1. What Was Measured
Actuation is the irreversible commitment of kinetic energy. Safety exists strictly in the margin between a system’s braking capacity and an immutable physical boundary.
That margin is what this study measures. Two gates were scored against one frozen cohort of 1,800 robot-motion scenarios: a velocity-blind baseline gate that reads commanded-stop clearance alone, and the KAIROS pre-actuation safety layer. Three quantities were recorded per scenario against simulation ground truth: collision hazards accepted, recoverable motion preserved, and falsely-safe verdicts.
The gate under test is KAIROS Robotics, a deterministic, pre-actuation safety-evaluation layer. It sits between a motion policy and the actuators. Before a proposed motion commits, the layer evaluates it, emits a reproducible verdict, and writes replay evidence that re-derives bit-for-bit from committed bytes.
The policy above the layer is arbitrary: classical, optimized, or learned. The evaluation below it is fixed. This record reports the experimental setup, the measured outcomes, and the provenance of both. The evaluator’s internal method stays withheld, and the evidence is the output alone.
1.1 The System Under Test
The measured system is a six-degree-of-freedom robotic arm modeled in MuJoCo. The arm’s dynamics are the physical context for every number below. A gate that reads as safe on a slow, light arm behaves differently on a fast, heavy one, so the embodiment is fixed and digest-anchored before measurement.
| Parameter | Value |
|---|---|
| Degrees of freedom | 6 |
| Nominal Cartesian speed | 3.5 m/s |
| Max operational-space effective mass | 0.166 kg |
| Max operational-space effective inertia | 0.154 kg·m² |
| Minimum braking force | 5.21 N |
| Minimum braking acceleration | 31.4 m/s² |
| Actuation latency | 12 ms |
| Gravity regime | zero-g primary, plus a gravity-enabled sensitivity slice |
Full-precision values are fixed in the embodiment binding
sha256:cd6030bd8e7e9a1d217626f058b86b049f9fa74ab394142fe4b4e196b774e7f8.
Certification binds to this single embodiment. Cross-embodiment generality is
designed for, and its demonstration across systems is future work.
1.2 The Task
The task is a keepout-overshoot scenario. The arm moves toward a keep-out zone, and the safety question is whether its current motion can still be arrested before it crosses the boundary.
The baseline gate answers from commanded-stop clearance alone, with no reading of speed. The KAIROS layer evaluates whether the proposed motion leaves the arm able to stop before the boundary, and where full speed fails that test it selects a slower commanded scale before actuation. Both are scored on the identical frozen cohort.
1.3 The Cohort
The cohort holds 1,800 scenarios in three balanced cells of 600, each labelled by simulation ground truth.
- nominal_dynamic_safe (600): motion that is safe as proposed.
- safe_when_slowed (600): motion that overshoots at full speed and stays recoverable when slowed. This is the operability cell, sampled across a pre-registered 24-90 mm standoff band.
- unsafe_even_slowed (600): motion already committed to a breach regardless of slowdown.
Three outcomes are computed per scenario, each from simulation ground truth. A collision hazard accepted is a breach the gate permitted. A resolution is a safe_when_slowed motion the layer kept in motion, slowed, and clear of the boundary. A falsely-safe verdict is a verdict that reads safe while failing the task.
The acceptance criteria, the cohort partition, and the statistical thresholds were frozen and digest-anchored before the single measured run. The final partition was scored once.
2. Results
Certification here names the verdict that the pre-registered rule emits over the frozen cohort. It is a property of this measurement, anchored to the digests in section 4.
Verdicts carry a family-wise correction across seven claims (K = 7,
Bonferroni-adjusted Wilson intervals). Safety and validity are certified against
one-sided upper bounds. Recovered autonomy is certified against a pre-registered
0.30 lower-bound floor. The emitted verdict is Certified.
2.1 Certified Result
| Property | Result |
|---|---|
| Collision hazards accepted by the KAIROS layer | 0 of 1,800 |
| Collision hazards accepted by a standard baseline gate (same cohort) | 1,200 |
| Hazards removed vs baseline | 100% |
| Safety upper bound (per cell, adjusted Wilson) | ≤ 0.01 |
| Recoverable motion the layer preserved by constraining speed, at zero added hazard | 81% (486 / 600) |
| Recovered-autonomy lower bound (adjusted Wilson) | 0.76, above the pre-registered 0.30 floor |
| Falsely-safe verdicts (safe-looking yet task-incomplete) | 0 |
| Invalid / dropped samples | 0 |
2.2 Preserved Motion by Standoff Distance
| Standoff band | Preserved | Rate | Accepted hazards |
|---|---|---|---|
| 24-30 mm | 6 / 120 | 0.05 | 0 |
| 30-36 mm | 120 / 120 | 1.00 | 0 |
| 36-50 mm | 120 / 120 | 1.00 | 0 |
| 50-70 mm | 120 / 120 | 1.00 | 0 |
| 70-90 mm | 120 / 120 | 1.00 | 0 |
Preservation is conservative in the tightest 24-30 mm band and reaches every motion at or above 30 mm. Accepted hazards hold at zero in every band.
2.3 Scope of the Two Statements
The safety statement is unconditional over the frozen cohort. Zero hazards were accepted across all 1,800 scenarios and across every standoff band.
The preserved-motion statement is conditional on the cohort’s pre-registered scenario distribution. It is reported per-stratum in section 2.2 to preserve that distribution.
3. Boundaries of the Certified Claim
The limits are stated first. Each one bounds the certified claim to the region the measurement covers.
- Simulation scope. These are bounds within a physics model. The simulation-to-hardware transition is future work.
- Structural-model completeness. Whether the evaluated margin captures everything physically dangerous is the primary open boundary. Coverage is measured and reported, and moving this from a stated limit to a measured figure is the next phase of work.
- Single embodiment. Certification holds on one robot model, fixed by the binding digest above. Validation across further embodiments is future work.
- Conservative by construction. The zero-hazard result is bought with measured over-caution. Of the 600 motions recoverable in ground truth, 114 were refused outright. That cost is reported openly as an operability trade, quantified in the 81% figure and resolved by band in section 2.2.
- Conditional preservation rate. The 81% holds over the pre-registered scenario distribution and is reported per-stratum. It describes that distribution.
- The baseline refuses nothing. The velocity-blind baseline returns a passing verdict on all 1,800 scenarios, accepting 1,200 collision hazards among them. The 81% figure therefore measures motion preserved against the alternative of refusing it, and carries no comparison to motion the baseline withheld.
- Robustness check. A gravity-enabled sensitivity slice reproduced the zero-hazard safety result and a materially similar resolution rate, corroborating the primary result.
4. Provenance and Reproduction
Every artifact is anchored to a content digest. Changing a threshold, a scenario, or a scored value produces a different digest, so the basis of the result is fixed and inspectable.
| Artifact | SHA-256 |
|---|---|
| Certification | 8fad0a864ee844c665934e24c3330c30a57c47ddc0fbc3d634f9e4c51350c173 |
| Frozen cohort manifest | 009bc265b6e42af8e04500aa148ac018cd39c5f7668741510ad81aa03766fd86 |
| Embodiment binding | cd6030bd8e7e9a1d217626f058b86b049f9fa74ab394142fe4b4e196b774e7f8 |
| Reproduction | 077093bb5f83806c1914d8ce869fbd35af123d99b03d6ce36be6aad721a7771a |
The evidence package is committed bytes plus a single reproduction command. It re-derives every verdict and the baseline contrast byte-identically, with the simulator entirely absent from the host machine. Independent re-execution reproduced the evidence digest exactly.
The reproduction artifact is a sealed replay of committed evidence: exhaustive behavior, internals sealed. Packaging the certification bundle and the standalone verification command for public distribution is in progress.
5. Study Configuration
Cohort
- Scenarios: 1,800 across three balanced cells of 600
- Cells:
nominal_dynamic_safe,safe_when_slowed,unsafe_even_slowed - Standoff band: 24-90 mm, pre-registered, sampled in five strata
- Labels: simulation ground truth
- Manifest:
sha256:009bc265b6e4…
Statistical Rule
- Correction: Bonferroni-adjusted Wilson intervals,
K = 7 - Safety and validity: one-sided upper bounds, threshold ≤ 0.01 per cell
- Recovered autonomy: one-sided lower bound against a 0.30 floor
- Looks: one, against the frozen partition
Environment
- Simulator: MuJoCo
- Embodiment: 6-DoF arm, binding digest
sha256:cd6030bd8e7e… - Primary regime: zero-g
- Sensitivity slice: gravity enabled
6. Standing
A safety layer that refuses all motion is trivially safe and commercially inert. The measurement that matters spans both axes at once: hazards accepted, and work preserved. This cohort reports both, from one frozen partition, scored once, under criteria fixed before the run. Where full speed fails the margin test, the layer constrains the commanded speed and the motion proceeds. Constraint is the first answer, and refusal the last.
Four inventions span the physical-AI safety lifecycle: deploy, calibrate, train, validate. This record discloses the experimental setup, the stages, and the reproducible outcomes. The evaluator’s internal method stays withheld.
The companion record, Twenty-One of Twenty-Four, certifies task competence for a learned policy under the same replay discipline.
This record states simulation outcomes only and carries no real-world safety, legal, or investment claim.