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diff --git a/docs/lurk/all.html b/docs/lurk/all.html
diff --git a/docs/lurk/circuit/gadgets/pointer/struct.AllocatedContPtr.html b/docs/lurk/circuit/gadgets/pointer/struct.AllocatedContPtr.html
diff --git a/docs/lurk/circuit/gadgets/pointer/struct.AllocatedPtr.html b/docs/lurk/circuit/gadgets/pointer/struct.AllocatedPtr.html
diff --git a/docs/lurk/coprocessor/gadgets/fn.a_ptr_as_z_ptr.html b/docs/lurk/coprocessor/gadgets/fn.a_ptr_as_z_ptr.html
@@ -1,4 +1,4 @@
 <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `a_ptr_as_z_ptr` fn in crate `lurk`."><title>a_ptr_as_z_ptr in lurk::coprocessor::gadgets - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-ac92e1bbe349e143.css"><meta name="rustdoc-vars" data-root-path="../../../" data-static-root-path="../../../static.files/" data-current-crate="lurk" data-themes="" data-resource-suffix="" data-rustdoc-version="1.76.0 (07dca489a 2024-02-04)" data-channel="1.76.0" data-search-js="search-2b6ce74ff89ae146.js" data-settings-js="settings-4313503d2e1961c2.js" ><script src="../../../static.files/storage-f2adc0d6ca4d09fb.js"></script><script defer src="sidebar-items.js"></script><script defer src="../../../static.files/main-305769736d49e732.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-feafe1bb7466e4bd.css"></noscript><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc fn"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">&#9776;</button></nav><nav class="sidebar"><div class="sidebar-crate"><h2><a href="../../../lurk/index.html">lurk</a><span class="version">0.3.1</span></h2></div><div class="sidebar-elems"><h2><a href="index.html">In lurk::coprocessor::gadgets</a></h2></div></nav><div class="sidebar-resizer"></div>
-    <main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><div id="sidebar-button" tabindex="-1"><a href="../../../lurk/all.html" title="show sidebar"></a></div><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" tabindex="-1"><a href="../../../help.html" title="help">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Function <a href="../../index.html">lurk</a>::<wbr><a href="../index.html">coprocessor</a>::<wbr><a href="index.html">gadgets</a>::<wbr><a class="fn" href="#">a_ptr_as_z_ptr</a><button id="copy-path" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/lurk/coprocessor/gadgets.rs.html#596-607">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><pre class="rust item-decl"><code>pub fn a_ptr_as_z_ptr&lt;T: Tag, F: <a class="trait" href="../../field/trait.LurkField.html" title="trait lurk::field::LurkField">LurkField</a>&gt;(
+    <main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><div id="sidebar-button" tabindex="-1"><a href="../../../lurk/all.html" title="show sidebar"></a></div><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" tabindex="-1"><a href="../../../help.html" title="help">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Function <a href="../../index.html">lurk</a>::<wbr><a href="../index.html">coprocessor</a>::<wbr><a href="index.html">gadgets</a>::<wbr><a class="fn" href="#">a_ptr_as_z_ptr</a><button id="copy-path" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/lurk/coprocessor/gadgets.rs.html#680-691">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><pre class="rust item-decl"><code>pub fn a_ptr_as_z_ptr&lt;T: Tag, F: <a class="trait" href="../../field/trait.LurkField.html" title="trait lurk::field::LurkField">LurkField</a>&gt;(
     a: &amp;<a class="struct" href="../../circuit/gadgets/pointer/struct.AllocatedPtr.html" title="struct lurk::circuit::gadgets::pointer::AllocatedPtr">AllocatedPtr</a>&lt;F&gt;
 ) -&gt; <a class="enum" href="https://doc.rust-lang.org/1.76.0/core/option/enum.Option.html" title="enum core::option::Option">Option</a>&lt;<a class="struct" href="../../z_data/z_ptr/struct.ZPtr.html" title="struct lurk::z_data::z_ptr::ZPtr">ZPtr</a>&lt;T, F&gt;&gt;</code></pre></section></div></main></body></html>
diff --git a/docs/lurk/coprocessor/gadgets/fn.chain_car_cdr.html b/docs/lurk/coprocessor/gadgets/fn.chain_car_cdr.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Chains `car_cdr` calls `n` times, returning the accumulated `car`s, the final `cdr` and the (explored) actual length (`&lt;= n`) of the cons-like `data`. For example, calling `chain_car_cdr` on “ab” with `n = 4` should return the full actual length `2` of such string. But if `n` is set to `1`, it will return `1` as the (explored) length."><title>chain_car_cdr in lurk::coprocessor::gadgets - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-ac92e1bbe349e143.css"><meta name="rustdoc-vars" data-root-path="../../../" data-static-root-path="../../../static.files/" data-current-crate="lurk" data-themes="" data-resource-suffix="" data-rustdoc-version="1.76.0 (07dca489a 2024-02-04)" data-channel="1.76.0" data-search-js="search-2b6ce74ff89ae146.js" data-settings-js="settings-4313503d2e1961c2.js" ><script src="../../../static.files/storage-f2adc0d6ca4d09fb.js"></script><script defer src="sidebar-items.js"></script><script defer src="../../../static.files/main-305769736d49e732.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-feafe1bb7466e4bd.css"></noscript><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc fn"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">&#9776;</button></nav><nav class="sidebar"><div class="sidebar-crate"><h2><a href="../../../lurk/index.html">lurk</a><span class="version">0.3.1</span></h2></div><div class="sidebar-elems"><h2><a href="index.html">In lurk::coprocessor::gadgets</a></h2></div></nav><div class="sidebar-resizer"></div>
-    <main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><div id="sidebar-button" tabindex="-1"><a href="../../../lurk/all.html" title="show sidebar"></a></div><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" tabindex="-1"><a href="../../../help.html" title="help">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Function <a href="../../index.html">lurk</a>::<wbr><a href="../index.html">coprocessor</a>::<wbr><a href="index.html">gadgets</a>::<wbr><a class="fn" href="#">chain_car_cdr</a><button id="copy-path" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/lurk/coprocessor/gadgets.rs.html#565-593">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><pre class="rust item-decl"><code>pub fn chain_car_cdr&lt;F: <a class="trait" href="../../field/trait.LurkField.html" title="trait lurk::field::LurkField">LurkField</a>, CS: ConstraintSystem&lt;F&gt;&gt;(
+    <main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><div id="sidebar-button" tabindex="-1"><a href="../../../lurk/all.html" title="show sidebar"></a></div><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" tabindex="-1"><a href="../../../help.html" title="help">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Function <a href="../../index.html">lurk</a>::<wbr><a href="../index.html">coprocessor</a>::<wbr><a href="index.html">gadgets</a>::<wbr><a class="fn" href="#">chain_car_cdr</a><button id="copy-path" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/lurk/coprocessor/gadgets.rs.html#649-677">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><pre class="rust item-decl"><code>pub fn chain_car_cdr&lt;F: <a class="trait" href="../../field/trait.LurkField.html" title="trait lurk::field::LurkField">LurkField</a>, CS: ConstraintSystem&lt;F&gt;&gt;(
     cs: <a class="primitive" href="https://doc.rust-lang.org/1.76.0/std/primitive.reference.html">&amp;mut CS</a>,
     g: &amp;<a class="struct" href="../../lem/circuit/struct.GlobalAllocator.html" title="struct lurk::lem::circuit::GlobalAllocator">GlobalAllocator</a>&lt;F&gt;,
     store: &amp;<a class="struct" href="../../lem/store/struct.Store.html" title="struct lurk::lem::store::Store">Store</a>&lt;F&gt;,

diff --git a/docs/lurk/coprocessor/gadgets/index.html b/docs/lurk/coprocessor/gadgets/index.html
@@ -1,5 +1,5 @@
 <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Helper gadgets for synthesis"><title>lurk::coprocessor::gadgets - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-ac92e1bbe349e143.css"><meta name="rustdoc-vars" data-root-path="../../../" data-static-root-path="../../../static.files/" data-current-crate="lurk" data-themes="" data-resource-suffix="" data-rustdoc-version="1.76.0 (07dca489a 2024-02-04)" data-channel="1.76.0" data-search-js="search-2b6ce74ff89ae146.js" data-settings-js="settings-4313503d2e1961c2.js" ><script src="../../../static.files/storage-f2adc0d6ca4d09fb.js"></script><script defer src="../sidebar-items.js"></script><script defer src="../../../static.files/main-305769736d49e732.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-feafe1bb7466e4bd.css"></noscript><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc mod"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">&#9776;</button></nav><nav class="sidebar"><div class="sidebar-crate"><h2><a href="../../../lurk/index.html">lurk</a><span class="version">0.3.1</span></h2></div><h2 class="location"><a href="#">Module gadgets</a></h2><div class="sidebar-elems"><section><ul class="block"><li><a href="#functions">Functions</a></li></ul></section><h2><a href="../index.html">In lurk::coprocessor</a></h2></div></nav><div class="sidebar-resizer"></div>
-    <main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><div id="sidebar-button" tabindex="-1"><a href="../../../lurk/all.html" title="show sidebar"></a></div><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" tabindex="-1"><a href="../../../help.html" title="help">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Module <a href="../../index.html">lurk</a>::<wbr><a href="../index.html">coprocessor</a>::<wbr><a class="mod" href="#">gadgets</a><button id="copy-path" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/lurk/coprocessor/gadgets.rs.html#1-894">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><details class="toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Helper gadgets for synthesis</p>
+    <main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><div id="sidebar-button" tabindex="-1"><a href="../../../lurk/all.html" title="show sidebar"></a></div><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" tabindex="-1"><a href="../../../help.html" title="help">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Module <a href="../../index.html">lurk</a>::<wbr><a href="../index.html">coprocessor</a>::<wbr><a class="mod" href="#">gadgets</a><button id="copy-path" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/lurk/coprocessor/gadgets.rs.html#1-985">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><details class="toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>Helper gadgets for synthesis</p>
 </div></details><h2 id="functions" class="section-header"><a href="#functions">Functions</a></h2><ul class="item-table"><li><div class="item-name"><a class="fn" href="fn.a_ptr_as_z_ptr.html" title="fn lurk::coprocessor::gadgets::a_ptr_as_z_ptr">a_ptr_as_z_ptr</a></div></li><li><div class="item-name"><a class="fn" href="fn.chain_car_cdr.html" title="fn lurk::coprocessor::gadgets::chain_car_cdr">chain_car_cdr</a></div><div class="desc docblock-short">Chains <code>car_cdr</code> calls <code>n</code> times, returning the accumulated <code>car</code>s, the final
 <code>cdr</code> and the (explored) actual length (<code>&lt;= n</code>) of the cons-like <code>data</code>. For
 example, calling <code>chain_car_cdr</code> on “ab” with <code>n = 4</code> should return the full