MacBookPro.lan 2026-5-2:23:34:24

.obsidian/plugins/obsidian-pandoc-reference-list/data.json

@@ -5,7 +5,7 @@
     {
       "id": 1,
       "name": "Ma bibliothèque",
-      "lastUpdate": 1777592858082
+      "lastUpdate": 1777756541919
     }
   ],
   "renderCitations": true,

désintégration audioactive.md

@@ -538,7 +538,10 @@ Conway leur donne des noms d'éléments (de l'hydrogène à l'uranium, ce qui fa
 > Il est évident que $\lambda$ est un nombre algébrique de degré $92$.
 
 > [!proposition]+ Théorème cosmologique
-> Toute chaine (autre que $[\;]$ et $[22]$) finit, après assez de dérivations, par 
+> Toute chaine (autre que $[\;]$ et $[22]$) finit, après assez de dérivations, par engendrer des chaines communes. Cela permet d'appliquer le théorème chimique à toutes les chaines.
+> > [!démonstration]- Démonstration
+> > La démonstration serait trop complexe pour le cadre de ce devoir. Conway lui-même ne l'a pas publiée dans son article *The weird and wonderful chemistry of audioactive decay*.
+> > Des preuves existent, prenant de l'ordre de 15 pages : [@lairezConwaysCosmologicalTheorem2025], 
 
 # Annexes
 
@@ -693,3 +696,9 @@ for elt_num in range(2, 93):
                              nb_derivations_engendre_tous_les_elements(elt_num))
 print("Borne pour le théorème chimique :", min_steps_required)
 ```
+
+# Bibliographie
+
+Lairez, P., & Storozhenko, A. (2025). Conway’s cosmological theorem and automata theory. _The American Mathematical Monthly_, _132_(9), 867–882. [https://doi.org/10.1080/00029890.2025.2549225](https://doi.org/10.1080/00029890.2025.2549225)
+Ekhad, S. B., & Zeilberger, D. (n.d.). _Proof of Conway’s lost cosmological theorem_. Retrieved [https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/horton.pdf](https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/horton.pdf)
+

sources/zotero/bibliographie/biblio.bib

@@ -511,6 +511,27 @@
   file = {/Users/oscarplaisant/Zotero/storage/767E3XLT/what-is-functional-programming.html}
 }
 
+@article{lairezConwaysCosmologicalTheorem2025,
+  title = {Conway's Cosmological Theorem and Automata Theory},
+  author = {Lairez, Pierre and Storozhenko, Aleksandr},
+  date = {2025-10-21},
+  journaltitle = {The American Mathematical Monthly},
+  shortjournal = {The American Mathematical Monthly},
+  volume = {132},
+  number = {9},
+  eprint = {2409.20341},
+  eprinttype = {arXiv},
+  eprintclass = {cs},
+  pages = {867--882},
+  issn = {0002-9890, 1930-0972},
+  doi = {10.1080/00029890.2025.2549225},
+  url = {http://arxiv.org/abs/2409.20341},
+  urldate = {2026-05-02},
+  abstract = {John Conway proved that every audioactive sequence (a.k.a. look-and-say) decays into a compound of 94\textasciitilde elements, a statement he termed the cosmological theorem. The underlying audioactive process can be modeled by a finite-state machine, mapping one sequence of integers to another. Leveraging automata theory, we propose a new proof of Conway's theorem based on a few simple machines, using a computer to compose and minimize them.},
+  keywords = {Computer Science - Formal Languages and Automata Theory},
+  file = {/Users/oscarplaisant/Zotero/storage/8MAWWH76/Lairez and Storozhenko - 2025 - Conway's cosmological theorem and automata theory.pdf;/Users/oscarplaisant/Zotero/storage/JF782S4T/2409.html}
+}
+
 @article{linEffectsWhiteNoise2022,
   title = {The {{Effects}} of {{White Noise}} on {{Attentional Performance}} and {{On-Task Behaviors}} in {{Preschoolers}} with {{ADHD}}},
   author = {Lin, Hung-Yu},
@@ -625,10 +646,8 @@
   file = {/Users/oscarplaisant/Zotero/storage/42P5K7TK/Okasaki - 1999 - Purely Functional Data Structures.pdf}
 }
 
-@online{OpenProblemsCommunication,
+@book{OpenProblemsCommunication,
   title = {Open Problems in Communication and Computation - {{Anna}}’s {{Archive}}},
-  url = {https://annas-archive.gd/md5/47f7db963973665771542f4578a8302f},
-  urldate = {2026-03-27},
   file = {/Users/oscarplaisant/Zotero/storage/822E4RYV/47f7db963973665771542f4578a8302f.html}
 }
 
@@ -833,3 +852,10 @@
   keywords = {communication,modèle,paradigme,schéma,théorie},
   file = {/Users/oscarplaisant/Zotero/storage/LFD49R3K/Willett - 1996 - Paradigme, théorie, modèle, schéma  qu’est-ce donc .pdf}
 }
+
+@article{ZeilbergerDoronCosmologicalTheorem,
+  title = {Proof of {{Conway}}'s Lost Cosmological Theorem},
+  author = {Ekhad, Shalosh B. and Zeilberger, Doron},
+  url = {https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/horton.pdf},
+  file = {/Users/oscarplaisant/Zotero/storage/NDV3AFE4/horton.pdf}
+}