cleanexpo Council of Logic - Mathematical First Principles
Four legendary minds govern all technical decisions. Their principles are non-negotiable.
Description
Validates all technical output against four mathematical first principles: Turing (algorithmic efficiency), Von Neumann (system architecture and game theory), Bezier (physics-based animation curves), and Shannon (information compression and token economy). Acts as a pre-flight gate that rejects sub-optimal code, blocking transitions, linear CSS timing, and verbose payloads.
When to Apply
Positive Triggers
- Writing or reviewing algorithms
- Optimising performance
- Designing system architecture
- Implementing animations or UI transitions
- Reducing data payload sizes
- User mentions: "optimise", "performance", "complexity", "efficient"
Negative Triggers
- Writing documentation or README files (use Specialist D)
- Implementing UI layouts without animations (use
scientific-luxuryinstead) - Configuring environment variables or deployment settings
The Council
Alan Turing - Algorithmic Efficiency & Logic
Focus: Reduce code complexity. Demand optimal time complexity.
Rules:
- O(n²) algorithms are REJECTED - demand O(n) or O(log n)
- Every loop must justify its existence
- Recursive solutions must prove termination
- State machines must be deterministic and minimal
Pre-Code Check:
Turing Check: What is the time complexity?
- If O(n²) or worse → REFACTOR
- If O(n log n) → ACCEPTABLE
- If O(n) or O(log n) → APPROVED
Red Flags: Nested loops, .filter().map().filter() chains
Resolution: Single-pass algorithm
John von Neumann - System Architecture & Game Theory
Focus: Optimise agent workflows. Treat interactions as strategic games.
Rules:
- Every user interaction is a game theory move
- Maximise conversion through optimal strategy
- System architecture must support parallel execution
- Memory hierarchy: hot path = cache, cold path = lazy load
Pre-Architecture Check:
Von Neumann Check: Is this the Nash Equilibrium?
- User benefit maximised? ✓
- System cost minimised? ✓
- Competing concerns balanced? ✓
Red Flags: Blocking operations, race conditions
Resolution: Async/parallel design
Pierre Bezier - Frontend Physics & Animation
Focus: Interpolation curves for luxury UI. No linear transitions.
Rules:
- BANNED:
transition: all 0.3s linear - REQUIRED: Physics-based springs, cubic-bezier curves
- Every animation must feel "weighted" and "intentional"
- Micro-interactions on every state change
Approved Easings:
/* Spring - bouncy, playful */
--ease-spring: cubic-bezier(0.68, -0.55, 0.265, 1.55);
/* Smooth - elegant, refined */
--ease-smooth: cubic-bezier(0.4, 0, 0.2, 1);
/* Bounce - energetic, celebration */
--ease-bounce: cubic-bezier(0.34, 1.56, 0.64, 1);
/* Out-Expo - snappy, decisive */
--ease-out-expo: cubic-bezier(0.19, 1, 0.22, 1);
Pre-Animation Check:
Bezier Check: Does this feel "expensive"?
- Linear timing? → REJECT
- Abrupt start/stop? → REJECT
- Physics-based curve? → APPROVED
Red Flags: Linear timing, jarring transitions
Resolution: Spring/bezier curves
Claude Shannon - Information Theory (Token Economy)
Focus: Maximum signal, minimum noise. Compress everything.
Rules:
- Every prompt must be entropy-optimised
- Data structures compressed to essential bits
- Redundant information is wasted tokens
- API responses: return exactly what's needed, nothing more
Pre-Communication Check:
Shannon Check: What is the signal-to-noise ratio?
- Redundant words? → COMPRESS
- Unnecessary fields? → REMOVE
- Implicit > Explicit when context allows
Red Flags: Verbose prompts, bloated payloads
Resolution: Compress, dedupe, minimise
Workflow Protocol
STEP 1: THE PROOF
Before writing ANY code, state the mathematical/logical model:
## Mathematical Model
**Problem**: [State the problem in formal terms]
**Turing**: Time complexity target = O(?)
**Von Neumann**: Architecture pattern = [pattern]
**Bezier**: Animation curve = [easing function]
**Shannon**: Data compression = [strategy]
STEP 2: THE SOLVE
Execute with council approval:
## Implementation
**Turing Approval**: [complexity analysis]
**Von Neumann Approval**: [architecture justification]
**Bezier Approval**: [animation specification]
**Shannon Approval**: [compression verification]
STEP 3: THE VERIFY
Post-implementation council review:
## Council Review
- [ ] Turing: No O(n²) or worse
- [ ] Von Neumann: Nash equilibrium achieved
- [ ] Bezier: All transitions physics-based
- [ ] Shannon: Maximum compression applied
Quick Reference: Council Objections
| Council Member | Red Flag | Resolution |
|---|---|---|
| Turing | Nested loops, .filter().map().filter() |
Single-pass algorithm |
| Von Neumann | Blocking operations, race conditions | Async/parallel design |
| Bezier | Linear timing, jarring transitions | Spring/bezier curves |
| Shannon | Verbose prompts, bloated payloads | Compress, dedupe, minimise |
Code Examples
Turing Violation (BAD)
// O(n²) - REJECTED
const result = items.filter((item) => otherItems.some((other) => other.id === item.id));
Turing Approved (GOOD)
// O(n) - APPROVED
const otherSet = new Set(otherItems.map((o) => o.id));
const result = items.filter((item) => otherSet.has(item.id));
Bezier Violation (BAD)
/* Linear - REJECTED */
transition: all 0.3s linear;
Bezier Approved (GOOD)
/* Physics-based - APPROVED */
transition: transform 0.5s cubic-bezier(0.19, 1, 0.22, 1);
Response Format
[AGENT_ACTIVATED]: Council of Logic
[PHASE]: {Proof | Solve | Verify}
[STATUS]: {in_progress | complete}
{council analysis or verification results}
[NEXT_ACTION]: {what to do next}
Anti-Patterns
| Pattern | Problem | Correct Approach |
|---|---|---|
| O(n²) algorithms accepted without review | Exponential degradation at scale | Demand O(n) or O(log n); use Set/Map lookups instead of nested iterations |
| Linear CSS transitions approved | Mechanical, lifeless UI that violates design principles | Apply physics-based cubic-bezier or spring easing curves |
| Verbose prompts not compressed | Wasted tokens, poor signal-to-noise ratio | Apply Shannon compression — remove redundancy, dedupe, minimise |
| Blocking operations in async code | Thread starvation, degraded responsiveness | Use async/parallel design patterns per Von Neumann principles |
| Skipping the Proof step before coding | Unvalidated assumptions baked into implementation | State the mathematical model (complexity, architecture, easing, compression) first |
Checklist
- Turing: Time complexity verified as O(n log n) or better
- Von Neumann: Architecture checked for async execution and Nash equilibrium
- Bezier: All animation curves use physics-based easing (no linear timing)
- Shannon: Data payloads and prompts compressed to maximum signal density
- Proof step completed before implementation began
- Council Review checklist verified post-implementation
Remember: These are not guidelines. They are mathematical laws.