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    <loc>https://mfg-lab.vercel.app/</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>weekly</changefreq>
    <priority>1.0</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.9</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/ai-verify</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.9</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/alien-science</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.85</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/mfg-congest</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.9</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/wardrop-repro</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.9</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/mfg-cap</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.8</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/stock-constraint</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.8</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/program</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.8</priority>
  </url>
  <!-- /about is priority 0.9, ABOVE /program and level with the reports. It is the page a
       name search has to land on, and the only one carrying Person structured data. -->
  <url>
    <loc>https://mfg-lab.vercel.app/about</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.9</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/mfg-lab</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.7</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/certificates</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.85</priority>
  </url>
<!-- SUPERSEDED 2026-08-05, kept as the record of what was true (C35). This said "/defects is
     deliberately NOT listed" because the page was noindex. It IS listed now, below: the owner
     directed on 2026-08-05 that every exported page be flipped to indexed, and /defects went
     with them. The reasoning the old note gave was sound and is exactly why the contradiction
     had to be resolved in one direction or the other rather than left standing. -->
  <url>
    <loc>https://mfg-lab.vercel.app/contact</loc>
    <lastmod>2026-07-30</lastmod>
    <changefreq>yearly</changefreq>
    <priority>0.5</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/catalogue</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/cap-for-mfg</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/certified-multiplicity</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/certified-price-formation</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/circuit-path-truncation</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/cobb-douglas-bracket</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/degree-sensitivity</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/edge-of-chaos</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/equilibrium-geometry</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/geometry-approaches</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/huggett-rational</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/interval-transcendentals</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/rational-attention</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/refusal-as-output</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/refusal-taxonomy</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/seaport-uniqueness</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/emergent-geometry</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/price-saturation</loc>
    <lastmod>2026-07-31</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.55</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/erdos290</loc>
    <lastmod>2026-08-03</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.8</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/defects</loc>
    <lastmod>2026-08-05</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.5</priority>
  </url>
  <!-- ADDED 2026-08-05. These nine routes were LIVE and self-declared robots index,follow while
       being absent from this file — so the pages asked to be indexed and the sitemap did not say
       they existed. Found by cross-checking PAGES.json exported:true routes against this file's
       own <loc> set; no gate performed that check, which is why it went unnoticed. THE GATE NOW
       EXISTS: tools/check-discoverable.js, run inside `make check-refs`, with a two-direction
       self-test flag.
       WHAT THE NEW GATE THEN FOUND, and what the owner then decided: 21 routes in this sitemap
       belonged to pages whose OWN robots tag said noindex — ai-verify, alien-science,
       mfg-congest, wardrop-repro, /defects and the exploratory notes. The owner directed on
       2026-08-05 that all of them be flipped to indexed, so the contradiction is resolved toward
       visibility and this file now lists every exported page. Nothing carries noindex any more. -->
  <!-- A NOTE THIS FILE OWES ITSELF: an earlier version of the comment above contained a double
       hyphen inside an XML comment, which is illegal, and it shipped live UNPARSEABLE for about
       an hour. Every text-level check kept passing, because they read this file as text rather
       than as XML. check-discoverable.js now parses it first: a sitemap that does not parse tells
       a crawler nothing at all, so validity is the one thing worth checking before anything else
       and it was the one thing nobody was checking. -->
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/faithfulness-ceiling</loc>
    <lastmod>2026-08-05</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.9</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/verification-lane</loc>
    <lastmod>2026-08-04</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.9</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/verify-maxwell</loc>
    <lastmod>2026-08-04</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.85</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/verify-lemniscate</loc>
    <lastmod>2026-08-04</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.85</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/verify-ranteng</loc>
    <lastmod>2026-08-04</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.8</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/verify-poisson</loc>
    <lastmod>2026-08-04</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.75</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/verify-mathieu</loc>
    <lastmod>2026-08-04</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.75</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/verify-korenblum</loc>
    <lastmod>2026-08-04</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.75</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/stack</loc>
    <lastmod>2026-08-05</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.7</priority>
  </url>
  <!-- ADDED 2026-08-05, second pass. These two were CORRECTLY absent until an hour ago because
       they carried noindex; the owner's flip left them asking to be indexed with no entry here,
       and check-discoverable.js caught both immediately — the gate doing the exact job it was
       written for, on a change made after it was written. -->
  <url>
    <loc>https://mfg-lab.vercel.app/technical-reports/attention-geometry</loc>
    <lastmod>2026-08-05</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.8</priority>
  </url>
  <url>
    <loc>https://mfg-lab.vercel.app/sin-mfg/water-value</loc>
    <lastmod>2026-08-05</lastmod>
    <changefreq>monthly</changefreq>
    <priority>0.6</priority>
  </url>
</urlset>
