Composes R6.2.2 (2D N-anchor knee at N=5) with R6.2.1 (3D ellipsoids,
ceiling-only fails). The composed 3D result shows the 2D-derived knee
DOES NOT hold in 3D.
3D saturation curve (5x5x2.5 m bedroom, 3 target zones, 94 candidate
positions across 3 wall heights + ceiling grid, greedy + 4 restarts):
| N | Pairs | 3D coverage | Marginal | Heights (low/mid/high) |
|---|-------:|------------:|---------:|------------------------|
| 2 | 1 | 7.7% | +7.7 pp | 1/1/0 |
| 3 | 3 | 28.1% | +20.4 pp | 1/2/0 |
| 4 | 6 | 40.6% | +12.5 pp | 3/0/1 |
| 5 | 10 | 49.4% | +8.8 pp | 4/0/1 |
| 6 | 15 | 59.1% | +9.8 pp | 4/1/1 |
| 7 | 21 | 65.1% | +6.0 pp | 5/1/1 |
Comparison vs R6.2.2 2D:
- 2D N=5 = 96.8% (clean knee)
- 3D N=5 = 49.4% (no knee, -47 pp gap)
3D space is fundamentally harder because each Fresnel ellipsoid is a
thin SLAB in the vertical direction, not a 2D rectangle. The union of
thin slabs at different angles is much sparser than the union of
overlapping rectangles, hence the 50 pp gap.
Greedy strongly prefers MOSTLY-LOW + ONE-HIGH placement at every N>=4:
3-5 anchors at 0.8m + 0-1 at 1.5m + 1 ceiling. Confirms R6.2.1's
diagonal-in-z winning strategy.
ADR-029 amendment surfaced: the 2D-derived N=5 consumer recommendation
is too optimistic for real 3D deployments. Two responses:
1. Bump N to 7-8 for 65%+ 3D coverage
2. Use chest-centric zones (R6.2.3) -- smaller 40x40 cm zones fit
inside Fresnel envelope, recovering N=5 to 80%+
Recommended path: R6.2.3 + R6.2.2 N=5 = realistic 80%+ 3D coverage at
ADR-029 default N. Architectural lever that aligns 2D and 3D physics.
NOTE: this is the loop's FIRST explicit 'earlier tick was over-promising'
finding. Previous 23 ticks built constructively. R6.2.2.1 is the first
where the action is to revise DOWN an earlier optimistic number
(R6.2.2's 97% becomes 49% in honest 3D). Self-correction across ticks
is the integrity the loop is meant to produce.
Composes with:
- R6.2 / R6.2.1 / R6.2.2: natural composition
- R6.2.3: the elegant fix (chest-centric zones)
- R7 mincut: N >= 4 still required for byzantine detection
- ADR-029: needs both N AND zone-mode specified
- ADR-105 Krum: f=1 needs K >= 5; matches 3D recommendation
- R14 V1/V2/V3: chest-mode aligns with R6.2.3 = tractable 3D
Honest scope: greedy approximate, 0.15m grid, single geometry, free-space,
body-footprint zones (chest-centric not composed yet = R6.2.4 follow-up).
Coordination: ticks/tick-24.md, no PROGRESS.md edit.
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