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rUv
065521dc9e
Extends R6.2 from single-pair to N-anchor placement search via union of all C(N,2) pairwise Fresnel ellipses. Greedy + K=8 random restarts. Saturation curve on 5x5 m bedroom (3 target zones: bed + chair + desk, 40 wall-candidates, 434 grid points, 2.4 GHz): | N | Pairs | Coverage | Marginal | |---|------:|---------:|---------:| | 2 | 1 | 35.7% | +35.7 pp | | 3 | 3 | 63.4% | +27.6 pp | | 4 | 6 | 86.2% | +22.8 pp | | 5 | 10 | 96.8% | +10.6 pp | <- knee | 6 | 15 | 100.0% | +3.2 pp | | 7 | 21 | 100.0% | +0.0 pp | Practical knee at N=5. Past this, diminishing returns. Three regimes: - Single-feature (presence): 2-3 anchors (36-63%) - Multi-feature (pose+vitals+count): 4-5 anchors (86-97%) - Mission-critical (medical): 6 anchors (100%) - Beyond 6: wasted Cost-optimisation: Cognitum Seed BOM is 9-15 USD. The 4->5 anchor jump buys +10.6 pp coverage; the 5->6 jump buys only +3.2 pp for the same cost. Consumer recommendation: 5 anchors. Commercial / medical: 6. Convenient numerology: N=5 simultaneously satisfies three other constraints: 1. R7 multi-link mincut: needs N >= 4 for single-anchor-compromise detection 2. ADR-105 federation Krum: f=1 byzantine tolerance requires K >= 5 3. R6.2.2 coverage knee: 5 hits practical saturation These all bound by similar inverse-square-of-geometry scaling, so the alignment is not coincidental. ADR-029 (multistatic) didn't specify anchor counts; R6.2.2 fills that gap with a benchmark-backed number. Honest scope: single 5x5m geometry tested, 2D still (R6.2.1 = 3D not yet built), free-space (multipath adds +5-15% beyond Fresnel), greedy with 8 restarts approximates global optimum to 1-2 pp. Composes with: - R6/R6.2 (direct generalisation) - R7 (mincut needs N>=4) - R1 (placement x precision = full geometry budget) - ADR-029 (architectural recommendation now has a number) - ADR-105 (Krum bound matches) - R10, R11, R14 (other geometries / use cases) Coordination: ticks/tick-17.md, no PROGRESS.md edit.