FOUNDER FINANCE ARCADE

1. THE BASELINE IS CALIBRATED, NOT ASSUMED

Every free constant is solved so that at the current knob positions the model reproduces today's reported numbers exactly — customers, ARPU, churn, gross margin, burn. If the baseline did not reproduce the present, nothing it said about the future would be worth reading.

2. EVERY RESPONSE CURVE BENDS

• Paid acquisition follows a saturating response, q = A(1 - e^(-S/θ)). Average CAC is what you have paid; marginal CAC is what the next customer costs, and it is always higher.
• Demand and closing capacity are complements, combined through a CES aggregator with an elasticity of substitution of 0.2. Reps with no leads do nothing; leads with no reps do nothing.
• Price uses constant elasticity: conversion moves by (1+Δp)^-1.1 and churn by (1+Δp)^0.6. That produces a genuine interior optimum rather than a free lunch.
• Retention spend and cost-of-serve decay exponentially toward a floor and a ceiling. You cannot buy zero churn or 100% margin.
• Headcount ramps over three months, cuts land immediately and carry severance, and an engineering team below the minimum viable size makes churn rise convexly.

3. SCORED THE WAY A BUDGET OFFICE SCORES A MEASURE

The static cost is the direct incremental spend with no behavioural response. The dynamic cost credits back the gross profit that the measure itself induces. The gap between them is the entire argument for spending money, expressed as a number.

4. THE OPTIMISER EQUALISES MARGINAL RETURN

Auto-tune hill-climbs on the full simulator, repeatedly spending the next dollar wherever it buys the most objective, subject to your budget, your runway floor and your growth floor. It stops when no affordable single step improves the result — the discrete version of equalising marginal return per dollar across every armed knob. The shadow price reports what one more $1,000/month of budget would have been worth.

5. THE FAN IS THE HONEST PART

A central projection is not a promise. The P10–P90 band comes from a seeded Monte Carlo that perturbs what a founder genuinely cannot observe: channel ceiling, price elasticity, quota attainment, churn, referral rate, ARPU realisation and cost overruns. The seed is fixed, so the same knobs always produce the same fan.

6. THE PIPELINE DECIDES NOTHING ON ITS OWN

Language models propose; they never enact. Each proposed move is checked by deterministic arithmetic for range, budget, cash and runway, and returned as supported, flagged_for_human or refuted — the same vocabulary the claim auditor uses. A move that spends money the company does not hold is refuted no matter how confidently it was argued.