diff --git a/content/essays/index-period-normal-forms/index.md b/content/essays/index-period-normal-forms/index.md
index 46c3aa4..6b1b70d 100644
--- a/content/essays/index-period-normal-forms/index.md
+++ b/content/essays/index-period-normal-forms/index.md
@@ -25,8 +25,6 @@ tags:
   - research/graph-theory
 authors:
   - "Levi Neuwirth | /me.html"
-affiliation:
-  - "Brown University | https://www.brown.edu"
 no-collapse: true
 status: "Working model"
 confidence: 80
@@ -467,21 +465,6 @@ summary $P$. [□]{.proof-qed}
 
 :::
 
-::: {.annotation .annotation--static #rem-right-object}
-<div class="annotation-header">
-<span class="annotation-label">Remark 4.5</span>
-<span class="annotation-name">Why this is the right object</span>
-</div>
-<div class="annotation-body">
-
-The old bound used only the size of $M^{D(\mathcal{R})}$. That is enough to
-prove eventual pumping, but it ignores the actual contribution elements
-$\gamma_b$. The exact bound for a child type $b$ is controlled by the cyclic
-submonoid generated by $\gamma_b$, not by the whole product monoid.
-
-</div>
-:::
-
 ## Index-period decomposition in a finite monoid
 
 We now isolate the elementary finite-monoid fact used throughout the note.