Beyond Certification — Building Real Software with 128 Monomers
The previous article showed PCD as a fortress. But real software isn't pure. Games, simulations, AI pipelines — and the power of open circuits.
Games, Simulations, AI Pipelines, and the Power of Open Circuits
The previous article showed PCD as a fortress: certified monomers, exact arithmetic, Φc= 1, impenetrable correctness. That's the pure vision.
But real software isn't pure. Games need graphics. AI pipelines need network calls. Simulations need floating-point math. Trading systems need websockets. And that's exactly what the extended monomers are for.
The Spectrum of Certification
PCD doesn't force you into a binary choice between "fully certified" and "not certified at all." It gives you a spectrum:
Φ_c = 1.0 — Pure. All 64 core monomers. Mathematical proof.
Φ_c = OPEN 87% — Mixed. Core + some extended. 87% proven, 13% contracted.
Φ_c = OPEN 50% — Balanced. Half proven, half contracted.
Φ_c = OPEN 12% — Mostly external. Heavy I/O, network, graphics.
Φ_c = CONTRACT — All extended. No proof, but bounded contracts.The compiler tells you exactly where you stand. No guessing. No "it probably works."
Example 1: A Multiplayer Game Score System
A game needs graphics (extended monomers), but the scoring logic can be certified:
PC game_scores {
// CERTIFIED CORE — exact, proven
domain score: Range [0, 999999];
domain level: Range [1, 100];
domain combo: Range [0, 50];
fn calculate_score(base_points, current_level, combo_count) {
let level_bonus = base_points * current_level / 10;
let combo_bonus = base_points * combo_count * combo_count / 100;
return base_points + level_bonus + combo_bonus;
}
fn is_high_score(new_score, current_high) {
if (new_score > current_high) { return 1; }
return 0;
}
// EXTENDED — interacts with outside world
// Graphics: framebuffer for rendering
// Network: connection to multiplayer server
// Interop: decode server messages
let player_score = calculate_score(500, 7, 3);
OUTPUT player_score;
return player_score;
}Result: BRIK-64 OPEN 78%— the score logic is certified, the rendering and networking operate under contract. You KNOW which parts are proven and which aren't.
Example 2: AI Pipeline with LLM Integration
An AI agent that validates its own outputs before sending them:
PC ai_pipeline {
// CERTIFIED — the guardrails
domain confidence: Range [0, 100];
domain token_count: Range [0, 32000];
domain cost_cents: Range [0, 100000];
fn validate_output(conf, tokens, max_tokens, max_cost) {
if (conf < 20) { return 0; }
if (tokens > max_tokens) { return 0; }
let estimated_cost = (tokens * 3) / 1000;
if (estimated_cost > max_cost) { return 0; }
return 1;
}
fn calculate_cost(input_tokens, output_tokens) {
// GPT-4 pricing: $30/1M input, $60/1M output (in microcents)
let input_cost = (input_tokens * 30) / 1000;
let output_cost = (output_tokens * 60) / 1000;
return input_cost + output_cost;
}
// EXTENDED — the I/O
// Network: HTTP request to LLM API
// Interop: JSON encode/decode
// String: manipulation for prompts
let cost = calculate_cost(2000, 500);
let allowed = validate_output(85, 500, 4000, 1000);
OUTPUT allowed;
return allowed;
}The cost calculation and validation are CERTIFIED (Φc= 1). The HTTP call to the LLM is CONTRACT. You can't bypass the budget check — it's a closed circuit.
Example 3: Physics Simulation
Simulating gravity with fixed-point arithmetic for deterministic results:
PC gravity_sim {
// Scale: x 1000 for 3 decimal places
domain position: Range [0, 10000000];
domain velocity: Range [0 - 50000, 50000];
domain gravity: Range [9800, 9810];
fn step(pos, vel, g, dt) {
let new_vel = vel + (g * dt) / 1000;
let new_pos = pos + (new_vel * dt) / 1000;
return new_pos;
}
fn simulate(initial_height, steps) {
let pos = initial_height;
let vel = 0;
loop(steps) as i {
let pos = step(pos, vel, 9806, 16);
let vel = vel + (9806 * 16) / 1000;
}
return pos;
}
let final_pos = simulate(5000000, 60);
OUTPUT final_pos;
return final_pos;
}9806 = 9.806 m/s² (gravity × 1000). 16 = 16ms timestep. Every client, every machine, every runtime produces THE SAME simulation. No floating-point divergence. No desync in multiplayer. BRIK-64 CERTIFIED Φc = 1.
Example 4: Trading Bot Risk Engine
The core risk logic is untouchable. The market data flows through extended monomers:
PC risk_engine {
domain position_size: Range [0, 1000000000];
domain price_bps: Range [1, 100000000];
domain risk_pct_bps: Range [0, 10000];
fn max_position(balance, risk_bps, stop_loss_bps) {
if (stop_loss_bps < 1) { return 0; }
let risk_amount = (balance * risk_bps) / 10000;
return (risk_amount * 10000) / stop_loss_bps;
}
fn should_trade(current_drawdown, max_drawdown, open_positions, max_positions) {
if (current_drawdown > max_drawdown) { return 0; }
if (open_positions > max_positions) { return 0; }
return 1;
}
fn calculate_pnl(entry_price, exit_price, size) {
return ((exit_price - entry_price) * size) / entry_price;
}
let max_pos = max_position(100000000, 200, 500);
let can_trade = should_trade(150, 500, 3, 10);
OUTPUT can_trade;
return can_trade;
}The risk engine is a closed circuit. Max position, drawdown limits, and PnL calculations are exact integer arithmetic. The WebSocket feed and order execution use extended monomers. BRIK-64 OPEN 72%.
Example 5: Procedural World Generator
PC world_gen {
domain seed: Range [0, 2147483647];
domain tile_type: Range [0, 7];
domain height: Range [0, 255];
fn pseudo_random(current_seed) {
let next = (current_seed * 1103515245 + 12345);
let masked = next - ((next / 2147483648) * 2147483648);
return masked;
}
fn tile_at(world_seed, x, y) {
let combined = world_seed + x * 31 + y * 37;
let rand = pseudo_random(combined);
return rand - ((rand / 8) * 8);
}
fn height_at(world_seed, x, y) {
let combined = world_seed + x * 17 + y * 23;
let rand = pseudo_random(combined);
return rand - ((rand / 256) * 256);
}
let tile = tile_at(42, 10, 20);
let h = height_at(42, 10, 20);
OUTPUT tile;
return tile;
}Fully certified (Φc = 1). Same seed, same world, everywhere. Add graphics extended monomers for rendering = BRIK-64 OPEN 65%. The generation logic is proven. The rendering is contracted.
You Choose the Mix
Use Case Core % Extended % Badge
────────────────────── ─────── ────────── ─────────────────────
Banking / Finance 100% 0% Φ_c = 1 CERTIFIED
AI Safety Policy 95% 5% OPEN 95%
Game Score + Render 70% 30% OPEN 70%
Physics Simulation 100% 0% Φ_c = 1 CERTIFIED
Trading Bot 72% 28% OPEN 72%
AI + LLM Pipeline 60% 40% OPEN 60%
World Gen + Graphics 65% 35% OPEN 65%
Full Network App 30% 70% OPEN 30%The point isn't "everything must be certified." The point is: you always know exactly how much is proven.
Traditional software gives you 0% certainty. PCD gives you a number.
The Extended Monomers: Your Peripherals
The 64 extended monomers cover 8 families: floating-point math, transcendentals, networking, graphics, audio, filesystem, concurrency, and foreign interop. Each family has CONTRACT certification because the outside world is inherently non-deterministic.
They're CONTRACT because the outside world is unpredictable. A network packet can be lost. A file can be deleted mid-read. A GPU can render differently. That's physics, not a bug.
But the logic AROUND them — the validation, the scoring, the risk checks, the policy decisions — that can be certified. And that's where bugs actually kill.
Getting Started with Mixed Circuits
# Install
curl -L https://brik64.dev/install | sh
# Write a mixed circuit
brikc run my_game.pcd # runs the certified parts via BIR
brikc build my_game.pcd -t js # compiles everything to JavaScript
brikc check my_game.pcd # shows: "BRIK-64 OPEN 72%"The compiler shows you exactly which functions are certified and which operate under contract. No surprises.
PCD with all the full monomer catalog isn't just for banking and safety-critical systems. It's for anything where you want measurable certainty alongside real-world I/O. Games. Simulations. AI pipelines. Trading bots. IoT. Robotics.
The question isn't "is it fully certified?" The question is: "how much of it is proven, and is that enough for my use case?"
PCD always has the answer. Traditional software never does.