<?xml version="1.0" encoding="UTF-8"?><?xml-stylesheet type="text/xsl" href="//blog.alexpetty.com/sitemap.xsl"?><urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9" xmlns:image="http://www.google.com/schemas/sitemap-image/1.1"><url><loc>https://blog.alexpetty.com/silent-primes/</loc><lastmod>2026-05-21T06:50:07.068Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b13a-cover.png</image:loc><image:caption>b13a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-character-structure-of-the-collision-fluctuation/</loc><lastmod>2026-05-21T05:36:41.706Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b7a-cover.png</image:loc><image:caption>b7a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/bin-derangements-and-the-gate-width-theorem/</loc><lastmod>2026-05-21T05:19:48.695Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b11a-cover.png</image:loc><image:caption>b11a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/phase-filtered-ramanujan-sums-and-the-spectral-gate/</loc><lastmod>2026-05-21T05:10:16.219Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b12a-cover.png</image:loc><image:caption>b12a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-autocorrelation-formula/</loc><lastmod>2026-05-21T03:18:42.368Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b10a-cover.png</image:loc><image:caption>b10a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-analytic-collision-transform/</loc><lastmod>2026-05-21T01:01:21.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/04/analytic-collision-transform-cover-a-1.png</image:loc><image:caption>analytic-collision-transform-cover-a-1.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-alignment-deficit-lattice/</loc><lastmod>2026-05-21T01:01:14.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/04/phi-and-major-scale-cover-a-1.png</image:loc><image:caption>phi-and-major-scale-cover-a-1.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-spectral-power-of-the-digit-function/</loc><lastmod>2026-05-20T18:40:56.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b9a-cover.png</image:loc><image:caption>b9a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-spectral-structure-of-fractional-fields/</loc><lastmod>2026-05-20T18:15:33.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b8a-cover.png</image:loc><image:caption>b8a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-cross-alignment-matrix/</loc><lastmod>2026-05-20T18:03:46.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b6a-cover.png</image:loc><image:caption>b6a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-coherence-decomposition/</loc><lastmod>2026-05-20T17:34:13.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b5a-cover.png</image:loc><image:caption>b5a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-three-tier-theorem/</loc><lastmod>2026-05-20T16:51:39.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b4d-cover.png</image:loc><image:caption>b4d-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-alignment-limit-for-all-primes/</loc><lastmod>2026-05-20T16:44:51.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b3-cover.png</image:loc><image:caption>b3-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/digit-partitioning-primes-and-the-alignment-formula/</loc><lastmod>2026-05-20T16:37:56.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b2-cover.png</image:loc><image:caption>b2-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/why-the-golden-ratio-selects-the-prime-three/</loc><lastmod>2026-05-20T16:16:19.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b1b-cover.png</image:loc><image:caption>b1b-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-collision-spectrum/</loc><lastmod>2026-04-18T05:22:28.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/04/collision-transform-cover-c.png</image:loc><image:caption>collision-transform-cover-c.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-collision-spectrum-and-the-l-function-landscape/</loc><lastmod>2026-04-18T05:21:25.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b22a-cover.png</image:loc><image:caption>b22a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/long-division-and-euclids-lemma/</loc><lastmod>2026-04-17T19:59:18.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/Figure-21.-Petty-Foundational-Division-Lemma-for-a-equals-1-through-32-2-1.png</image:loc><image:caption>Figure-21.-Petty-Foundational-Division-Lemma-for-a-equals-1-through-32-2-1.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/geometries-hidden-in-the-number-system/</loc><lastmod>2026-04-17T19:59:17.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/47fns.png</image:loc><image:caption>47fns.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-effect-of-base-on-numeric-fields/</loc><lastmod>2026-04-17T19:59:17.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b2m1-fns-web.png</image:loc><image:caption>b2m1-fns-web.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/foundational-tables-of-multiplication/</loc><lastmod>2026-04-17T19:59:16.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/fives-table-chart-1-v2.png</image:loc><image:caption>fives-table-chart-1-v2.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/arithmetic-foundations/</loc><lastmod>2026-04-17T19:59:16.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/fns-circle-chart-round-2x-v2.png</image:loc><image:caption>fns-circle-chart-round-2x-v2.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-golden-ratio/</loc><lastmod>2026-04-17T19:59:16.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/simple-construction-of-phi-v2.png</image:loc><image:caption>simple-construction-of-phi-v2.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/on-numeric-polarity-and-the-distribution-of-primes/</loc><lastmod>2026-04-17T19:59:15.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/numeric-polarity1-1.png</image:loc><image:caption>numeric-polarity1-1.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-structure-that-survives/</loc><lastmod>2026-04-17T19:59:15.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/04/structure-survives-cover-b.png</image:loc><image:caption>structure-survives-cover-b.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-double-transversality/</loc><lastmod>2026-04-17T19:59:12.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b20a-cover.png</image:loc><image:caption>b20a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-spectral-repulsion/</loc><lastmod>2026-04-17T19:59:12.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b21a-cover.png</image:loc><image:caption>b21a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-neutrality-theorem/</loc><lastmod>2026-04-17T19:59:11.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b18a-cover.png</image:loc><image:caption>b18a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-general-neutrality-theorem/</loc><lastmod>2026-04-17T19:59:11.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b19a-cover.png</image:loc><image:caption>b19a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-centered-collision-sum/</loc><lastmod>2026-04-17T19:59:10.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b16a-cover.png</image:loc><image:caption>b16a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-collision-transform-and-the-critical-strip/</loc><lastmod>2026-04-17T19:59:10.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b17a-cover.png</image:loc><image:caption>b17a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-collision-periodic-table/</loc><lastmod>2026-04-17T19:59:10.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/04/collision-pnt-cover-c.png</image:loc><image:caption>collision-pnt-cover-c.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-collision-fluctuation-sum/</loc><lastmod>2026-04-17T19:59:09.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/03/b14a-cover.png</image:loc><image:caption>b14a-cover.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-collision-invariant/</loc><lastmod>2026-04-14T23:52:49.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/04/collision-invariant-cover-a.png</image:loc><image:caption>collision-invariant-cover-a.png</image:caption></image:image></url><url><loc>https://blog.alexpetty.com/the-collision-transform/</loc><lastmod>2026-04-14T19:31:08.000Z</lastmod><image:image><image:loc>https://blog.alexpetty.com/content/images/2026/04/collision-transform-cover-e.png</image:loc><image:caption>collision-transform-cover-e.png</image:caption></image:image></url></urlset>