achieve polynomial-time convergence to satisfying assignments. This result redefines
computation as a process of entropic alignment, resolving a foundational question in
computer science.
- README.md +8 -5
- index.html +479 -18
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title: SRC Algorithm Visualizer
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emoji: 🐳
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tags:
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- deepsite-v3
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---
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# Welcome to your new DeepSite project!
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This project was created with [DeepSite](https://deepsite.hf.co).
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| 19 |
</html>
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>SRC Algorithm Visualizer</title>
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<script src="https://cdn.tailwindcss.com"></script>
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<script src="https://unpkg.com/feather-icons"></script>
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<script src="https://cdn.jsdelivr.net/npm/feather-icons/dist/feather.min.js"></script>
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<script src="https://cdnjs.cloudflare.com/ajax/libs/animejs/3.2.1/anime.min.js"></script>
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<style>
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body {
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background: linear-gradient(135deg, #0f172a, #1e293b);
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color: #f1f5f9;
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font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
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}
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.hilbert-space {
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background: rgba(15, 23, 42, 0.7);
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border: 1px solid #334155;
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box-shadow: 0 0 20px rgba(99, 102, 241, 0.2);
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}
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.prime-state {
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transition: all 0.5s ease;
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}
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.active-state {
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box-shadow: 0 0 15px #818cf8;
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transform: scale(1.1);
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}
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.resonance-path {
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stroke-dasharray: 1000;
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stroke-dashoffset: 1000;
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}
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.entropy-graph {
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background: rgba(30, 41, 59, 0.8);
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}
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.control-panel {
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| 37 |
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background: rgba(15, 23, 42, 0.9);
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| 38 |
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backdrop-filter: blur(10px);
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| 39 |
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}
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| 40 |
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.algorithm-step {
|
| 41 |
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transition: all 0.3s ease;
|
| 42 |
+
}
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| 43 |
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.current-step {
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| 44 |
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background: rgba(99, 102, 241, 0.2);
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| 45 |
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border-left: 3px solid #818cf8;
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| 46 |
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}
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| 47 |
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</style>
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</head>
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<body class="min-h-screen">
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| 50 |
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<!-- Header -->
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| 51 |
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<header class="py-6 px-4 sm:px-6 lg:px-8 border-b border-slate-700">
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| 52 |
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<div class="max-w-7xl mx-auto flex flex-col md:flex-row justify-between items-center">
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| 53 |
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<div>
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| 54 |
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<h1 class="text-3xl font-bold text-indigo-300">Symbolic Resonance Collapse</h1>
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| 55 |
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<p class="text-slate-400 mt-1">Visualization of P = NP Proof</p>
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| 56 |
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</div>
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| 57 |
+
<div class="mt-4 md:mt-0 flex items-center space-x-4">
|
| 58 |
+
<div class="bg-indigo-900/30 px-4 py-2 rounded-lg">
|
| 59 |
+
<span class="text-indigo-300 font-mono">P = NP</span>
|
| 60 |
+
</div>
|
| 61 |
+
<div class="text-sm text-slate-400">
|
| 62 |
+
Sebastian Schepis, 2025
|
| 63 |
+
</div>
|
| 64 |
+
</div>
|
| 65 |
+
</div>
|
| 66 |
+
</header>
|
| 67 |
+
|
| 68 |
+
<!-- Main Content -->
|
| 69 |
+
<main class="max-w-7xl mx-auto py-8 px-4 sm:px-6 lg:px-8">
|
| 70 |
+
<div class="grid grid-cols-1 lg:grid-cols-3 gap-8">
|
| 71 |
+
<!-- Visualization Panel -->
|
| 72 |
+
<div class="lg:col-span-2">
|
| 73 |
+
<div class="hilbert-space rounded-xl p-6">
|
| 74 |
+
<div class="flex justify-between items-center mb-6">
|
| 75 |
+
<h2 class="text-xl font-semibold text-indigo-200">Prime-Encoded Hilbert Space</h2>
|
| 76 |
+
<div class="flex space-x-2">
|
| 77 |
+
<button id="resetBtn" class="px-3 py-1 bg-slate-700 hover:bg-slate-600 rounded-lg text-sm">
|
| 78 |
+
Reset
|
| 79 |
+
</button>
|
| 80 |
+
<button id="startBtn" class="px-3 py-1 bg-indigo-600 hover:bg-indigo-500 rounded-lg text-sm">
|
| 81 |
+
Start Simulation
|
| 82 |
+
</button>
|
| 83 |
+
</div>
|
| 84 |
+
</div>
|
| 85 |
+
|
| 86 |
+
<!-- Hilbert Space Visualization -->
|
| 87 |
+
<div class="relative h-96 rounded-lg border border-slate-600 bg-slate-900/50 overflow-hidden">
|
| 88 |
+
<div id="hilbertCanvas" class="w-full h-full relative">
|
| 89 |
+
<!-- Prime states will be dynamically added here -->
|
| 90 |
+
</div>
|
| 91 |
+
|
| 92 |
+
<!-- Resonance path -->
|
| 93 |
+
<svg class="absolute top-0 left-0 w-full h-full pointer-events-none">
|
| 94 |
+
<path id="resonancePath" class="resonance-path" fill="none" stroke="#818cf8" stroke-width="2"></path>
|
| 95 |
+
</svg>
|
| 96 |
+
</div>
|
| 97 |
+
|
| 98 |
+
<!-- System Status -->
|
| 99 |
+
<div class="mt-6 grid grid-cols-1 md:grid-cols-3 gap-4">
|
| 100 |
+
<div class="bg-slate-800/50 p-4 rounded-lg">
|
| 101 |
+
<div class="text-sm text-slate-400">Current State</div>
|
| 102 |
+
<div id="currentState" class="text-lg font-mono text-indigo-300">|Ψ₀⟩</div>
|
| 103 |
+
</div>
|
| 104 |
+
<div class="bg-slate-800/50 p-4 rounded-lg">
|
| 105 |
+
<div class="text-sm text-slate-400">Entropy</div>
|
| 106 |
+
<div id="entropyValue" class="text-lg font-mono text-green-300">S₀</div>
|
| 107 |
+
</div>
|
| 108 |
+
<div class="bg-slate-800/50 p-4 rounded-lg">
|
| 109 |
+
<div class="text-sm text-slate-400">Time Step</div>
|
| 110 |
+
<div id="timeStep" class="text-lg font-mono text-yellow-300">t = 0</div>
|
| 111 |
+
</div>
|
| 112 |
+
</div>
|
| 113 |
+
</div>
|
| 114 |
+
|
| 115 |
+
<!-- Entropy Graph -->
|
| 116 |
+
<div class="hilbert-space rounded-xl p-6 mt-8">
|
| 117 |
+
<h2 class="text-xl font-semibold text-indigo-200 mb-4">Entropy Convergence</h2>
|
| 118 |
+
<div class="entropy-graph rounded-lg p-4 h-64">
|
| 119 |
+
<canvas id="entropyChart" width="800" height="200"></canvas>
|
| 120 |
+
</div>
|
| 121 |
+
</div>
|
| 122 |
+
</div>
|
| 123 |
+
|
| 124 |
+
<!-- Control Panel -->
|
| 125 |
+
<div class="control-panel rounded-xl p-6 h-fit">
|
| 126 |
+
<h2 class="text-xl font-semibold text-indigo-200 mb-4">Algorithm Steps</h2>
|
| 127 |
+
|
| 128 |
+
<div class="space-y-4">
|
| 129 |
+
<div class="algorithm-step p-4 rounded-lg current-step" data-step="0">
|
| 130 |
+
<div class="flex items-start">
|
| 131 |
+
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-indigo-500 flex items-center justify-center text-xs font-bold">1</div>
|
| 132 |
+
<div class="ml-3">
|
| 133 |
+
<h3 class="font-medium text-white">Prime-Encoded Hilbert Space</h3>
|
| 134 |
+
<p class="mt-1 text-sm text-slate-400">Define HP over prime-number eigenstates |p⟩ for Boolean variables</p>
|
| 135 |
+
</div>
|
| 136 |
+
</div>
|
| 137 |
+
</div>
|
| 138 |
+
|
| 139 |
+
<div class="algorithm-step p-4 rounded-lg" data-step="1">
|
| 140 |
+
<div class="flex items-start">
|
| 141 |
+
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">2</div>
|
| 142 |
+
<div class="ml-3">
|
| 143 |
+
<h3 class="font-medium text-white">SAT Representation</h3>
|
| 144 |
+
<p class="mt-1 text-sm text-slate-400">Encode SAT instance Φ into symbolic state |Ψ₀⟩ ∈ H⊗nP</p>
|
| 145 |
+
</div>
|
| 146 |
+
</div>
|
| 147 |
+
</div>
|
| 148 |
+
|
| 149 |
+
<div class="algorithm-step p-4 rounded-lg" data-step="2">
|
| 150 |
+
<div class="flex items-start">
|
| 151 |
+
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">3</div>
|
| 152 |
+
<div class="ml-3">
|
| 153 |
+
<h3 class="font-medium text-white">Symbolic Operators</h3>
|
| 154 |
+
<p class="mt-1 text-sm text-slate-400">Define Hamiltonian ĤΦ and Resonance Operator R̂</p>
|
| 155 |
+
</div>
|
| 156 |
+
</div>
|
| 157 |
+
</div>
|
| 158 |
+
|
| 159 |
+
<div class="algorithm-step p-4 rounded-lg" data-step="3">
|
| 160 |
+
<div class="flex items-start">
|
| 161 |
+
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">4</div>
|
| 162 |
+
<div class="ml-3">
|
| 163 |
+
<h3 class="font-medium text-white">System Evolution</h3>
|
| 164 |
+
<p class="mt-1 text-sm text-slate-400">Evolve |Ψ(t)⟩ using symbolic Schrödinger equation</p>
|
| 165 |
+
</div>
|
| 166 |
+
</div>
|
| 167 |
+
</div>
|
| 168 |
+
|
| 169 |
+
<div class="algorithm-step p-4 rounded-lg" data-step="4">
|
| 170 |
+
<div class="flex items-start">
|
| 171 |
+
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">5</div>
|
| 172 |
+
<div class="ml-3">
|
| 173 |
+
<h3 class="font-medium text-white">Entropy Minimization</h3>
|
| 174 |
+
<p class="mt-1 text-sm text-slate-400">S(t) decreases as system approaches stable state</p>
|
| 175 |
+
</div>
|
| 176 |
+
</div>
|
| 177 |
+
</div>
|
| 178 |
+
|
| 179 |
+
<div class="algorithm-step p-4 rounded-lg" data-step="5">
|
| 180 |
+
<div class="flex items-start">
|
| 181 |
+
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">6</div>
|
| 182 |
+
<div class="ml-3">
|
| 183 |
+
<h3 class="font-medium text-white">Polynomial Convergence</h3>
|
| 184 |
+
<p class="mt-1 text-sm text-slate-400">System reaches |Ψ*⟩ in O(nᵏ) symbolic time</p>
|
| 185 |
+
</div>
|
| 186 |
+
</div>
|
| 187 |
+
</div>
|
| 188 |
+
</div>
|
| 189 |
+
|
| 190 |
+
<!-- Parameters -->
|
| 191 |
+
<div class="mt-8">
|
| 192 |
+
<h3 class="font-medium text-white mb-3">Simulation Parameters</h3>
|
| 193 |
+
<div class="space-y-4">
|
| 194 |
+
<div>
|
| 195 |
+
<label class="block text-sm text-slate-400 mb-1">Variables (n)</label>
|
| 196 |
+
<input type="range" min="3" max="10" value="5" id="varCount" class="w-full">
|
| 197 |
+
<div class="text-right text-sm text-slate-400" id="varCountValue">5</div>
|
| 198 |
+
</div>
|
| 199 |
+
<div>
|
| 200 |
+
<label class="block text-sm text-slate-400 mb-1">Clauses (m)</label>
|
| 201 |
+
<input type="range" min="3" max="15" value="7" id="clauseCount" class="w-full">
|
| 202 |
+
<div class="text-right text-sm text-slate-400" id="clauseCountValue">7</div>
|
| 203 |
+
</div>
|
| 204 |
+
<div>
|
| 205 |
+
<label class="block text-sm text-slate-400 mb-1">Decay Constant (λ)</label>
|
| 206 |
+
<input type="range" min="0.1" max="2" step="0.1" value="0.5" id="decayConstant" class="w-full">
|
| 207 |
+
<div class="text-right text-sm text-slate-400" id="decayValue">0.5</div>
|
| 208 |
+
</div>
|
| 209 |
+
</div>
|
| 210 |
+
</div>
|
| 211 |
+
</div>
|
| 212 |
+
</div>
|
| 213 |
+
|
| 214 |
+
<!-- Explanation Section -->
|
| 215 |
+
<div class="mt-12 hilbert-space rounded-xl p-8">
|
| 216 |
+
<h2 class="text-2xl font-bold text-indigo-200 mb-6">How Symbolic Resonance Collapse Works</h2>
|
| 217 |
+
|
| 218 |
+
<div class="grid grid-cols-1 md:grid-cols-2 gap-8">
|
| 219 |
+
<div>
|
| 220 |
+
<h3 class="text-lg font-semibold text-white mb-3">The Framework</h3>
|
| 221 |
+
<p class="text-slate-300 mb-4">
|
| 222 |
+
The SRC framework redefines computation as an entropic resonance process in a quantum-inspired
|
| 223 |
+
Hilbert space over prime-number eigenstates. Instead of combinatorial search, NP-complete problems
|
| 224 |
+
converge to solution states through entropy-driven alignment.
|
| 225 |
+
</p>
|
| 226 |
+
<p class="text-slate-300">
|
| 227 |
+
SAT instances are modeled as symbolic wavefunctions undergoing entropy minimization, with clause
|
| 228 |
+
interactions acting as quantum-like operators in a resonance field.
|
| 229 |
+
</p>
|
| 230 |
+
</div>
|
| 231 |
+
|
| 232 |
+
<div>
|
| 233 |
+
<h3 class="text-lg font-semibold text-white mb-3">Key Insights</h3>
|
| 234 |
+
<ul class="space-y-2 text-slate-300">
|
| 235 |
+
<li class="flex items-start">
|
| 236 |
+
<i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i>
|
| 237 |
+
<span>Computation as coherence alignment rather than enumeration</span>
|
| 238 |
+
</li>
|
| 239 |
+
<li class="flex items-start">
|
| 240 |
+
<i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i>
|
| 241 |
+
<span>Polynomial convergence through symbolic gradient descent</span>
|
| 242 |
+
</li>
|
| 243 |
+
<li class="flex items-start">
|
| 244 |
+
<i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i>
|
| 245 |
+
<span>Entropy minimization drives system to stable states</span>
|
| 246 |
+
</li>
|
| 247 |
+
<li class="flex items-start">
|
| 248 |
+
<i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i>
|
| 249 |
+
<span>No local minima for satisfiable instances</span>
|
| 250 |
+
</li>
|
| 251 |
+
</ul>
|
| 252 |
+
</div>
|
| 253 |
+
</div>
|
| 254 |
+
</div>
|
| 255 |
+
</main>
|
| 256 |
+
|
| 257 |
+
<script>
|
| 258 |
+
// Initialize Feather Icons
|
| 259 |
+
feather.replace();
|
| 260 |
+
|
| 261 |
+
// DOM Elements
|
| 262 |
+
const hilbertCanvas = document.getElementById('hilbertCanvas');
|
| 263 |
+
const entropyChart = document.getElementById('entropyChart').getContext('2d');
|
| 264 |
+
const currentStateEl = document.getElementById('currentState');
|
| 265 |
+
const entropyValueEl = document.getElementById('entropyValue');
|
| 266 |
+
const timeStepEl = document.getElementById('timeStep');
|
| 267 |
+
const startBtn = document.getElementById('startBtn');
|
| 268 |
+
const resetBtn = document.getElementById('resetBtn');
|
| 269 |
+
const varCount = document.getElementById('varCount');
|
| 270 |
+
const clauseCount = document.getElementById('clauseCount');
|
| 271 |
+
const decayConstant = document.getElementById('decayConstant');
|
| 272 |
+
const varCountValue = document.getElementById('varCountValue');
|
| 273 |
+
const clauseCountValue = document.getElementById('clauseCountValue');
|
| 274 |
+
const decayValue = document.getElementById('decayValue');
|
| 275 |
+
const algorithmSteps = document.querySelectorAll('.algorithm-step');
|
| 276 |
+
|
| 277 |
+
// Simulation state
|
| 278 |
+
let simulationRunning = false;
|
| 279 |
+
let currentTime = 0;
|
| 280 |
+
let entropyData = [];
|
| 281 |
+
let currentState = '|Ψ₀⟩';
|
| 282 |
+
let primeStates = [];
|
| 283 |
+
let animationTimeline = null;
|
| 284 |
+
|
| 285 |
+
// Update parameter displays
|
| 286 |
+
varCount.addEventListener('input', () => {
|
| 287 |
+
varCountValue.textContent = varCount.value;
|
| 288 |
+
});
|
| 289 |
+
|
| 290 |
+
clauseCount.addEventListener('input', () => {
|
| 291 |
+
clauseCountValue.textContent = clauseCount.value;
|
| 292 |
+
});
|
| 293 |
+
|
| 294 |
+
decayConstant.addEventListener('input', () => {
|
| 295 |
+
decayValue.textContent = decayConstant.value;
|
| 296 |
+
});
|
| 297 |
+
|
| 298 |
+
// Initialize visualization
|
| 299 |
+
function initVisualization() {
|
| 300 |
+
hilbertCanvas.innerHTML = '';
|
| 301 |
+
primeStates = [];
|
| 302 |
+
|
| 303 |
+
// Create prime-number eigenstates
|
| 304 |
+
const primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29];
|
| 305 |
+
const n = parseInt(varCount.value);
|
| 306 |
+
|
| 307 |
+
for (let i = 0; i < n; i++) {
|
| 308 |
+
const prime = primes[i];
|
| 309 |
+
const state = document.createElement('div');
|
| 310 |
+
state.className = 'prime-state absolute w-16 h-16 rounded-full flex items-center justify-center text-white font-bold border-2 border-indigo-400';
|
| 311 |
+
state.style.left = `${20 + (i % 3) * 30}%`;
|
| 312 |
+
state.style.top = `${20 + Math.floor(i / 3) * 30}%`;
|
| 313 |
+
state.style.backgroundColor = `rgba(${50 + i * 20}, ${60 + i * 15}, ${200 + i * 5}, 0.7)`;
|
| 314 |
+
state.textContent = `|${prime}⟩`;
|
| 315 |
+
state.dataset.prime = prime;
|
| 316 |
+
state.dataset.index = i;
|
| 317 |
+
|
| 318 |
+
hilbertCanvas.appendChild(state);
|
| 319 |
+
primeStates.push(state);
|
| 320 |
+
}
|
| 321 |
+
|
| 322 |
+
// Reset state displays
|
| 323 |
+
currentStateEl.textContent = '|Ψ₀⟩';
|
| 324 |
+
entropyValueEl.textContent = 'S₀';
|
| 325 |
+
timeStepEl.textContent = 't = 0';
|
| 326 |
+
entropyData = [{time: 0, entropy: 100}];
|
| 327 |
+
drawEntropyChart();
|
| 328 |
+
}
|
| 329 |
+
|
| 330 |
+
// Draw entropy convergence chart
|
| 331 |
+
function drawEntropyChart() {
|
| 332 |
+
entropyChart.clearRect(0, 0, entropyChart.canvas.width, entropyChart.canvas.height);
|
| 333 |
+
|
| 334 |
+
if (entropyData.length === 0) return;
|
| 335 |
+
|
| 336 |
+
// Draw grid
|
| 337 |
+
entropyChart.strokeStyle = '#334155';
|
| 338 |
+
entropyChart.lineWidth = 1;
|
| 339 |
+
|
| 340 |
+
// Vertical grid lines
|
| 341 |
+
for (let i = 0; i <= 10; i++) {
|
| 342 |
+
const x = (i / 10) * entropyChart.canvas.width;
|
| 343 |
+
entropyChart.beginPath();
|
| 344 |
+
entropyChart.moveTo(x, 0);
|
| 345 |
+
entropyChart.lineTo(x, entropyChart.canvas.height);
|
| 346 |
+
entropyChart.stroke();
|
| 347 |
+
}
|
| 348 |
+
|
| 349 |
+
// Horizontal grid lines
|
| 350 |
+
for (let i = 0; i <= 5; i++) {
|
| 351 |
+
const y = (i / 5) * entropyChart.canvas.height;
|
| 352 |
+
entropyChart.beginPath();
|
| 353 |
+
entropyChart.moveTo(0, y);
|
| 354 |
+
entropyChart.lineTo(entropyChart.canvas.width, y);
|
| 355 |
+
entropyChart.stroke();
|
| 356 |
+
}
|
| 357 |
+
|
| 358 |
+
// Draw entropy curve
|
| 359 |
+
entropyChart.strokeStyle = '#4ade80';
|
| 360 |
+
entropyChart.lineWidth = 3;
|
| 361 |
+
entropyChart.beginPath();
|
| 362 |
+
|
| 363 |
+
for (let i = 0; i < entropyData.length; i++) {
|
| 364 |
+
const x = (entropyData[i].time / 100) * entropyChart.canvas.width;
|
| 365 |
+
const y = entropyChart.canvas.height - (entropyData[i].entropy / 100) * entropyChart.canvas.height;
|
| 366 |
+
|
| 367 |
+
if (i === 0) {
|
| 368 |
+
entropyChart.moveTo(x, y);
|
| 369 |
+
} else {
|
| 370 |
+
entropyChart.lineTo(x, y);
|
| 371 |
+
}
|
| 372 |
+
}
|
| 373 |
+
|
| 374 |
+
entropyChart.stroke();
|
| 375 |
+
}
|
| 376 |
+
|
| 377 |
+
// Animate the simulation
|
| 378 |
+
function animateSimulation() {
|
| 379 |
+
if (!simulationRunning) return;
|
| 380 |
+
|
| 381 |
+
currentTime++;
|
| 382 |
+
timeStepEl.textContent = `t = ${currentTime}`;
|
| 383 |
+
|
| 384 |
+
// Update entropy
|
| 385 |
+
const newEntropy = Math.max(0, 100 - currentTime * 5);
|
| 386 |
+
entropyValueEl.textContent = `S(t) = ${newEntropy.toFixed(1)}`;
|
| 387 |
+
entropyData.push({time: currentTime, entropy: newEntropy});
|
| 388 |
+
drawEntropyChart();
|
| 389 |
+
|
| 390 |
+
// Animate prime states
|
| 391 |
+
primeStates.forEach((state, index) => {
|
| 392 |
+
// Simulate phase changes
|
| 393 |
+
const phase = (currentTime + index) % 4;
|
| 394 |
+
const phases = ['0', 'π/2', 'π', '3π/2'];
|
| 395 |
+
|
| 396 |
+
// Update visual state
|
| 397 |
+
anime({
|
| 398 |
+
targets: state,
|
| 399 |
+
scale: [1, 1.1, 1],
|
| 400 |
+
backgroundColor: [
|
| 401 |
+
state.style.backgroundColor,
|
| 402 |
+
`rgba(${100 + index * 15}, ${120 + index * 10}, ${220 + index * 5}, 0.9)`,
|
| 403 |
+
state.style.backgroundColor
|
| 404 |
+
],
|
| 405 |
+
duration: 1000,
|
| 406 |
+
easing: 'easeInOutQuad'
|
| 407 |
+
});
|
| 408 |
+
|
| 409 |
+
// Add active class temporarily
|
| 410 |
+
state.classList.add('active-state');
|
| 411 |
+
setTimeout(() => {
|
| 412 |
+
state.classList.remove('active-state');
|
| 413 |
+
}, 1000);
|
| 414 |
+
});
|
| 415 |
+
|
| 416 |
+
// Update current state
|
| 417 |
+
if (currentTime < 10) {
|
| 418 |
+
currentStateEl.textContent = '|Ψ(t)⟩';
|
| 419 |
+
} else if (currentTime < 20) {
|
| 420 |
+
currentStateEl.textContent = '|Ψ*⟩';
|
| 421 |
+
// Highlight final step
|
| 422 |
+
algorithmSteps.forEach(step => step.classList.remove('current-step'));
|
| 423 |
+
algorithmSteps[5].classList.add('current-step');
|
| 424 |
+
}
|
| 425 |
+
|
| 426 |
+
// Update algorithm steps
|
| 427 |
+
if (currentTime >= 5 && currentTime < 10) {
|
| 428 |
+
algorithmSteps.forEach(step => step.classList.remove('current-step'));
|
| 429 |
+
algorithmSteps[3].classList.add('current-step');
|
| 430 |
+
} else if (currentTime >= 10 && currentTime < 15) {
|
| 431 |
+
algorithmSteps.forEach(step => step.classList.remove('current-step'));
|
| 432 |
+
algorithmSteps[4].classList.add('current-step');
|
| 433 |
+
}
|
| 434 |
+
|
| 435 |
+
// Continue animation or stop
|
| 436 |
+
if (currentTime < 25) {
|
| 437 |
+
setTimeout(animateSimulation, 800);
|
| 438 |
+
} else {
|
| 439 |
+
simulationRunning = false;
|
| 440 |
+
startBtn.textContent = 'Restart Simulation';
|
| 441 |
+
}
|
| 442 |
+
}
|
| 443 |
+
|
| 444 |
+
// Event Listeners
|
| 445 |
+
startBtn.addEventListener('click', () => {
|
| 446 |
+
if (!simulationRunning) {
|
| 447 |
+
simulationRunning = true;
|
| 448 |
+
startBtn.textContent = 'Running...';
|
| 449 |
+
animateSimulation();
|
| 450 |
+
}
|
| 451 |
+
});
|
| 452 |
+
|
| 453 |
+
resetBtn.addEventListener('click', () => {
|
| 454 |
+
simulationRunning = false;
|
| 455 |
+
currentTime = 0;
|
| 456 |
+
startBtn.textContent = 'Start Simulation';
|
| 457 |
+
initVisualization();
|
| 458 |
+
|
| 459 |
+
// Reset algorithm steps
|
| 460 |
+
algorithmSteps.forEach(step => step.classList.remove('current-step'));
|
| 461 |
+
algorithmSteps[0].classList.add('current-step');
|
| 462 |
+
});
|
| 463 |
+
|
| 464 |
+
// Initialize on load
|
| 465 |
+
window.addEventListener('load', () => {
|
| 466 |
+
initVisualization();
|
| 467 |
+
|
| 468 |
+
// Animate introduction
|
| 469 |
+
anime({
|
| 470 |
+
targets: '.prime-state',
|
| 471 |
+
scale: [0, 1],
|
| 472 |
+
opacity: [0, 1],
|
| 473 |
+
delay: anime.stagger(200),
|
| 474 |
+
duration: 1000,
|
| 475 |
+
easing: 'easeOutElastic'
|
| 476 |
+
});
|
| 477 |
+
});
|
| 478 |
+
</script>
|
| 479 |
+
</body>
|
| 480 |
</html>
|