s2s-certify 1.4.1

Physics-certified motion data toolkit for Physical AI training

S2S — Physics-Certified Sensor Data

Physics-certified motion data for prosthetics, robotics, and Physical AI.

S2S is a physics validation layer for human motion sensor data. Before training a prosthetic hand, surgical robot, or humanoid — run your IMU data through S2S. It verifies the data obeys 11 biomechanical laws and issues a certificate. Bad data gets rejected before it reaches your model.

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Live Demos

• 📊 Interactive Data Explorer — 104,160 real certified records, hover to explore
• 📱 Phone IMU Demo — real-time physics certification on your phone
• 🎥 Pose Camera Demo — 17-joint live certification

No install needed. All processing runs on your device. No data sent anywhere.

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The Problem

Physical AI (robots, prosthetics, exoskeletons) is trained on motion data. But most datasets contain synthetic data that violates physics, corrupted recordings, and mislabeled actions — with no way to verify the data came from a real human moving in physically valid ways.

A robot trained on bad data learns bad motion. A prosthetic hand trained on uncertified data fails its user.

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Four Proven Training Benefits

S2S is not just a filter. It improves model performance at every stage of the training pipeline. All results validated across two independent datasets (WISDM 20Hz, PAMAP2 100Hz).

Level 1 — Quality Floor

Remove data that fails physics before training.

Dataset	Corruption	Recovery	Result
WISDM 20Hz	35% corrupted	108% of damage recovered	+0.23% net vs clean
PAMAP2 100Hz	35% corrupted	Confirmed cross-dataset	+0.51% F1

Physics floor removes bad data and beats the clean baseline with 46% less data.

Level 2 — Curriculum Training

Train in physics quality order: GOLD → SILVER → BRONZE.

Dataset	Result
WISDM 20Hz	+1.03% F1 vs clean baseline, 46% less data

The model learns the ceiling first. Marginal data is introduced only after the model understands perfect motion.

Level 3 — Adaptive Reconstruction

Repair marginal (BRONZE) records using frequency-appropriate methods. Every repaired record carries full provenance.

Hz	Method	Result
≤50Hz (20Hz WISDM)	Kalman RTS smoother	+1.44% F1
≥100Hz (PAMAP2)	Savitzky-Golay	Spectral sim=0.997 — signal needs no repair

Dual acceptance: physics re-score ≥75 AND spectral similarity ≥0.8. Both must pass.

At low Hz, noise is separable from signal — Kalman removes it. At high Hz, every micro-movement is real — smoothing destroys features. S2S adapts automatically.

Level 4 — Kinematic Chain Consistency (headline result)

Verify that multiple sensors tell a consistent biomechanical story.

Condition	F1	Δ
Single chest IMU	0.7969	baseline
3 IMUs naive concat	0.8308	+3.39%
3 IMUs + chain filter	0.8399	+0.91% over naive
Net vs single sensor	+4.23% F1	← headline

Tested on PAMAP2 12-class activity recognition (hand + chest + ankle IMU, 100Hz).

Why this catches synthetic data: Synthetic motion generators produce each sensor channel independently. Real walking produces a 50–100ms ankle-to-chest jerk lag from heel-strike propagating up the skeleton. This timing cannot be faked without full rigid-body simulation. S2S Level 4 is the first physics-based cross-sensor consistency check for IMU data.

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11 Physics Laws

Single-Sensor Laws (Levels 1–3)

#	Law	What It Catches
1	Newton's Second Law (F=ma, 75ms EMG delay)	Synthetic data missing lagged EMG-accel correlation
2	Segment Resonance (ω=√(K/I))	Tremor at impossible frequency for body segment
3	Rigid Body Kinematics (a=α×r+ω²×r)	Gyro and accel generated independently
4	Ballistocardiography (F=ρQv)	IMU missing cardiac recoil
5	Joule Heating (Q=0.75×P×t)	Sustained EMG without thermal elevation
6	Motor Control Jerk (∂³x/∂t³ ≤ 5000 m/s³)	Robotic or keyframe animation artefacts
7	IMU Consistency (Var(accel) ~ f(Var(gyro)))	Accel and gyro from independent generators

Multi-Sensor Chain Laws (Level 4)

#	Law	What It Catches
8	Locomotion Coherence (freq spread <2.5Hz)	Sensors recording different activities
9	Segment Coupling (chest-ankle r >0.3)	Independent synthetic channels
10	Gyro-Accel Coupling (per IMU)	Rotation without corresponding acceleration
11	Cross-Sensor Jerk Timing (ankle leads chest 0–200ms)	Reversed or zero lag — not real heel-strike

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Tier System

Tier	Score	Meaning
GOLD	≥87	All physics laws passed. Pristine.
SILVER	75–86	Trusted. Minor deviations within noise.
BRONZE	60–74	Marginal. Candidate for reconstruction at ≤50Hz.
RECONSTRUCTED	—	Repaired, re-scored ≥75, spectral sim ≥0.8. Weight 0.5.
REJECTED	<floor	Removed from pipeline.

Floor = p25 of clean score distribution per dataset (adaptive). GOLD always means the same thing everywhere.

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Install

pip install s2s-certify

Zero dependencies. Pure Python 3.9+. Works on any platform.

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Quick Start

from s2s_certify import certify

# Single window — list of [ax, ay, az] samples
result = certify(accel_window, sample_rate_hz=20)

print(result['tier'])        # GOLD / SILVER / BRONZE / REJECTED
print(result['score'])       # 0–100
print(result['laws_passed']) # which of 7 single-sensor laws passed

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Datasets Validated

Dataset	Hz	Sensors	Windows	Used for
WISDM 2019	20Hz	Wrist accel	46,946	Levels 1, 2, 3
PAMAP2	100Hz	Hand+Chest+Ankle IMU	13,094	Levels 1, 3, 4

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Paper

S2S: Physics-Certified Sensor Data — Four Proven Training Benefits Across Two Independent Datasets

→ Read paper (PDF) | → DOI: 10.5281/zenodo.18878307

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Project Structure

s2s_standard_v1_3/     # Physics engine (zero dependencies)
experiments/           # All 4 level experiments + results JSON
  level3_adaptive_reconstruction.py  # Kalman + SavGol adaptive
  level4_multisensor_fusion.py       # Kinematic chain consistency
  results_level4_pamap2.json         # +4.23% chain result
  results_level3_adaptive_wisdm.json # +1.44% Kalman result
docs/paper/            # S2S_Paper_v5.pdf + .docx
dashboard/app.py       # Streamlit human review UI
train_classifier.py    # Domain classifier (v1.4, 76.6% acc)
wisdm_adapter.py       # WISDM 2019 dataset adapter

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License

BSL-1.1 — free for research and non-commercial use. Contact for commercial licensing.