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GROUND-WP-0002 T06: the group cannot win below 5 seats

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Confirmed by play and by reproduction. The maintainer could not win any
3-player game on 2026-08-03; the engine computes why from its own
constants: GR-S01 deals 2/3/4 Problems and GR-E01 asks for 5/7/9, so a
perfect group still loses at 2, 3 and 4 seats.

Not a dataset problem -- the stand-in gives 3/6/10 and this repo's
Problems.csv gives 4/6/9 against the same thresholds. No edition data
reconciles them.

Reproduction named so the ruling can be checked against it:
gd0001_group_success_is_unreachable_below_five_seats in clay-borg.

Three possibilities offered rather than one assumed: the deal is too
small, the thresholds are too high, or low seat counts are deliberately
not SHARED GROUND games -- in which case nothing currently says so and
the engine will keep offering an unwinnable game.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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@ -229,6 +229,60 @@ T01 may dissolve it.
| `gr-e02-shared-ground` | **Confirm** — encode `Modes.csv` MODE_COOP as printed |
| `gr-e04-coalitions` | **Confirm** — encode `Modes.csv` MODE_COALITION as printed |
## Task: GR-E01 vs GR-S01 — the group cannot win below 5 seats
```task
id: GROUND-WP-0002-T06
status: todo
priority: high
```
**This is the sharpest finding the engine has produced, it is confirmed by
play, and it has a reproduction.**
The maintainer played several 3-player games on 2026-08-03 and could not
win any of them. The engine says why, computed from its own constants:
| seats | Problems dealt (GR-S01) | maximum achievable | GR-E01 threshold | |
|---:|---:|---:|---:|---|
| 2 | 2 | 3 | 5 | **unreachable** |
| 3 | 3 | 6 | 7 | **unreachable** |
| 4 | 3 | 6 | 7 | **unreachable** |
| 5 | 4 | 10 | 9 | reachable |
| 6 | 4 | 10 | 9 | reachable |
**Claim every Problem in play, concede nothing, play perfectly — and at 2,
3 and 4 seats the group still loses.** In SHARED GROUND (GR-E02), where
the group total *is* the outcome, those games cannot be won.
**It is not a dataset problem.** The stand-in the engine used gives
3 / 6 / 10; this repository's `Problems.csv` gives 4 / 6 / 9. Both fall
short of the same 5 / 7 / 9. No edition data reconciles them.
**Reproduction:** `games/ground/src/lib.rs` →
`gd0001_group_success_is_unreachable_below_five_seats`, run with
`cargo test -p games-ground --all-features gd0001 -- --nocapture`. It
reads `problem_priorities` (GR-S01) and `threshold` (GR-E01) out of the
engine, so it cannot drift from the rules it is testing.
### The ruling needed
Two numbers disagree and **only one of them can be right**:
- **GR-S01's deal** — 2 / 3 / 4 Problems by player count, from a scenario
of five. Should more of the five be in play at low seat counts?
- **GR-E01's thresholds** — 5 / 7 / 9. Were these set for a game that
deals more Problems than GR-S01 deals?
A third possibility worth ruling out explicitly: **the thresholds may be
intended to be unreachable at low seat counts**, with SHARED GROUND being
a 5–6 player mode and the smaller counts played in another mode. If so,
say it, because nothing currently does and the engine will keep offering
a game that cannot be won.
**Until this is ruled the engine cannot claim a working scoring mode**, and
`gr-e01-threshold-unreachable-2p` stays as a failing-in-fact record.
## Task: GR-E03 and GR-E04 have never been played to the end
```task