--- title: The Lemma Said This Couldn’t Happen | daily.dev description: A developer implemented a cutting-edge deterministic shortest-path algorithm (arXiv:2602.07868) that had never been run on a machine before, and discovered... canonical: https://daily.dev/posts/the-lemma-said-this-couldn-t-happen-9z1welulp twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: The Lemma Said This Couldn’t Happen | daily.dev og:description: A developer implemented a cutting-edge deterministic shortest-path algorithm (arXiv:2602.07868) that had never been run on a machine before, and discovered... og:url: https://daily.dev/posts/the-lemma-said-this-couldn-t-happen-9z1welulp og:image: https://api.daily.dev/og/posts/9z1wELULp.png og:image:alt: The Lemma Said This Couldn’t Happen og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # The Lemma Said This Couldn’t Happen **[Medium](https://daily.dev/sources/medium_js)** · 9 min read · 0 upvotes · 0 comments ## Summary A developer implemented a cutting-edge deterministic shortest-path algorithm (arXiv:2602.07868) that had never been run on a machine before, and discovered multiple critical issues: two crash-inducing bugs from empty argmin operations, a parameter prescription that requires n ≥ 2^4096 to be valid (making it unusable on any real input), and a false completeness clause in Lemma 3.7 that causes incorrect distances when applying the most standard Dijkstra optimization. The algorithm itself still produces correct results by accidentally re-settling vertices, but the proof that licenses skipping re-settlements is demonstrably false on a 70-vertex graph. After nine engine variants and a hand-written proof, the best implementation runs at 1.8–2.2× Dijkstra's speed — essentially becoming Dijkstra with extra label overhead. The conclusion: both papers represent genuine theoretical progress, but neither should be shipped in production. The practical recommendation remains: use Dijkstra. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Similar posts on daily.dev - [Faster than Dijkstra?](https://daily.dev/posts/faster-than-dijkstra--luk6oiopf) · Hacker News · 3 upvotes · 0 comments --- Tags: [#python](https://daily.dev/tags/python) [View this post on daily.dev](https://daily.dev/posts/the-lemma-said-this-couldn-t-happen-9z1welulp) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"The Lemma Said This Couldn’t Happen","url":"https://daily.dev/posts/the-lemma-said-this-couldn-t-happen-9z1welulp","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/the-lemma-said-this-couldn-t-happen-9z1welulp"},"datePublished":"2026-07-27T07:30:40.221Z","dateModified":"2026-07-27T07:31:13.640Z","description":"A developer implemented a cutting-edge deterministic shortest-path algorithm (arXiv:2602.07868) that had never been run on a machine before, and discovered...","image":"https://miro.medium.com/v2/da:true/resize:fit:1050/1*PmhcttiCvrpqKG_1wnZMlQ.gif","thumbnailUrl":"https://miro.medium.com/v2/da:true/resize:fit:1050/1*PmhcttiCvrpqKG_1wnZMlQ.gif","isAccessibleForFree":true,"articleSection":"Medium","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"Medium","logo":"https://media.daily.dev/image/upload/t_logo,f_auto/v1/logos/medium","url":"https://daily.dev/sources/medium_js"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/the-lemma-said-this-couldn-t-happen-9z1welulp","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":0},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"python","timeRequired":"PT9M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"Medium","item":"https://daily.dev/sources/medium_js"},{"@type":"ListItem","position":3,"name":"The Lemma Said This Couldn’t Happen"}]} ```