diff --git a/README.md b/README.md
index dd0f4e3..04dfc0f 100644
--- a/README.md
+++ b/README.md
@@ -34,4 +34,42 @@ If you want to run the demo directly with golang from the root of the repo:
 ```
 cd integrity
 go run .
+```
+
+## Completeness Demo
+
+The completenesss demo will verify the integrity of a list of datatrails events.
+
+This is achieved by checking that ONLY the events in the list exist on the log within a range
+starting from the first event ending at the last event in the list.
+
+Every event in the list then has an inclusion proof generated.
+
+If all the inclusion proofs are verified successfully, we can say that the list of
+datatrails events is complete and all are included on the merkle log.
+
+### Docker Demo
+To run the completeness demo with docker:
+
+```
+docker run -v ./completeness:/usr/src/myapp -w /usr/src/myapp  golang:1.22-alpine go run .
+```
+
+Where the docker command is run from the root of the repo.
+
+### Task Demo
+
+To run the demo with a task (https://taskfile.dev/installation/) rune:
+
+```
+task demos:completeness
+```
+
+### Go Demo
+
+If you want to run the demo directly with golang from the root of the repo:
+
+```
+cd completeness
+go run .
 ```
\ No newline at end of file
diff --git a/completeness/go.mod b/completeness/go.mod
index c40231e..ba7a0f6 100644
--- a/completeness/go.mod
+++ b/completeness/go.mod
@@ -4,7 +4,7 @@ go 1.22
 
 require (
 	github.com/datatrails/go-datatrails-common v0.16.1
-	github.com/datatrails/go-datatrails-demos/logverification v0.0.3-0.20240530102756-109763df17b4
+	github.com/datatrails/go-datatrails-demos/logverification v0.0.3-0.20240530114926-8e28942cc526
 	github.com/stretchr/testify v1.9.0
 )
 
diff --git a/completeness/go.sum b/completeness/go.sum
index d0fa1b0..b83207c 100644
--- a/completeness/go.sum
+++ b/completeness/go.sum
@@ -45,8 +45,8 @@ github.com/datatrails/go-datatrails-common v0.16.1 h1:kaNOwyu8EmBbIR44daWDiUZxBt
 github.com/datatrails/go-datatrails-common v0.16.1/go.mod h1:IEcuwUaFl+bI1tt30r+Ov2+nvpcAZH/kXmAPGFjkwT4=
 github.com/datatrails/go-datatrails-common-api-gen v0.4.8 h1:IzrhGHi9TyEASjk06QjsayjtpXYCKuDt78+ffLuOCNM=
 github.com/datatrails/go-datatrails-common-api-gen v0.4.8/go.mod h1:zlwFPJXYAK7yqgLtxKUgkF5gw9ddxoqWS+Ruhf+Ksw0=
-github.com/datatrails/go-datatrails-demos/logverification v0.0.3-0.20240530102756-109763df17b4 h1:f8c13P302U0EA54FOQKMijUv7j8HuUMb5ohXByaSQIs=
-github.com/datatrails/go-datatrails-demos/logverification v0.0.3-0.20240530102756-109763df17b4/go.mod h1:5uMSYrfH8l3RNtiu934BXhwym9TorhSp375O188MJrM=
+github.com/datatrails/go-datatrails-demos/logverification v0.0.3-0.20240530114926-8e28942cc526 h1:S3/QdoZZsf+Q0fFGTPw+AL6ezHry0tsoL1ce+Mmbq8w=
+github.com/datatrails/go-datatrails-demos/logverification v0.0.3-0.20240530114926-8e28942cc526/go.mod h1:5uMSYrfH8l3RNtiu934BXhwym9TorhSp375O188MJrM=
 github.com/datatrails/go-datatrails-merklelog/massifs v0.0.5 h1:HfOvtpydHxFeBs3CMLVn4tliHrxfusI5cX8n/y23lYI=
 github.com/datatrails/go-datatrails-merklelog/massifs v0.0.5/go.mod h1:9gVKGJXWmQru2TlWF7Ho+jVCQRJTZKoT2L7Lda1batI=
 github.com/datatrails/go-datatrails-merklelog/mmr v0.0.1 h1:XggMVejsJ72cAL/msjPhQUSQNeElSh/O1zZcvX4d4JU=
diff --git a/taskfiles/Taskfile_demos.yml b/taskfiles/Taskfile_demos.yml
index e2a3567..614e279 100644
--- a/taskfiles/Taskfile_demos.yml
+++ b/taskfiles/Taskfile_demos.yml
@@ -14,6 +14,14 @@ tasks:
   integrity:
     desc: "run the intgrity demo"
     dir: ../integrity
+    cmds:
+      - cmd: |
+          
+          go run .
+
+  completeness:
+    desc: "run the completeness demo"
+    dir: ../completeness
     cmds:
       - cmd: |