protocolcompany/embodied-physics-trajectories

Embodied Physics Trajectories

100+ million physics trajectories across 10 substrates, generated from 200KB of hand-rolled Rust on a single Apple M4 Pro. No external physics libraries. No game engines. No Unity. No MuJoCo.

This dataset contains sample trajectories (50-100 per substrate) from the full corpus. Every trajectory is SHA-256 sealed at generation time. Every result is deterministically reproducible from its RNG seed.

This is not synthetic data from a rendering pipeline. This is physics ground truth — bodies in substrates experiencing forces.

Full corpus access and discovery reports available at Protocol Company.

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Quick Start

from datasets import load_dataset

# Load Mars EDL trajectories
mars = load_dataset("protocolcompany/embodied-physics-trajectories", "mars", split="train")
print(mars[0])  # First data point: altitude, velocity, atmospheric density, phase

# Load Orbital attitude recovery
orbital = load_dataset("protocolcompany/embodied-physics-trajectories", "orbital", split="train")

# Load any of the 10 substrates
# Options: mars, orbital, marine, terran, mycelial, atheric, asteroid, plutonian, celestial, energy

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What This Contains

Time-series trajectory data from Monte Carlo physics simulations across 10 physical domains. Each trajectory records the full state evolution of a body moving through a physically-grounded environment.

Substrate	Physics	Bodies	Rate (traj/s)	Sample Trajectories
Mars	CO2 atmospheric drag, supersonic deceleration, suicide burn	EDL Lander	144	100
Orbital	Quaternion attitude dynamics, reaction wheels, gyroscopic coupling	MAVEN-class satellite	353	100
Marine	Pressure gradients, buoyancy, IMU drift, GPS-denied navigation	Submarine, Autonomous Boat	11	100
Terran	Boussinesq soil stress, glomalin coupling, moisture transport	8 body types (tracked, wheeled, legged, drone, humanoid, agrover, scout drone, titanhauler)	10,750	100
Mycelial	Hyphal conductance, Kirchhoff flow, percolation threshold	Mycorrhizal Mesh	760	50
Atheric	Shannon capacity, Friis path loss, frequency hopping	Coherent Signal	15,830	100
Asteroid	O(N^2) N-body gravity, Hookean contact mechanics	Rubble Pile (GPU-accelerated via Apple Metal)	9	100
Celestial	Yoshida 4th-order symplectic integration, N-body ephemeris	Spacecraft (gravity assist)	71	100
Plutonian	Entropy decay, phase crystallization, deep-time evolution	Phase System	71	100
Energy	Swing equation, nuclear/solar/wind/hydro dispatch	Grid Node	186,060	100

Generation rates are live-measured on Apple M4 Pro (14-core CPU, 20-core GPU, 24GB unified memory). All physics is pure CPU Rust except Asteroid, which uses Metal GPU compute for N-body gravity.

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Discoveries in This Data

These sample trajectories contain the signatures of three physics discoveries documented in our Tier 1 reports:

The Suicide Burn Cliff (Mars EDL)

Mars EDL survival rate: 0.7%. One equation changes it to 87.27%. The ignition boundary is a cliff, not a gradient. 1,377,638 trajectories found it. The boundary equation: alt <= v^2 / (2*(T/m - g)) * 1.2. Look at the score_final_velocity and score_mission_success fields — the transition is visible in this sample.

The Gyroscopic Discontinuity (Orbital)

Single-axis satellite tumble recovery: ~100% success. Three-axis with full Euler coupling: 17.6%. The gap is invisible to linearized control models. 300,041 trajectories found the discontinuity. Examine the omega_x, omega_y, omega_z fields and correlate with score_recovered — the coupling torque cross-terms are what kills recovery.

The Glomalin Bridge (Terran + Mycelial)

A 15-ton robot on dry sand: 94,077 Pa contact stress vs 29,967 Pa yield stress. It sinks. Add glomalin (fungal protein) and the yield stress rises. Biology changes what technology is allowed to do on living earth. Cross-reference score_pressure_yield_ratio in the Terran data with health in the Mycelial data — the coupling was invisible until two substrates talked to each other.

Purchase full reports — instant download after payment:

Report	Price	Buy
The Suicide Burn Cliff — Mars EDL	$750	Purchase Report
The Gyroscopic Discontinuity — Orbital	$1,500	Purchase Report
The Glomalin Bridge — Terran + Mycelial	$750	Purchase Report

Each includes a discovery report (15-16 pages), curated trajectory dataset, SHA-256 verification package, and Python loader.

Infrastructure modules ($15K+) and enterprise licensing ($150K/yr): View all products

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Per-Substrate Schema

Every row represents one data point within a trajectory. Trajectory-level fields are repeated on each row.

Common Fields (all substrates)

Field	Type	Description
trajectory_id	string	Unique trajectory identifier
type	string	Mission/scenario type
scenario	string	Specific scenario parameters
steps	int	Total integration steps in full trajectory
proof_hash	string	SHA-256 cryptographic proof (64 hex chars)
reasoning_context	string	JSON-encoded anomaly metadata
data_point_index	int	Index of this data point within the trajectory

Mars

Field	Type	Description
alt	float	Altitude above Mars surface (m)
vel	float	Total velocity magnitude (m/s)
rho	float	CO2 atmospheric density (kg/m^3)
phase	string	ENTRY, POWERED_DESCENT, or TERMINAL
pos_x/y/z	float	3D position (m)
t	float	Time (seconds)
score_mission_success	bool	Survived landing
score_final_velocity	float	Touchdown velocity (m/s)
score_dispersion	float	Landing accuracy (m)
score_max_deceleration_g	float	Peak deceleration (g)

Orbital

Field	Type	Description
omega_x/y/z	float	Angular velocity components (rad/s)
omega_mag	float	Angular velocity magnitude (rad/s)
wheel_h_x/y/z	float	Reaction wheel angular momentum (Nms)
fuel_kg	float	Remaining RCS propellant (kg)
battery_pct	float	Battery state of charge (%)
in_sunlight	bool	Solar illumination state
measured_mag	float	Measured magnetic field magnitude
phase	string	TUMBLE, RECOVERY, or STABILIZED
t	float	Time (seconds)
score_recovered	bool	Successfully stabilized
score_recovery_time_s	float	Time to stabilize (s)
score_fuel_remaining_pct	float	Fuel remaining at end (%)

Marine

Field	Type	Description
depth	float	Depth below surface (m)
drift	float	Accumulated IMU drift (m)
nav_error	float	Navigation error from true position (m)
battery	float	Battery fraction (0-1)
p_x/y/z	float	3D position (m)
v_x/y/z	float	3D velocity (m/s)
current_x/y/z	float	Ocean current vector (m/s)
waypoint	int	Current waypoint index
t	float	Time (seconds)
score_mission_success	bool	Reached all waypoints
score_nav_error_m	float	Final navigation error (m)

Terran

Field	Type	Description
pressure_pa	float	Contact pressure (Pascals)
yield_pa	float	Soil yield stress (Pascals)
compaction	float	Soil compaction fraction
moisture	float	Soil moisture fraction
phase	string	APPROACH, CONTACT, SEEDING, or WITHDRAWAL
t	float	Time (seconds)
score_mission_success	bool	Successful operation
score_pressure_yield_ratio	float	Contact/yield ratio (>1 = sinkage)
score_seed_emerged	bool	Seed germination success

Mycelial

Field	Type	Description
density	float	Network node density
health	float	Average network health (0-1)
delivery	float	Nutrient delivery ratio (0-1)
components	int	Connected components (lower = healthier)
phase	string	ESTABLISH, PROPAGATE, or DEGRADE
t	float	Time (seconds)
score_survived	bool	Network survived
score_delivery_ratio	float	Final nutrient delivery

Atheric

Field	Type	Description
snr_db	float	Signal-to-noise ratio (dB)
channel	int	Active frequency channel
delivery_pct	float	Packet delivery percentage
packet	int	Packet sequence number
received	bool	Packet successfully received
phase	string	TRANSMIT, RECEIVE, or IDLE
score_sealed	bool	Communication sealed (all packets delivered)
score_delivery_rate	float	Overall delivery rate (0-1)

Asteroid

Field	Type	Description
boulder_count	int	Active boulders in simulation
center_x/y/z	float	Center of mass position (km)
t	float	Time (seconds)
score_survived_cohesion	bool	Rubble pile held together
score_max_dispersion_km	float	Maximum boulder spread (km)
score_energy_dissipation	float	Total energy dissipated (J)

Plutonian

Field	Type	Description
avg_entropy	float	Average system entropy
avg_coherence	float	Average phase coherence
avg_energy	float	Average energy (normalized)
phase_shifts	int	Cumulative phase transitions
t_years	float	Time (millions of years)
score_survived	bool	System persisted
score_final_entropy	float	Terminal entropy

Celestial

Field	Type	Description
d_mars	float	Distance to Mars (km)
probe_pos_x/y/z	float	Probe position (km, heliocentric)
v_probe	float	Probe velocity (km/s)
t_days	float	Time (days from launch)
score_survived	bool	Mission survived
score_delta_v	float	Total delta-v expended (km/s)
score_closest_approach_km	float	Closest Mars flyby distance (km)

Energy

Field	Type	Description
frequency	float	Grid frequency (Hz, nominal 60)
demand	float	Power demand (MW)
gen_nuclear	float	Nuclear generation (MW)
gen_solar	float	Solar generation (MW)
gen_wind	float	Wind generation (MW)
gen_hydro	float	Hydro generation (MW)
t_hours	float	Time (hours)
score_survived	bool	Grid maintained stability
score_min_frequency	float	Minimum frequency reached (Hz)
score_blackout_time_s	float	Total blackout duration (s)

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Verification

Every trajectory carries a SHA-256 proof_hash. The proof chain works like this:

1. Physics engine generates trajectory with deterministic LCG PRNG
2. Final state vector is hashed: SHA-256(trajectory_data)
3. Hash is chained: SHA-256(prev_proof + current_proof)
4. Chain anchor stored on Internet Computer (ICP) canister: ad7wi-4aaaa-aaaad-aeijq-cai

To verify any trajectory:

• Check the proof_hash field (64-character hex string)
• The hash can be independently recomputed from the RNG seed
• The master proof chain is anchored on-chain (immutable)

Master Proof Hash: a9db821f2793cc91bba6a1d07caabffce64417edc37759ad6182025b8569fa54

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Generation Details

• Language: Pure Rust (no external physics libraries)
• Integration: Euler (1000Hz for Mars/Marine, 100Hz for Orbital/Terran) and Yoshida 4th-order symplectic (Celestial)
• Hardware: Apple M4 Pro (14-core CPU, 20-core GPU, 24GB unified memory)
• GPU: Metal compute shader for Asteroid N-body gravity (O(N^2), GPU-authoritative)
• RNG: Deterministic LCG (seed-based, fully reproducible)
• Total corpus: 100,009,600 trajectories SHA-256 sealed
• Exported corpus: 85,200 trajectories with full state vectors (10.6 GB)
• This sample: 950 trajectories, 264,161 data points (~13 MB Parquet)

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Licensing

This sample dataset is provided for evaluation purposes. The data is generated by Protocol Company and subject to the Protocol Commercial License v1.

You may:

• Download and evaluate the sample data
• Use for academic research with citation
• Benchmark your models against this data

For commercial use, training production models, or access to the full corpus: Visit Protocol Company or contact kruze@aijesusbro.com

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Citation

@dataset{kruze_embodied_physics_2026,
  author = {Kruze, John},
  title = {Embodied Physics Trajectories: 100M+ Monte Carlo Simulations Across 10 Physical Substrates},
  organization = {Protocol Company},
  year = {2026},
  url = {https://huggingface.co/datasets/protocolcompany/embodied-physics-trajectories},
  note = {Hand-rolled Rust physics, SHA-256 proof chain, ICP on-chain verification}
}

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About Protocol Company

Protocol Company builds physics ground truth for autonomous systems. 10 substrates. 100+ million trajectories. Hand-rolled Rust on bare metal. No game engines, no approximations, no synthetic slop.

The thesis: autonomous systems operating without human-in-the-loop require embodied intelligence, not information retrieval. When GPS is denied, when communication is blacked out, when the Dark Window opens — the body must reason from physics priors alone.

Website: www.aijesusbro.com ICP Backend: ad7wi-4aaaa-aaaad-aeijq-cai SOMA Ledger: mwtw4-wiaaa-aaaak-qx57a-cai (ICRC-1/2/3) Author: John Kruze | Products | Articles