Axiom

A compact Rule Definition Language (RDL) for AI coding agents. Compiles verbose markdown rules into self-describing tabular format with 87% token reduction and no compliance degradation.

Empirical Results

Tested across 20 A/B runs on 8 coding tasks with Claude Sonnet 4.6:

Metric	Markdown (1195 tok)	Axiom S/D (159 tok)
Mean compliance	91.0%	90.5%
Token savings	--	86.7%
Wins / Losses / Ties	5 / 5 / 10	5 / 5 / 10

Key finding: Axiom achieves compliance parity at 87% token reduction. Same compliance, fraction of the cost.

The path to 100%: static format (Axiom, ~91%) + dynamic PostToolUse compliance hook (~9% remaining) = ~100%.

See paper.md for the full research paper and bench/ for the benchmark.

Before & After

Markdown rule (87 tokens):

## Git Safety
- Never use `git push --force` on any branch. Force pushing rewrites
  remote history and can destroy other contributors' work. If you need
  to update a remote branch, use `git push --force-with-lease` instead,
  which will fail if the remote has commits you haven't seen.

Axiom compiled (18 tokens):

GOVERNANCE[1]{id,effect,domain,trigger,message}:
no-force-push,forbid,Git,push --force,Use --force-with-lease instead

Format

Axiom uses TOON-style self-describing tabular headers:

SECTION_NAME[N]{col1,col2,...}:
value1,value2,value3,...
value1,value2,value3,...

• SECTION_NAME -- uppercase category (GOVERNANCE, CODING, SECURITY, etc.)
• [N] -- row count (optional, derivable from rows)
• {col1,col2,...} -- inline column schema
• Rows are CSV-like, one rule per line

Core Schemas

Category	Columns
GOVERNANCE	id, effect, domain, trigger, condition, message
CODING	id, language, scope, pattern, effect, fix_hint, severity
SECURITY	id, risk_level, data_type, trigger, effect, response
TESTING	id, effect, target, threshold, action, message
WORKFLOW	id, effect, phase, actor, condition, message

Source Format

Rules are authored as markdown with YAML frontmatter. Axiom's frontmatter is a superset of Claude Code's description/paths/when_to_use fields, so .claude/rules/*.md files work with both CC and Axiom without modification.

---
id: no-force-push
description: Prevent force-push to protected branches
category: governance
effect: forbid
priority: critical
trigger: push --force
globs: ["*.sh"]
when_to_use: When reviewing or executing git push commands
---
Never use `git push --force`. Use `--force-with-lease` instead.

Pressure Zones

Zone	Context	Behavior
FRESH	0-40%	All rules
MODERATE	40-70%	Drop inform, drop message
DEPLETED	70-90%	Critical + high only
CRITICAL	90%+	Safety floor (critical + forbid)

How to Validate

Run the compliance benchmark yourself:

# Install dependency
pip install tiktoken

# Dry run (no Claude invocation, validates rules + format generation)
python bench/runner.py --mode dry

# Full A/B comparison (requires Claude CLI, costs money)
python bench/runner.py --mode ab

# Aggregate results from all runs
python bench/aggregate.py

See bench/README.md for details.

Orchestration & Complexity Stratification (v0.6.0)

Axiom §17 standardizes how runners report multi-dimensional dispatch results: orchestration shape vocabulary (flat / waves / scatter-gather / team-mode / subagents), complexity tier vocabulary (display / crud / transactional / cross_cutting), the fixture_gap terminal status, verification_runs[], and artifact_quality. Inspired by Fabian Wesner's One-Shot Shop Challenge — the empirical demonstration that orchestration architecture beats model choice (Team Mode 85% vs Sub-Agents 57% on the same model). Reference implementation: pawbench. See spec.md §17.

Documentation

• Paper -- research paper with empirical results (arXiv-style)
• Specification -- normative format definition (v0.6.0)
• Benchmark -- compliance benchmark (10 rules, 8 tasks, 20 runs)
• Compliance Hook -- PostToolUse hook for ~100% compliance
• Examples -- sample .axiom files

License

MIT

---