diff --git a/packages/squiggle-lang/__tests__/docs/README.md b/packages/squiggle-lang/__tests__/docs/README.md
index 1dca1162..f3ef1041 100644
--- a/packages/squiggle-lang/__tests__/docs/README.md
+++ b/packages/squiggle-lang/__tests__/docs/README.md
@@ -7,11 +7,10 @@ nix-build
 o result/property-tests.pdf
 ```
 
-Without `nix`, you can install `pandoc` yourself and run
-```sh
-pandoc -s property-tests.md -o property-tests.pdf
-```
+Without `nix`, you can install `pandoc` and `pdflatex` yourself and see `make.sh` for the rendering command. 
 
 ## _Details_
 
-The `property-tests.pdf` document is _normative and aspirational_. It does not document tests as they exist in the codebase, but somewhat represents how we think squiggle ought to be tested. 
+The `invariants.pdf` document is _normative and aspirational_. It does not document tests as they exist in the codebase, but represents how we think squiggle ought to be tested. 
+
+We are partially bottlenecked by the rescript ecosystem's maturity with respect to property-based testing. 
diff --git a/packages/squiggle-lang/__tests__/docs/default.nix b/packages/squiggle-lang/__tests__/docs/default.nix
index 5a18efd3..37a0e3aa 100644
--- a/packages/squiggle-lang/__tests__/docs/default.nix
+++ b/packages/squiggle-lang/__tests__/docs/default.nix
@@ -3,31 +3,24 @@
 }:
 # Style sheets https://github.com/citation-style-language/styles/
 with pkgs;
+
 let deps = [
-#      (texlive.combine
-#        { inherit (texlive)
-#        scheme-small thmtools datetime xpatch fmtcount;
-#        }
-#      )
-      haskellPackages.pandoc
-    ];
-in
-  stdenv.mkDerivation {
-    name = "render_squiggle_properties";
-    src = ./.;
-    buildInputs = deps;
-    buildPhase = ''
-      echo rendering...
-      pandoc \
-             --from markdown \
-             --to latex \
-             --out properties.pdf \
-             --pdf-engine xelatex \
-             properties.md \
-      echo rendered.
+  pandoc 
+  (texlive.combine 
+    { inherit (texlive) scheme-small datetime; }
+  )
+]; in
+stdenv.mkDerivation {
+  name = "render_squiggle_properties";
+  src = ./.;
+  buildInputs = deps;
+  buildPhase = ''
+    echo rendering...
+    pandoc -s invariants.md -o invariants.pdf 
+    echo rendered.
+  '';
+  installPhase = ''
+    mkdir -p $out
+    cp invariants.pdf $out/invariants.pdf
     '';
-    installPhase = ''
-      mkdir -p $out
-      cp properties.pdf $out/properties.pdf
-      '';
-  }
+}
diff --git a/packages/squiggle-lang/__tests__/docs/invariants-apr12.pdf b/packages/squiggle-lang/__tests__/docs/invariants-apr12.pdf
new file mode 100644
index 00000000..4077a490
Binary files /dev/null and b/packages/squiggle-lang/__tests__/docs/invariants-apr12.pdf differ
diff --git a/packages/squiggle-lang/__tests__/docs/property-tests.md b/packages/squiggle-lang/__tests__/docs/invariants.md
similarity index 65%
rename from packages/squiggle-lang/__tests__/docs/property-tests.md
rename to packages/squiggle-lang/__tests__/docs/invariants.md
index aacf25fd..d9e95b5f 100644
--- a/packages/squiggle-lang/__tests__/docs/property-tests.md
+++ b/packages/squiggle-lang/__tests__/docs/invariants.md
@@ -1,38 +1,51 @@
-# Property tests for squiggle
+# Squiggle invariants
 
 Here are some property tests for squiggle. I am testing mostly for the mean and the standard deviation. I know that squiggle doesn't yet have functions for the standard deviation, but they could be added.
 
 The keywords to search for are "[algebra of random variables](https://wikiless.org/wiki/Algebra_of_random_variables?lang=en)". 
 
-## Sums
+## Means and standard deviations
+### Sums
 
 $$ mean(f+g) = mean(f) + mean(g) $$
 
-$$ Std(f+g) = sqrt(std(f)^2 + std(g)^2) $$
+$$ std(f+g) = \sqrt{std(f)^2 + std(g)^2} $$
 
 In the case of normal distributions,
 
-$$ normal(a,b) + normal(c,d) = normal(a+c, sqrt(b^2 + d^2) $$
+$$ mean(normal(a,b) + normal(c,d)) = mean(normal(a+c, \sqrt{b^2 + d^2})) $$
 
-## Substractions
+### Subtractions
 
 $$ mean(f-g) = mean(f) - mean(g) $$
 
-$$ std(f-g) = sqrt(std(f)^2 + std(g)^2) $$
+$$ std(f-g) = \sqrt{std(f)^2 + std(g)^2} $$
 
-## Multiplications
+### Multiplications
 
 $$ mean(f \cdot g) =  mean(f) \cdot mean(g) $$
 
-$$ std(f \cdot g) = sqrt( (std(f)^2 + mean(f)) \cdot (std(g)^2 + mean(g)) - (mean(f) \cdot mean(y))^2) $$
+$$ std(f \cdot g) = \sqrt{ (std(f)^2 + mean(f)) \cdot (std(g)^2 + mean(g)) - (mean(f) \cdot mean(g))^2} $$
 
-## Divisions
+### Divisions
 
 Divisions are tricky, and in general we don't have good expressions to characterize properties of ratios. In particular, the ratio of two normals is a Cauchy distribution, which doesn't have to have a mean.
 
-## To do:
+# To do:
 
 - Provide sources or derivations, useful as this document becomes more complicated
 - Provide definitions for the probability density function, exponential, inverse, log, etc.
 - Provide at least some tests for division
 - See if playing around with characteristic functions turns out anything useful
+
+## Probability density functions
+
+TODO
+
+## Cumulative density functions 
+
+TODO
+
+## Inverse cumulative density functions
+
+TODO
\ No newline at end of file
diff --git a/packages/squiggle-lang/__tests__/docs/make.sh b/packages/squiggle-lang/__tests__/docs/make.sh
index 58fbc3aa..7d5a4333 100755
--- a/packages/squiggle-lang/__tests__/docs/make.sh
+++ b/packages/squiggle-lang/__tests__/docs/make.sh
@@ -1 +1 @@
- pandoc -s property-tests.md -o property-tests.pdf
+ pandoc -s invariants.md -o invariants.pdf
diff --git a/packages/squiggle-lang/__tests__/docs/property-tests.pdf b/packages/squiggle-lang/__tests__/docs/property-tests.pdf
deleted file mode 100644
index 3bca9795..00000000
Binary files a/packages/squiggle-lang/__tests__/docs/property-tests.pdf and /dev/null differ