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R6.2.5 — Multi-subject occupancy union: N=5 hits 100% for 4 occupants

Status: clean positive result · 2026-05-22

Premise

R6.2 / R6.2.3 picked one chest position per zone. Real households have 2-4 occupants who can be in different positions simultaneously. R6.2.5 extends to union of chest envelopes across all expected occupant positions. The practical question: does coverage degrade gracefully as occupant count grows?

Result: graceful saturation at N=5

Scenario	# zones	Total area	Coverage @ N=5
1 occupant (chair)	1	0.16 m²	100%
2 occupants (chair + bed)	2	0.40 m²	100%
3 occupants (chair + bed + desk)	3	0.48 m²	100%
4 occupants (+ 2nd chair)	4	0.64 m²	100%

N=5 hits 100% coverage for all configurations up to 4 occupants. The chest-centric small-zone approach (R6.2.3) generalises trivially to multi-subject.

4-occupant saturation curve

N	Coverage	Marginal
2	14.5%	+14.5 pp
3	72.9%	+58.4 pp
4	99.0%	+26.1 pp
5	100%	+1.0 pp
6	100%	+0 pp
7	100%	+0 pp

Knee returns to N=4 — even for 4 occupants, 4 anchors get us to 99%. This is the 2D chest-centric multi-subject regime, which is the most demanding 2D configuration tested in the R6 family — and it still hits the knee at N=4.

Cross-eval: single-subject placement is bad for multi-subject

Placement	Coverage on 4-zone target
Single-subject-optimised	70.6%
Multi-subject-optimised	100%
Gain from multi-subject optimisation	+29.4 pp

The CLI must accept multiple --target arguments and optimise for their union — not pick a representative zone and hope.

Updated CLI recommendation

wifi-densepose plan-antennas \
    --room 5 5 \
    --target chair_chest 3.7 3.7 0.4 0.4 \
    --target bed_chest   2.2 0.8 0.6 0.4 \
    --target desk_chest  0.5 2.7 0.4 0.2 \
    --target chair2_chest 1.0 4.2 0.4 0.4 \
    --freq-ghz 2.4

Output: N=5 anchors hitting 100% coverage of the union.

R6 family summary (8 ticks + this)

Tick	Configuration	Headline number
R6.2	2D body, single-subject	51% N=5
R6.2.1	3D body, single-subject	26% N=2 (mixed-height)
R6.2.2	2D body, N-anchor	97% N=5
R6.2.2.1	3D body, N-anchor	49% N=5
R6.2.3	2D chest, single-subject	82% N=5
R6.2.4	3D chest, N-anchor	77% N=5 / 82% N=6
R6.2.5 (this)	2D chest, multi-subject (1-4)	100% N=5

The R6 family's headline finding: 2D chest-centric + multi-subject + N=5 = 100% coverage. This is the placement recipe to ship.

Composes with prior threads

R6.2 / R6.2.3: directly extends — single-subject → multi-subject union
R6.2.2 / R6.2.4: same saturation behaviour at the multi-subject level
R14 (empathic appliances): V1 lighting / V2 HVAC / V3 attention in households of 2-4 occupants → use multi-subject placement
R3 / ADR-024: per-subject identity (AETHER) + multi-subject placement = full empathic-appliance stack
ADR-105 / ADR-106 / ADR-107: federation operates on the same model across occupant counts; placement is orthogonal
R12 PABS: works per-subject within the union; multi-subject coverage = multi-subject intrusion detection

Why N=4 knee returns for multi-subject

Each chest zone is small (40×40 cm) and fits inside a single Fresnel ellipsoid (which is ~40 cm wide at midpoint of a 5 m link). With N=4 anchors, we get 6 pairwise links — enough Fresnel ellipsoids to cover 4 disjoint 40×40 cm zones without much waste. Beyond N=4 the marginal gain drops to <1 pp.

This is more saturated than the single-subject R6.2 setup (which used 3 m² bed footprint and couldn't be covered fully even at N=8 with body-centric zones). Chest-centric multi-subject is the sweet spot for the Fresnel envelope geometry.

Honest scope

2D only — multi-subject 3D not benchmarked (extension is mechanical; expect N=6 to retain the chest-centric N=5 advantage).
Static positions — real occupants move; the union should be conservative (larger than any instantaneous configuration).
Single 5×5 m geometry — larger or oddly-shaped rooms need separate benchmarks.
Greedy + 4 restarts — global optimum may be 1-2 pp higher.
4 occupants — beyond 4-5 the coverage may degrade. Extreme density (e.g. classroom with 20 people) is a different regime.

What this DOES enable

A clean cap on the placement complexity story: 4-occupant households are fully sensable at N=5 with multi-subject-aware placement.
A required CLI feature: support multiple --target arguments.
An updated installer recipe: for households of 1-4, the same N=5 chest-centric placement works.
R6 family closes with a positive result that ships directly.

What this DOES NOT enable

Beyond 4-5 occupants — separate regime, not tested.
Time-varying occupancy (people moving between zones) — would benefit from pose-trajectory data (out of scope).
3D multi-subject — mechanical extension, not done here.

Final R6.2 CLI surface

After this tick, the productisation of R6.2 should support:

wifi-densepose plan-antennas
    --room W H [Z]                       # 2D or 3D
    --target NAME X Y W H [DX DY DZ]    # repeatable
    --target-mode {body, chest}          # R6.2.3
    --freq-ghz F                         # 2.4, 5.0, 6.0
    --n-anchors N                        # auto-saturation if omitted
    --restarts K                         # 4 default

This covers the R6.2 / R6.2.1 / R6.2.2 / R6.2.2.1 / R6.2.3 / R6.2.4 / R6.2.5 use cases in a single CLI tool. ~50 LOC over the original R6.2.

Connection back

R6 / R6.1: physical foundation
R6.2 / R6.2.3: single-subject body / chest
R6.2.1 / R6.2.2 / R6.2.2.1 / R6.2.4: 3D / N-anchor / composition
R6.2.5 (this): multi-subject completes the matrix
R14: empathic-appliance deployment recipe is now: N=5 + chest-centric + multi-subject-union targets, with mixed-height anchors for full-body coverage when needed

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