{"id":56436,"date":"2025-10-02T19:40:23","date_gmt":"2025-10-02T18:40:23","guid":{"rendered":"https:\/\/4.exstyle.fr\/le-blog-photo\/blog-2\/"},"modified":"2025-10-04T13:30:29","modified_gmt":"2025-10-04T12:30:29","slug":"blog-2","status":"publish","type":"page","link":"https:\/\/4.exstyle.fr\/le-blog-photo\/blog-2\/","title":{"rendered":"Blog"},"content":{"rendered":"\n<div class=\"wp-block-query is-layout-flow wp-block-query-is-layout-flow\"><ul class=\"wp-block-post-template is-layout-flow wp-block-post-template-is-layout-flow\"><li class=\"wp-block-post post-56570 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-d2\/\" target=\"_self\" >Fr &#8211; D2<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Couture par distances et potentiel d\u00e9croissant pour la dynamique Collatz (odd-only) TL;DR. On code chaque pas impair par une distance paire \\( D=2d \\) et une branche \\((\\,-\\,)\\) ou \\( (+) \\). On obtient une couture explicite \\( D \\mapsto D&rsquo; \\) via \\( s=\\nu_2(9d\\pm\\text{const}) \\). Puis on construit un potentiel \\[ \\Phi=\\log_2(D+\\kappa)\\;-\\;\\gamma\\cdot \\mathrm{clip}(k-2,\\,\\le 2)\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-29T23:54:00+01:00\">29 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56568 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-preuve-par-tape\/\" target=\"_self\" >Fr &#8211; Preuve par tape<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Tape de base : r\u00e8gles et convergence R\u00e8gles (telles qu\u2019on les fige ici) : pair + : devient impair + (on reste c\u00f4t\u00e9 + et on atteint une valeur impaire). impair + : devient impair \u2212 (on change de signe en restant impaire). pair \u2212 : halving jusqu\u2019\u00e0 l\u2019impair \u2212 suivant (ex. : -14 \u2192\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-26T13:54:35+01:00\">26 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56563 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-tape-d\/\" target=\"_self\" >FR &#8211; Tape D<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Collatz \u201caplati\u201d : deux courbes pli\u00e9es, un pont de longueur 1 R\u00e9sum\u00e9. On projette la dynamique impaire compress\u00e9e du Collatz sur deux suites tr\u00e8s clairsem\u00e9es : la branche positive (d\u00e9calage \u22121 puis un impair sur deux) et la branche n\u00e9gative (d\u00e9calage +1 puis un impair sur trois). Ces deux sous-dynamiques s\u2019identifient aux triangulaires \\( T(n)=\\frac{n(n+1)}{2}\\;\\)\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-24T14:18:37+01:00\">24 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56558 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-d-et-mise-a-lechelle-24\/\" target=\"_self\" >FR -> D et mise \u00e0 l&rsquo;\u00e9chelle 24<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">UPdelta \u2014 \u00c9chelle 24 = 1 : un \u00ab mod\u00e8le dans le mod\u00e8le \u00bb pour comprendre l\u2019anti-cycle Id\u00e9e cl\u00e9 : en divisant toutes les quantit\u00e9s par 24, chaque rang\u00e9e (distance D) devient le m\u00eame gabarit g\u00e9om\u00e9trique \u2014 un \u00ab ruban \u00bb constant \u2014 et toute la dynamique int\u00e9ress\u00e9e par les cycles se concentre alors sur\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-20T13:29:55+01:00\">20 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56546 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-updelta\/\" target=\"_self\" >FR -> UPdelta<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Dynamique \u00ab ultra-compress\u00e9e \u00bb sur l\u2019ossature Collatz : potentiel, contraction r+\u2192r+ et certificats On conserve la g\u00e9om\u00e9trie compress\u00e9e de Collatz (colonnes, fratries, diagonales), mais on \u00ab avale \u00bb la cascade de divisions par 2 en ne visitant que les impairs. On exhibe un potentiel entier \\(D\\) qui d\u00e9cro\u00eet pour la r\u00e8gle \u00e9tudi\u00e9e, puis on construit\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-15T12:08:58+01:00\">15 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56541 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/collatz-preuve-variante-2x-1-mod-basee-sur-structure-compresse\/\" target=\"_self\" >Collatz \u2013 Preuve variante 2x-1 mod bas\u00e9e sur structure compress\u00e9<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">R\u00e9sum\u00e9 \u2014 Dynamique \u00ab ultra-compress\u00e9e \u00bb sur l\u2019ossature Collatz &amp; pont vers la classique R\u00e8gle \u00e9tudi\u00e9e (entiers&nbsp;\u2265&nbsp;0)&nbsp;: \\(f(x)=\\begin{cases}\\frac{x-1}{4},&#038; x\\equiv 1\\ (\\mathrm{mod}\\ 4),\\\\[4pt]2x-1,&#038; \\text{sinon.}\\end{cases}\\) Id\u00e9e&nbsp;: on garde la g\u00e9om\u00e9trie compress\u00e9e de Collatz (colonnes \\(L_{r,n}\\), fratries, diagonales), mais on \u00ab avale \u00bb la cascade des pairs en ne visitant que les fr\u00e8res impairs. 1) Ossature Collatz conserv\u00e9e\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-15T08:58:32+01:00\">15 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56537 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/collatz-variante-mod-basee-sur-structure-compresse\/\" target=\"_self\" >Collatz &#8211; Variante mod bas\u00e9e sur structure compress\u00e9<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Dynamique affine sur l\u2019ossature Collatz R\u00e8gle \u00e0 trois branches (entiers&nbsp;\u2265&nbsp;0) : \\(f(x)=\\begin{cases} \\frac{x-1}{4}&#038; \\text{si }x\\equiv1\\ (\\mathrm{mod}\\ 4),\\\\[4pt] 3x-1&#038; \\text{si }x\\equiv1\\ (\\mathrm{mod}\\ 2)\\ \\text{(i.e. }x\\equiv3\\ (\\mathrm{mod}\\ 4)\\text{)},\\\\[4pt] 3x+1&#038; \\text{si }x\\equiv0\\ (\\mathrm{mod}\\ 2). \\end{cases}\\) Id\u00e9e : on conserve la g\u00e9om\u00e9trie compress\u00e9e de Collatz (colonnes \\(L_{r,n}\\), racines minimales, \u00ab liens \u00bb, diagonales NE\/SE), mais on fige la\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-14T16:17:49+01:00\">14 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56534 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-pont-conjoncture-%e2%88%921-4-1-%e2%86%94-collatz-compresse-distance-d\/\" target=\"_self\" >FR &#8211; PONT CONJONCTURE (\u22121\/4 \/ +1) \u2194 COLLatz compress\u00e9, DISTANCE D<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Conjoncture \u201c\u22121\/4 si possible, sinon +1\u201d \u2014 Lien complet avec Collatz compress\u00e9 et la distance D R\u00e8gle (sur les entiers) : \\[ f(n)= \\begin{cases} \\frac{n-1}{4}, &#038; \\text{si } n\\equiv 1\\pmod 4,\\\\[4pt] n+1, &#038; \\text{sinon.} \\end{cases} \\] On montre : (i) pas de cycle non trivial (tout converge vers \\(0\\leftrightarrow 1\\)) ; (ii) traduction exacte dans\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-13T08:37:12+01:00\">13 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56529 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-collatz-distance-et-frere-innaccessibles\/\" target=\"_self\" >FR &#8211; Collatz distance et fr\u00e8re innaccessibles<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Fr\u00e8res \u00ab double \u2212 1 \u00bb non divisibles par 3 \u2014 lecture en distance D (rep\u00e8re MCC) But. Pour une fratrie impaire \\(r\\), on consid\u00e8re les nombres \\(\\;y_k(r)=r\\cdot4^k-1\\;\\) (les \u00ab fr\u00e8res \u22121 \u00bb). On veut : (i) les reclasser par liens \\(Y_\\pm=3D\\pm1\\) (distance \\(D\\) paire), (ii) d\u00e9crire leur dynamique compress\u00e9e \\(T(y)=\\mathrm{oddize}(3y+1)\\) en \\(D\\), et (iii)\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-10T10:58:33+01:00\">10 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56524 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-collatz-ennonce-par-les-distances\/\" target=\"_self\" >FR &#8211; Collatz ennonc\u00e9 par les Distances<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Collatz \u00ab&nbsp;en distances&nbsp;\u00bb : d\u00e9finition, it\u00e9ration, exemples et pistes anti-cycle Id\u00e9e. On remplace l\u2019impair visit\u00e9 x par une distance enti\u00e8re D et un signe de branche \\( \\sigma\\in\\{-,+\\} \\) tels que \\(\\;x=Y_\\sigma(D)=\\begin{cases} 3D-1 &#038;(\\sigma=-),\\\\ 3D+1 &#038;(\\sigma=+). \\end{cases}\\) C\u2019est une formulation strictement \u00e9quivalente \u00e0 la Collatz compress\u00e9e classique (impair \\(\\mapsto\\) diviser par \\(2^k\\) jusqu\u2019\u00e0 l\u2019impair suivant),\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-09T11:08:06+01:00\">9 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56515 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-approche-par-racine-minimal\/\" target=\"_self\" >FR &#8211; Approche par racine minimal<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Retours \u22121\/4, squelette MCC et \u00ab&nbsp;distance&nbsp;\u00bb : pourquoi c\u2019est utile (et comment s\u2019en servir) Id\u00e9e g\u00e9n\u00e9rale. Les retours (y\u22121)\/4 ne sont pas la r\u00e8gle Collatz compress\u00e9e, mais l\u2019inverse du pas fratrie NE&nbsp;:&nbsp;x\u21a64x+1. Ils permettent de remonter le squelette MCC jusqu\u2019\u00e0 la racine minimale et fournissent des congruences fortes modulo \\(4^{j}\\) qui forcent des poids 2-adiques\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-07T13:20:55+01:00\">7 octobre 2025<\/time><\/div>\n<\/li><li class=\"wp-block-post post-56502 post type-post status-publish format-standard hentry category-non-classe tag-math\">\n<h2 class=\"wp-block-post-title\"><a href=\"https:\/\/4.exstyle.fr\/le-blog-photo\/fr-preuve-avec-3\/\" target=\"_self\" >FR Preuve avec \/3<\/a><\/h2>\n\n\n\n<div class=\"wp-block-post-excerpt\"><p class=\"wp-block-post-excerpt__excerpt\">Variante \u00ab \/3 sinon *2\u22121 \u00bb vs Collatz classique : \u00e9quations de cycle et seuils critiques But. Mettre en parall\u00e8le la variante T(n)=n\/3 si 3|n, sinon T(n)=2n\u22121 (o\u00f9 l\u2019on prouve qu\u2019il n\u2019y a aucun cycle non trivial), et la Collatz classique compress\u00e9e (o\u00f9 il faut certifier une marge sur la moyenne des valuations). Les deux\u2026 <\/p><\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<div class=\"wp-block-post-date\"><time datetime=\"2025-10-06T13:34:23+01:00\">6 octobre 2025<\/time><\/div>\n<\/li><\/ul><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"full-width","meta":{"saved_in_kubio":true,"footnotes":""},"categories":[],"tags":[],"class_list":["post-56436","page","type-page","status-publish","hentry"],"kubio_ai_page_context":{"short_desc":"","purpose":"general"},"_links":{"self":[{"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/pages\/56436","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/comments?post=56436"}],"version-history":[{"count":5,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/pages\/56436\/revisions"}],"predecessor-version":[{"id":56481,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/pages\/56436\/revisions\/56481"}],"wp:attachment":[{"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/media?parent=56436"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/categories?post=56436"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/4.exstyle.fr\/le-blog-photo\/wp-json\/wp\/v2\/tags?post=56436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}