Double Check AI Math Manually

Double-Check AI Math Manually (Deterministic Verification) (AI Skill)

Overview

Because Large Language Models are probabilistic language generators rather than algebraic engines, they can generate an impeccable financial breakdown where the individual line items look flawless, but the sum at the bottom is subtly wrong by $150 or 2.5%.

The 3-Tier Math Verification Ladder provides a safety net to ensure that no AI-generated financial quote, invoice, equity cap table, or budget is delivered without deterministic proof of accuracy.

The 3-Tier Math Verification Ladder

┌─────────────────────────────────────────────────────────────┐
│                 3-Tier Math Safety Ladder                   │
│                                                             │
│  [ TIER 1: AI Formula Derivation ]                          │
│  • Define variables, logic, and standard formulas           │
│                           │                                 │
│                           ▼                                 │
│  [ TIER 2: Code / Python Execution ]                        │
│  • Force the AI to execute Python math programmatically     │
│                           │                                 │
│                           ▼                                 │
│  [ TIER 3: Deterministic Human Check ]                      │
│  • Paste values into Excel, Google Sheets, or a calculator  │
│  • 100% Guaranteed Mathematical Integrity                   │
└─────────────────────────────────────────────────────────────┘

High-Risk Math Scenarios Requiring Tier-3 Verification

1. Client Invoices & Estimates: Multi-line hourly rates with discounts and tax percentages.
2. Cap Tables & Equity Dilution: Post-money SAFE notes, option pools, and vesting calculations.
3. Loan & Mortgage Amortization: Compound interest formulas ($M = P \frac{r(1+r)^n}{(1+r)^n - 1}$).
4. Tax Withholdings & Deductions: Progressive bracket brackets and FICA thresholds.

Master Deterministic Math Prompt Templates

Pattern 1: The Spreadsheet Formula Generator (Safest Approach)

Instead of asking the AI to calculate the total, ask it for the exact Excel/Google Sheets formula:

I have the following billing items: [LIST ITEMS, HOURS, & RATES].

Do NOT just calculate the total yourself.
Provide:
1. A Markdown table of the items.
2. The exact **Excel / Google Sheets formulas** (e.g. `=SUM(C2:C10)`, `=B2*C2*(1-D2)`) so I can paste this directly into a spreadsheet to calculate the verified numbers.

Pattern 2: The Multi-Check Python Verification Block

Calculate [FINANCIAL / COMPOUND MATH PROBLEM].

Output Requirements:
1. Show the mathematical formula with named variables.
2. Provide a standalone Python 3 script using `decimal.Decimal` (not floating point) to compute the exact figures.
3. Print intermediate line items and the final sum.

Real-World Case Study

Scenario: Freelance Project Quote with Retainer Discount

Unverified AI Output (Subtle Arithmetic Drift)

Item A: 40 hrs @ $125/hr = $5,000
Item B: 15 hrs @ $150/hr = $2,250
Item C: Server Setup Flat Fee = $800
Subtotal = $8,050
10% Early Bird Discount = $805
Total Due: $7,145

⚠️ Look closely: $8,050 - $805 = $7,245, NOT $7,145. An unverified quote would lose you $100 on the invoice!

The Excel-Verified Output

| Item | Hours | Rate | Total Formula |
| :--- | :--- | :--- | :--- |
| **Development** | 40 | $125.00 | `=B2*C2` ($5,000.00) |
| **UX Review** | 15 | $150.00 | `=B3*C3` ($2,250.00) |
| **Infrastructure**| 1 | $800.00 | `=B4*C4` ($800.00) |
| **Subtotal** | | | `=SUM(D2:D4)` ($8,050.00) |
| **10% Discount** | | | `=D5*0.10` ($805.00) |
| **Final Total** | | | `=D5-D6` (**$7,245.00**) |

Core Rule of Financial Safety

"Never sign or send an AI calculation without letting a deterministic engine (Python, Excel, Calculator) sum the final line."