diff --git a/jcp/jcp-rs/crates/jcp-efficiency/examples/session.rs b/jcp/jcp-rs/crates/jcp-efficiency/examples/session.rs
index e7b0fdb0b..d7667a575 100644
--- a/jcp/jcp-rs/crates/jcp-efficiency/examples/session.rs
+++ b/jcp/jcp-rs/crates/jcp-efficiency/examples/session.rs
@@ -59,7 +59,7 @@ fn main() {
             "  {:16} {:>5} tok  {:>7} µJ/tok  {:>6.0} tok/s   {}",
             t.task,
             t.tokens_out,
-            t.uj_per_accepted_token(),
+            dash(t.uj_per_accepted_token()),
             t.tokens_per_sec(),
             mark
         );
@@ -75,12 +75,20 @@ fn main() {
     println!("  wasted units     : {}   (tokens burned, no result)", t.wasted_units);
     println!(
         "  tokens/completed : {}   ← charges EVERY attempt (incl. failures) to results delivered",
-        t.tokens_per_completed_unit()
+        dash(t.tokens_per_completed_unit())
     );
-    println!("  µJ/completed     : {}", t.uj_per_completed_unit());
+    println!("  µJ/completed     : {}", dash(t.uj_per_completed_unit()));
     println!("  value / joule    : {:.4} µUSD/J", t.value_per_joule());
     println!(
-        "  WASTE FRACTION   : {:.0}%   ← the number a 'cost per token' rate hides",
-        t.waste_fraction() * 100.0
+        "  WASTE FRACTION   : {}   ← the number a 'cost per token' rate hides",
+        t.waste_fraction()
+            .map_or_else(|| "—  (no tokens spent)".to_string(), |f| format!("{:.0}%", f * 100.0))
     );
 }
+
+/// Render a figure that may be undefined. An undefined cost-per-result ratio is
+/// shown as "—", never as 0: zero is the optimum of these figures, so printing it
+/// would rank spend that bought nothing above every run that delivered.
+fn dash(v: Option<u64>) -> String {
+    v.map_or_else(|| "—".to_string(), |n| n.to_string())
+}
diff --git a/jcp/jcp-rs/crates/jcp-efficiency/src/lib.rs b/jcp/jcp-rs/crates/jcp-efficiency/src/lib.rs
index dbe47cc84..57b232263 100644
--- a/jcp/jcp-rs/crates/jcp-efficiency/src/lib.rs
+++ b/jcp/jcp-rs/crates/jcp-efficiency/src/lib.rs
@@ -83,9 +83,17 @@ impl Efficiency {
     }
 
     /// Microjoules per accepted output token — the headline energy figure, matching
-    /// the family's `uj_per_accepted_token` convention. `0` if no tokens accepted.
-    pub fn uj_per_accepted_token(&self) -> u64 {
-        self.energy.uj().checked_div(self.tokens_out).unwrap_or(0)
+    /// the family's `uj_per_accepted_token` convention: `None` when no tokens were
+    /// accepted, because the division is undefined then.
+    ///
+    /// It is not `0`. This is a cost-per-result figure, so `0` is its *optimum* —
+    /// returning it for an uncomputable ratio reported the worst outcome (spend
+    /// that bought nothing, `completed: false`) as the best one, and the figure is
+    /// sealed and read straight back out rather than recomputed. `mesh/SPEC.md`
+    /// §6 states the family convention this matches: "omitted when no tokens were
+    /// accepted".
+    pub fn uj_per_accepted_token(&self) -> Option<u64> {
+        self.energy.uj().checked_div(self.tokens_out)
     }
 
     /// Accepted tokens per second — real decode throughput. `0.0` if no time
@@ -101,7 +109,10 @@ impl Efficiency {
     /// Micro-USD of value per accepted token — economic efficiency — when a value
     /// figure is given. `None` otherwise (never invented).
     pub fn uusd_per_accepted_token(&self) -> Option<u64> {
-        self.value_uusd.map(|v| v.checked_div(self.tokens_out).unwrap_or(0))
+        // `and_then`, not `map(... .unwrap_or(0))`: with no accepted tokens the
+        // ratio is undefined, and this function's contract is that a value figure
+        // is never invented.
+        self.value_uusd.and_then(|v| v.checked_div(self.tokens_out))
     }
 
     /// Commit this measurement to an external energy attestation — the raw report
@@ -141,14 +152,22 @@ impl Efficiency {
             "energy_uj": self.energy.uj(),
             "provenance": self.energy.provenance.jcr1_label(),
             "wall_ns": self.wall_ns,
-            "uj_per_accepted_token": self.uj_per_accepted_token(),
             "seq": seq,
             "prev": prev.to_hex(),
             "steward": steward,
         });
+        // Omitted when undefined, never sealed as 0 — the same shape
+        // `mesh-receipt` seals its wedge metric with, and what `mesh/SPEC.md` §6
+        // specifies. Canonical CBOR sorts keys, so insertion order here never
+        // reaches the wire.
+        if let Some(uj) = self.uj_per_accepted_token() {
+            o["uj_per_accepted_token"] = json!(uj);
+        }
         if let Some(v) = self.value_uusd {
             o["value_uusd"] = json!(v);
-            o["uusd_per_accepted_token"] = json!(self.uusd_per_accepted_token().unwrap_or(0));
+            if let Some(per) = self.uusd_per_accepted_token() {
+                o["uusd_per_accepted_token"] = json!(per);
+            }
         }
         if let Some(a) = &self.energy_attestation {
             o["energy_attestation"] = json!(a);
@@ -242,8 +261,10 @@ pub struct EfficiencyReceipt {
     pub provenance: String,
     /// Wall-clock nanoseconds.
     pub wall_ns: u64,
-    /// Microjoules per accepted token (headline).
-    pub uj_per_accepted_token: u64,
+    /// Microjoules per accepted token (headline). `None` when the receipt sealed
+    /// no figure because no tokens were accepted — an undefined ratio, not zero
+    /// cost per token.
+    pub uj_per_accepted_token: Option<u64>,
     /// Value delivered, micro-USD (when stated).
     pub value_uusd: Option<u64>,
     /// Hex content-id commitment to an external energy attestation (when present) —
@@ -298,7 +319,7 @@ pub fn verify(envelope: &[u8], steward: &str, pubkey: &[u8; 32]) -> Result<Effic
         energy_uj: u("energy_uj")?,
         provenance: s("provenance")?,
         wall_ns: u("wall_ns")?,
-        uj_per_accepted_token: u("uj_per_accepted_token")?,
+        uj_per_accepted_token: v.get("uj_per_accepted_token").and_then(Value::as_u64),
         value_uusd: v.get("value_uusd").and_then(Value::as_u64),
         energy_attestation: v.get("energy_attestation").and_then(Value::as_str).map(str::to_string),
         seq: u("seq")?,
@@ -356,24 +377,33 @@ pub struct Totals {
 impl Totals {
     /// Total tokens per completed unit — *including* the waste of failed attempts.
     /// The number that beats "cost per token": it charges every attempt against the
-    /// results actually delivered. `0` if nothing completed.
-    pub fn tokens_per_completed_unit(&self) -> u64 {
+    /// results actually delivered. `None` when nothing completed.
+    ///
+    /// The claim is that it "charges every attempt against the results actually
+    /// delivered", which it stops doing precisely when nothing was delivered: the
+    /// denominator is zero and the ratio is undefined. Reporting `0` there named
+    /// the cheapest possible cost per result for spend that produced none.
+    pub fn tokens_per_completed_unit(&self) -> Option<u64> {
         self.completed_tokens
             .saturating_add(self.wasted_tokens)
             .checked_div(self.completed_units)
-            .unwrap_or(0)
     }
 
-    /// Total microjoules per completed unit, including waste.
-    pub fn uj_per_completed_unit(&self) -> u64 {
+    /// Total microjoules per completed unit, including waste. `None` when nothing
+    /// completed — see [`Self::tokens_per_completed_unit`].
+    pub fn uj_per_completed_unit(&self) -> Option<u64> {
         self.completed_uj
             .saturating_add(self.wasted_uj)
             .checked_div(self.completed_units)
-            .unwrap_or(0)
     }
 
     /// Micro-USD of value delivered per joule spent (including waste) — the ultimate
     /// efficiency figure. `0.0` if no energy spent.
+    ///
+    /// Kept as `0.0`, unlike the cost-per-unit ratios above: higher is better here,
+    /// so the fallback is this figure's *worst* value, not its optimum. The same
+    /// holds for [`Efficiency::tokens_per_sec`]. A zero that understates is not the
+    /// defect those `Option`s fix.
     pub fn value_per_joule(&self) -> f64 {
         let total_uj = self.completed_uj.saturating_add(self.wasted_uj);
         if total_uj == 0 {
@@ -384,13 +414,15 @@ impl Totals {
         }
     }
 
-    /// The share of spent tokens that bought nothing (0.0–1.0).
-    pub fn waste_fraction(&self) -> f64 {
+    /// The share of spent tokens that bought nothing (0.0–1.0). `None` when no
+    /// tokens were spent at all, since `0.0` is this figure's optimum — an empty
+    /// ledger reported a perfect zero-waste record.
+    pub fn waste_fraction(&self) -> Option<f64> {
         let total = self.completed_tokens.saturating_add(self.wasted_tokens);
         if total == 0 {
-            0.0
+            None
         } else {
-            self.wasted_tokens as f64 / total as f64
+            Some(self.wasted_tokens as f64 / total as f64)
         }
     }
 }
@@ -438,7 +470,7 @@ mod tests {
     #[test]
     fn the_four_metrics_compute_from_the_inputs() {
         let e = measurement("t", true, 500, 1_000_000, Some(2_000_000));
-        assert_eq!(e.uj_per_accepted_token(), 2_000); // 1e6 µJ / 500 tok
+        assert_eq!(e.uj_per_accepted_token(), Some(2_000)); // 1e6 µJ / 500 tok
         assert_eq!(e.tokens_per_sec(), 500.0); // 500 tok / 1 s
         assert_eq!(e.uusd_per_accepted_token(), Some(4_000)); // 2e6 µUSD / 500
         assert_eq!(e.tokens_total(), 2_500); // 4×500 in + 500 out
@@ -450,6 +482,96 @@ mod tests {
         assert_eq!(e.uusd_per_accepted_token(), None);
     }
 
+    /// The case the sealed headline figure used to misreport: 10 J spent,
+    /// nothing accepted, `completed: false` — which the crate documents as
+    /// meaning "the tokens/joules below bought nothing".
+    ///
+    /// The ratio is undefined, and `0` is the *optimum* of a cost-per-result
+    /// figure — better than any successful run — so the receipt seals no figure
+    /// rather than the best possible one. `mesh/SPEC.md` §6 specifies the same
+    /// convention: "omitted when no tokens were accepted".
+    #[test]
+    fn spend_that_bought_nothing_seals_no_headline_figure() {
+        let sk = key();
+        let e = measurement("t", false, 0, 10_000_000, None);
+        assert_eq!(e.energy.uj(), 10_000_000, "the spend is real");
+        assert_eq!(
+            e.uj_per_accepted_token(),
+            None,
+            "0 uJ/token would read as free, and as better than any completed run"
+        );
+
+        let wire = e.wire(0, &ContentId([0u8; 32]), "did:jcp:eff");
+        assert!(
+            wire.get("uj_per_accepted_token").is_none(),
+            "an undefined figure is omitted from the signed core, not sealed as 0: {wire}"
+        );
+
+        let env = e.seal(0, &ContentId([0u8; 32]), &sk, "did:jcp:eff");
+        let rec = verify(&env, "did:jcp:eff", &sk.verifying_key().to_bytes())
+            .expect("a receipt without the figure still verifies");
+        assert_eq!(rec.uj_per_accepted_token, None);
+        assert_eq!(rec.energy_uj, 10_000_000, "and the spend is still on it");
+    }
+
+    /// The value projection is not invented either. `value_uusd` is an input and
+    /// still seals; the per-token ratio derived from it does not.
+    #[test]
+    fn a_value_figure_is_not_invented_without_accepted_tokens() {
+        let e = measurement("t", false, 0, 10_000_000, Some(2_000_000));
+        assert_eq!(e.uusd_per_accepted_token(), None);
+
+        let wire = e.wire(0, &ContentId([0u8; 32]), "did:jcp:eff");
+        assert_eq!(
+            wire.get("value_uusd").and_then(Value::as_u64),
+            Some(2_000_000),
+            "the stated value is an input, not a ratio"
+        );
+        assert!(wire.get("uusd_per_accepted_token").is_none());
+    }
+
+    /// The aggregate half, through the real seal -> verify -> aggregate path:
+    /// units that spent energy and completed nothing have no cost per completed
+    /// unit. Not 0, which would be the cheapest ledger expressible.
+    #[test]
+    fn a_ledger_with_nothing_completed_reports_no_cost_per_unit() {
+        let sk = key();
+        let pk = sk.verifying_key().to_bytes();
+        let recs: Vec<EfficiencyReceipt> = (0..3)
+            .map(|i| {
+                let e = measurement("t", false, 0, 10_000_000, None);
+                let env = e.seal(i, &ContentId([0u8; 32]), &sk, "did:jcp:eff");
+                verify(&env, "did:jcp:eff", &pk).expect("seals and verifies")
+            })
+            .collect();
+        for r in &recs {
+            assert_eq!(r.uj_per_accepted_token, None);
+        }
+
+        let t = aggregate(&recs);
+        assert_eq!(t.completed_units, 0);
+        assert_eq!(t.wasted_units, 3);
+        assert_eq!(t.wasted_uj, 30_000_000, "30 J of real spend");
+        assert_eq!(
+            t.uj_per_completed_unit(),
+            None,
+            "0 uJ per completed unit would be the cheapest record possible"
+        );
+        assert_eq!(t.tokens_per_completed_unit(), None);
+
+        // An empty ledger has no waste share at all, rather than a perfect one.
+        assert_eq!(Totals::default().waste_fraction(), None);
+    }
+
+    /// The figures whose zero fallback is their *worst* value keep it: a zero
+    /// that understates is not the defect the `Option`s above fix.
+    #[test]
+    fn a_fallback_toward_the_worst_value_is_left_alone() {
+        let e = measurement("t", true, 0, 1_000, None);
+        assert_eq!(e.tokens_per_sec(), 0.0, "throughput: higher is better");
+        assert_eq!(Totals::default().value_per_joule(), 0.0, "value: higher is better");
+    }
+
     #[test]
     fn seal_verify_round_trips_and_tamper_fails() {
         let sk = key();
@@ -459,7 +581,7 @@ mod tests {
         assert_eq!(rec.task, "fix-123");
         assert!(rec.completed);
         assert_eq!(rec.tokens_out, 400);
-        assert_eq!(rec.uj_per_accepted_token, 2_000);
+        assert_eq!(rec.uj_per_accepted_token, Some(2_000));
         assert_eq!(rec.value_uusd, Some(1_000_000));
         assert_eq!(rec.tokens_per_sec(), 400.0);
 
@@ -520,9 +642,9 @@ mod tests {
         assert_eq!(t.completed_tokens, 3_000);
         assert_eq!(t.wasted_tokens, 4_500);
         // tokens per completed unit charges ALL spend (7500) to the 2 done units.
-        assert_eq!(t.tokens_per_completed_unit(), 3_750);
+        assert_eq!(t.tokens_per_completed_unit(), Some(3_750));
         assert_eq!(t.value_uusd, 1_000_000);
         // more than half the tokens bought nothing — the number "cost/token" hides.
-        assert!(t.waste_fraction() > 0.5);
+        assert!(t.waste_fraction().expect("tokens were spent") > 0.5);
     }
 }
diff --git a/jouledesk/jouledesk-rs/crates/jouledesk/examples/channel.rs b/jouledesk/jouledesk-rs/crates/jouledesk/examples/channel.rs
index 652e02f6f..62d6819dc 100644
--- a/jouledesk/jouledesk-rs/crates/jouledesk/examples/channel.rs
+++ b/jouledesk/jouledesk-rs/crates/jouledesk/examples/channel.rs
@@ -66,7 +66,10 @@ fn main() {
     println!("    wasted units    : {}   (ran, produced no result)", s.wasted_units);
     println!(
         "    µJ / completed  : {}   (charges the failed build's energy across the completed work)",
+        // "—" when nothing completed: 0 is this figure's optimum, so printing it
+        // would name the cheapest possible cost for work that delivered none.
         s.uj_per_completed_unit()
+            .map_or_else(|| "—  (nothing completed)".to_string(), |uj| uj.to_string())
     );
     println!(
         "\n  Note: 'deploy' was refused (no held skill) and the third 'summarize' was refused\n  \
diff --git a/jouledesk/jouledesk-rs/crates/jouledesk/examples/room.rs b/jouledesk/jouledesk-rs/crates/jouledesk/examples/room.rs
index 6af85c7d9..82f3e3b77 100644
--- a/jouledesk/jouledesk-rs/crates/jouledesk/examples/room.rs
+++ b/jouledesk/jouledesk-rs/crates/jouledesk/examples/room.rs
@@ -53,7 +53,9 @@ fn main() {
     println!("  tokens          : {} in · {} out", r.tokens_in, r.tokens_out);
     println!(
         "  energy (derived): {} µJ   ({} µJ / accepted token)",
-        r.energy_uj, r.uj_per_accepted_token
+        r.energy_uj,
+        r.uj_per_accepted_token
+            .map_or_else(|| "—".to_string(), |uj| uj.to_string())
     );
     println!("  verified under  : {}", call.steward());
     println!(
diff --git a/jouledesk/jouledesk-rs/crates/jouledesk/src/lib.rs b/jouledesk/jouledesk-rs/crates/jouledesk/src/lib.rs
index 928372ed8..4b8f6ffe5 100644
--- a/jouledesk/jouledesk-rs/crates/jouledesk/src/lib.rs
+++ b/jouledesk/jouledesk-rs/crates/jouledesk/src/lib.rs
@@ -531,7 +531,9 @@ mod tests {
         // The per-completed-unit cost charges the wasted build across the two summaries,
         // so it exceeds the summaries' own per-unit cost — the ROI a count would hide.
         assert!(
-            s.uj_per_completed_unit() > s.completed_uj / s.completed_units,
+            s.uj_per_completed_unit()
+                .expect("two units completed, so the ratio is defined")
+                > s.completed_uj / s.completed_units,
             "waste inflates joules-per-completed-unit"
         );
         assert_eq!(t.efficiency_ledger().len(), 3, "one efficiency/1 per task that ran");
diff --git a/joulehook/joulehook-rs/crates/joulehook-meter/src/lib.rs b/joulehook/joulehook-rs/crates/joulehook-meter/src/lib.rs
index a56f7363a..c09fe7ab9 100644
--- a/joulehook/joulehook-rs/crates/joulehook-meter/src/lib.rs
+++ b/joulehook/joulehook-rs/crates/joulehook-meter/src/lib.rs
@@ -172,7 +172,7 @@ mod tests {
         let r = jcp_efficiency::verify(&sealed, steward, &pk).expect("efficiency/1 verifies");
         assert_eq!(r.tokens_out, 900);
         assert_eq!(r.energy_uj, 2_700_000);
-        assert_eq!(r.uj_per_accepted_token, 2_700_000 / 900); // 3000 µJ/accepted token
+        assert_eq!(r.uj_per_accepted_token, Some(2_700_000 / 900)); // 3000 µJ/accepted token
         assert_eq!(r.provenance, "ModelBased");
     }
 
diff --git a/sandbox/sandbox-rs/crates/sandbox-tee/examples/attested_efficiency.rs b/sandbox/sandbox-rs/crates/sandbox-tee/examples/attested_efficiency.rs
index ecf63fbf7..b24ddfc5b 100644
--- a/sandbox/sandbox-rs/crates/sandbox-tee/examples/attested_efficiency.rs
+++ b/sandbox/sandbox-rs/crates/sandbox-tee/examples/attested_efficiency.rs
@@ -185,7 +185,12 @@ fn main() {
         r.receipt.provenance
     );
     println!("  nonce            : fresh (matches the issued challenge)");
-    println!("  efficiency       : {} µJ / link", r.receipt.uj_per_accepted_token);
+    println!(
+        "  efficiency       : {} µJ / link",
+        r.receipt
+            .uj_per_accepted_token
+            .map_or_else(|| "—".to_string(), |uj| uj.to_string())
+    );
     println!("  TRUST LEVEL      : {:?}, over a `{}` figure", r.trust, counter.tag());
     println!();