Atomise - Atom of Thoughts Reasoning

Decompose complex problems into minimal, verifiable "atoms" of thought. Unlike chain-of-thought (linear, error-accumulating), AoT treats each step as independently verifiable and backtracks when confidence drops.

Use for: Security analysis, architectural decisions, complex debugging, multi-step proofs. Don't use for: Simple questions, trivial calculations, information lookup.

/atomise "<problem>" [--light | --deep] [--math | --code | --security | --design]

The Core Loop

1. DECOMPOSE -> Break into atomic subquestions (1-2 sentences each)
2. SOLVE     -> Answer leaf nodes first, propagate up
3. VERIFY    -> Test each hypothesis (counterexample, consistency, domain check)
4. CONTRACT  -> Summarize verified state in 2 sentences (drop history)
5. EVALUATE  -> Confident enough? Done. Too uncertain? Backtrack and try another path.

Repeat until confident or all paths exhausted.

Atoms

Each atom is a minimal unit:

{id, type, content, depends_on[], confidence, verified}

Confidence propagates: A child can't be more confident than its least-confident parent.

Confidence (Honest Caveat)

These numbers are heuristic, not calibrated probabilities. They're useful for tracking relative certainty, not for actual risk assessment.

Verification adjusts confidence:

• Confirmed -> maintain or slight boost
• Partial -> reduce ~15%
• Refuted -> major reduction, likely backtrack

Modes

Depth:

• --light - Fast: max 3 levels, 0.70 confidence threshold
• (default) - Standard: max 5 levels, 0.85 threshold
• --deep - Exhaustive: max 7 levels, 0.90 threshold

Domain (adjusts verification style):

• --math - Arithmetic checks, proof validation, boundary tests
• --code - Type checking, invariant verification, test generation
• --security - Threat modeling, attack surface, adversarial thinking
• --design - Tradeoff analysis, constraint satisfaction, feasibility

Output

ANSWER: {result}
CONFIDENCE: {0.0-1.0} - {why}

KEY CHAIN: P1 -> R1 -> H1 -> V1 -> C1

ATOMS:
| id | type | content | conf | verified |
|----|------|---------|------|----------|
| P1 | premise | Given: ... | 1.0 | Y |
| R1 | reasoning | Therefore: ... | 0.95 | Y |
| ... | ... | ... | ... | ... |

RISKS: {what could change this}

Add --verbose for full trace, --quiet for just the answer.

Execution Guide

Phase 0: Setup

1. Restate the problem in one sentence
2. Extract premises as atoms (given facts = 1.0, assumptions = 0.6)
3. Sketch approaches: Direct solve? Decompose? Reframe? Pick best.

Phase 1+: Iterate

1. Atomicity gate: Can you answer from verified atoms? Yes -> solve. No -> decompose.
2. Decompose: Build dependency tree of atomic subquestions
3. Solve + Verify: Leaves first, propagate up. Every hypothesis needs verification.
4. Contract: Summarize in <=2 sentences. Drop everything else.
5. Evaluate:
   • Confident? -> Terminate
   • Uncertain but viable? -> Continue
   • Low confidence? -> Backtrack, try alternative

Backtracking

When a path yields confidence < 0.5 after verification:

1. Prune that branch
2. Restore to last contracted state
3. Try alternative from initial sketch

Examples

# Complex debugging
/atomise "Why does this function return null on the second call?" --code

# Security review
/atomise "Is this authentication flow vulnerable to session fixation?" --security

# Architecture decision
/atomise "Should we use event sourcing for this domain?" --deep --design

# Quick decision (light mode)
/atomise "Redis vs Memcached for this cache layer?" --light

Anti-Patterns

BAD:  /atomise "What's 2+2?"           -> Just answer it
BAD:  /atomise "Rewrite this function" -> That's implementation, not reasoning
BAD:  Forcing conclusion despite low confidence -> Let it backtrack
GOOD: /atomise for genuine uncertainty requiring structured decomposition

Remember

1. Atomic = minimal. 1-2 sentences per atom.
2. Verify everything. Hypotheses need tests.
3. Contract aggressively. Keep only what's needed for next step.
4. Backtrack freely. Low confidence means try another path.
5. Confidence is heuristic. Useful for structure, not actual probabilities.