<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content/"><channel><title>Clocks · XB Field Notes</title><link>https://www.xbcatm.com/tags/clocks/</link><description>Illustrated field notes on HTTP, DNS, TLS, Caddy, SSH, releases, and recovery.</description><generator>Hugo</generator><language>en-us</language><atom:link href="https://www.xbcatm.com/tags/clocks/index.xml" rel="self" type="application/rss+xml"/><item><title>Vector clocks order concurrent writes</title><link>https://www.xbcatm.com/posts/vector-clocks-order-concurrent-writes/</link><pubDate>Sat, 18 Sep 2027 00:00:00 +0000</pubDate><guid>https://www.xbcatm.com/posts/vector-clocks-order-concurrent-writes/</guid><description>A single clock cannot order events across machines. A vector clock tracks each participant's impression, letting replicas decide whether two writes conflict or one causally follows the other.</description><content:encoded>&lt;p&gt;Each node keeps a counter per participant. Comparing vectors reveals a causal edge or a true concurrent write, which decides whether to merge or to ask.&lt;/p&gt;
&lt;h2 id="one-timestamp-is-not-enough"&gt;One timestamp is not enough&lt;/h2&gt;
&lt;p&gt;A single timestamp cannot order concurrent events, because a clock is not a cause, so two nodes that each wrote something at the same label may still disagree about which came first. Vector clocks solve that by giving every participant its own counter: a process bumps its own slot whenever it does something, and merges the sender&amp;rsquo;s vector into its own whenever it receives a message. The result is a vector that grows as events happen, and comparing two vectors tells you whether one event provably preceded the other, or whether neither did.&lt;/p&gt;
&lt;h2 id="compare-vectors-to-see-causality"&gt;Compare vectors to see causality&lt;/h2&gt;
&lt;p&gt;To compare vectors, look element by element: if every value in one vector is less than or equal to the matching value in the other, the first event happened before the second; otherwise the two events are concurrent. Because a causal order accumulates everywhere the two paths crossed, a vector captures the transitive and direct edges that a single scalar time forfeits. The moment a message passes from A to B, B&amp;rsquo;s vector reflects both B&amp;rsquo;s own progress and everything A had seen, which is how the model traces causality instead of guessing it.&lt;/p&gt;
&lt;h2 id="concurrent-means-someone-decides"&gt;Concurrent means someone decides&lt;/h2&gt;
&lt;p&gt;Concurrency in the vector sense does not produce a winner; it only says two events are unrelated or tied, so someone else must decide the order when the application needs one. That decision is usually made by comparing a key or by ordering on the vector values themselves, and it must be deterministic so every replica agrees. The design is honest: vector clocks do not fabricate a total order among unrelated writes, they only expose that no such order exists; the final ordering decision belongs to the rule above them.&lt;/p&gt;
&lt;h2 id="when-it-breaks"&gt;When it breaks&lt;/h2&gt;
&lt;p&gt;Vector clocks fail first by growing. One entry exists per participant, so a key written by hundreds of short-lived clients carries hundreds of counters on every read, and every write ships them back. Dynamo reported exactly this pressure: reconciliation metadata grows with the writer set, and Riak operators see the same symptom as oversized causal context that slows reads and multiplies siblings. Evicting the oldest entries feels like relief, but it deletes causality.&lt;/p&gt;
&lt;p&gt;Once node C is pruned from &lt;code&gt;[A:3, B:2, C:5]&lt;/code&gt;, later comparisons read the missing slot as zero, so an event C had already observed looks brand new, and a write that should have stayed subsumed resurrects as a false sibling.&lt;/p&gt;
&lt;p&gt;The second failure misreads concurrent vectors as ordered. Comparing only the sum, the maximum, or a wall-clock timestamp beside the vector elects a winner between &lt;code&gt;[A:2, B:1]&lt;/code&gt; and &lt;code&gt;[A:1, B:2]&lt;/code&gt;, yet neither dominates the other element by element, so the honest answer is concurrent, not before or after. The discarded sibling is a lost update the clock had flagged correctly. The mirror mistake treats one equal slot as equal history: &lt;code&gt;[A:2]&lt;/code&gt; seen twice is the same event replayed, but &lt;code&gt;[A:2]&lt;/code&gt; against &lt;code&gt;[A:2, B:1]&lt;/code&gt; is a strict before relation, and overwriting the longer vector with the shorter one rewinds history.&lt;/p&gt;
&lt;p&gt;The guard is strict: return causal context on every write, merge with element-wise maximum, increment only your own slot, and prune only with a dominance-preserving scheme such as dotted version vectors. A write without its read vector forks a sibling every time.&lt;/p&gt;
&lt;h2 id="check-it-quickly"&gt;Check it quickly&lt;/h2&gt;
&lt;p&gt;Save this as &lt;code&gt;check_vector_clocks.py&lt;/code&gt; and run &lt;code&gt;python3 check_vector_clocks.py&lt;/code&gt;. It stores vectors as plain dicts with missing entries read as zero, then asserts all three outcomes: happens-before with equality in both directions, plus a concurrent pair whose merge dominates both parents.&lt;/p&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-python" data-lang="python"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s2"&gt;&amp;#34;&amp;#34;&amp;#34;Return &amp;#39;equal&amp;#39;, &amp;#39;before&amp;#39;, &amp;#39;after&amp;#39;, or &amp;#39;concurrent&amp;#39;.&amp;#34;&amp;#34;&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;nodes&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;set&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="nb"&gt;set&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;le&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;all&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;nodes&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;ge&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;all&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;nodes&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;le&lt;/span&gt; &lt;span class="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;ge&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;equal&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;le&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;before&amp;#34;&lt;/span&gt; &lt;span class="c1"&gt;# a happens-before b&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;ge&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;after&amp;#34;&lt;/span&gt; &lt;span class="c1"&gt;# b happens-before a&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;concurrent&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;merge&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nb"&gt;set&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="nb"&gt;set&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;tick&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;clock&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;nxt&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;clock&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;nxt&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;nxt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;nxt&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;# 1. Happens-before: b extends a with one new event from B.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;assert&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;before&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;assert&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;after&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;# 2. Equal: the same causal history seen twice.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;assert&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;equal&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;# 3. Concurrent: each side saw something the other missed.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;assert&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;concurrent&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;# Merge of concurrent histories dominates both parents.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;m&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;merge&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;assert&lt;/span&gt; &lt;span class="n"&gt;m&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;B&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;assert&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;m&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;before&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;assert&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;m&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;before&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;# A truncated vector lies: dropping B makes m look merely later.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;truncated&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;A&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;assert&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;truncated&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;m&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;before&amp;#34;&lt;/span&gt; &lt;span class="c1"&gt;# missing B reads as 0, hiding what was pruned&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="nb"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;PASS: before/after/equal/concurrent and merge all behave as expected&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;Expect before and after on the extended vector, equal on identical histories, and concurrent on the split pair. The merge reads &lt;code&gt;[A:2, B:2]&lt;/code&gt; and follows each parent, while truncated &lt;code&gt;[A:2]&lt;/code&gt; still reports before, showing how pruning hides causality. The assertions passed with CPython 3.12 on macOS; the sketch omits pruning, dotted versions, and persistence, so treat it as a comparison demo, not a store.&lt;/p&gt;
&lt;h2 id="further-reading"&gt;Further reading&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.xbcatm.com/posts/gossip-protocols-converge-eventually/"&gt;Gossip protocols converge eventually&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://www.xbcatm.com/posts/clock-sync-keeps-distributed-time-honest/"&gt;Clock synchronization bounds time disagreement&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;h2 id="sources"&gt;Sources&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.allthingsdistributed.com/files/amazon-dynamo-sosp2007.pdf"&gt;Dynamo: Amazon&amp;rsquo;s highly available key-value store&lt;/a&gt;, reconciliation with version vectors and sibling retention, checked 2026-09-12.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://docs.riak.com/riak/kv/2.2.3/learn/concepts/causal-context/"&gt;Riak KV 2.2.3: Causal context (vector clocks and dotted version vectors)&lt;/a&gt;, vector-clock growth, pruning hazards, and dotted version vectors, checked 2026-09-12.&lt;/li&gt;
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