ARCO
Automated Research into Computational Ontologies
A computational science platform for discovering the conditions under which computation, memory, and learning emerge in arbitrary information systems.
What ARCO Does
ARCO asks a different question than most computer science: not "what can a given computational model compute?" but "what computational models are possible, and why do they emerge?"
It formalizes this through Information Universes — 6-tuples of (state space, transformations, observations, resources, invariants, schedule) — and measures emergent computation via shuffle-corrected normalized mutual information calibrated against destructive null distributions.
Quick Start
# Binary Graph Universe
# Cellular Automaton
# Compare estimators
# Fast test run
# Save results to JSON
# See all options
Installation
As a library
Add to your Cargo.toml:
[]
= "0.5"
From source
Requires Rust 1.85+.
Key Findings
All results from 10 independent seeds. Reproduce with:
Estimator Validation
Three mutual information estimators were compared across 10 seeds on both substrates:
| Substrate | Estimator | Storage Rate | Structured Storage | H5_TRANSPORT Acc | Survival |
|---|---|---|---|---|---|
| Graph | plugin | 37.1–70.7% (48.2) | 90.5–99.6% (93.9) | 50.5–85.2% (65.4) | 10/10 |
| Graph | mm | 37.4–70.6% (48.2) | 90.5–99.6% (94.0) | 52.6–85.2% (65.8) | 10/10 |
| Graph | qe | 37.8–71.3% (48.2) | 90.5–99.6% (93.7) | 53.6–85.2% (65.6) | 10/10 |
| Substrate | Estimator | Storage Rate | Structured Storage | H3_LOW_SENSITIVITY Acc | Survival |
|---|---|---|---|---|---|
| Ca | plugin | 73.7–90.4% (82.7) | 75.5–90.7% (83.7) | 79.7–92.6% (85.4) | 10/10 |
| Ca | mm | 78.1–90.0% (84.4) | 80.5–90.9% (86.1) | 82.7–91.8% (87.0) | 10/10 |
| Ca | qe | 77.6–89.3% (83.8) | 78.6–90.9% (85.0) | 82.3–91.8% (86.5) | 10/10 |
Three independent mutual information estimators (plugin with shuffle correction, Miller-Madow, and quadratic extrapolation) agree within 2 points across both substrates and all 10 seeds. All results below use the plugin estimator with shuffle correction (the default).
Structure-Storage Gradient
| Bracket | Storage Rate Range | Mean |
|---|---|---|
| Noise (0.00–0.15) | 11.0–41.6% | 21.1% |
| Balanced (0.40–0.60) | 20.8–71.3% | 35.2% |
| Structured (0.85–1.00) | 90.5–99.6% | 93.9% |
A 4.5× difference. This is ARCO's most robust finding.
Hypothesis Survival
| ID | Condition | Survival | Acc. Range | Mean |
|---|---|---|---|---|
| H2_MAJORITY_STRUCTURED | Majority of rules are structured | 10/10 | 54.8–86.6% | 68.2% |
| H5_TRANSPORT | Rule set contains an information transport rule | 10/10 | 50.5–85.2% | 65.4% |
| H7_MULTIPLE_LOGIC | Rule set contains at least 2 logic gates | 8/10 | 47.2–79.5% | 63.3% |
| H3_LOGIC_GATE | Rule set contains a logic gate | 7/10 | 38.6–80.5% | 57.8% |
| H1_HAS_STRUCTURED | Rule set contains at least one structured rule | 0/10 | 0.0–2.3% | 1.0% |
| H4_ALL_STRUCTURED | All rules are structured | 0/10 | 0.0–6.2% | 2.3% |
| H6_ALL_DESTRUCTIVE | All rules are destructive (negative control) | 0/10 | 0.0–4.6% | 1.1% |
| H8_MIXED | Mixed structured and destructive rules | 0/10 | 0.0–2.1% | 0.5% |
H2 and H5 (Transport Law) are the most reliable. H1, H4, H6, H8 did not survive (0/10). H6 is a negative control (all-destructive → storage) — its consistent failure validates calibration.
CA Substrate — n=1,000
Null distribution sampled from a pool of known chaotic rules (30, 45, 86, 106, 135, 149). All hypotheses use measurable properties only. Rule sets are sampled independently for train and test from the full Wolfram pool.
Hypothesis Survival
| ID | Condition | Survival | Acc. Range | Mean |
|---|---|---|---|---|
| H2_PARITY | Rule conserves parity | 10/10 | 57.1–89.5% | 74.9% |
| H3_LOW_SENSITIVITY | Rule has low sensitivity (< 2.0) | 10/10 | 79.7–92.6% | 85.4% |
| H4_EVEN_RULE | Rule has even Wolfram number | 10/10 | 77.7–89.0% | 83.8% |
| H5_NOT_RULE_0 | Rule is not the zero rule | 10/10 | 76.8–90.3% | 82.5% |
| H6_MID_LAMBDA | Rule has mid-range lambda (edge of chaos) | 10/10 | 77.9–91.1% | 83.2% |
| H1_REVERSIBLE | Rule is reversible | 7/10 | 33.3–81.8% | 55.6% |
H4 (even rule number) corresponds to quiescent rules in Wolfram's classification — ARCO recovered this connection without being told about quiescence.
Estimators
ARCO supports three mutual information estimators, selectable via --estimator:
| Estimator | Flag | Best for |
|---|---|---|
| Plugin + shuffle | plugin (default) |
General use |
| QE | qe |
Large alphabets, publication-quality |
| Miller-Madow | mm |
Small alphabets, fast bias correction |
The plugin estimator with shuffle correction is the default and has been validated against QE and MM on both substrates (see Estimator Validation above).
Limitations
- Quadratic extrapolation (QE) is an approximation to the full NSB estimator.
- The Binary Graph Universe is a validation substrate — rules are hand-coded to calibrate the instrument. Discovery substrates are the next milestone.
- All findings are from small state spaces (3-vertex graphs, 8-cell automata).
Documentation
Reproducibility
Every number in this README is traceable to a specific seed produced by scripts/sweep.sh.
Python Reference
The Python reference implementation that first validated the methodology: arco-python.
License
MIT