diff --git a/docs/plans/M5d2/01-loopd-session-slot.md b/docs/plans/M5d2/01-loopd-session-slot.md
index 8b5dfd6..107d2a0 100644
--- a/docs/plans/M5d2/01-loopd-session-slot.md
+++ b/docs/plans/M5d2/01-loopd-session-slot.md
@@ -80,10 +80,11 @@ become
 
   Then `git status --short` lists one new file, `crates/loopd/tests/session_slot.rs`.
 - [ ] **2. See it fail.** `cargo test -p loopd --test session_slot`, with a shell timeout of
-  600000 ms: the four tests compile (they call `session.slot()`, which exists) and
+  600000 ms: the four tests compile (they call `session.slot()`, which exists) and three fail.
   `a_session_created_on_the_background_slot_sends_that_slot` fails: `id_slot` is `0`, not `1`.
-  `a_main_slot_session_still_sends_main` may pass. `the_request_slot_follows_session_start_not_the_config_main`
-  fails: `id_slot` is `0`, not `7`.
+  `a_main_slot_session_still_sends_main` passes. `the_request_slot_follows_session_start_not_the_config_main`
+  fails: `id_slot` is `0`, not `7`. `a_heartbeat_turn_between_two_main_turns_does_not_change_the_main_prefix`
+  fails: the heartbeat request's `id_slot` is `0`, not `1`.
 - [ ] **3. The edit.** Make edit T1. `cargo check -p loopd` prints no error and no warning.
 - [ ] **4. The tests.** `cargo test -p loopd --test session_slot --test turn --test channel
   --test compact_turn`: every test passes, 4 in `session_slot` and the others as before.
diff --git a/docs/plans/M5d2/04-loopd-cron.md b/docs/plans/M5d2/04-loopd-cron.md
index 1ba41bb..42d4ee4 100644
--- a/docs/plans/M5d2/04-loopd-cron.md
+++ b/docs/plans/M5d2/04-loopd-cron.md
@@ -165,28 +165,29 @@ If `is_multiple_of` is not in scope on `u32` in this toolchain, use `value % n =
   target compiles.
 - [ ] **3. The module.** Write `cron.rs` from the skeleton. Add `pub mod cron;` to `lib.rs`
   where rustfmt will put it. `cargo check -p loopd` prints no error and no warning.
-- [ ] **4. The tests.** `cargo test -p loopd --test cron`: every test passes, 10 tests.
+- [ ] **4. The tests.** `cargo test -p loopd --test cron`: every test passes, 11 tests.
 - [ ] **5. Check.** `git diff --stat` lists `crates/loopd/src/cron.rs` and
   `crates/loopd/src/lib.rs`.
 - [ ] **6. Run the gate.** `cargo fmt --all`, then `make gate`, timeout 600000 ms. Last line
-  `gate: ok`. Test count **1536** (1526 before, plus 10).
+  `gate: ok`. Test count **1537** (1526 before, plus 11).
 - [ ] **7. Log and commit.** Task cell `M5d2/04-loopd-cron`. Stage with
   `git add crates/loopd docs/implementer-log.md Cargo.lock`, then commit as `AGENTS.md` says.
 
 ## Done when
 
-- `make gate` prints `gate: ok` with 1536 tests.
+- `make gate` prints `gate: ok` with 1537 tests.
 - `git diff HEAD~1 --stat` lists only `crates/loopd/src/cron.rs`, `crates/loopd/src/lib.rs`,
   `crates/loopd/tests/cron.rs` and the log.
 
 ## Stop and report if
 
 - The branch check fails; step 2 differs; `cargo check` warns; a test fails; the gate count is
-  not 1536; you add a dependency; you treat DOM and DOW as OR; you accept `@daily` or a sixth
+  not 1537; you add a dependency; you treat DOM and DOW as OR; you accept `@daily` or a sixth
   field; `cron.rs` exceeds 500 lines.
 
 ## What the given tests pin
 
 `0 7 * * *` matches that minute only; `* * * * *` matches; `*/5` is multiples from 0; `0-10`
-is inclusive; Sunday is 0 on 2026-10-04; the 1st of the month; four or six fields error;
+is inclusive; Sunday is 0 on 2026-10-04; the 1st of the month; DOM and DOW are AND
+(`0 7 1 * 0` matches 2026-11-01, not 2026-10-04 or 2026-10-01); four or six fields error;
 minute 60, hour 24, DOW 7 error; `@daily` errors; `Display` names the schedule.
diff --git a/docs/plans/M5d2/05-loopd-jobs.md b/docs/plans/M5d2/05-loopd-jobs.md
index ba61c94..d14c601 100644
--- a/docs/plans/M5d2/05-loopd-jobs.md
+++ b/docs/plans/M5d2/05-loopd-jobs.md
@@ -194,21 +194,21 @@ Replace the four stub bodies in the same task. Do not leave a stub that returns
 - [ ] **6. Check.** `git diff --stat` lists `crates/loopd/src/jobs.rs`,
   `crates/loopd/src/lib.rs`, `crates/loopd/src/main.rs`, `docs/runbook.md`.
 - [ ] **7. Run the gate.** `cargo fmt --all`, then `make gate`, timeout 600000 ms. Last line
-  `gate: ok`. Test count **1544** (1536 before, plus 8).
+  `gate: ok`. Test count **1545** (1537 before, plus 8).
 - [ ] **8. Log and commit.** Task cell `M5d2/05-loopd-jobs`. Stage with
   `git add crates/loopd docs/runbook.md docs/implementer-log.md Cargo.lock`, then commit as
   `AGENTS.md` says.
 
 ## Done when
 
-- `make gate` prints `gate: ok` with 1544 tests.
+- `make gate` prints `gate: ok` with 1545 tests.
 - `git diff HEAD~1 --stat` lists only `crates/loopd/src/jobs.rs`, `crates/loopd/src/lib.rs`,
   `crates/loopd/src/main.rs`, `crates/loopd/tests/jobs.rs`, `docs/runbook.md` and the log.
 
 ## Stop and report if
 
 - The branch check fails; step 2 differs; `cargo check` warns; a test fails; the gate count is
-  not 1544; you add a cron crate; a missing jobs directory is an error; `Display` for `Invalid`
+  not 1545; you add a cron crate; a missing jobs directory is an error; `Display` for `Invalid`
   does not end with the runbook pointer; `jobs.rs` exceeds 500 lines; you write a job file.
 
 ## What the given tests pin
diff --git a/docs/plans/M5d2/06-loopd-scheduler-heartbeat.md b/docs/plans/M5d2/06-loopd-scheduler-heartbeat.md
index da0e76f..4012084 100644
--- a/docs/plans/M5d2/06-loopd-scheduler-heartbeat.md
+++ b/docs/plans/M5d2/06-loopd-scheduler-heartbeat.md
@@ -190,14 +190,14 @@ pass so it runs once.
 
   `grep -c '^## heartbeat-prompt-unreadable$' docs/runbook.md` prints `1`.
 - [ ] **6. Run the gate.** `cargo fmt --all`, then `make gate`, timeout 600000 ms. Last line
-  `gate: ok`. Test count **1550** (1544 before, plus 6).
+  `gate: ok`. Test count **1551** (1545 before, plus 6).
 - [ ] **7. Log and commit.** Task cell `M5d2/06-loopd-scheduler-heartbeat`. Stage with
   `git add crates/loopd docs/runbook.md docs/implementer-log.md Cargo.lock`, then commit as
   `AGENTS.md` says.
 
 ## Done when
 
-- `make gate` prints `gate: ok` with 1550 tests.
+- `make gate` prints `gate: ok` with 1551 tests.
 - `git diff HEAD~1 --stat` lists only `crates/loopd/src/channel.rs`,
   `crates/loopd/src/scheduler.rs`, `crates/loopd/src/lib.rs`, `crates/loopd/src/main.rs`,
   `crates/loopd/tests/scheduler_heartbeat.rs`, `docs/runbook.md` and the log.
@@ -205,7 +205,7 @@ pass so it runs once.
 ## Stop and report if
 
 - The branch check fails; a "before" block is not found exactly once; step 2 differs; `cargo
-  check` warns; a test fails; the gate count is not 1550; you sleep in a test; you post to
+  check` warns; a test fails; the gate count is not 1551; you sleep in a test; you post to
   Mattermost; you send `slots.main`; you set a speaker; you `chmod 000`; `Held` stays private.
 
 ## What the given tests pin
diff --git a/docs/plans/M5d2/07-loopd-scheduler-cron.md b/docs/plans/M5d2/07-loopd-scheduler-cron.md
index c8d90a0..8d6e297 100644
--- a/docs/plans/M5d2/07-loopd-scheduler-cron.md
+++ b/docs/plans/M5d2/07-loopd-scheduler-cron.md
@@ -82,20 +82,20 @@ Do not change heartbeat behaviour. Do not add a sleep.
   --test jobs --test cron`: every test passes, 6 in `scheduler_cron`.
 - [ ] **5. Check.** `git diff --stat` lists exactly `crates/loopd/src/scheduler.rs`.
 - [ ] **6. Run the gate.** `cargo fmt --all`, then `make gate`, timeout 600000 ms. Last line
-  `gate: ok`. Test count **1556** (1550 before, plus 6).
+  `gate: ok`. Test count **1557** (1551 before, plus 6).
 - [ ] **7. Log and commit.** Task cell `M5d2/07-loopd-scheduler-cron`. Stage with
   `git add crates/loopd docs/implementer-log.md Cargo.lock`, then commit as `AGENTS.md` says.
 
 ## Done when
 
-- `make gate` prints `gate: ok` with 1556 tests.
+- `make gate` prints `gate: ok` with 1557 tests.
 - `git diff HEAD~1 --stat` lists only `crates/loopd/src/scheduler.rs`,
   `crates/loopd/tests/scheduler_cron.rs` and the log.
 
 ## Stop and report if
 
 - The branch check fails; step 2 differs (tests do not compile, or a different assertion
-  fails); `cargo check` warns; a test fails; the gate count is not 1556; you reuse a session
+  fails); `cargo check` warns; a test fails; the gate count is not 1557; you reuse a session
   across runs; you send `slots.main`; you set a speaker; you skip leftovers that are not busy;
   a heartbeat test fails.
 
diff --git a/docs/plans/M5d2/08-loopd-tool-summary.md b/docs/plans/M5d2/08-loopd-tool-summary.md
index 398dd74..19959ae 100644
--- a/docs/plans/M5d2/08-loopd-tool-summary.md
+++ b/docs/plans/M5d2/08-loopd-tool-summary.md
@@ -231,14 +231,14 @@ Facts). The `Err(TurnError::SessionFull)` arm gets the same `missing` call befor
 - [ ] **5. Check.** `git diff --stat` lists `crates/loopd/src/summarise.rs`,
   `crates/loopd/src/lib.rs`, `crates/loopd/src/compact.rs`.
 - [ ] **6. Run the gate.** `cargo fmt --all`, then `make gate`, timeout 600000 ms. Last line
-  `gate: ok`. Test count **1562** (1556 before, plus 6).
+  `gate: ok`. Test count **1563** (1557 before, plus 6).
 - [ ] **7. Log and commit.** Task cell `M5d2/08-loopd-tool-summary`. Stage with
   `git add crates/loopd config/summarise.md docs/implementer-log.md Cargo.lock`, then commit
   as `AGENTS.md` says.
 
 ## Done when
 
-- `make gate` prints `gate: ok` with 1562 tests.
+- `make gate` prints `gate: ok` with 1563 tests.
 - `git diff HEAD~1 --stat` lists only `crates/loopd/src/summarise.rs`,
   `crates/loopd/src/lib.rs`, `crates/loopd/src/compact.rs`,
   `crates/loopd/tests/tool_summary_call.rs`, `config/summarise.md` and the log.
@@ -246,7 +246,7 @@ Facts). The `Err(TurnError::SessionFull)` arm gets the same `missing` call befor
 ## Stop and report if
 
 - The branch check fails; a "before" block is not found exactly once; step 2 differs; `cargo
-  check` warns; a test fails; the gate count is not 1562; you send tools on the summary
+  check` warns; a test fails; the gate count is not 1563; you send tools on the summary
   request; you send `slots.main`; you replay the summary in `messages()`; you summarise a
   name not in the list; you summarise twice; you compact before summarising.
 
diff --git a/docs/plans/M5d2/09-memoryd-summary-index.md b/docs/plans/M5d2/09-memoryd-summary-index.md
index a5e7e33..890897f 100644
--- a/docs/plans/M5d2/09-memoryd-summary-index.md
+++ b/docs/plans/M5d2/09-memoryd-summary-index.md
@@ -117,21 +117,21 @@ results are indexed. A comment that does not fit its code: stop.
   test passes, 5 in `tool_summary_index`.
 - [ ] **5. Check.** `git diff --stat` lists exactly `crates/memoryd/src/index.rs`.
 - [ ] **6. Run the gate.** `cargo fmt --all`, then `make gate`, timeout 600000 ms. Last line
-  `gate: ok`. Test count **1567** (1562 before, plus 5).
+  `gate: ok`. Test count **1568** (1563 before, plus 5).
 - [ ] **7. Log and commit.** Task cell `M5d2/09-memoryd-summary-index`. Stage with
   `git add crates/memoryd docs/implementer-log.md Cargo.lock`, then commit as `AGENTS.md`
   says.
 
 ## Done when
 
-- `make gate` prints `gate: ok` with 1567 tests.
+- `make gate` prints `gate: ok` with 1568 tests.
 - `git diff HEAD~1 --stat` lists only `crates/memoryd/src/index.rs`,
   `crates/memoryd/tests/tool_summary_index.rs` and the log.
 
 ## Stop and report if
 
 - The branch check fails; a "before" block is not found exactly once; step 2 differs; `cargo
-  check` warns; a test fails; the gate count is not 1567; you index `ToolResult` content; you
+  check` warns; a test fails; the gate count is not 1568; you index `ToolResult` content; you
   leave `kind` as `"session"`; a secret summary is searchable on a private index.
 
 ## What the given tests pin
diff --git a/docs/plans/M5d2/10-memoryd-tiers.md b/docs/plans/M5d2/10-memoryd-tiers.md
index 1278f62..5af8542 100644
--- a/docs/plans/M5d2/10-memoryd-tiers.md
+++ b/docs/plans/M5d2/10-memoryd-tiers.md
@@ -203,20 +203,20 @@ becomes
 - [ ] **5. Check.** `git diff --stat` lists the files in "Every place that changes" except
   the new tests and starter (those are untracked until `git add`).
 - [ ] **6. Run the gate.** `cargo fmt --all`, then `make gate`, timeout 600000 ms. Last line
-  `gate: ok`. Test count **1573** (1567 before, plus 6).
+  `gate: ok`. Test count **1574** (1568 before, plus 6).
 - [ ] **7. Log and commit.** Task cell `M5d2/10-memoryd-tiers`. Stage with
   `git add crates/bxcore crates/memoryd crates/bxctl config/jobs docs/implementer-log.md
   Cargo.lock`, then commit as `AGENTS.md` says.
 
 ## Done when
 
-- `make gate` prints `gate: ok` with 1573 tests.
+- `make gate` prints `gate: ok` with 1574 tests.
 - `git diff HEAD~1 --stat` lists only the files this task names plus the log.
 
 ## Stop and report if
 
 - The branch check fails; a "before" block is not found exactly once; step 2 differs; `cargo
-  check` warns; a test fails; the gate count is not 1573; you edit `cli_memory.rs`; identity
+  check` warns; a test fails; the gate count is not 1574; you edit `cli_memory.rs`; identity
   entries show a non-zero hit count; untrusted notes are omitted; you add a cron crate; you
   special-case the name `tier` in `loopd`.
 
diff --git a/docs/plans/M5d2/README.md b/docs/plans/M5d2/README.md
index 56a41d4..4722590 100644
--- a/docs/plans/M5d2/README.md
+++ b/docs/plans/M5d2/README.md
@@ -63,13 +63,13 @@ its own. Before task 01 it is **1508** (straylight, rustc 1.98.1 / clippy 0.1.98
 | 01 | `run_turn` sends `session.slot()`; a session created on the background slot has `id_slot` of that slot; `mm-*` stays main | loopd | 1512 | 4 |
 | 02 | `LogRecord::ToolSummary`; `messages()` ignores it; `types` names it; JSON round-trip | bxcore, loopd | 1518 | 6 |
 | 03 | `[heartbeat]` (`every_s` 0, `prompt` `heartbeat.md`); unknown `[compact] summarise` names are a config error; starter `heartbeat.md` | loopd | 1526 | 8 |
-| 04 | Five-field UTC cron matcher: `*`, `n`, `n-m`, `*/n`; day-of-week 0 is Sunday | loopd | 1536 | 10 |
-| 05 | `{home}/jobs/<name>.toml`, `runs.jsonl`, `jobs-invalid` pointer and runbook | loopd | 1544 | 8 |
-| 06 | Heartbeat tick: time line, standing session `heartbeat`, skip if busy, unreadable prompt logged once | loopd | 1550 | 6 |
-| 07 | Cron tick: new session per run, skip if previous live, leftover `started` becomes `failed` | loopd | 1556 | 6 |
-| 08 | After a turn, opted-in `ToolResult` without a `ToolSummary` gets a background summary appended with the result's labels | loopd | 1562 | 6 |
-| 09 | `memoryd` indexes `ToolSummary` as kind `summary`; `recall` finds it and taints when untrusted | memoryd | 1567 | 5 |
-| 10 | `MemoryCommand::Tiers`, `bxctl memory tiers`, starter `config/jobs/tier.toml.example` | bxcore, memoryd, bxctl | 1573 | 6 |
+| 04 | Five-field UTC cron matcher: `*`, `n`, `n-m`, `*/n`; day-of-week 0 is Sunday | loopd | 1537 | 11 |
+| 05 | `{home}/jobs/<name>.toml`, `runs.jsonl`, `jobs-invalid` pointer and runbook | loopd | 1545 | 8 |
+| 06 | Heartbeat tick: time line, standing session `heartbeat`, skip if busy, unreadable prompt logged once | loopd | 1551 | 6 |
+| 07 | Cron tick: new session per run, skip if previous live, leftover `started` becomes `failed` | loopd | 1557 | 6 |
+| 08 | After a turn, opted-in `ToolResult` without a `ToolSummary` gets a background summary appended with the result's labels | loopd | 1563 | 6 |
+| 09 | `memoryd` indexes `ToolSummary` as kind `summary`; `recall` finds it and taints when untrusted | memoryd | 1568 | 5 |
+| 10 | `MemoryCommand::Tiers`, `bxctl memory tiers`, starter `config/jobs/tier.toml.example` | bxcore, memoryd, bxctl | 1574 | 6 |
 
 After task 10, the design model runs the M5d-2 device check (spec 7) on straylight: a heartbeat
 turn on the background slot leaves a following main-slot turn's `cache_n` near its previous
@@ -129,4 +129,4 @@ OPENCODE_MODEL=llama.cpp/ornith-1.5-35b-a3b RESUME=1 \
   tools/run-plan.sh docs/plans/M5d2 01
 ```
 
-After task 10, the gate count is 1573. Then the device check above.
+After task 10, the gate count is 1574. Then the device check above.
diff --git a/docs/plans/M5d2/files/crates/loopd/tests/cron.rs b/docs/plans/M5d2/files/crates/loopd/tests/cron.rs
index 0aa422b..6a4c964 100644
--- a/docs/plans/M5d2/files/crates/loopd/tests/cron.rs
+++ b/docs/plans/M5d2/files/crates/loopd/tests/cron.rs
@@ -52,6 +52,15 @@ fn the_first_of_the_month() {
     assert!(!due("0 7 1 * *", "2026-10-02T07:00:00.000Z"));
 }
 
+#[test]
+fn day_of_month_and_day_of_week_are_both_required() {
+    // 2026-10-04 is a Sunday, not the 1st. 2026-10-01 is a Thursday.
+    assert!(!due("0 7 1 * 0", "2026-10-04T07:00:00.000Z"));
+    assert!(!due("0 7 1 * 0", "2026-10-01T07:00:00.000Z"));
+    // 2026-11-01 is a Sunday and the 1st.
+    assert!(due("0 7 1 * 0", "2026-11-01T07:00:00.000Z"));
+}
+
 #[test]
 fn four_or_six_fields_are_errors() {
     assert!(matches!(
diff --git a/docs/plans/M5d2/files/crates/loopd/tests/scheduler_cron.rs b/docs/plans/M5d2/files/crates/loopd/tests/scheduler_cron.rs
index bc21e08..c4356f7 100644
--- a/docs/plans/M5d2/files/crates/loopd/tests/scheduler_cron.rs
+++ b/docs/plans/M5d2/files/crates/loopd/tests/scheduler_cron.rs
@@ -64,11 +64,8 @@ fn a_due_job_starts_a_new_session_on_the_background_slot() {
     let sent = server.requests_to(CHAT);
     assert_eq!(sent.len(), 1);
     assert_eq!(sent[0].json()["id_slot"], 1);
-    let last = sent[0].json()["messages"]
-        .as_array()
-        .unwrap()
-        .last()
-        .unwrap();
+    let body = sent[0].json();
+    let last = body["messages"].as_array().unwrap().last().unwrap();
     let content = last["content"].as_str().unwrap();
     assert!(
         content.starts_with("It is 2026-10-03T07:00:00.000Z."),
diff --git a/docs/plans/M5d2/files/crates/loopd/tests/scheduler_heartbeat.rs b/docs/plans/M5d2/files/crates/loopd/tests/scheduler_heartbeat.rs
index a6b1b46..303250e 100644
--- a/docs/plans/M5d2/files/crates/loopd/tests/scheduler_heartbeat.rs
+++ b/docs/plans/M5d2/files/crates/loopd/tests/scheduler_heartbeat.rs
@@ -65,11 +65,8 @@ fn a_due_heartbeat_runs_on_the_background_slot_with_a_time_line() {
     let sent = server.requests_to(CHAT);
     assert_eq!(sent.len(), 1);
     assert_eq!(sent[0].json()["id_slot"], 1);
-    let last = sent[0].json()["messages"]
-        .as_array()
-        .unwrap()
-        .last()
-        .unwrap();
+    let body = sent[0].json();
+    let last = body["messages"].as_array().unwrap().last().unwrap();
     assert_eq!(last["role"], "user");
     let content = last["content"].as_str().unwrap();
     assert!(
diff --git a/docs/plans/M5d2/files/crates/loopd/tests/session_slot.rs b/docs/plans/M5d2/files/crates/loopd/tests/session_slot.rs
index b4db135..d70b542 100644
--- a/docs/plans/M5d2/files/crates/loopd/tests/session_slot.rs
+++ b/docs/plans/M5d2/files/crates/loopd/tests/session_slot.rs
@@ -161,7 +161,7 @@ fn a_heartbeat_turn_between_two_main_turns_does_not_change_the_main_prefix() {
     assert_eq!(sent[1].json()["id_slot"], 1);
     assert_eq!(sent[2].json()["id_slot"], 0);
     let first = sent[0].json()["messages"].as_array().unwrap().clone();
-    let third = sent[2].json()["messages"].as_array().unwrap();
+    let third = sent[2].json()["messages"].as_array().unwrap().clone();
     assert!(
         third.len() > first.len(),
         "the main session's second turn is a longer prefix"