MICROGRID (Linear Channel)

1. INJECTION

Watermark modulates power_draw, storage_dispatch, local_generation

params[i] += amplitude * sin(2π * trial / period)

SIGNAL: STRONG — clean sinusoidal modulation

▼

2. SENDER'S NET LOAD

Net load changes with watermarked parameters

net = power_draw - generation - storage

SIGNAL: PRESERVED — linear combination

▼

3. COUPLING CHANNEL

Neighbor's load → direct additive term on objectives

direct_coupling = (neighbor_load / base) × factor × 10.0

SIGNAL: PRESERVED — additive, proportional to factor

▼

4. RECEIVER OBJECTIVES

throughput = base + direct_coupling

obj_val += direct_coupling (for obj0, obj1, obj2)

SIGNAL: DETECTABLE — additive on 3 of 4 objectives

▼

5. DETECTION

FFT finds clean spectral peak at watermark frequency

p = 0.0002 (coupling=0.9), p = 0.005 (coupling=0.5)

RESULT: DETECTED at all coupling levels

GREENHOUSE (Nonlinear Channel)

1. INJECTION

Watermark modulates heating, vents, CO2, light, irrigation

params[i] += amplitude * sin(2π * trial / period)

SIGNAL: STRONG — clean sinusoidal modulation

▼

2. COUPLING DELTAS

4 hidden deltas computed from neighbor state

δT = (neighbor_avg_temp - 20) × factor × 0.1

δCO₂ = neighbor_energy × factor × 2.0

δlight = neighbor_energy × factor × 0.01

δhumidity = (neighbor_avg_hum - 0.5) × factor × 0.05

SIGNAL: WEAKENED — depends on neighbor state deviation from baseline

▼

3. OUTSIDE CONDITIONS MODIFIED

Deltas fold into outside_temp, outside_co2, outside_humidity, effective_light

outside_temp += δT (~0.5°C at factor=0.9)

KILL #1: Thermal inertia — zone temp changes by 0.01°C per tick

Signal enters a low-pass filter (insulation × dt)

▼

4. ZONE PHYSICS (6 nonlinear transforms)

Signal passes through cascaded nonlinear dynamics

heat_loss = (zone_temp - outside_temp) × 0.1

vent_cooling = vent × (zone_temp - outside_temp) × 0.3

wall_transfer = (neighbor_avg - zone.temp) × 0.05

KILL #2: Multiple interacting heat terms compete with coupling signal

KILL #3: Zone-to-zone wall conduction creates feedback loops

▼

5. MULTIPLICATIVE GROWTH MODEL

Growth = temp × light × CO₂ × water × humidity × damage

temp_factor: 0 if temp<5 or >40, ramps, plateau in optimal range

co2_factor: optimal range shifts with crop phase (seedling→flowering→fruiting)

KILL #4: FLAT REGIONS — if temp is in optimal range, ±0.1°C = ZERO change

KILL #5: PHASE DEPENDENCE — CO2 sensitivity jumps 1×→3× at tick 400

KILL #6: MULTIPLICATIVE — any factor at 0 kills entire signal

▼

6. IRREVERSIBLE DAMAGE

Extreme temps cause permanent damage_factor reduction (floor 0.3)

damage_factor -= 0.002 per extreme tick (temp > 42 or < 3)

KILL #7: Permanent attenuation — once damaged, all future signal reduced

▼

7. SENSOR NOISE

Metrics add gaussian noise to all readings

temp ± 0.3°C, humidity ± 0.02, CO₂ ± 15ppm, growth ± 0.02

KILL #8: Noise exceeds the already-tiny coupling signal

▼

8. RECEIVER'S OWN EXPLORATION

Evolutionary optimizer changes parameters every trial

Each trial: new heating, vent, CO2, light, irrigation values

KILL #9: Receiver's own parameter changes produce variance 100× larger than coupling

▼

9. DETECTION ATTEMPT

FFT / MI / Transfer Entropy / Granger / Cross-correlation

All methods: p > 0.05 (not significant)

RESULT: NOT DETECTED — signal died at stages 4-7, noise buried remainder at 8-9

The Core Problem

The coupling signal starts at ~0.5°C temperature shift (stage 3). After thermal inertia (×0.01), it becomes ~0.005°C zone temp change. If the zone is in the optimal temp range (stage 5), this produces exactly zero change in growth rate. The piecewise-linear growth model has dead zones where small perturbations are invisible.

Even when the zone is near a threshold (where the signal would be nonzero), the receiver's own exploration (stage 8) changes zone temperature by several degrees per trial — completely overwhelming the 0.005°C coupling signal. The SNR is approximately 0.005 / 3.0 ≈ 0.002. The signal is 500× weaker than the noise.

The microgrid works because the coupling is additive on the output: throughput += direct_coupling. The greenhouse fails because the coupling is multiplicative through intermediate state, passing through nonlinear dead zones before reaching the output.

Possible Paths Forward

Stronger coupling: Increase factor beyond 0.9 — unrealistic but would confirm the signal is there
Larger watermark amplitude: Aggressive probing during dedicated analysis phase
Detect on intermediate state: Instead of objectives, detect on raw zone temps, CO₂, humidity (before the growth model kills the signal)
Operate near thresholds: Deliberately keep zones near growth model thresholds where small coupling changes produce nonzero output
Accept the limitation: Some channels have inherent SNR too low for detection at realistic trial budgets

Signal Death in the Greenhouse vs Microgrid

MICROGRID (Linear Channel)

GREENHOUSE (Nonlinear Channel)

The Core Problem

Possible Paths Forward