GD-0001: group success is unreachable below 5 seats, with its reproduction

The maintainer played several 3-player games on 2026-08-03 and could not
win any. This says why, from the engine's own constants rather than my
arithmetic: claim every Problem the deal puts in play, concede nothing,
and the total still falls short of GR-E01's threshold at 2, 3 and 4
seats.

  2p: 2 problems worth 3  vs threshold 5 — UNREACHABLE
  3p: 3 problems worth 6  vs threshold 7 — UNREACHABLE
  4p: 3 problems worth 6  vs threshold 7 — UNREACHABLE
  5p: 4 problems worth 10 vs threshold 9 — reachable
  6p: 4 problems worth 10 vs threshold 9 — reachable

The test reads problem_priorities (GR-S01's deal) and threshold (GR-E01)
out of the engine, so it cannot drift from the rules it tests, and it
holds for either dataset -- the stand-in gives 3/6/10 and Problems.csv
gives 4/6/9 against the same 5/7/9.

It ASSERTS THE DEFECT and is expected to keep passing until ground-game
rules, then be inverted. This is CB-WP-0022's reproduction rule applied
before the register exists, because delivering feedback should not block
on building the tool that tracks it.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

games/ground/src/lib.rs

@@ -2162,6 +2162,19 @@ mod replay_probe {
     use cb_kernel::EventSeq;
     use std::time::Instant;
 
+    /// A fresh game at `seats` players, for the seat-count sweep.
+    fn fresh_n(seats: u8) -> GroundState {
+        GroundState::setup(
+            &Setup {
+                players: seats,
+                preset: format!("standard-{seats}p"),
+                patch: BTreeMap::new(),
+            },
+            42,
+        )
+        .expect("a standard deal")
+    }
+
     fn fresh(seed: u64) -> GroundState {
         GroundState::setup(
             &Setup {
@@ -2441,6 +2454,56 @@ mod replay_probe {
         }
     }
 
+    /// **GD-0001: group success is arithmetically unreachable below 5
+    /// seats**, and this is the reproduction rather than an argument.
+    ///
+    /// The maintainer played several 3-player games on 2026-08-03 and
+    /// could not win any of them. This says why: claim *every* Problem
+    /// the deal puts in play, concede nothing, and the total still falls
+    /// short of GR-E01's threshold at 2, 3 and 4 seats.
+    ///
+    /// It reads both numbers out of the engine — `problem_priorities`
+    /// (GR-S01's deal) and `threshold` (GR-E01) — so it cannot drift from
+    /// the rules it is testing, and it holds for **either dataset**: the
+    /// stand-in gives 3/6/10 and `Problems.csv` gives 4/6/9, against the
+    /// same 5/7/9.
+    ///
+    /// **This test asserts the defect.** It is expected to keep passing
+    /// until ground-game rules, and to be inverted when it does — either
+    /// the deal count rises or the thresholds fall.
+    #[test]
+    fn gd0001_group_success_is_unreachable_below_five_seats() {
+        let mut verdicts = Vec::new();
+        for seats in 2..=6u8 {
+            let state = fresh_n(seats);
+            let best: u32 = state.problems.values().map(|p| u32::from(p.value)).sum();
+            let need = state.threshold();
+            verdicts.push((seats, state.problems.len(), best, need, best >= need));
+            println!(
+                "  {seats}p: {} problem(s) worth {best} against a threshold of {need} \u{2014} {}",
+                state.problems.len(),
+                if best >= need { "reachable" } else { "UNREACHABLE" }
+            );
+        }
+        let unreachable: Vec<u8> = verdicts
+            .iter()
+            .filter(|(_, _, _, _, ok)| !ok)
+            .map(|(s, _, _, _, _)| *s)
+            .collect();
+        // Positive control: a run where everything is reachable would
+        // report a clean sheet and prove nothing.
+        assert!(
+            !verdicts.is_empty() && verdicts.iter().any(|(_, _, _, _, ok)| *ok),
+            "no seat count was reachable; the harness measured nothing useful"
+        );
+        assert_eq!(
+            unreachable,
+            vec![2, 3, 4],
+            "GD-0001 has changed: ground-game may have ruled. Re-read the \
+             finding before editing this test."
+        );
+    }
+
     /// AM-7 scaling floor from GameKernel §5: fold throughput at 100k
     /// events must be at least this fraction of throughput at 5k.
     ///