diff --git a/trees/ag-000I.tree b/trees/ag-000I.tree
index 3ad3567f..48601891 100644
--- a/trees/ag-000I.tree
+++ b/trees/ag-000I.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative
 
-\card{Definition}{Signed distance function \citewiki{sdf}{Signed_distance_function}}{
+\card{Definition}{signed distance function \citewiki{sdf}{Signed_distance_function}}{
 
 \p{
 Let #{\Omega} be a subset of a [metric space](https://en.wikipedia.org/wiki/Metric_space) #{X} with metric #{d}, and #{\partial \Omega} be its boundary. The distance between a point #{\point{p}} of #{X} and the subset #{\partial \Omega} of #{X} is defined as usual as
diff --git a/trees/ag-000J.tree b/trees/ag-000J.tree
index 847a98fc..4206feca 100644
--- a/trees/ag-000J.tree
+++ b/trees/ag-000J.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative
 
-\card{Convention}{Sign}{
+\card{Convention}{sign}{
 \p{Simply put, SDFs are the minimum possible distance from a point to an implicit surface defined by #{f(\point{p})=0}.}
 
 \p{The convention adopted in this note is that the #{+} and #{-} signs indicate whether the point is outside or inside the surface, respectively, so that when a ray marches towards the surface from the outside, the distance is positive, becomes smaller when approaching the surface.
diff --git a/trees/ag-000K.tree b/trees/ag-000K.tree
index 2f3ffa7a..b8f949f2 100644
--- a/trees/ag-000K.tree
+++ b/trees/ag-000K.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere
 
-\refdeft{Implicit surface}{sec. 1}{hart1996sphere}{
+\refdeft{implicit surface}{sec. 1}{hart1996sphere}{
 \p{If an SDF #{f} is a continuous mapping, the subset #{\Omega}  can be implicitly described as the [locus](https://en.wikipedia.org/wiki/Locus_(mathematics)) of points
 
 ##{ \Omega = \{ p : f(p) \le 0 \} }
diff --git a/trees/ag-000R.tree b/trees/ag-000R.tree
index 6e339d04..34adb468 100644
--- a/trees/ag-000R.tree
+++ b/trees/ag-000R.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere
 
-\refdeft{Point-to-set distance}{def. 1}{hart1996sphere}{
+\refdeft{point-to-set distance}{def. 1}{hart1996sphere}{
 \p{
 The \newvocab{point-to-set distance} defines the distance from a point #{\point{x} \in \mathbb{R}^3} to a set #{A \subset \mathbb{R}^3} as the distance from #{x} to the closest point in #{A},
 
diff --git a/trees/ag-000S.tree b/trees/ag-000S.tree
index 8b3cb7cb..41174e2f 100644
--- a/trees/ag-000S.tree
+++ b/trees/ag-000S.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray
 
-\refdeft{Signed distance bound}{def. 2}{hart1996sphere}{
+\refdeft{signed distance bound}{def. 2}{hart1996sphere}{
 \p{
 A function #{f: \mathbb{R}^3 \rightarrow \mathbb{R}} is a \newvocab{signed distance bound} of its implicit surface #{f^{-1}(0)} if and only if
 
diff --git a/trees/ag-000V.tree b/trees/ag-000V.tree
index 563063d3..2a6b9087 100644
--- a/trees/ag-000V.tree
+++ b/trees/ag-000V.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray
 
-\refdeft{Ray equation}{sec. 1.1 eq. 3}{gillespie2024ray}{
+\refdeft{ray equation}{sec. 1.1 eq. 3}{gillespie2024ray}{
 \p{
 A \vocab{ray} anchored at origin #{\boldsymbol{r}_o} in the direction of the unit vector #{\boldsymbol{r}_d} can be parametrically defined as a \newvocab{ray equation}
 
diff --git a/trees/ag-000W.tree b/trees/ag-000W.tree
index 8eb69b16..59167e6b 100644
--- a/trees/ag-000W.tree
+++ b/trees/ag-000W.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray
 
-\refdeft{Ray intersection}{sec. 1.1 eq. 4}{gillespie2024ray}{
+\refdeft{ray intersection}{sec. 1.1 eq. 4}{gillespie2024ray}{
 \p{Plugging the \vocab{ray equation} #{r: \mathbb{R} \rightarrow \mathbb{R}^n} into the function #{f: \mathbb{R}^n \rightarrow \mathbb{R}} that defines the implicit surface produces the composite real function #{F: \mathbb{R} \rightarrow \mathbb{R}} where #{F=f \circ \boldsymbol{r}} such that the \vocab{solution}s to
 
 ##{
diff --git a/trees/ag-000X.tree b/trees/ag-000X.tree
index ab0f14fb..4986e62a 100644
--- a/trees/ag-000X.tree
+++ b/trees/ag-000X.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\refdeft{Implicit surface}{sec. 1}{winchenbach2024lipschitz}{
+\refdeft{implicit surface}{sec. 1}{winchenbach2024lipschitz}{
 \p{Let #{\Omega} be a subset of a [topological space](https://en.wikipedia.org/wiki/Topological_space) #{X}, and #{\partial \Omega} be its [boundary](https://en.wikipedia.org/wiki/Boundary_(topology)).
 }
 
diff --git a/trees/ag-000Y.tree b/trees/ag-000Y.tree
index 6c0fe8d5..b228567e 100644
--- a/trees/ag-000Y.tree
+++ b/trees/ag-000Y.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Definition}{Level set \citewiki{level-set}{https://en.wikipedia.org/wiki/Level_set}}{
+\card{Definition}{level set \citewiki{level-set}{https://en.wikipedia.org/wiki/Level_set}}{
 A \newvocab{level set} of a real-valued function #{f} (a.k.a. an iso-contour of a scalar field in 3D)
 
 ##{L_c(f)=\left\{\point{x} \mid \forall \point{x} \in X, f(\point{x})=c  \right\} }
diff --git a/trees/ag-0018.tree b/trees/ag-0018.tree
index e0c52b63..8056791e 100644
--- a/trees/ag-0018.tree
+++ b/trees/ag-0018.tree
@@ -26,7 +26,7 @@
 \def\eps{\varepsilon}
 \def\tmax{t_{\max}}
 
-\card{Algorithm}{Ray marching (naïve)}{
+\card{Algorithm}{ray marching (naïve)}{
 \minialg{
 % \begin{algorithm*}{Ray marching (naive)}{}
 \alg/input{$\ro \in \RR^3$, ray origin}
diff --git a/trees/ag-0019.tree b/trees/ag-0019.tree
index d107e41d..ee2afd48 100644
--- a/trees/ag-0019.tree
+++ b/trees/ag-0019.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Example}{Ray marching (naïve)}{
+\card{Example}{ray marching (naïve)}{
 
 \p{The following renders a scene with a unit sphere at the origin, the camera at #{(0,0,8)} and looking at the origin, through a screen of height 1.0, centered at 5.0 from the camera.
 }
diff --git a/trees/ag-001A.tree b/trees/ag-001A.tree
index f521aeee..350ea659 100644
--- a/trees/ag-001A.tree
+++ b/trees/ag-001A.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Definition}{Ray}{
+\card{Definition}{ray}{
 \p{A \newvocab{ray} is a half-line that starts at a point and extends indefinitely in one direction.
 }
 
diff --git a/trees/ag-001B.tree b/trees/ag-001B.tree
index 7f1c3a3d..28cc74c2 100644
--- a/trees/ag-001B.tree
+++ b/trees/ag-001B.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Definition}{Ray marching (naïve)}{
+\card{Definition}{ray marching (naïve)}{
 \p{The \newvocab{ray marching (naïve)} algorithm is to march a ray by a \em{fixed step size}, check if a \vocab{ray intersection} occurs at each step, until the ray reaches a maximum distance or step count.
 }
 
diff --git a/trees/ag-001C.tree b/trees/ag-001C.tree
index 34332da3..337c495d 100644
--- a/trees/ag-001C.tree
+++ b/trees/ag-001C.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Definition}{Ray marching}{
+\card{Definition}{ray marching}{
 \p{To render a scene, the \newvocab{Ray marching} algorithm marches a ray from an origin towards a direction. At each step, the algorithm marches a short (possibly changing) distance and checks if a \vocab{ray intersection} occurs. This process continues until a \em{stopping condition} is met. The information obtained from the ray intersection is then used to determine the color of a pixel on the screen.
 }
 }
\ No newline at end of file
diff --git a/trees/ag-001D.tree b/trees/ag-001D.tree
index e74dd1ce..992ec5a6 100644
--- a/trees/ag-001D.tree
+++ b/trees/ag-001D.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Example}{Ray-marching for different types of rays}{
+\card{Example}{ray-marching for different types of rays}{
 
 \p{A \vocab{view ray} has the origin at the camera, the direction is determined by the pixel on the screen that it passes through. It may intersect with a surface in the scene, and the information obtained from the intersection is used to determine the color of the corresponding pixel on the screen.}
 
diff --git a/trees/ag-001E.tree b/trees/ag-001E.tree
index de57bcda..76ca6641 100644
--- a/trees/ag-001E.tree
+++ b/trees/ag-001E.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\card{Remark}{Ray-casting/ray-tracing/ray-marching}{
+\card{Remark}{ray-casting/ray-tracing/ray-marching}{
 \p{The \newvocab{ray-casting}/\newvocab{ray-tracing}/\newvocab{ray-marching} algorithms simply apply one of the multitude of root finding methods to solve the \vocab{ray intersection} equation.
 }
 
diff --git a/trees/ag-001I.tree b/trees/ag-001I.tree
index f2e77ba6..825cefa4 100644
--- a/trees/ag-001I.tree
+++ b/trees/ag-001I.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative hart1996sphere gillespie2024ray winchenbach2024lipschitz
 
-\refdeft{Sphere tracing}{sec. 2.3, eq. 12}{hart1996sphere}{
+\refdeft{sphere tracing}{sec. 2.3, eq. 12}{hart1996sphere}{
 \p{The \newvocab{sphere tracing} algorithm is to march a ray by an adaptive safe step size, which is the absolute value of the \vocab{signed distance bound} calculated by #{F/\lambda} per \ref{ag-000T}, the rest is the same as \vocabk{ray marching (naïve)}{ag-001B}.
 }
 
diff --git a/trees/ca-000P.tree b/trees/ca-000P.tree
index c083b3c7..ec20e586 100644
--- a/trees/ca-000P.tree
+++ b/trees/ca-000P.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative
 
-\note{basics: from groups to modules}{
+\note{Basics: from groups to modules}{
 \transclude{ca-000O}
 \transclude{ca-000Q}
 \transclude{ca-000R}
diff --git a/trees/ca-0013.tree b/trees/ca-0013.tree
index d7ad83cd..58467fd4 100644
--- a/trees/ca-0013.tree
+++ b/trees/ca-0013.tree
@@ -12,7 +12,7 @@
 
 % cox1997ideals gathmann2013commutative
 
-\note{algebras}{
+\note{Algebras}{
 \transclude{ca-0014}
 \transclude{ca-0015}
 \transclude{ca-0016}
diff --git a/trees/uts-000C.tree b/trees/uts-000C.tree
index cecbca73..6ed5c0ed 100644
--- a/trees/uts-000C.tree
+++ b/trees/uts-000C.tree
@@ -21,7 +21,7 @@
 
 \put\transclude/numbered{false}
 
-\block{disclaimer}{
+\block{Disclaimer}{
   \p{This is a manual translation of a portion of \em{Chapitre 9 Formes sesquilinéaires et formes quadratiques} of Bourbaki's \em{Éléments de Mathématique} \citek{bourbaki2007algebra} from French to English.}
   
   \p{Such a translation is not available eleswhere, to the best of our knowledge. We claim no rights to the original text, and all mistakes in the translation are our own. The translation is for educational purposes only.}
@@ -29,7 +29,7 @@
   \p{So far, we have only translated the portion that is related to Clifford algebras, namely \em{§ 9. Clifford Algebra}. The translation is still in progress.}
 }
 
-\block{editorial remarks}{
+\block{Editorial remarks}{
   \p{We always keep the original notation, and the numbering of equations, definitions, propositions, sections etc.}
 
   \p{Equation labels are placed on the right side of the equations unlike the original text where they are placed on the left side.}