diff --git a/cli/tri/src/leanvac.rs b/cli/tri/src/leanvac.rs
new file mode 100644
index 0000000000..cecf7b708d
--- /dev/null
+++ b/cli/tri/src/leanvac.rs
@@ -0,0 +1,235 @@
+//! `tri lean vacuous` -- completeness theorems whose model is empty.
+//!
+//! `proofs/lean4/.../Completeness.lean` holds 250 hand-transcribed models, one per
+//! spec, each with a theorem asserting the module is Icarus-lowerable. A model with
+//! `functions := []` makes its theorem true by construction: `native_decide` on an
+//! empty structure proves something, and that something is not about the spec.
+//!
+//! 114 of the 250 are empty. The ledger's `max_vacuous` ratchet, which exists to stop
+//! that number growing, counts **44** -- because it only sees models that ALSO disagree
+//! with the Rust classifier. The other 70 are vacuous and invisible to it.
+//!
+//! A ratchet measuring a subset of its own subject is worse than no ratchet, because
+//! the number it reports looks like the number you care about.
+
+use anyhow::Result;
+use clap::Subcommand;
+use std::path::PathBuf;
+
+#[derive(Subcommand)]
+pub enum LeanCmd {
+    /// Completeness theorems whose model has no functions.
+    Vacuous {
+        /// Print every name, not just the count and the gap.
+        #[arg(long)]
+        all: bool,
+    },
+}
+
+/// One model as the file states it.
+pub struct Model {
+    pub name: String,
+    pub empty_fns: bool,
+    pub empty_env: bool,
+}
+
+/// Every `<name>_module` in the file, with whether its function list and its Env are
+/// empty.
+///
+/// Text-scanned rather than parsed, and that is a limit worth stating: this reads what
+/// the file SAYS, and only a Lean build can say what it MEANS. No workflow in this
+/// repository builds these proofs (#2747), so a text scan is the strongest instrument
+/// available here, not the weakest one chosen.
+pub fn models_in(src: &str) -> Vec<Model> {
+    let mut envs: Vec<(String, bool)> = Vec::new();
+    let mut out: Vec<Model> = Vec::new();
+    let mut cur: Option<(String, bool, bool)> = None; // name, is_module, saw_empty
+    let mut empty_env_names: Vec<String> = Vec::new();
+    for line in src.split('\n') {
+        let t = line.trim();
+        if let Some(rest) = t.strip_prefix("def ") {
+            // flush
+            if let Some((name, is_module, saw)) = cur.take() {
+                if is_module {
+                    out.push(Model {
+                        empty_env: empty_env_names.contains(&name),
+                        name,
+                        empty_fns: saw,
+                    });
+                } else if saw {
+                    empty_env_names.push(name);
+                }
+            }
+            if let Some(n) = rest.strip_suffix(" : Env := {") {
+                cur = Some((n.trim_end_matches("_env").to_string(), false, false));
+            } else if let Some(n) = rest.strip_suffix(" : Module := {") {
+                cur = Some((n.trim_end_matches("_module").to_string(), true, false));
+            }
+            continue;
+        }
+        if let Some((_, is_module, saw)) = cur.as_mut() {
+            if (*is_module && t.starts_with("functions := []"))
+                || (!*is_module && t.starts_with("structs := []"))
+            {
+                *saw = true;
+            }
+        }
+    }
+    if let Some((name, is_module, saw)) = cur.take() {
+        if is_module {
+            out.push(Model {
+                empty_env: empty_env_names.contains(&name),
+                name,
+                empty_fns: saw,
+            });
+        }
+    }
+    let _ = &mut envs;
+    out
+}
+
+fn repo_root() -> Result<PathBuf> {
+    let out = std::process::Command::new("git")
+        .args(["rev-parse", "--show-toplevel"])
+        .output()?;
+    if !out.status.success() {
+        anyhow::bail!("not inside a git repository");
+    }
+    Ok(PathBuf::from(
+        String::from_utf8_lossy(&out.stdout).trim().to_string(),
+    ))
+}
+
+pub fn run(cmd: &LeanCmd) -> Result<()> {
+    let LeanCmd::Vacuous { all } = cmd;
+    let root = repo_root()?;
+    let lean = root.join("proofs/lean4/Trinity/IcarusLowerable/Completeness.lean");
+    let src = std::fs::read_to_string(&lean)
+        .map_err(|e| anyhow::anyhow!("cannot read {}: {}", lean.display(), e))?;
+    let models = models_in(&src);
+    if models.is_empty() {
+        anyhow::bail!(
+            "read {} and found no `<name>_module : Module := {{` -- the file's shape \
+             changed, and a count of zero here would be the scanner, not the proofs",
+            lean.display()
+        );
+    }
+    let vacuous: Vec<&Model> = models.iter().filter(|m| m.empty_fns).collect();
+    let both: usize = vacuous.iter().filter(|m| m.empty_env).count();
+
+    let ledger = root.join("docs/reports/lean_completeness_mismatches.json");
+    let marked: usize = std::fs::read_to_string(&ledger)
+        .ok()
+        .and_then(|r| serde_json::from_str::<serde_json::Value>(&r).ok())
+        .and_then(|v| {
+            v.get("entries")?.as_object().map(|o| {
+                o.values()
+                    .filter(|e| e.get("model_empty").and_then(|b| b.as_bool()) == Some(true))
+                    .count()
+            })
+        })
+        .unwrap_or(0);
+
+    println!("VACUOUS COMPLETENESS THEOREMS");
+    println!();
+    println!("  models in the file            {}", models.len());
+    println!("  with `functions := []`        {}", vacuous.len());
+    println!("  ...and an empty Env too       {}", both);
+    println!("  counted by max_vacuous        {}", marked);
+    println!(
+        "  vacuous and INVISIBLE to it   {}",
+        vacuous.len().saturating_sub(marked)
+    );
+    println!();
+    if *all {
+        for m in &vacuous {
+            println!("    {}{}", m.name, if m.empty_env { "  (env empty too)" } else { "" });
+        }
+        println!();
+    }
+    println!(
+        "`max_vacuous` counts only models that ALSO disagree with the Rust classifier.\n\
+         A theorem about an empty module says nothing about its spec whether or not the\n\
+         classifier happens to disagree, so the ratchet measures a subset of its own\n\
+         subject -- and the number it reports looks like the number you care about."
+    );
+    println!();
+    println!(
+        "Read from the file's text. Only a Lean build can say what these theorems MEAN,\n\
+         and no workflow in this repository builds them (#2747)."
+    );
+    Ok(())
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    const SAMPLE: &str = "\
+def a_env : Env := {
+  structs := [],
+  enums := []
+}
+
+def a_module : Module := {
+  name := \"a\",
+  functions := [],
+  tests := []
+}
+
+def b_env : Env := {
+  structs := [(\"S\", [])],
+  enums := []
+}
+
+def b_module : Module := {
+  name := \"b\",
+  functions := [{ name := \"f\" }],
+  tests := []
+}
+";
+
+    #[test]
+    fn an_empty_function_list_is_vacuous_and_a_populated_one_is_not() {
+        let ms = models_in(SAMPLE);
+        assert_eq!(ms.len(), 2, "two modules");
+        assert!(ms[0].empty_fns, "a has functions := []");
+        assert!(!ms[1].empty_fns, "b lists a function");
+    }
+
+    #[test]
+    fn an_empty_env_is_reported_separately_from_an_empty_module() {
+        let ms = models_in(SAMPLE);
+        assert!(ms[0].empty_env, "a's Env has structs := []");
+        assert!(!ms[1].empty_env, "b's Env declares a struct");
+    }
+
+    #[test]
+    fn a_file_with_no_modules_yields_nothing_rather_than_a_wrong_zero() {
+        // The command turns this into a refusal, because a zero from a scanner
+        // that matched nothing is indistinguishable from a clean file.
+        assert!(models_in("-- just a comment\n").is_empty());
+    }
+
+    #[test]
+    fn the_env_belonging_to_a_module_is_the_one_with_its_name() {
+        // `a_env` empty, `b_env` not: the pairing is by name, not by position,
+        // so a file that declares them out of order still pairs correctly.
+        let reordered = "\
+def b_env : Env := {
+  structs := [(\"S\", [])]
+}
+
+def a_env : Env := {
+  structs := []
+}
+
+def a_module : Module := {
+  functions := []
+}
+";
+        let ms = models_in(reordered);
+        assert_eq!(ms.len(), 1);
+        assert!(ms[0].empty_env);
+    }
+}
diff --git a/cli/tri/src/main.rs b/cli/tri/src/main.rs
index cc7c0cb880..c37675b90b 100644
--- a/cli/tri/src/main.rs
+++ b/cli/tri/src/main.rs
@@ -26,6 +26,7 @@ mod quant;
 mod red;
 mod rtl;
 mod kinddrift;
+mod leanvac;
 mod skillnum;
 mod seals;
 mod sweep;
@@ -52,6 +53,11 @@ enum Commands {
         #[command(subcommand)]
         action: kinddrift::KindsCmd,
     },
+    /// Completeness theorems whose Lean model is empty.
+    Lean {
+        #[command(subcommand)]
+        action: leanvac::LeanCmd,
+    },
     Cell {
         #[command(subcommand)]
         action: CellAction,
@@ -758,6 +764,7 @@ fn main() -> Result<()> {
             cmd_status(&root)?;
         }
         Commands::Kinds { action } => kinddrift::run(action)?,
+        Commands::Lean { action } => leanvac::run(action)?,
         Commands::Skill { action } => {
             let root = find_trinity_root()?;
             match action {
diff --git a/docs/now/2026-08-30-a-ratchet-measuring-a-subset-of-itself.md b/docs/now/2026-08-30-a-ratchet-measuring-a-subset-of-itself.md
new file mode 100644
index 0000000000..4a704c4596
--- /dev/null
+++ b/docs/now/2026-08-30-a-ratchet-measuring-a-subset-of-itself.md
@@ -0,0 +1,17 @@
+# NOW -- A ratchet measuring a subset of its own subject (2026-08-30)
+
+## 114 vacuous completeness theorems; the ratchet counts 44 (Refs #2747)
+
+- `Completeness.lean` holds 250 hand-transcribed models; **114** have `functions := []`, and 104 of those have an empty `Env` too
+- a theorem about an empty module says nothing about its spec: `native_decide` on an empty structure proves something true and useless
+- `max_vacuous`, the ratchet that exists to stop that number growing, counts **44** -- only the models that ALSO disagree with the Rust classifier
+- **70 vacuous theorems are invisible to it**, and the number it reports looks like the number you care about
+- all 44 of its marks are correct: zero entries marked `model_empty` that are not empty
+- measured twice, by a throwaway Python scan and by the shipped Rust, and the two agree at 250/114/104/44/70
+
+## What I proposed last pass and am NOT doing
+
+- I named "write real Lean models for those four" as the only honest way to lower `max_vacuous`
+- `lean`, `lake` and `elan` are not installed here; `.github/workflows/lean-proofs.yml` has a `lake build` but I cannot run it locally
+- a faithful model may make its theorem FALSE -- the classifier says `Rust=false` for those four specs -- and that is the correct outcome, not a bug
+- writing a proof I cannot check and pushing it to see what CI says is exactly what this repository exists to prevent, so the count is reported instead