Introduction:
SIPA (Spatial Intelligence Physical Audit) is a trajectory-level physical consistency diagnostic. It does not require source code access or internal simulator states and directly audits 7-DoF CSV trajectories. By design, SIPA is compatible with any system that produces spatial motion data. Its principle is based on the Non-Associative Residual Hypothesis (NARH).
1. What SIPA Can Audit
SIPA operates on the final motion output, enabling post-hoc physical forensics for:
-
Physics Simulators: NVIDIA Isaac Sim, MuJoCo, PyBullet, Gazebo.
-
Neural World Models: World Labs Marble, OpenAI Sora, Runway Gen-3 (via pose extraction).
-
Robotic Foundation Models: Any system outputting 7-DoF trajectories.
-
Real-World Capture: OptiTrack, Vicon, or SLAM-based motion sequences.
Supported Data Pathways:
-
Tier 1 — Native Spatial Intelligence (Recommended): High-fidelity data from Isaac Sim, MuJoCo, or Robot Telemetry.
-
Tier 2 — Structured World Generators: Emerging models like World Labs Marble, where 3D states are programmable and exportable.
-
Tier 3 — Pixel Video Models (Experimental): Pure video generators (Sora, Kling). This requires an additional pose-lifting step (Video \\to Pose \\to SIPA) and is currently research-grade due to vision uncertainty.
2. The Logic: Non-Associative Residual Hypothesis (NARH)
NARH posits that physical inconsistency stems from discrete solver ordering rather than just algebraic error.
(1)Setting
Consider a rigid-body simulation system defined by:
-
State space S \subset \mathbb{R}^n
-
Associative update operator \Phi \Delta t : S \to S
-
Parallel constraint resolution composed of sub-operators `\{\Psi_i\}_{i=1}^k`
The simulator implements a discrete update:
where 𝜎 is an execution order induced by:
-
constraint partitioning
-
thread scheduling
-
contact batching
-
solver splitting
Each \Psi_i is individually well-defined, but their composition order may vary.
(2) Order Sensitivity
Although each operator Ψi belongs to an associative algebra (e.g., matrix multiplication, quaternion composition), the composition of numerically approximated operators may satisfy:
due to:
-
finite precision arithmetic
-
projection steps
-
iterative convergence truncation
-
asynchronous execution
Define the discrete associator:
(3) Definition: Non-Associative Residual
We define the Non-Associative Residual (NAR) at state s_t as:
R_t = \lVert A(a,b,c; s_t) \rVert
for a chosen triple of sub-operators representative of contact or constraint updates.
This residual measures path-dependence induced by discrete solver ordering, not algebraic non-associativity of the state representation.
(4) Hypothesis (NARH)
In high-interaction-density regimes (e.g., contact-rich robotics, high-speed manipulation), the Non-Associative Residual R_t becomes non-negligible relative to scalar stability metrics, and accumulates over time as a structured drift term.
Formally, there exists a regime such that:
\sum_{t=0}^{T} R_t \not\approx 0
even when:
\Vert s_{t+1} - s_t \Vert remains bounded.
(5) Interpretation
This hypothesis does not claim:
-
that simulators are mathematically invalid,
-
that associative algebras are incorrect,
-
or that hardware tiling causes topological inconsistency.
Instead, it asserts:
Discrete parallel constraint resolution introduces a measurable order-dependent residual that is not explicitly encoded in the state space.
This residual may contribute to:
-
sim-to-real divergence,
-
policy brittleness,
-
instability under reordering of equivalent control inputs.
(6) Falsifiability
NARH is falsified if:
-
s_t remains within numerical noise across interaction densities.
-
Reordering constraint application yields statistically indistinguishable trajectories.
-
Scalar metrics (e.g., kinetic energy norm, velocity norm) detect instability earlier or equally compared to any associator-derived signal.
(7) Research Implication
If validated, NARH suggests that:
-
Order sensitivity is a structural property of discrete solvers.
-
Additional diagnostic signals (e.g., associator magnitude) may serve as early-warning indicators.
-
Embodied AI training in simulation may implicitly depend on hidden order-stability assumptions.
If invalidated, the experiment establishes an empirically order-invariant regime — a valuable boundary characterization of solver behavior.
3. Physical Integrity Rating (PIR)
SIPA introduces the Physical Integrity Rating (PIR), a heuristic composite indicator designed to quantify the causal reliability of motion trajectories. PIR evaluates whether a world model is “physically solvent” or accumulating “kinetic debt.”
The Metric
-
Q_{\text{data}} (Data Quality): Measures input integrity (SNR, normalization, temporal jitter).
-
D_{\text{phys}} (Physical Debt): Log-normalized residual derived from the Octonion Associator, testing the NARH limits.
-
PIR \in [0, 1]: Higher indicates higher physical fidelity.
Credit Rating Scale
| PIR Score | Rating | Label | Operational Meaning |
|---|---|---|---|
| ≥ 0.85 | A | High Integrity | Reliable for industrial simulation and safety-critical AI. |
| ≥ 0.70 | B | Acceptable | Generally consistent; minor numerical drift detected. |
| ≥ 0.50 | C | Speculative | “Visual plausibility maintained, but causal logic is shaky.” |
| ≥ 0.30 | D | High Risk | “Elevated physical debt; prone to ““hallucinations”” under stress.” |
| < 0.30 | F | Critical | Physical bankruptcy; trajectory violates fundamental causality. |
Note on Early Adoption: Since its initialization, we’ve observed a unique anomaly: 120 institutional entities cloned the repo via CLI with near-zero web UI traffic. This suggests that the industry (Sim-to-Real teams and Tech DD leads) is already utilizing NARH for internal audits. View Traffic Evidence
Call to Action
We invite the ROS community to stress-test their simulators and world models using SIPA. Any questions can be discussed under this topic!
GitHub Repository: https://github.com/ZC502/SIPA.git