docs/README.md

# STEM: eight domains, 40 tasks, 55 recorded Argon attempts

This package combines the latest five-task samples for Astronomy, Biology,
Chemistry, Earth science, Engineering, Mathematics, Medicine, and Physics.
All task folders share one `tasks/` directory; all corresponding attempt folders
share one `trajectory/` directory. There are no domain-level wrapper directories,
nested archives, duplicated `runs/` trees, or original-ID mapping tables.

**40 independent tasks · 55 recorded attempts · 19 passes · 34.55% pooled attempt pass rate.**

The retained task and trajectory files are preserved byte-for-byte from the eight
normalized five-task samples. Task IDs are unique, and each domain uses IDs numbered 1–5.
This combines the later five-task Chemistry sample, not the earlier six-task
Chemistry set whose IDs overlap. Shared grading utilities, the inventory under `docs/`,
documentation, and checksums have been consolidated for this package.

## Domain inventory and observed outcomes

| Domain | Task IDs | Tasks | Recorded attempts | Passes | Attempt pass rate |
| --- | --- | ---: | ---: | ---: | ---: |
| Astronomy | `ASTRO1`–`ASTRO5` | 5 | 5 | 2 | 40.00% |
| Biology | `BIO1`–`BIO5` | 5 | 5 | 2 | 40.00% |
| Chemistry | `CHEM1`–`CHEM5` | 5 | 10 | 2 | 20.00% |
| Earth science | `EARTH1`–`EARTH5` | 5 | 5 | 2 | 40.00% |
| Engineering | `ENG1`–`ENG5` | 5 | 5 | 2 | 40.00% |
| Mathematics | `MATH1`–`MATH5` | 5 | 15 | 5 | 33.33% |
| Medicine | `MED1`–`MED5` | 5 | 5 | 2 | 40.00% |
| Physics | `PHYS1`–`PHYS5` | 5 | 5 | 2 | 40.00% |
| **Total** | **Eight domains** | **40** | **55** | **19** | **34.55%** |

These were deliberately selected samples. The pass rates describe the included
recorded attempts, not general model performance, independent estimates of task
difficulty, or prospective success probabilities. A pass requires the complete
answer to satisfy its included verifier; fractional field reward is not a pass.

The pooled rate weights every recorded attempt equally. It combines different
capture modes and model labels and is not a common pass@1 or pass@k estimate.
Separately, **19 of 40 tasks (47.5%)** were solved at least once; that is a different
measure from the requested 20%–40% per-attempt sample rate. Each domain's attempt
pass rate remains within that range.

## Directory layout

```text
STEM-final.zip
├── tasks/
│   ├── ASTRO1/ ... ASTRO5/
│   ├── BIO1/   ... BIO5/
│   ├── CHEM1/  ... CHEM5/
│   ├── EARTH1/ ... EARTH5/
│   ├── ENG1/   ... ENG5/
│   ├── MATH1/  ... MATH5/
│   ├── MED1/   ... MED5/
│   └── PHYS1/  ... PHYS5/
├── trajectory/
│   ├── ASTRO1/ ... ASTRO5/
│   ├── BIO1/   ... BIO5/
│   ├── CHEM1/  ... CHEM5/
│   ├── EARTH1/ ... EARTH5/
│   ├── ENG1/   ... ENG5/
│   ├── MATH1/  ... MATH5/
│   ├── MED1/   ... MED5/
│   └── PHYS1/  ... PHYS5/
├── environment/
│   ├── __init__.py
│   ├── grade.py
│   └── stem_env.py
└── docs/
    ├── README.md
    ├── tasks.json
    └── SHA256SUMS.json
```

The ZIP opens directly to these folders; it does not contain an extra `STEM/`
wrapper. Each `tasks/<TASK_ID>/` includes `instruction.md`, `instance.json`,
`task.json`, `verify.py`, and `solution/solution.json`. Optional Mathematics
reference solvers are retained where present. Per-task READMEs have been removed;
`docs/README.md` is the single authoritative package guide.

Each `trajectory/<TASK_ID>/attempt_<N>/` contains:

- `trajectory.json`: the available captured model/tool record in its original normalized format.
- `submitted_action.json`: the complete answer actually submitted for grading.
- `result.json`: the recorded pass/fail outcome, reward, and available diagnostics.

Chemistry has `attempt_1` and `attempt_2`; Mathematics has `attempt_1` through
`attempt_3`; all other domains have `attempt_1`. Attempt numbering is local to a
task. `docs/tasks.json` is the unified machine-readable inventory and contains each
task's domain, paths, attempt count, and recorded outcomes. In that manifest,
`path` and `trajectory_path` are relative to the package root. Within each
`task.json`, instruction, instance, verifier, and reference-solution paths are
relative to the task folder; `trajectory_path`, where present, is root-relative.
Explicit file links inside a trajectory are relative to its attempt folder.

## Grade answers offline

Use **Python 3.10 or newer**. All 40 numerical verifiers and the shared grading
utilities use only the Python standard library. No network connection, private
image, external dataset, or separately downloaded reference answer is required.
The `environment/` folder contains utilities, not a container image.

From the extracted package root:

```bash
# Grade all 40 bundled reference answers.
python environment/grade.py --all

# Regrade all 55 saved submissions and compare their recorded outcomes.
python environment/grade.py --check-trajectories

# Check every packaged file against the combined SHA-256 manifest.
python environment/grade.py --check-integrity

# Restrict bulk grading or trajectory checking to one domain.
python environment/grade.py --all --domain BIO
python environment/grade.py --check-trajectories --domain MATH

# Grade a new answer or one saved attempt.
python environment/grade.py --task CHEM1 --candidate candidate.json
python environment/grade.py --task MATH1 --attempt 2

# Run an individual task verifier directly, with an explicit candidate path.
python tasks/ASTRO1/verify.py tasks/ASTRO1/solution/solution.json
```

`--domain` accepts `ASTRO`, `BIO`, `CHEM`, `EARTH`, `ENG`, `MATH`, `MED`, and
`PHYS`. Bulk checks use up to eight workers. The CLI returns JSON; bulk modes
include a summary and per-entry results. For individual grading, exit code 0
means pass and 1 means fail. For `--check-trajectories`, exit code 0 means every
saved result matches, **including correctly reproduced failures**. Invalid CLI
arguments return exit code 2. With `--task` and no candidate or attempt, the shared
grader checks that task's reference solution.

Read each task's full instruction and exact schema before submitting. Depending
on the original normalized task, the schema appears as `submission_schema` or
`action_schema` in `instance.json`. Keep required keys, units, numeric types, and
any required `problem_id` exactly as specified. Mathematics answers can include
arrays, integers, or rational strings; do not assume every task accepts only
scalar floats. The per-candidate size limit is recorded in `docs/tasks.json`.

## One-step environment

```python
from environment import STEMEnv

# Fix a task; alternatively, use STEMEnv(domain="BIO") or STEMEnv().
env = STEMEnv(task_id="BIO1")
observation, info = env.reset(seed=0)

# Supply your answer as a JSON-compatible dictionary, JSON string, or bytes.
# observation, reward, terminated, truncated, info = env.step(answer)
```

One episode accepts one submitted answer. Call `reset()` before another episode.
The environment is a convenience interface, **not a security sandbox**. For a
blind assessment, expose only problem instructions and instances to the solving
agent. Keep reference solutions, verifiers, saved trajectories, and result data
in evaluator-side storage. Verifier feedback may reveal reference values.

## Models, capture fidelity, and limits

Astronomy records identify the model as `gemini-4-argon-high`; the other domains
identify it as `gemini-4-argon`. These labels come from the supplied records, not
newly verified provider identities. No new model runs were generated.

Chemistry preserves one single-turn, no-tool attempt and one agentic Python-tool
attempt per task. Mathematics preserves three recorded tool-use attempts per
task. The remaining domains preserve one captured tool-use attempt per task.
The `trajectory.json` schemas differ between source samples and are intentionally
preserved rather than forcing heterogeneous capture records into a lossy format.
The shared directory layout, complete submitted answers, and task-level inventory
provide consistent access across all eight domains.

**Medical capture limitation:** the supplied medical records cap or truncate
some tool-code and console-output snippets. These are not fully executable
transcripts. Their complete saved submitted answers remain independently
gradeable. The capture metadata identifies these limitations; missing code and
conversation content have not been reconstructed.

More generally, captured reasoning summaries, tool traces, stdout, or stderr may
be excerpts rather than complete API conversations. Available content, order,
recorded usage, and timing are retained as provided. Regrading checks final
answers; it does not rerun Argon, replay historical tool execution, or certify
that the captured code is sufficient to regenerate an answer.

Optional Mathematics `solution/solver.py` files are reference implementations,
not required by the grading commands. The MATH2 solver imports SciPy. Historical
tool snippets may also depend on optional numerical libraries; those libraries
are not required to grade the packaged reference or submitted JSON answers.

## Selected task catalog

Outcomes below follow `attempt_1`, `attempt_2`, and `attempt_3` where available.

| Task | Area | Problem | Recorded outcomes |
| --- | --- | --- | --- |
| `ASTRO1` | Cosmology / recombination and CMB damping | Coupled Peebles Recombination with $s+p$-Wave Dirac Dark-Matter Annihilation & Silk Damping | Fail |
| `ASTRO2` | Strong-field gravity / black-hole superradiance | Kerr Superradiant $2p$ Scalar Cloud with Self-Gravity Shift, Boson Number & Annihilation GW Signal | Pass |
| `ASTRO3` | Compact stars / relativistic stellar structure | MIT Bag Model Strange Quark Star TOV Structure, ISM Dispersion & Bare-Surface Thermal Flux | Fail |
| `ASTRO4` | Interstellar medium / gravitational stability | Bonnor–Ebert Critical Stability Limit via Emden–Chandrasekhar ODE Turning Point & Submm Flux | Fail |
| `ASTRO5` | Exoplanets / orbital irradiation and radiative transfer | Eccentric Exoplanet Orbital Insolation: Flux-Averaged vs. Time-Averaged Temperatures & Periastron Flux | Pass |
| `BIO1` | Enzyme kinetics and biochemical networks | Theorell–Chance enzyme kinetics and coupled carrier-buffered thermodynamics | Fail |
| `BIO2` | Molecular biophysics and nonequilibrium thermodynamics | Single-molecule work fluctuations with Donnan partitioning | Pass |
| `BIO3` | Cellular electrophysiology and ion transport | Eyring ion-channel permeation with thermal and electrolyte linkage | Fail |
| `BIO4` | Population genetics and evolutionary dynamics | Underdominant-inversion traveling waves with viscoelastic and homeostatic coupling | Fail |
| `BIO5` | Ecological biogeochemistry and nutrient cycling | Soil nitrification–denitrification with crowding and mass-transfer coupling | Pass |
| `CHEM1` | Electrochemistry / impedance spectroscopy | Electrochemical impedance with coupled conformational equilibrium | Pass, Fail |
| `CHEM2` | Polymer / soft-matter thermodynamics | Polyelectrolyte hydrogel swelling and nonlinear mechanics | Fail, Pass |
| `CHEM3` | Theoretical / quantum chemistry | Radical-cation Hückel molecular-orbital analysis | Fail, Fail |
| `CHEM4` | Organometallic catalysis / reaction kinetics | Wilkinson-catalyzed hydrogenation microkinetics | Fail, Fail |
| `CHEM5` | Thermodynamics / reaction equilibrium | Non-ideal ammonia synthesis using a cubic equation of state | Fail, Fail |
| `EARTH1` | Earthquake physics / rate-and-state fault dynamics | Inverse Dieterich–Ruina Nonlinear Phase-Plane Excursion, Hopf Bifurcation, and Rebound Peak | Pass |
| `EARTH2` | Geothermal convection / porous-media stability | Inverse Variable-Conductivity Anisotropic Porous Thermal Convection Sturm–Liouville BVP | Fail |
| `EARTH3` | Glaciology / Antarctic ice-shelf hydrofracture | Antarctic Ice-Shelf Firn-Aquifer Meltwater Percolation & Hydrofracture BVP | Fail |
| `EARTH4` | Chemical oceanography / marine iron cycling | Hydrothermal-to-Abyssal Dissolved Iron Organic-Siderophore Stabilization BVP | Fail |
| `EARTH5` | Atmospheric chemistry / polar ozone depletion | Polar Stratospheric Cloud (PSC) Type Ia NAT Denitrification & ClONO2-HCl Activation BVP | Pass |
| `ENG1` | Magnetohydrodynamics and liquid-metal cooling | Hartmann-channel ohmic dissipation and microwave-transducer heat flow | Fail |
| `ENG2` | Geotechnical mechanics and optical sensing | Strip-foundation stress and causal optical-sensor pulse dispersion | Pass |
| `ENG3` | Information theory and signal processing | Gaussian source reverse water-filling and coupled quantum ground-state energy | Pass |
| `ENG4` | Control systems and electrochemical transduction | Control-loop stability and coupled electrostatic–osmotic free energy | Fail |
| `ENG5` | Chemical process engineering and electro-optics | Fixed-bed adsorption breakthrough and Pockels-waveguide pulse propagation | Fail |
| `MATH1` | Algebraic geometry / arithmetic curves | Frobenius Slopes and Hasse-Witt Invariants of a Genus 2 Curve over $\mathbb{F}_7$ | Fail, Pass, Fail |
| `MATH2` | Partial differential equations / nonlinear elasticity | Radial Equilibria and Non-Homogeneous Annular Deformations for Polyconvex Hyperelasticity | Fail, Pass, Fail |
| `MATH3` | Probability / random matrix theory | Normalized Expected Sum of Singular Values of Gaussian Matrices | Fail, Pass, Fail |
| `MATH4` | Analytic number theory / modular forms | Analytic Invariants of the Normalized Ramanujan Delta L-Function | Pass, Fail, Fail |
| `MATH5` | Topology / knot invariants | Determinant, Signature, and Cyclotomic Tristram-Levine Invariants of Pretzel Knots | Pass, Fail, Fail |
| `MED1` | Cardiovascular hemodynamics | Womersley blood flow coupled to a three-element Windkessel | Fail |
| `MED2` | Renal physiology | Glomerular ultrafiltration with tubuloglomerular feedback and protein transport | Pass |
| `MED3` | Cancer genetics and Bayesian risk modeling | Two-hit retinoblastoma, mosaic selection, and sequencing-biased genetic risk | Pass |
| `MED4` | Medical imaging physics | SPGR MRI T1 mapping with field scaling, protein binding, and T2* decay | Fail |
| `MED5` | Clinical-trial biostatistics | Non-inferiority trials with constancy drift and crossover correction | Fail |
| `PHYS1` | Condensed-matter physics | Quantum oscillations and polariton wavepacket dispersion | Pass |
| `PHYS2` | Quantum optics and open quantum systems | Quantum-jump photon statistics and driven-probe heat transport | Pass |
| `PHYS3` | Kinetic plasma physics | Vlasov–Landau plasma damping and driven-probe heat transport | Fail |
| `PHYS4` | Fluid mechanics and hydrodynamic stability | Görtler boundary-layer instability and dispersive waveguide pulses | Fail |
| `PHYS5` | General relativity and spin dynamics | Relativistic gyroscope precession and dispersive waveguide pulses | Fail |

## Validation and integrity

All **40 reference answers pass** the unchanged packaged verifiers. All **55 saved
Argon outcomes reproduce**, including pass/fail, reward, and applicable recorded
field diagnostics. The **370 retained task and trajectory files** are byte-identical to
the eight normalized input samples; merging has not changed numerical answers,
reference targets, tolerances, or historical content. Task IDs are unique and
metadata file links are checked against the merged directory layout.

`docs/SHA256SUMS.json` lists every delivered file except itself. Its paths are
relative to the package root, not to `docs/`. It is regenerated for this final
package, not copied from any individual domain archive.
Runtime Python bytecode caches are ignored by the integrity checker. No private
images, duplicate run trees, nested ZIPs, or temporary build reports are shipped.

Passing a bundled verifier establishes compatibility with that benchmark's
reference answers and tolerances. It does not constitute independent scientific
peer review of the problem statements or reference calculations. The Medicine
entries are benchmark problems, not guidance for patient care.