feedback from stejabc, change the script for better uniformity and optimization

Author: ChrisSon15

concept/MuSig2adaptor-rust.md

@@ -60,7 +60,7 @@ Up to here, its independent of the message and can be precalculated.
 
 ### Sign round 2
 
-From collected Nonce the aggregated Nonce $R$ is calculated:
+At this point in time the public Adaptor $T$ must be known to both parties. From collected Nonce the aggregated Nonce $R$ is calculated:
 
 $$\begin{aligned}
 (2)~~ R_1 &= R_{a,1} + R_{b,1} \\

concept/STx7.drawio

@@ -1,6 +1,6 @@
-<mxfile host="drawio-plugin" modified="2026-03-04T13:44:54.239Z" agent="Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/137.0.0.0 Safari/537.36" etag="N3SYCEXVYOUo0RP3hA44" version="22.1.22" type="embed">
+<mxfile host="drawio-plugin" modified="2026-03-05T14:00:00.567Z" agent="Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/137.0.0.0 Safari/537.36" etag="HtWYuJCgjJPmr4AlW5qf" version="22.1.22" type="embed">
   <diagram name="Page-1" id="4t2JOigZqfDRrmz9JXpL">
-    <mxGraphModel dx="1560" dy="1241" grid="1" gridSize="10" guides="1" tooltips="1" connect="1" arrows="1" fold="1" page="0" pageScale="1" pageWidth="827" pageHeight="1169" background="#FFFFFF" math="1" shadow="0">
+    <mxGraphModel dx="1168" dy="1236" grid="1" gridSize="10" guides="1" tooltips="1" connect="1" arrows="1" fold="1" page="0" pageScale="1" pageWidth="827" pageHeight="1169" background="#FFFFFF" math="1" shadow="0">
       <root>
         <mxCell id="0" />
         <mxCell id="1" parent="0" />
@@ -27,7 +27,7 @@
         <mxCell id="8" value="Deposit Tx" style="swimlane;fontStyle=0;childLayout=stackLayout;horizontal=1;startSize=30;horizontalStack=0;resizeParent=1;resizeParentMax=0;resizeLast=0;collapsible=1;marginBottom=0;whiteSpace=wrap;html=1;labelBackgroundColor=none;fillColor=#d5e8d4;strokeColor=#82b366;gradientColor=#97d077;" parent="1" vertex="1">
           <mxGeometry x="250" y="180" width="220" height="280" as="geometry" />
         </mxCell>
-        <mxCell id="10" value="&lt;b&gt;Output&lt;/b&gt;&amp;nbsp;0: Seller deposit and trade amount&lt;br&gt;Taproot key spend: P&#39;&lt;br&gt;script spend 0:&lt;br&gt;&amp;lt;PubKey Alice U&amp;gt;&lt;br&gt;OP_CHECKSIG_VERIFY&lt;br&gt;&amp;lt;PubKey Bob V&amp;gt;&lt;br&gt;OP_CHECKSIG&lt;br&gt;&lt;br&gt;" style="text;strokeColor=none;fillColor=none;align=left;verticalAlign=middle;spacingLeft=4;spacingRight=4;overflow=hidden;points=[[0,0.5],[1,0.5]];portConstraint=eastwest;rotatable=0;whiteSpace=wrap;html=1;labelBackgroundColor=none;" parent="8" vertex="1">
+        <mxCell id="10" value="&lt;b&gt;Output&lt;/b&gt;&amp;nbsp;0: Seller deposit and trade amount&lt;br&gt;Taproot key spend: P&#39;&lt;br&gt;script spend 0:&lt;br&gt;&amp;lt;PubKey Bob V&amp;gt;&lt;br&gt;OP_CHECKSIG_VERIFY&lt;br&gt;&amp;lt;PubKey Alice U&amp;gt;&lt;br&gt;OP_CHECKSIG&lt;br&gt;" style="text;strokeColor=none;fillColor=none;align=left;verticalAlign=middle;spacingLeft=4;spacingRight=4;overflow=hidden;points=[[0,0.5],[1,0.5]];portConstraint=eastwest;rotatable=0;whiteSpace=wrap;html=1;labelBackgroundColor=none;" parent="8" vertex="1">
           <mxGeometry y="30" width="220" height="130" as="geometry" />
         </mxCell>
         <mxCell id="14" value="&lt;b&gt;Output&lt;/b&gt;&amp;nbsp;1: Buyer deposit&lt;br&gt;Taproot key spent: Q&#39;&lt;br&gt;script spend 0:&lt;br style=&quot;border-color: rgb(218, 220, 224);&quot;&gt;&amp;lt;PubKey Alice U&amp;gt;&lt;br style=&quot;border-color: rgb(218, 220, 224);&quot;&gt;OP_CHECKSIG_VERIFY&lt;br style=&quot;border-color: rgb(218, 220, 224);&quot;&gt;&amp;lt;PubKey Bob V&amp;gt;&lt;br style=&quot;border-color: rgb(218, 220, 224);&quot;&gt;OP_CHECKSIG" style="text;strokeColor=none;fillColor=none;align=left;verticalAlign=middle;spacingLeft=4;spacingRight=4;overflow=hidden;points=[[0,0.5],[1,0.5]];portConstraint=eastwest;rotatable=0;whiteSpace=wrap;html=1;labelBackgroundColor=none;" parent="8" vertex="1">
@@ -44,7 +44,7 @@
         <mxCell id="16" value="Warning Tx Alice / Bob" style="swimlane;fontStyle=0;childLayout=stackLayout;horizontal=1;startSize=30;horizontalStack=0;resizeParent=1;resizeParentMax=0;resizeLast=0;collapsible=1;marginBottom=0;whiteSpace=wrap;html=1;labelBackgroundColor=none;fillColor=#e1d5e7;strokeColor=#9673a6;" parent="1" vertex="1">
           <mxGeometry x="580" y="20" width="260" height="300" as="geometry" />
         </mxCell>
-        <mxCell id="17" value="&lt;b style=&quot;&quot;&gt;&lt;font style=&quot;font-size: 14px;&quot;&gt;Output 0&lt;/font&gt;&lt;span style=&quot;font-size: 13px;&quot;&gt;: &lt;/span&gt;&lt;/b&gt;buyer deposit&amp;nbsp;seller deposit and trade amount&lt;br&gt;&lt;br&gt;&lt;b&gt;key spend&lt;/b&gt;: &lt;br&gt;Q&#39; / P&#39;&amp;nbsp;(Bob / Alice can claim if key exchange already happened)&lt;br&gt;&lt;b style=&quot;border-color: var(--border-color);&quot;&gt;&lt;br&gt;script spend 0&lt;/b&gt;: &lt;br&gt;Alice / Bob can claim the hole amount after time t_1 with script:&lt;br style=&quot;border-color: var(--border-color);&quot;&gt;push t_1&lt;br style=&quot;border-color: var(--border-color);&quot;&gt;OP_CSV&lt;br style=&quot;border-color: var(--border-color);&quot;&gt;OP_DROP&lt;br style=&quot;border-color: var(--border-color);&quot;&gt;push pubkey R&lt;br style=&quot;border-color: var(--border-color);&quot;&gt;OP_CHECKSIG" style="text;strokeColor=none;fillColor=none;align=left;verticalAlign=middle;spacingLeft=4;spacingRight=4;overflow=hidden;points=[[0,0.5],[1,0.5]];portConstraint=eastwest;rotatable=0;whiteSpace=wrap;html=1;labelBackgroundColor=none;opacity=0;" parent="16" vertex="1">
+        <mxCell id="17" value="&lt;b style=&quot;&quot;&gt;&lt;font style=&quot;font-size: 14px;&quot;&gt;Output 0&lt;/font&gt;&lt;span style=&quot;font-size: 13px;&quot;&gt;: &lt;/span&gt;&lt;/b&gt;buyer deposit&amp;nbsp;seller deposit and trade amount&lt;br&gt;&lt;br&gt;&lt;b&gt;key spend&lt;/b&gt;: &lt;br&gt;Q&#39; / P&#39;&amp;nbsp;(Bob / Alice can claim if key exchange already happened)&lt;br&gt;&lt;b style=&quot;border-color: var(--border-color);&quot;&gt;&lt;br&gt;script spend 0&lt;/b&gt;: &lt;br&gt;Alice / Bob can claim the hole amount after time t_1 with script:&lt;br style=&quot;border-color: var(--border-color);&quot;&gt;push pubkey R&lt;br style=&quot;border-color: var(--border-color);&quot;&gt;OP_CHECKSIGVERIFY&lt;br&gt;push t_1&lt;br style=&quot;border-color: rgb(218, 220, 224);&quot;&gt;OP_CSV" style="text;strokeColor=none;fillColor=none;align=left;verticalAlign=middle;spacingLeft=4;spacingRight=4;overflow=hidden;points=[[0,0.5],[1,0.5]];portConstraint=eastwest;rotatable=0;whiteSpace=wrap;html=1;labelBackgroundColor=none;opacity=0;" parent="16" vertex="1">
           <mxGeometry y="30" width="260" height="230" as="geometry" />
         </mxCell>
         <mxCell id="74" value="&lt;b style=&quot;&quot;&gt;&lt;font style=&quot;font-size: 14px;&quot;&gt;Output 1&lt;/font&gt;&lt;span style=&quot;font-size: 13px;&quot;&gt;: &lt;/span&gt;&lt;/b&gt;anchor output 330 sats.&lt;br&gt;&lt;b&gt;key spend&lt;/b&gt;: Pubkey from Alice / Bob" style="text;strokeColor=none;fillColor=none;align=left;verticalAlign=middle;spacingLeft=4;spacingRight=4;overflow=hidden;points=[[0,0.5],[1,0.5]];portConstraint=eastwest;rotatable=0;whiteSpace=wrap;html=1;labelBackgroundColor=none;opacity=0;" parent="16" vertex="1">