diff --git a/crates/eureka-pipeline/src/lib.rs b/crates/eureka-pipeline/src/lib.rs
index a071572..11f4f65 100644
--- a/crates/eureka-pipeline/src/lib.rs
+++ b/crates/eureka-pipeline/src/lib.rs
@@ -96,6 +96,12 @@ impl<T> Absent for Option<T> {
     }
 }
 
+impl Absent for bool {
+    fn absent(&self) -> bool {
+        !*self
+    }
+}
+
 impl<T> Absent for Vec<T> {
     fn absent(&self) -> bool {
         self.is_empty()
@@ -591,7 +597,10 @@ fn pulse_is_well_formed(pulse: &PipelinePulse, at: &str) -> Result<(), PipelineR
     {
         return Err(format_error(&format!("{at}.urgency_permille"), &urgency.to_string()));
     }
-    if pulse.tempo_vote_beat_s.is_none() && pulse.urgency_permille.is_none() {
+    if pulse.tempo_vote_withdrawn && pulse.tempo_vote_beat_s.is_some() {
+        return Err(format_error(&format!("{at}.tempo_vote_withdrawn"), "a pulse that votes a beat and withdraws the vote"));
+    }
+    if pulse.tempo_vote_beat_s.is_none() && !pulse.tempo_vote_withdrawn && pulse.urgency_permille.is_none() {
         return Err(format_error(&format!("{at}.tempo_vote_beat_s"), "a pulse that votes and declares nothing"));
     }
     Ok(())
@@ -736,12 +745,14 @@ value_types! {
         budget_usd: Short, claims: Vec<PipelineRef>[64], campaigns: Vec<Slug>[8],
     } => run_is_well_formed
     /// One Mind's heartbeat vote, in her own mind: the beat she wants (the swarm's
-    /// tempo is the lower median of every Mind's newest vote) and the urgency she
-    /// declares for herself until her next Persona turn. Either may be absent, not
-    /// both. Instance-rooted: the key is `<instance>:pulse:<label>`, the label
+    /// tempo is the lower median of every Mind's newest vote), the withdrawal of
+    /// her standing vote (`tempo_vote_withdrawn`, an explicit null: she counts as
+    /// silent again), and the urgency she declares for herself until her next
+    /// Persona turn. A pulse says at least one of the three; a withdrawal and a
+    /// beat are never both. Instance-rooted: the key is `<instance>:pulse:<label>`, the label
     /// time-ordered like a run's.
     pub struct PipelinePulse {
-        instance: Slug, label: Label, tempo_vote_beat_s: Option<u32>, urgency_permille: Option<u16>, note: Line,
+        instance: Slug, label: Label, tempo_vote_beat_s: Option<u32>, tempo_vote_withdrawn: bool = absent, urgency_permille: Option<u16>, note: Line,
     } => pulse_is_well_formed
 }
 
@@ -1407,7 +1418,7 @@ mod tests {
                 campaigns: vec![slug(CAMPAIGN)],
             }), format!("{INSTANCE}:run:mind-2026-10-09-1")),
             (D::Pulse(PipelinePulse {
-                instance: slug(INSTANCE), label: l("2026-10-31t041200-t0"), tempo_vote_beat_s: Some(600), urgency_permille: Some(250),
+                instance: slug(INSTANCE), label: l("2026-10-31t041200-t0"), tempo_vote_beat_s: Some(600), tempo_vote_withdrawn: false, urgency_permille: Some(250),
                 note: "The swarm is idle; a shorter beat.".into(),
             }), format!("{INSTANCE}:pulse:2026-10-31t041200-t0")),
         ]
@@ -1703,7 +1714,7 @@ mod tests {
     #[test]
     fn a_pulse_is_in_bounds_and_says_something() {
         let validated = |beat: Option<u32>, urgency: Option<u16>| {
-            PipelineDocument::Pulse(PipelinePulse { instance: slug(INSTANCE), label: l("2026-10-31t041200-t0"), tempo_vote_beat_s: beat, urgency_permille: urgency, note: "".into() }).validate()
+            PipelineDocument::Pulse(PipelinePulse { instance: slug(INSTANCE), label: l("2026-10-31t041200-t0"), tempo_vote_beat_s: beat, tempo_vote_withdrawn: false, urgency_permille: urgency, note: "".into() }).validate()
         };
         for (beat, urgency) in [(Some(60), None), (Some(86_400), None), (None, Some(0)), (None, Some(1000)), (Some(600), Some(250))] {
             assert_eq!(validated(beat, urgency), Ok(()), "{beat:?} {urgency:?}");
diff --git a/crates/huginn-mind/src/admission.rs b/crates/huginn-mind/src/admission.rs
index 302b27f..eb1b6bc 100644
--- a/crates/huginn-mind/src/admission.rs
+++ b/crates/huginn-mind/src/admission.rs
@@ -2453,7 +2453,7 @@ mod tests {
     fn a_pulse_of_another_mind_is_a_foreign_instance_and_her_own_is_admitted() {
         let mut mind = with_specs();
         let pulse = |instance: &str| {
-            D::Pulse(eureka_pipeline::PipelinePulse { instance: slug(instance), label: l("p1"), tempo_vote_beat_s: Some(600), urgency_permille: None, note: "".into() })
+            D::Pulse(eureka_pipeline::PipelinePulse { instance: slug(instance), label: l("p1"), tempo_vote_beat_s: Some(600), tempo_vote_withdrawn: false, urgency_permille: None, note: "".into() })
         };
         assert_eq!(
             refusal(admit(&mut mind, vec![pulse(OTHER_INSTANCE)])),
diff --git a/crates/huginn-mind/src/query.rs b/crates/huginn-mind/src/query.rs
index c7743f5..e77346a 100644
--- a/crates/huginn-mind/src/query.rs
+++ b/crates/huginn-mind/src/query.rs
@@ -141,7 +141,7 @@ pub enum PipelineFacts {
     Stewardship { instance: Slug, repo: OrgRepo, sequence: u32, assigned_on: Date, note: Line },
     HandOff { from_instance: Slug, to_instance: Slug, repo: OrgRepo, handed_on: Date },
     Run { label: Label, operated_by: RunOperator, turn: RunTurn, started_on: Date, claims: Vec<PipelineRef> },
-    Pulse { label: Label, tempo_vote_beat_s: Option<u32>, urgency_permille: Option<u16> },
+    Pulse { label: Label, tempo_vote_beat_s: Option<u32>, #[serde(default)] tempo_vote_withdrawn: bool, urgency_permille: Option<u16> },
 }
 
 impl PipelineFacts {
@@ -243,6 +243,7 @@ impl PipelineFacts {
             D::Pulse(value) => Self::Pulse {
                 label: value.label.clone(),
                 tempo_vote_beat_s: value.tempo_vote_beat_s,
+                tempo_vote_withdrawn: value.tempo_vote_withdrawn,
                 urgency_permille: value.urgency_permille,
             },
         }
@@ -1468,6 +1469,7 @@ mod tests {
                 instance: Slug(INSTANCE.into()),
                 label: Label(label.into()),
                 tempo_vote_beat_s: beat,
+                tempo_vote_withdrawn: false,
                 urgency_permille: urgency,
                 note: "n".into(),
             })
diff --git a/crates/huginn-mind/src/rows.rs b/crates/huginn-mind/src/rows.rs
index 3f49993..d404369 100644
--- a/crates/huginn-mind/src/rows.rs
+++ b/crates/huginn-mind/src/rows.rs
@@ -48,7 +48,7 @@ pub(crate) enum Alias {
     /// unrun, so a reader of her last real turn skips the withdrawn ones in the
     /// index instead of walking past them.
     Ran,
-    /// `true` on a pulse that casts a tempo vote.
+    /// `true` on a pulse that casts a tempo vote or withdraws the standing one.
     Voted,
     /// `true` on a pulse that declares an urgency.
     Urged,
@@ -244,7 +244,7 @@ impl SelectionRow {
                 put(Alias::Ran, if withdrawn { Vec::new() } else { vec!["true".into()] });
             }
             D::Pulse(pulse) => {
-                put(Alias::Voted, if pulse.tempo_vote_beat_s.is_some() { vec!["true".into()] } else { Vec::new() });
+                put(Alias::Voted, if pulse.tempo_vote_beat_s.is_some() || pulse.tempo_vote_withdrawn { vec!["true".into()] } else { Vec::new() });
                 put(Alias::Urged, if pulse.urgency_permille.is_some() { vec!["true".into()] } else { Vec::new() });
             }
             _ => {}
diff --git a/crates/mind-body/src/heartbeat.rs b/crates/mind-body/src/heartbeat.rs
index 7998a15..bd9f06b 100644
--- a/crates/mind-body/src/heartbeat.rs
+++ b/crates/mind-body/src/heartbeat.rs
@@ -450,12 +450,13 @@ fn label_of(run: &eureka_pipeline::PipelineRef) -> String {
     run.id.0.rsplit(':').next().unwrap_or_default().to_string()
 }
 
-/// Her standing vote: the newest pulse that carries one, by admission ordinal. A
-/// vote stands until she replaces it, however many pulses of other kinds follow.
+/// Her standing vote: the newest pulse that votes or withdraws, by admission
+/// ordinal. A vote stands until she casts another or withdraws it, however many
+/// pulses of other kinds follow; a withdrawal leaves her silent.
 fn standing_vote(mind: &dyn MindPort, instance: &Slug) -> Result<Option<u32>> {
     let pulses = any_of(any_of(of_kind(PipelineKind::Pulse), "root", &[&instance.0]), "voted", &["true"]);
     Ok(newest(mind, pulses)?.and_then(|header| match header.facts {
-        PipelineFacts::Pulse { tempo_vote_beat_s, .. } => tempo_vote_beat_s,
+        PipelineFacts::Pulse { tempo_vote_beat_s, tempo_vote_withdrawn: false, .. } => tempo_vote_beat_s,
         _ => None,
     }))
 }
diff --git a/crates/mind-body/src/heartbeat/tests.rs b/crates/mind-body/src/heartbeat/tests.rs
index 241c45c..0df4956 100644
--- a/crates/mind-body/src/heartbeat/tests.rs
+++ b/crates/mind-body/src/heartbeat/tests.rs
@@ -220,6 +220,7 @@ impl Rig {
             instance: Slug(NAMES[who].into()),
             label: eureka_pipeline::Label(label),
             tempo_vote_beat_s: beat,
+            tempo_vote_withdrawn: false,
             urgency_permille: urgency,
             note: "test".into(),
         })]);
@@ -603,6 +604,7 @@ fn ann_queries_with(pulses: usize, beat: Option<u32>, urgency: Option<u16>) -> u
                         instance: Slug("ann".into()),
                         label: eureka_pipeline::Label(format!("c{}", done + n)),
                         tempo_vote_beat_s: beat,
+                        tempo_vote_withdrawn: false,
                         urgency_permille: urgency,
                         note: "cost".into(),
                     })
@@ -655,3 +657,28 @@ fn her_standing_vote_is_the_newest_by_admission_not_by_the_clock() {
     let trace = rig.store.traces.borrow().last().cloned().unwrap();
     assert_eq!(trace.instances[ANN].vote_beat_s, Some(7200), "admitted second, stamped earlier");
 }
+
+#[test]
+fn a_null_vote_withdraws_the_standing_one_and_an_urgency_only_pulse_leaves_it() {
+    let rig = Rig::new();
+    rig.turn(ANN, 3000);
+    rig.turn(BOB, 3000);
+    rig.pulse(ANN, 300, Some(60), None);
+    rig.pulse(ANN, 200, None, Some(5));
+    rig.poll();
+    let kept = rig.store.traces.borrow().last().cloned().unwrap();
+    assert_eq!(kept.instances[ANN].vote_beat_s, Some(60), "an urgency-only pulse leaves her vote standing");
+    rig.minds[ANN].admit_at(rig.now() - Duration::seconds(100));
+    rig.minds[ANN].committed(vec![eureka_pipeline::PipelineDocument::Pulse(eureka_pipeline::PipelinePulse {
+        instance: Slug("ann".into()),
+        label: eureka_pipeline::Label("withdraw".into()),
+        tempo_vote_beat_s: None,
+        tempo_vote_withdrawn: true,
+        urgency_permille: None,
+        note: "test".into(),
+    })]);
+    rig.poll();
+    let withdrawn = rig.store.traces.borrow().last().cloned().unwrap();
+    assert_eq!(withdrawn.instances[ANN].vote_beat_s, None, "an explicit null withdraws it");
+    assert_eq!(withdrawn.tempo_s, 900, "she counts as silent again");
+}
diff --git a/crates/mind-body/src/persona.rs b/crates/mind-body/src/persona.rs
index 5861e98..8b91e7d 100644
--- a/crates/mind-body/src/persona.rs
+++ b/crates/mind-body/src/persona.rs
@@ -179,6 +179,11 @@ impl Config {
     }
 }
 
+/// A key that is present, null or not, reads as `Some`; an omitted key stays `None`.
+fn present<'de, D: serde::Deserializer<'de>, T: Deserialize<'de>>(deserializer: D) -> Result<Option<T>, D::Error> {
+    T::deserialize(deserializer).map(Some)
+}
+
 /// Her one reply to a turn. The connector is asked for exactly this and the
 /// answer is decoded into exactly this.
 #[derive(Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]
@@ -188,9 +193,10 @@ pub struct PersonaReply {
     /// Required, null when she starts nothing: a reply that omits it is not a reply.
     #[serde(deserialize_with = "Option::deserialize")]
     pub start_self_run: Option<StartSelfRun>,
-    /// The beat she votes for, in seconds; null votes nothing.
-    #[serde(deserialize_with = "Option::deserialize")]
-    pub tempo_vote_beat_s: Option<u32>,
+    /// The beat she votes for, in seconds. Omitted, she says nothing about her
+    /// vote and her standing one stands; an explicit null withdraws it.
+    #[serde(default, deserialize_with = "present")]
+    pub tempo_vote_beat_s: Option<Option<u32>>,
     /// The urgency she declares for herself until her next turn, in thousandths; null declares none.
     #[serde(deserialize_with = "Option::deserialize")]
     pub urgency_permille: Option<u16>,
@@ -230,7 +236,7 @@ fn campaign_in_bounds(campaign: &str) -> bool {
 }
 
 fn vote_in_bounds(reply: &PersonaReply) -> bool {
-    reply.tempo_vote_beat_s.is_none_or(|beat| (TEMPO_VOTE_MIN_S..=TEMPO_VOTE_MAX_S).contains(&beat)) && reply.urgency_permille.is_none_or(|urgency| urgency <= URGENCY_MAX_PERMILLE)
+    reply.tempo_vote_beat_s.flatten().is_none_or(|beat| (TEMPO_VOTE_MIN_S..=TEMPO_VOTE_MAX_S).contains(&beat)) && reply.urgency_permille.is_none_or(|urgency| urgency <= URGENCY_MAX_PERMILLE)
 }
 
 fn start_in_bounds(ask: &StartSelfRun) -> bool {
@@ -264,7 +270,7 @@ pub fn reply_schema(rooms: &[String], campaigns: &[String]) -> String {
     json!({
         "type": "object",
         "additionalProperties": false,
-        "required": ["say", "start_self_run", "tempo_vote_beat_s", "urgency_permille"],
+        "required": ["say", "start_self_run", "urgency_permille"],
         "properties": {
             "say": {
                 "type": "array",
@@ -815,7 +821,8 @@ fn admit_pulse(organs: &Organs, run: &PipelineRef, turn: u32, reply: &PersonaRep
     let pulse = PipelineDocument::Pulse(PipelinePulse {
         instance: organs.mind.instance().clone(),
         label: Label(format!("{}-t{turn}", label_of(run))),
-        tempo_vote_beat_s: reply.tempo_vote_beat_s,
+        tempo_vote_beat_s: reply.tempo_vote_beat_s.flatten(),
+        tempo_vote_withdrawn: reply.tempo_vote_beat_s == Some(None),
         urgency_permille: reply.urgency_permille,
         note: "Voted in a Persona turn.".into(),
     });
@@ -825,7 +832,7 @@ fn admit_pulse(organs: &Organs, run: &PipelineRef, turn: u32, reply: &PersonaRep
 /// The tempo the Minds hold between them, from the newest `heartbeat.cc` trace:
 /// the tally, and each Mind vote and declared urgency, her own marked.
 fn render_tempo(view: Option<&dyn TempoView>, instance: &Slug) -> String {
-    let guidance = "The swarm beat is the lower median of every Mind newest vote. You vote with tempo_vote_beat_s (60 to 86400 seconds per beat, null to vote nothing) and declare your own urgency with urgency_permille (0 to 1000, null for none); an urgency lasts until your next turn, so use it as etiquette, not as a habit.";
+    let guidance = "The swarm beat is the lower median of every Mind newest vote. You vote with tempo_vote_beat_s (60 to 86400 seconds per beat; omit the key to leave your standing vote as it is, and send null to withdraw it so you count as silent again) and declare your own urgency with urgency_permille (0 to 1000, null for none); an urgency lasts until your next turn, so use it as etiquette, not as a habit.";
     let latest: Option<PollTrace> = view.and_then(|view| view.latest().ok().flatten());
     let Some(trace) = latest else { return format!("Tempo: not yet read. {guidance}") };
     let mut out = format!("Tempo: the beat is {} s. {guidance}\nMinds:\n", trace.tempo_s);
diff --git a/crates/mind-body/src/persona/tests.rs b/crates/mind-body/src/persona/tests.rs
index 4125202..58cbecf 100644
--- a/crates/mind-body/src/persona/tests.rs
+++ b/crates/mind-body/src/persona/tests.rs
@@ -169,7 +169,7 @@ fn readout() -> UsageReadout {
 
 fn says(lines: &[(&str, &str)]) -> String {
     let say: Vec<_> = lines.iter().map(|(room, text)| json!({ "room": room, "text": text })).collect();
-    json!({ "say": say, "start_self_run": null, "tempo_vote_beat_s": null, "urgency_permille": null }).to_string()
+    json!({ "say": say, "start_self_run": null, "urgency_permille": null }).to_string()
 }
 
 impl Rig {
@@ -403,7 +403,7 @@ fn a_reply_is_decoded_as_the_one_type_and_nothing_else_is_scanned() {
     assert!(decode_reply(&says(&[("swarm", "x")]), &c.rooms).is_ok());
     for bad in [
         "I will start_self_run now",
-        r#"{"say":[],"start_self_run":null,"tempo_vote_beat_s":null,"urgency_permille":null} and more"#,
+        r#"{"say":[],"start_self_run":null,"urgency_permille":null} and more"#,
         r#"{"say":[],"start_self_run":null,"extra":1}"#,
         "",
     ] {
@@ -465,7 +465,7 @@ fn start_self_run_admits_brief_and_launches() {
 
 #[test]
 fn a_start_outside_the_reply_bounds_fails_the_turn_without_an_admission_or_an_ack() {
-    let reply = json!({ "say": [], "start_self_run": { "brief": "x", "repo": "not a repo", "campaign": CAMPAIGN }, "tempo_vote_beat_s": null, "urgency_permille": null }).to_string();
+    let reply = json!({ "say": [], "start_self_run": { "brief": "x", "repo": "not a repo", "campaign": CAMPAIGN }, "urgency_permille": null }).to_string();
     let rig = Rig::new(vec![operator_says(1, "go")], &[reply]);
     let Outcome::Served { failure, .. } = rig.go() else { panic!("served") };
     assert_eq!(failure, Some(Failure::Undecodable));
@@ -477,7 +477,7 @@ fn a_start_outside_the_reply_bounds_fails_the_turn_without_an_admission_or_an_ac
 fn a_reply_without_start_self_run_is_not_a_reply_though_null_is() {
     let c = config();
     assert_eq!(decode_reply(r#"{"say":[]}"#, &c.rooms), Err(Failure::Undecodable), "the schema requires the field, so does the decoder");
-    assert!(decode_reply(r#"{"say":[],"start_self_run":null,"tempo_vote_beat_s":null,"urgency_permille":null}"#, &c.rooms).is_ok());
+    assert!(decode_reply(r#"{"say":[],"start_self_run":null,"urgency_permille":null}"#, &c.rooms).is_ok());
     let rig = Rig::new(vec![operator_says(1, "go")], &[r#"{"say":[{"room":"operator","text":"hi"}]}"#.into()]);
     let Outcome::Served { failure, .. } = rig.go() else { panic!("served") };
     assert_eq!(failure, Some(Failure::Undecodable));
@@ -487,7 +487,7 @@ fn a_reply_without_start_self_run_is_not_a_reply_though_null_is() {
 #[test]
 fn the_decoder_holds_the_bounds_the_schema_states() {
     let c = config();
-    let start = |brief: &str, repo: &str, campaign: &str| json!({ "say": [], "start_self_run": { "brief": brief, "repo": repo, "campaign": campaign }, "tempo_vote_beat_s": null, "urgency_permille": null }).to_string();
+    let start = |brief: &str, repo: &str, campaign: &str| json!({ "say": [], "start_self_run": { "brief": brief, "repo": repo, "campaign": campaign }, "urgency_permille": null }).to_string();
     let ok = |brief: &str, repo: &str, campaign: &str| decode_reply(&start(brief, repo, campaign), &c.rooms).is_ok();
     assert!(ok("b", "GameCult/Huginn", "eureka-body"));
     assert!(ok(&"b".repeat(1000), "a-b/c.d_e-f", &"c".repeat(64)));
@@ -676,7 +676,7 @@ fn no_member_text_name_or_context_can_read_as_an_operator_line() {
 
 #[test]
 fn a_self_run_in_a_campaign_the_mind_does_not_hold_is_refused_before_anything_is_admitted() {
-    let reply = json!({ "say": [], "start_self_run": { "brief": "Work", "repo": REPO, "campaign": "no-such-campaign" }, "tempo_vote_beat_s": null, "urgency_permille": null }).to_string();
+    let reply = json!({ "say": [], "start_self_run": { "brief": "Work", "repo": REPO, "campaign": "no-such-campaign" }, "urgency_permille": null }).to_string();
     let rig = Rig::new(vec![operator_says(1, "go")], &[reply]);
     let Outcome::Served { failure, self_run, .. } = rig.go() else { panic!("served") };
     assert_eq!((failure, self_run), (Some(Failure::SelfRun), None));
@@ -684,7 +684,7 @@ fn a_self_run_in_a_campaign_the_mind_does_not_hold_is_refused_before_anything_is
     assert!(rig.launcher.started.borrow().is_empty());
     assert!(rig.chat.acked.borrow().is_empty());
     // A prefix of a real campaign's name is not that campaign.
-    let prefix = json!({ "say": [], "start_self_run": { "brief": "Work", "repo": REPO, "campaign": &CAMPAIGN[..CAMPAIGN.len() - 1] }, "tempo_vote_beat_s": null, "urgency_permille": null }).to_string();
+    let prefix = json!({ "say": [], "start_self_run": { "brief": "Work", "repo": REPO, "campaign": &CAMPAIGN[..CAMPAIGN.len() - 1] }, "urgency_permille": null }).to_string();
     let rig = Rig::new(vec![operator_says(1, "go")], &[prefix]);
     let Outcome::Served { failure, .. } = rig.go() else { panic!("served") };
     assert_eq!(failure, Some(Failure::SelfRun));
@@ -810,7 +810,7 @@ fn the_campaigns_in_force_are_listed_and_are_the_schemas_campaign_enum() {
 
 #[test]
 fn a_self_run_naming_a_listed_campaign_passes_the_campaign_check() {
-    let reply = json!({ "say": [], "start_self_run": { "brief": "Work", "repo": REPO, "campaign": CAMPAIGN }, "tempo_vote_beat_s": null, "urgency_permille": null }).to_string();
+    let reply = json!({ "say": [], "start_self_run": { "brief": "Work", "repo": REPO, "campaign": CAMPAIGN }, "urgency_permille": null }).to_string();
     let rig = Rig::new(vec![operator_says(1, "go")], &[reply]);
     let Outcome::Served { failure, self_run, .. } = rig.go() else { panic!("served") };
     assert_eq!(failure, None);
@@ -882,13 +882,18 @@ fn the_turn_input_says_how_to_read_an_addressee() {
     assert!(input_for(&[], "Aqua").contains("A message addressed to another Mind is theirs to answer. Answer it only if you hold something they need, and say so."));
 }
 
-fn voting(beat: serde_json::Value, urgency: serde_json::Value) -> String {
-    json!({ "say": [{ "room": "operator", "text": "ok" }], "start_self_run": null, "tempo_vote_beat_s": beat, "urgency_permille": urgency }).to_string()
+/// A reply that votes `beat` (`None` leaves the key out; `Some(null)` withdraws) and declares `urgency`.
+fn voting(beat: Option<serde_json::Value>, urgency: serde_json::Value) -> String {
+    let mut reply = json!({ "say": [{ "room": "operator", "text": "ok" }], "start_self_run": null, "urgency_permille": urgency });
+    if let Some(beat) = beat {
+        reply["tempo_vote_beat_s"] = beat;
+    }
+    reply.to_string()
 }
 
 #[test]
 fn a_vote_and_a_declared_urgency_in_the_reply_become_one_pulse_in_her_own_mind() {
-    let rig = Rig::new(vec![operator_says(1, "how fast should we go?")], &[voting(json!(600), json!(250))]);
+    let rig = Rig::new(vec![operator_says(1, "how fast should we go?")], &[voting(Some(json!(600)), json!(250))]);
     let Outcome::Served { failure, .. } = rig.go() else { panic!("served") };
     assert_eq!(failure, None);
     let pulses = rig.mind.ids(K::Pulse);
@@ -918,7 +923,7 @@ fn a_vote_or_urgency_outside_its_bounds_fails_the_turn_without_a_pulse_or_an_ack
 #[test]
 fn the_reply_schema_bounds_the_vote_and_the_urgency_to_the_pulse_kind() {
     let schema: serde_json::Value = serde_json::from_str(&reply_schema(&["operator".to_string()], &[])).unwrap();
-    assert_eq!(schema["required"], json!(["say", "start_self_run", "tempo_vote_beat_s", "urgency_permille"]));
+    assert_eq!(schema["required"], json!(["say", "start_self_run", "urgency_permille"]));
     assert_eq!(schema["properties"]["tempo_vote_beat_s"]["anyOf"][1], json!({ "type": "integer", "minimum": 60, "maximum": 86_400 }));
     assert_eq!(schema["properties"]["urgency_permille"]["anyOf"][1], json!({ "type": "integer", "minimum": 0, "maximum": 1000 }));
 }
@@ -1108,13 +1113,27 @@ fn the_persona_flags_come_from_the_environment_when_the_command_line_lacks_them(
 
 #[test]
 fn a_vote_alone_or_an_urgency_alone_is_still_one_pulse() {
-    for (beat, urgency) in [(json!(600), json!(null)), (json!(null), json!(250))] {
+    for (beat, urgency) in [(Some(json!(600)), json!(null)), (None, json!(250))] {
         let rig = Rig::new(vec![operator_says(1, "go")], &[voting(beat.clone(), urgency.clone())]);
         let Outcome::Served { failure, .. } = rig.go() else { panic!("served") };
-        assert_eq!(failure, None, "{beat} {urgency}");
+        assert_eq!(failure, None, "{beat:?} {urgency}");
         let pulses = rig.mind.ids(K::Pulse);
-        assert_eq!(pulses.len(), 1, "{beat} {urgency}");
+        assert_eq!(pulses.len(), 1, "{beat:?} {urgency}");
         let PipelineDocument::Pulse(pulse) = rig.mind.view(K::Pulse, &pulses[0]).unwrap().document else { panic!("a pulse") };
-        assert_eq!((pulse.tempo_vote_beat_s.map(i64::from), pulse.urgency_permille.map(i64::from)), (beat.as_i64(), urgency.as_i64()));
+        assert_eq!((pulse.tempo_vote_beat_s.map(i64::from), pulse.urgency_permille.map(i64::from)), (beat.as_ref().and_then(|beat| beat.as_i64()), urgency.as_i64()));
     }
 }
+
+#[test]
+fn an_explicit_null_vote_is_a_pulse_that_withdraws_and_an_omitted_vote_is_no_vote_at_all() {
+    let rig = Rig::new(vec![operator_says(1, "withdraw")], &[voting(Some(json!(null)), json!(null))]);
+    let Outcome::Served { failure, .. } = rig.go() else { panic!("served") };
+    assert_eq!(failure, None);
+    let pulses = rig.mind.ids(K::Pulse);
+    assert_eq!(pulses.len(), 1);
+    let PipelineDocument::Pulse(pulse) = rig.mind.view(K::Pulse, &pulses[0]).unwrap().document else { panic!("a pulse") };
+    assert_eq!((pulse.tempo_vote_beat_s, pulse.tempo_vote_withdrawn, pulse.urgency_permille), (None, true, None));
+    let silent = Rig::new(vec![operator_says(1, "nothing")], &[voting(None, json!(null))]);
+    let Outcome::Served { .. } = silent.go() else { panic!("served") };
+    assert!(silent.mind.ids(K::Pulse).is_empty(), "no vote key and no urgency is no pulse");
+}
diff --git a/crates/mind-body/src/tempo.rs b/crates/mind-body/src/tempo.rs
index d6d7b4f..527ccb1 100644
--- a/crates/mind-body/src/tempo.rs
+++ b/crates/mind-body/src/tempo.rs
@@ -19,7 +19,10 @@ pub const LOG_BOUND_ORDERS: f64 = 1.0;
 /// The swarm's tempo (ruling `eureka-body:ruling:tempo-silent-means-default`):
 /// the lower median over every Mind in the roster, each her newest vote in seconds
 /// per beat. A Mind with no standing vote, or whose mind cannot be read, is
-/// `None` and counts as `DEFAULT_BEAT_S`, so a lone voter cannot move the beat.
+/// `None` and counts as `DEFAULT_BEAT_S`. The lower median moves below the
+/// default only when at least half the roster, rounded up, votes at or below it
+/// (ruling `eureka-body:ruling:tempo-lower-median-stands`): on a roster of one or
+/// two a single Mind decides, on the live eight it takes four.
 pub fn tally(votes: &[Option<u32>]) -> u32 {
     let mut sorted: Vec<u32> = votes.iter().map(|vote| vote.unwrap_or(DEFAULT_BEAT_S)).collect();
     sorted.sort_unstable();