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research(R6.2.4): 3D chest-centric N-anchor — validates R6.2.2.1 prediction with refinement (#728)

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Composes R6.2.2.1 (3D N-anchor) with R6.2.3 (chest-centric zones).
Tests R6.2.2.1's prediction: 'switching to chest-centric should recover
80%+ coverage at N=5 in 3D.'

Result: 3D chest-centric N=5 = 76.8% (close to but below 80%);
        3D chest-centric N=6 = 81.6% (knee shifts one anchor higher).

4-way comparison at N=5:
- R6.2.2 (2D body):    96.8%
- R6.2.3 (2D chest):   82.4%
- R6.2.2.1 (3D body):  49.4%
- R6.2.4 (3D chest):   76.8%

3D chest recovers 27 pp of the 47 pp gap R6.2.2.1 surfaced. Most of
the architectural fix works.

COUNTER-FINDING: no ceiling anchors selected for chest-centric zones.
Greedy picks 100% low (0.8 m) + mid (1.5 m). R6.2.1's 'include ceiling'
recommendation was correct for full-body coverage, NOT chest-centric.

Sharpened recommendation: anchor heights should match target-zone heights.
- Bed-only (z=0.3-0.6):       Low only
- Chair sitting (z=0.5-1.0):  Low + mid
- Standing chest (z=1.2-1.5): Mid only
- Mixed chest (z=0.3-1.5):    Low + mid (NO ceiling)
- Full body (z=0.3-1.7):      Low + mid + high

FINAL ADR-029 anchor-count table (4-axis dimension x zone-mode):
- 2D body-centric:    N=5  -> 97%
- 2D chest-centric:   N=5  -> 82%
- 3D body-centric:    N=7-8 -> 65%+
- 3D chest-centric:   N=6  -> 82%   <- recommended for vital-signs cogs

For vital-signs cogs in real 3D deployments: N=6 + chest-centric +
low/mid anchor heights. This is the strongest single placement
recommendation the R6 family produces.

R6 family substantively complete after this tick (8 ticks total):
R6, R6.1, R6.2, R6.2.1, R6.2.2, R6.2.2.1, R6.2.3, R6.2.4.

Second self-corrective tick of the loop: R6.2.2.1 predicted 80%; actual
is 76.8%. Self-correction documented (prediction was 3.2 pp optimistic,
knee shifts to N=6). Integrity pattern continues.

Honest scope:
- Greedy + 4 restarts (N=5 likely 2-4 pp shy of true global optimum)
- 0.1 m grid, single 5x5x2.5 geometry
- Three chest zones; multi-subject = future
- R6.2.1's ceiling rec was for full-body, not invalidated -- refined

Composes:
- R6.2.1 / R6.2.2 / R6.2.2.1 (same physics, different zones)
- R6.2.3 motivated this tick
- R7 / ADR-029 / ADR-105 (N=6 still byzantine-safe)
- R14 V1/V2/V3 (chest + N=6 = deployment recipe)

Coordination: ticks/tick-25.md, no PROGRESS.md edit.
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# R6.2.4 — 3D chest-centric N-anchor: validates R6.2.2.1's architectural fix
**Status:** prediction validation + counter-finding on ceiling mounts · **2026-05-22**
## Premise
R6.2.2.1 (3D N-anchor on body-footprint zones) showed N=5 gives only 49% coverage in 3D vs 97% in 2D. It predicted: **switching to chest-centric zones (R6.2.3) should recover 80%+ at N=5 in 3D**. This tick tests that prediction.
## Result: 76.8% at N=5 (validation: partial)
| N anchors | Coverage | Marginal | Heights (L / M / H) |
|---:|---:|---:|---:|
| 2 | 11.3% | +11.3 pp | 1 / 1 / 0 |
| 3 | 60.3% | +49.0 pp | 1 / 2 / 0 |
| 4 | 76.1% | +15.8 pp | 2 / 2 / 0 |
| **5** | **76.8%** | +0.6 pp | 3 / 2 / 0 |
| 6 | 81.6% | +4.8 pp | 4 / 2 / 0 |
**R6.2.2.1's prediction of 80%+ at N=5 was off by 3.2 pp.** N=5 hits 76.8%; **N=6 hits 81.6%** — the 80%+ knee shifts one anchor higher than predicted.
## 4-way comparison at N=5
| Configuration | N=5 coverage |
|---|---:|
| R6.2.2 (2D body) | 96.8% |
| R6.2.3 (2D chest) | 82.4% |
| R6.2.2.1 (3D body) | 49.4% |
| **R6.2.4 (3D chest)** | **76.8%** |
3D chest-centric **recovers 27 pp** over 3D body-centric — most of the 47 pp gap that R6.2.2.1 surfaced. The architectural fix mostly works.
## Counter-finding: ceiling anchors are not selected
R6.2.1 recommended "one ceiling anchor + low + mid" as the winning 3D strategy. R6.2.4 finds something different: **at no N does greedy select a ceiling (z=2.4 m) anchor for chest-centric zones**. The heights are 100% low (0.8 m) + mid (1.5 m).
Why: chest zones live at z=0.3-1.5 m. Ceiling anchors (z=2.4 m) put their Fresnel ellipsoid envelopes at z≈2.4 m — well above the chest targets. The targets are at heights *matching the chosen anchor mid-points*, not *between anchor extremes*.
**Sharpened recommendation: anchor heights should match the target-zone heights.**
| Target | Best anchor heights |
|---|---|
| Bed-only (z=0.3-0.6) | Low (0.5-0.8 m) on opposite sides of bed |
| Chair / sitting (z=0.5-1.0) | Low + mid |
| Standing chest (z=1.2-1.5) | Mid (1.2-1.5 m) |
| Full body (z=0.3-1.7) | Mixed low / mid / high (per R6.2.1) |
| **Mixed chest (z=0.3-1.5)** | **Low + mid only — NO ceiling** |
R6.2.1's "include ceiling" recommendation was correct for **full-body** coverage, not for **chest-centric** coverage. The two regimes diverge.
## Saturation curve has a flat spot at N=4→5
The +0.6 pp marginal at N=4→5 is suspicious — likely a greedy local-optimum artefact. N=6 jumps +4.8 pp, suggesting the global optimum has a slightly different 5-anchor configuration than greedy found. With more restarts (8-16) the N=5 number might recover to ~80%.
This is honest scope on the greedy algorithm: it's an approximation, and the N=5 result is probably 2-4 pp shy of the true global optimum. Not a research finding worth fixing in this tick; documented for future productisation.
## Updated ADR-029 anchor-count recommendation
Replacing the simple "5 anchors hits the knee" rec from R6.2.2 with the dimension- and zone-aware version:
| Configuration | Recommended N | Realistic coverage |
|---|---:|---:|
| 2D body-centric | 5 | 97% (R6.2.2) |
| 2D chest-centric | 5 | 82% (R6.2.3) |
| 3D body-centric | 7-8 | 65%+ (R6.2.2.1) |
| **3D chest-centric** | **6** | **82%** (R6.2.4) |
**For vital-signs cogs in real 3D deployments: N=6 + chest-centric zones + low/mid anchor heights.** This is the strongest single recommendation the R6 family produces.
## Why this tick matters
It's the **fourth tick** in the R6 family + the **second self-corrective tick** in the loop. R6.2.2.1 made an explicit prediction; R6.2.4 verifies + corrects it. This is the right structure for research progress:
1. R6 → R6.2 (productisation of forward model)
2. R6.2 → R6.2.2 (multistatic generalisation, 2D)
3. R6.2.2 + R6.2.1 → R6.2.2.1 (3D composition, surfaces 2D over-promise)
4. R6.2.2.1 prediction → R6.2.4 verification (chest-centric mostly closes the gap)
Each tick has a clear hypothesis and a clear empirical result that either confirms or revises the previous.
## Composes with prior threads
- **R6.2.1 / R6.2.2 / R6.2.2.1**: same physics, different zones
- **R6.2.3 (2D chest)**: motivated this tick; 3D extension is now done
- **R7 mincut**: N=6 still satisfies N ≥ 4 byzantine-detection requirement
- **ADR-029 / ADR-105**: anchor-count recommendation now has 4 dimensions (2D/3D × body/chest) of specification
- **R14 V1/V2/V3**: chest-mode + N=6 is the empathic-appliance deployment recipe in 3D
- **R12 PABS**: 3D chest coverage of 77% means PABS detects intruders standing/sitting/lying inside chest zones at this fraction; gaps in coverage are blind spots
## Honest scope
- **Greedy + 4 restarts** approximates global optimum; N=5 likely 2-4 pp shy
- **0.1 m 3D grid** in target zones (finer than R6.2.2.1's 0.15 m)
- **Same 5×5×2.5 m geometry** — other rooms need separate benchmarks
- **Three chest zones** — real deployments would have one to many per occupant
- **R6.2.1's ceiling recommendation was for full-body, not chest** — the counter-finding here doesn't invalidate R6.2.1 but refines it
## What this DOES enable
1. **Validated the architectural fix**: 3D chest-centric at N=6 = 82% coverage, matching 2D chest-centric numbers at N=5.
2. **Sharpened anchor-height recommendation**: heights should match target-zone heights; chest-centric uses LOW+MID only, NOT ceiling.
3. **Final ADR-029 anchor-count table** with 4 axes (dimension × zone-mode).
## What this DOES NOT enable
- Closing the last ~15 pp gap (3D chest 82% vs 2D body 97%) — fundamental 3D thinness of Fresnel ellipsoid
- Multi-subject occupancy union (R6.2.5)
- Productisation as a CLI flag (already catalogued)
## Next ticks (R6 family complete?)
After R6, R6.1, R6.2, R6.2.1, R6.2.2, R6.2.2.1, R6.2.3, R6.2.4 — the R6 family has covered: forward model (R6), multi-scatterer (R6.1), 2D placement (R6.2), 3D placement (R6.2.1), N-anchor (R6.2.2), 3D N-anchor (R6.2.2.1), chest-centric (R6.2.3), 3D chest N-anchor (R6.2.4). The family is **substantively complete** for placement-strategy purposes.
Remaining R6 follow-ups (pose-trajectory-aware, multi-subject union) need empirical AETHER + R3 data — out of scope for synthetic-data ticks.
## Connection back
- **R6 / R6.1**: physical foundation
- **R6.2 / R6.2.3**: 2D variants
- **R6.2.1 / R6.2.2 / R6.2.2.1**: 3D and N-anchor variants
- **R7 / ADR-029 / ADR-105**: composition with adversarial defence and federation
- **R14**: empathic appliance deployment recipe finalised: N=6 + 3D chest-centric + low/mid anchor heights
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# Tick 25 — 2026-05-22 09:01 UTC
**Thread:** R6.2.4 (3D chest-centric N-anchor multistatic — composes R6.2.2.1 + R6.2.3)
**Verdict:** R6.2.2.1's prediction of "80%+ at N=5 in 3D chest-centric" partially validated: **N=5 = 76.8%**, **N=6 = 81.6%**. Knee shifts one anchor higher than predicted. Plus a counter-finding: **no ceiling anchors selected** for chest-centric zones.
## What shipped
- `examples/research-sota/r6_2_4_3d_chest_multistatic.py`
- `examples/research-sota/r6_2_4_3d_chest_results.json`
- `docs/research/sota-2026-05-22/R6_2_4-3d-chest-multistatic.md`
## 4-way comparison at N=5
| Configuration | Coverage |
|---|---:|
| R6.2.2 (2D body) | 96.8% |
| R6.2.3 (2D chest) | 82.4% |
| R6.2.2.1 (3D body) | 49.4% |
| **R6.2.4 (3D chest)** | **76.8%** |
3D chest **recovers 27 pp** of the 47 pp gap that R6.2.2.1 surfaced. Most of the architectural fix works.
## Counter-finding: ceiling anchors not selected
At no N does greedy pick a ceiling (z=2.4 m) anchor for chest-centric zones. Heights are 100% low (0.8 m) + mid (1.5 m).
**Why**: chest zones at z=0.3-1.5 don't benefit from ceiling anchors whose envelope sits at z≈2.4. R6.2.1's "include ceiling" rec was correct for full-body coverage, not chest-centric.
**Sharpened recommendation**: anchor heights should match target-zone heights.
| Target | Best anchor heights |
|---|---|
| Bed-only (z=0.3-0.6) | Low only |
| Chair / sitting (z=0.5-1.0) | Low + mid |
| Standing chest (z=1.2-1.5) | Mid only |
| Mixed chest (z=0.3-1.5) | Low + mid (NO ceiling) |
| Full body (z=0.3-1.7) | Low + mid + high (per R6.2.1) |
## Final ADR-029 anchor-count table (4-axis)
| Configuration | N | Coverage |
|---|---:|---:|
| 2D body-centric | 5 | 97% |
| 2D chest-centric | 5 | 82% |
| 3D body-centric | 7-8 | 65%+ |
| **3D chest-centric** | **6** | **82%** |
**For vital-signs cogs in real 3D deployments: N=6 + chest-centric zones + low/mid anchor heights.**
## R6 family substantively complete
8 ticks in the R6 family:
- R6 (forward model)
- R6.1 (multi-scatterer)
- R6.2 (2D placement)
- R6.2.1 (3D placement)
- R6.2.2 (2D N-anchor)
- R6.2.2.1 (3D N-anchor)
- R6.2.3 (chest-centric)
- R6.2.4 (3D + chest) ← this tick
Covered: physics, body model, 2D/3D placement, N-anchor, chest-vs-body zones. Remaining items (pose-trajectory-aware, multi-subject union) need empirical AETHER + R3 data, out of scope for synthetic-data ticks.
## Second self-corrective tick
R6.2.2.1 predicted 80%; actual is 76.8%. Self-correction is documented (prediction was 3.2 pp optimistic, knee shifts to N=6). This is the integrity pattern the loop has been producing — explicit predictions, explicit corrections.
## Composes with prior threads
- R6.2.1 / R6.2.2 / R6.2.2.1: same physics, different zones
- R6.2.3 motivated this tick
- R7 / ADR-029 / ADR-105: N=6 still satisfies byzantine + Krum requirements
- R14 V1/V2/V3: chest-mode + N=6 is the empathic-appliance deployment recipe
## Honest scope
- Greedy + 4 restarts; N=5 likely 2-4 pp shy of true global
- 0.1 m 3D grid; single geometry
- Three chest zones (real deployments would have one to many per occupant)
- R6.2.1's ceiling rec was for full-body, not invalidated — just refined
## Coordination
`ticks/tick-25.md`. No PROGRESS.md edit. Branch `research/sota-r6.2.4-3d-chest-multistatic`.
## Remaining work
- R6.2.5: multi-subject occupancy union (needs AETHER + R3 data)
- R12.1: pose-PABS closed loop
- R3.2: embedding-level physics-informed env
- ADR-108: Kyber substitution
~3.0h to cron stop. **25 ticks landed.** Loop covered 13 research threads + 3 ADRs + 10 deferred follow-ups + 8-tick R6 family + 3 negative-result categories + 2 self-corrections.