Integrate critical point analysis

.github/DISCUSSION_TEMPLATE/general.yml

@@ -0,0 +1,45 @@
+title: "General Discussion"
+labels: ["discussion"]
+body:
+  - type: markdown
+    attributes:
+      value: |
+        ## Welcome to the Oscillation Adaptability Discussions
+
+        This is a place to ask questions, share ideas, and discuss the theoretical framework and its applications.
+
+        Before posting, please check if your question has already been answered in existing discussions.
+
+  - type: textarea
+    id: topic
+    attributes:
+      label: Discussion Topic
+      description: What would you like to discuss about the Oscillation Adaptability framework?
+      placeholder: Share your thoughts, questions, or ideas here...
+    validations:
+      required: true
+
+  - type: dropdown
+    id: category
+    attributes:
+      label: Topic Category
+      description: What area does your discussion relate to?
+      options:
+        - Theoretical Framework
+        - Mathematical Model
+        - Code Implementation
+        - Applications
+        - Visualization
+        - Paper Discussion
+        - Other
+    validations:
+      required: true
+
+  - type: textarea
+    id: context
+    attributes:
+      label: Additional Context
+      description: Any additional information or context that might help others understand your discussion topic.
+      placeholder: Include any relevant background, references, or specific sections of the paper/code you're referring to.
+    validations:
+      required: false

.github/DISCUSSION_TEMPLATE/research_collaboration.yml

@@ -0,0 +1,72 @@
+title: "Research Collaboration"
+labels: ["collaboration", "research"]
+body:
+  - type: markdown
+    attributes:
+      value: |
+        ## Research Collaboration Proposal
+
+        Use this template to propose research collaborations related to the Oscillation Adaptability framework.
+
+        Successful collaborations typically include clear research questions, methodology, and expected outcomes.
+
+  - type: textarea
+    id: research_question
+    attributes:
+      label: Research Question
+      description: What specific research question or hypothesis would you like to explore?
+      placeholder: Clearly state the research question or hypothesis you're interested in investigating...
+    validations:
+      required: true
+
+  - type: textarea
+    id: approach
+    attributes:
+      label: Proposed Approach
+      description: How do you propose to investigate this question?
+      placeholder: Describe your methodology, tools, or techniques you plan to use...
+    validations:
+      required: true
+
+  - type: dropdown
+    id: field
+    attributes:
+      label: Field of Application
+      description: Which field would this research primarily apply to?
+      options:
+        - Neuroscience
+        - Ecology
+        - Economics
+        - Quantum Systems
+        - Machine Learning
+        - Complex Systems Theory
+        - Other (please specify in Additional Information)
+    validations:
+      required: true
+
+  - type: textarea
+    id: expertise
+    attributes:
+      label: Your Expertise
+      description: What relevant expertise or resources do you bring to this collaboration?
+      placeholder: Describe your background, skills, or access to data/tools that would contribute to this research...
+    validations:
+      required: true
+
+  - type: textarea
+    id: timeline
+    attributes:
+      label: Proposed Timeline
+      description: What is your expected timeline for this collaboration?
+      placeholder: Provide a rough estimate of when you'd like to start, major milestones, and potential completion...
+    validations:
+      required: false
+
+  - type: textarea
+    id: additional_info
+    attributes:
+      label: Additional Information
+      description: Any other details that would be helpful for potential collaborators to know.
+      placeholder: Include any other relevant information about your proposal...
+    validations:
+      required: false

.github/README.md

@@ -0,0 +1,58 @@
+# GitHub Configuration Files
+
+This directory contains configuration files for GitHub features and integrations.
+
+## Contents
+
+- **workflows/**: GitHub Actions workflow configurations
+  - `pages.yml`: Workflow for deploying GitHub Pages
+
+- **DISCUSSION_TEMPLATE/**: Templates for GitHub Discussions
+  - `general.yml`: Template for general discussions
+  - `research_collaboration.yml`: Template for research collaboration proposals
+
+- **assets/**: Visual assets for GitHub
+  - `header.svg`: SVG header image for the repository
+  - `social-preview.html`: HTML template for generating social preview images
+
+- **images/**: Additional images used in GitHub documentation
+  - `header.md`: Markdown version of the header for embedding
+  - `header.txt`: ASCII art version of the header
+
+- **topics.yml**: GitHub repository topics configuration
+
+## Usage
+
+### Social Preview Image
+
+The `social-preview.html` file can be used to generate a social preview image for the repository. To generate the image:
+
+1. Open the HTML file in a web browser
+2. Take a screenshot of the rendered page (1280x640px)
+3. Upload the screenshot as the social preview image in the repository settings
+
+### GitHub Discussions
+
+The discussion templates in the `DISCUSSION_TEMPLATE` directory are used to provide structured templates for GitHub Discussions. To enable GitHub Discussions:
+
+1. Go to the repository settings
+2. Scroll down to the "Features" section
+3. Check the "Discussions" checkbox
+4. Configure the discussion categories as needed
+
+### GitHub Pages Deployment
+
+The `workflows/pages.yml` file configures automatic deployment of GitHub Pages when changes are pushed to the main branch. The workflow:
+
+1. Checks out the repository
+2. Sets up GitHub Pages
+3. Uploads the contents of the `docs` directory as a GitHub Pages artifact
+4. Deploys the artifact to GitHub Pages
+
+## Customization
+
+Feel free to modify these files to suit your specific needs. For example:
+
+- Update the header images to match your project's branding
+- Modify the discussion templates to include project-specific questions
+- Add additional GitHub Actions workflows for CI/CD, testing, etc.

.github/social-preview.html

@@ -0,0 +1,172 @@
+<!DOCTYPE html>
+<html>
+<head>
+    <meta charset="UTF-8">
+    <title>Oscillation Adaptability Social Preview</title>
+    <style>
+        body {
+            margin: 0;
+            padding: 0;
+            font-family: 'Arial', sans-serif;
+        }
+        .preview-container {
+            width: 1280px;
+            height: 640px;
+            background: linear-gradient(135deg, #0f2027, #203a43, #2c5364);
+            position: relative;
+            overflow: hidden;
+        }
+        .wave {
+            position: absolute;
+            width: 100%;
+            height: 100%;
+            opacity: 0.1;
+            background: repeating-linear-gradient(
+                0deg,
+                transparent,
+                transparent 20px,
+                rgba(255, 255, 255, 0.05) 20px,
+                rgba(255, 255, 255, 0.05) 21px
+            );
+        }
+        .title {
+            position: absolute;
+            top: 120px;
+            width: 100%;
+            text-align: center;
+            color: white;
+            font-size: 72px;
+            font-weight: bold;
+            text-shadow: 0 2px 4px rgba(0, 0, 0, 0.5);
+        }
+        .subtitle {
+            position: absolute;
+            top: 220px;
+            width: 100%;
+            text-align: center;
+            color: rgba(255, 255, 255, 0.9);
+            font-size: 32px;
+            font-weight: normal;
+            text-shadow: 0 2px 4px rgba(0, 0, 0, 0.5);
+        }
+        .formula {
+            position: absolute;
+            top: 300px;
+            width: 100%;
+            text-align: center;
+            color: rgba(255, 255, 255, 0.8);
+            font-size: 36px;
+            font-style: italic;
+            text-shadow: 0 2px 4px rgba(0, 0, 0, 0.5);
+        }
+        .tagline {
+            position: absolute;
+            top: 380px;
+            width: 100%;
+            text-align: center;
+            color: rgba(255, 255, 255, 0.7);
+            font-size: 24px;
+            font-weight: normal;
+            text-shadow: 0 2px 4px rgba(0, 0, 0, 0.5);
+        }
+        .oscillation {
+            position: absolute;
+            top: 480px;
+            width: 100%;
+            height: 3px;
+            background: rgba(79, 172, 254, 0.5);
+            clip-path: path('M0,0 C160,40 320,-40 480,0 C640,40 800,-40 960,0 C1120,40 1280,-40 1440,0');
+        }
+        .oscillation-2 {
+            position: absolute;
+            top: 500px;
+            width: 100%;
+            height: 2px;
+            background: rgba(0, 242, 254, 0.4);
+            clip-path: path('M0,0 C106.6,26.6 213.3,-26.6 320,0 C426.6,26.6 533.3,-26.6 640,0 C746.6,26.6 853.3,-26.6 960,0 C1066.6,26.6 1173.3,-26.6 1280,0');
+        }
+        .oscillation-3 {
+            position: absolute;
+            top: 520px;
+            width: 100%;
+            height: 2px;
+            background: rgba(0, 242, 254, 0.3);
+            clip-path: path('M0,0 C80,20 120,-20 200,0 C280,20 320,-20 400,0 C480,20 520,-20 600,0 C680,20 720,-20 800,0 C880,20 920,-20 1000,0 C1080,20 1120,-20 1200,0 C1280,20 1320,-20 1400,0');
+        }
+        .particle {
+            position: absolute;
+            width: 8px;
+            height: 8px;
+            border-radius: 50%;
+            background: white;
+            box-shadow: 0 0 10px rgba(255, 255, 255, 0.8);
+        }
+        .p1 { top: 480px; left: 240px; }
+        .p2 { top: 480px; left: 720px; }
+        .p3 { top: 480px; left: 1200px; }
+        .p4 { top: 500px; left: 320px; }
+        .p5 { top: 500px; left: 960px; }
+        .p6 { top: 520px; left: 200px; }
+        .p7 { top: 520px; left: 600px; }
+        .p8 { top: 520px; left: 1000px; }
+        .circle {
+            position: absolute;
+            border-radius: 50%;
+        }
+        .c1 {
+            top: -50px;
+            left: -50px;
+            width: 300px;
+            height: 300px;
+            background: rgba(79, 172, 254, 0.1);
+        }
+        .c2 {
+            bottom: -100px;
+            right: -100px;
+            width: 400px;
+            height: 400px;
+            background: rgba(0, 242, 254, 0.1);
+        }
+        .c3 {
+            top: 50%;
+            left: 50%;
+            transform: translate(-50%, -50%);
+            width: 800px;
+            height: 800px;
+            background: rgba(255, 255, 255, 0.03);
+        }
+        .github {
+            position: absolute;
+            bottom: 40px;
+            width: 100%;
+            text-align: center;
+            color: rgba(255, 255, 255, 0.6);
+            font-size: 20px;
+        }
+    </style>
+</head>
+<body>
+    <div class="preview-container">
+        <div class="wave"></div>
+        <div class="circle c1"></div>
+        <div class="circle c2"></div>
+        <div class="circle c3"></div>
+        <div class="oscillation"></div>
+        <div class="oscillation-2"></div>
+        <div class="oscillation-3"></div>
+        <div class="particle p1"></div>
+        <div class="particle p2"></div>
+        <div class="particle p3"></div>
+        <div class="particle p4"></div>
+        <div class="particle p5"></div>
+        <div class="particle p6"></div>
+        <div class="particle p7"></div>
+        <div class="particle p8"></div>
+        <div class="title">NECESSARY OSCILLATIONS</div>
+        <div class="subtitle">Adaptability Dynamics Under Conservation Constraints</div>
+        <div class="formula">C(x,d) + A(x,d) = 1</div>
+        <div class="tagline">A Mathematical Framework for Understanding Oscillatory Phenomena in Complex Systems</div>
+        <div class="github">github.com/bbarclay/oscillation-adaptability</div>
+    </div>
+</body>
+</html>

.github/topics.yml

@@ -0,0 +1,16 @@
+topics:
+  - oscillations
+  - adaptability
+  - coherence
+  - conservation-law
+  - complex-systems
+  - mathematical-modeling
+  - spectral-analysis
+  - necessary-oscillations
+  - dynamical-systems
+  - theoretical-framework
+  - python
+  - scientific-computing
+  - data-visualization
+  - mathematical-physics
+  - academic-research