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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.
85 lines
3.7 KiB
Markdown
85 lines
3.7 KiB
Markdown
# Tick 17 — 2026-05-22 07:09 UTC
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**Thread:** R6.2.2 (N-anchor multistatic placement)
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**Verdict:** Practical knee at **N=5 anchors** for typical 5×5 m bedroom. Direct cost-optimisation conclusion + ADR-029 architectural update.
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## What shipped
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- `examples/research-sota/r6_2_2_multistatic_placement.py` — pure-numpy greedy multi-anchor placement search with random restarts.
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- `examples/research-sota/r6_2_2_multistatic_results.json` — full saturation curve for 5×5 m bedroom benchmark.
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- `docs/research/sota-2026-05-22/R6_2_2-multistatic-placement.md` — research note.
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## Saturation curve (5×5 m bedroom, 3 target zones, 2.4 GHz)
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| N anchors | Pairs | Coverage | Marginal |
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|---:|---:|---:|---:|
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| 2 | 1 | 35.7% | +35.7 pp |
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| 3 | 3 | 63.4% | +27.6 pp |
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| 4 | 6 | 86.2% | +22.8 pp |
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| **5** | **10** | **96.8%** | **+10.6 pp** ← knee |
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| 6 | 15 | 100% | +3.2 pp |
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| 7+ | 21+ | 100% | +0.0 pp |
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**Knee at N=5** — past this, diminishing returns.
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## Three regimes surfaced
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| Use case | Anchors | Coverage |
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|---|---:|---:|
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| Single-feature (presence only) | 2-3 | 36-63% |
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| Multi-feature (pose, vitals, count) | **4-5** | 86-97% |
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| Mission-critical (medical, security) | 6 | 100% |
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| Beyond 6 | wasted | 100% (no gain) |
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## Cost-optimisation conclusion
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Cognitum Seed BOM is $9-15. The +$9-15 from 4→5 anchors buys +10.6 pp coverage. The same cost from 5→6 buys only +3.2 pp. **Consumer recommendation: 5 anchors hits the knee.** Commercial / medical: 6.
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## Convenient numerology
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**N=5 happens to also satisfy three other constraints simultaneously:**
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1. **R7 multi-link mincut**: needs N ≥ 4 to detect single-anchor compromise
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2. **ADR-105 federation Krum**: f=1 byzantine tolerance requires K ≥ 5
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3. **R6.2.2 coverage knee**: 5 anchors hits practical saturation
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These three constraints all bound by similar inverse-square-of-geometry scaling, so the alignment is probably not coincidental — but it's a useful fact for the architectural roadmap.
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## ADR-029 recommendation update
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ADR-029 (multistatic sensing) didn't specify anchor counts. R6.2.2 fills the gap:
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> **Recommended anchor count: 5 for typical 5×5 m room.** 4 anchors gives 86% coverage (good for many use cases); 6 anchors gives 100% but is over-provisioned past the knee.
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## Composes with prior threads
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- **R6 / R6.2**: direct generalisation; greedy expansion to N anchors
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- **R7**: needs N ≥ 4 for multi-link adversarial detection; N=5 satisfies
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- **R1**: combined with R6.2.2 = full sensing geometry budget
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- **ADR-029**: architectural recommendation now has a number
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- **ADR-105**: Krum byzantine bound f < (K-2)/2 → K=5 = f=1 (matches R7 single-attacker case)
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- **R10**: wildlife corridors will have different saturation (more anchors for length, fewer for width)
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- **R11**: maritime cabins likely saturate earlier (N=3-4)
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- **R14**: V1/V2/V3 verticals all need ≥86% coverage = N=4 minimum
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## Honest scope
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- Single geometry tested (5×5 m bedroom). Other rooms have different knees.
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- 2D still (R6.2.1 = 3D ceiling/floor mounts not yet built).
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- Free-space (multipath probably adds +5-15% beyond Fresnel-only).
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- Greedy + 8 restarts → 1-2 pp shy of global optimum at most.
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## Coordination
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`ticks/tick-17.md`. No PROGRESS.md edit. Branch `research/sota-r6.2.2-multistatic-placement`.
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## Remaining work
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- **R3 follow-up**: physics-informed env_sig prediction (zero-shot cross-room via R6 forward operator + room map)
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- **R6.1**: multi-scatterer additive forward model
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- **R6.2.1**: 3D ceiling/floor placement
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- **R6.2.3**: pose-trajectory-aware zones (needs AETHER + R3 data)
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- **ADR-107**: cross-installation federation w/ secure aggregation
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~4.9h to cron stop. **17 ticks landed. 2 ADRs + 2 deferred follow-ups closed.**
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