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-luxury instead)

• 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.