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Logo for Axiom Math

Parity of the Partition Function in Quadratic Progressions

These files accompany the paper [TODO].

The formal proofs provided in this work were developed and verified using Lean 4.28.0 + mathlib 4.28.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and mathlib.

Input files

Output files

  • problem.lean: translation of the problem statement into formal language (Lean)
  • solution.lean: solution in formal language (Lean)

Verification

One can verify that each problem.lean and solution.lean are compatible using verify.py, which calls Axle's verify_proof:

python3 verify.py
okay=True (passed)

This is expected to complete very quickly, as the results are cached by Axle. To bypass this, pass --no-cache to the call, which will force Axle to recompute everything, at the cost of a slower time:

python3 verify.py --no-cache
okay=True (passed)

The files have been verified locally via the Comparator.

License

This repository uses the MIT License. See LICENSE for details.

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all 
 blocks\n(function() {\n function addCopyButtons() {\n document.querySelectorAll('pre code').forEach(function(codeBlock) {\n if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;\n codeBlock.parentElement.setAttribute('data-copy-added', 'true');\n \n var btn = document.createElement('button');\n btn.textContent = 'Copy';\n btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';\n btn.onmouseover = function() { this.style.opacity = '1'; };\n btn.onmouseout = function() { this.style.opacity = '0.7'; };\n btn.onclick = function() {\n navigator.clipboard.writeText(codeBlock.textContent).then(function() {\n btn.textContent = 'Copied!';\n setTimeout(function() { btn.textContent = 'Copy'; }, 1500);\n });\n };\n codeBlock.parentElement.style.position = 'relative';\n codeBlock.parentElement.appendChild(btn);\n });\n }\n \n addCopyButtons();\n \n // Re-run on dynamic content\n var observer = new MutationObserver(addCopyButtons);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Add Copy Buttons to Code Blocks");
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

Skip to content
BranchesTags
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Logo for Axiom Math
Parity of the Partition Function in Quadratic Progressions
These files accompany the paper [TODO].
The formal proofs provided in this work were developed and verified using Lean 4.28.0 + mathlib 4.28.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and mathlib.
Input files
Output files
  • problem.lean: translation of the problem statement into formal language (Lean)
  • solution.lean: solution in formal language (Lean)
Verification
One can verify that each problem.lean and solution.lean are compatible
using verify.py, which calls Axle's verify_proof:
python3 verify.py
okay=True (passed)
This is expected to complete very quickly, as the results are cached by Axle.
To bypass this, pass --no-cache to the call, which will force Axle to recompute everything,
at the cost of a slower time:
python3 verify.py --no-cache
okay=True (passed)
The files have been verified locally via the Comparator.
License
This repository uses the MIT License. See LICENSE for details.
About
No description, website, or topics provided.
Resources
Readme
MIT license
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0 watching
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0 forks
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
Repository files navigation
Logo for Axiom Math
Parity of the Partition Function in Quadratic Progressions
These files accompany the paper [TODO].
The formal proofs provided in this work were developed and verified using Lean 4.28.0 + mathlib 4.28.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and mathlib.
Input files
Output files
  • problem.lean: translation of the problem statement into formal language (Lean)
  • solution.lean: solution in formal language (Lean)
Verification
One can verify that each problem.lean and solution.lean are compatible
using verify.py, which calls Axle's verify_proof:
python3 verify.py
okay=True (passed)
This is expected to complete very quickly, as the results are cached by Axle.
To bypass this, pass --no-cache to the call, which will force Axle to recompute everything,
at the cost of a slower time:
python3 verify.py --no-cache
okay=True (passed)
The files have been verified locally via the Comparator.
License
This repository uses the MIT License. See LICENSE for details.
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Custom properties
Stars
0 stars
Watchers
0 watching
Forks
0 forks
Report repository
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
Repository files navigation
Logo for Axiom Math
Parity of the Partition Function in Quadratic Progressions
These files accompany the paper [TODO].
The formal proofs provided in this work were developed and verified using Lean 4.28.0 + mathlib 4.28.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and mathlib.
Input files
Output files
  • problem.lean: translation of the problem statement into formal language (Lean)
  • solution.lean: solution in formal language (Lean)
Verification
One can verify that each problem.lean and solution.lean are compatible
using verify.py, which calls Axle's verify_proof:
python3 verify.py
okay=True (passed)
This is expected to complete very quickly, as the results are cached by Axle.
To bypass this, pass --no-cache to the call, which will force Axle to recompute everything,
at the cost of a slower time:
python3 verify.py --no-cache
okay=True (passed)
The files have been verified locally via the Comparator.
License
This repository uses the MIT License. See LICENSE for details.
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Custom properties
Stars
0 stars
Watchers
0 watching
Forks
0 forks
Report repository
Releases
Packages
Contributors
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

Skip to content
BranchesTags
Repository files navigation
Logo for Axiom Math
Parity of the Partition Function in Quadratic Progressions
These files accompany the paper [TODO].
The formal proofs provided in this work were developed and verified using Lean 4.28.0 + mathlib 4.28.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and mathlib.
Input files
Output files
  • problem.lean: translation of the problem statement into formal language (Lean)
  • solution.lean: solution in formal language (Lean)
Verification
One can verify that each problem.lean and solution.lean are compatible
using verify.py, which calls Axle's verify_proof:
python3 verify.py
okay=True (passed)
This is expected to complete very quickly, as the results are cached by Axle.
To bypass this, pass --no-cache to the call, which will force Axle to recompute everything,
at the cost of a slower time:
python3 verify.py --no-cache
okay=True (passed)
The files have been verified locally via the Comparator.
License
This repository uses the MIT License. See LICENSE for details.
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Custom properties
Stars
0 stars
Watchers
0 watching
Forks
0 forks
Report repository
Releases
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
Repository files navigation
Logo for Axiom Math
Parity of the Partition Function in Quadratic Progressions
These files accompany the paper [TODO].
The formal proofs provided in this work were developed and verified using Lean 4.28.0 + mathlib 4.28.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and mathlib.
Input files
Output files
  • problem.lean: translation of the problem statement into formal language (Lean)
  • solution.lean: solution in formal language (Lean)
Verification
One can verify that each problem.lean and solution.lean are compatible
using verify.py, which calls Axle's verify_proof:
python3 verify.py
okay=True (passed)
This is expected to complete very quickly, as the results are cached by Axle.
To bypass this, pass --no-cache to the call, which will force Axle to recompute everything,
at the cost of a slower time:
python3 verify.py --no-cache
okay=True (passed)
The files have been verified locally via the Comparator.
License
This repository uses the MIT License. See LICENSE for details.
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Custom properties
Stars
0 stars
Watchers
0 watching
Forks
0 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
Repository files navigation
Logo for Axiom Math
Parity of the Partition Function in Quadratic Progressions
These files accompany the paper [TODO].
The formal proofs provided in this work were developed and verified using Lean 4.28.0 + mathlib 4.28.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and mathlib.
Input files
Output files
  • problem.lean: translation of the problem statement into formal language (Lean)
  • solution.lean: solution in formal language (Lean)
Verification
One can verify that each problem.lean and solution.lean are compatible
using verify.py, which calls Axle's verify_proof:
python3 verify.py
okay=True (passed)
This is expected to complete very quickly, as the results are cached by Axle.
To bypass this, pass --no-cache to the call, which will force Axle to recompute everything,
at the cost of a slower time:
python3 verify.py --no-cache
okay=True (passed)
The files have been verified locally via the Comparator.
License
This repository uses the MIT License. See LICENSE for details.
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Custom properties
Stars
0 stars
Watchers
0 watching
Forks
0 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

Skip to content
BranchesTags
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Logo for Axiom Math
Parity of the Partition Function in Quadratic Progressions
These files accompany the paper [TODO].
The formal proofs provided in this work were developed and verified using Lean 4.28.0 + mathlib 4.28.0. Compatibility with earlier or later versions is not guaranteed due to the evolving nature of the Lean 4 compiler and mathlib.
Input files
Output files
  • problem.lean: translation of the problem statement into formal language (Lean)
  • solution.lean: solution in formal language (Lean)
Verification
One can verify that each problem.lean and solution.lean are compatible
using verify.py, which calls Axle's verify_proof:
python3 verify.py
okay=True (passed)
This is expected to complete very quickly, as the results are cached by Axle.
To bypass this, pass --no-cache to the call, which will force Axle to recompute everything,
at the cost of a slower time:
python3 verify.py --no-cache
okay=True (passed)
The files have been verified locally via the Comparator.
License
This repository uses the MIT License. See LICENSE for details.
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Custom properties
Stars
0 stars
Watchers
0 watching
Forks
0 forks
Report repository
Releases
Packages
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