Opinion is not part of the calculation.

PLANEJA ENGINE · 02/03

Metrics arrive scattered across tools. Here, acquisition, ad return, customer value and media cost enter the same calculation. Each resulting number opens to show how it was calculated.

See the five steps Back to the Planeja Engine ↖ MATHEMATICAL ENGINE WHAT IT CALCULATES Metrics from different places, in the same calculation. R$ 18,900 + 150 customers THE CALCULATION IN VIEW Each number opens to show how it was calculated. 18,900 ÷ 150 = 126 · sources open FORMULA media ÷ customers TERMS investment + customers SOURCES media + orders RESULT R$ 126 PER CUSTOMER CONFIDENCE INTERVAL A projection without a margin of error is a guess that looks certain. comparable history WHAT CHANGES IF The variable that moves the result most appears first. cost per thousand +23% · conversion -22% WHEN IT CANNOT If a source is missing, it says so. organic without origin · excluded from the calculation

A number without the calculation behind it is an opinion in a pretty font.

01 Analysis and research Researches inside and outside. 02 Mathematical engine Combines metrics from every source. 03 Routes and scenarios Creates reviewable plans.

AI SHOULD NOT BE DOING EVERYTHING ALONE

Consider a clear example of the problem of letting AI do everything on its own

Customer acquisition cost (CAC), return on ad spend (ROAS), contribution margin, customer lifetime value (LTV) and break-even point come from combining sales, media, cost and cash, rather than a single spreadsheet.

PROBLEM Is basic arithmetic error acceptable in your personal and professional life?

Of course not. However, Claude 4.5 Sonnet, Claude Opus 4.1, ChatGPT 5.1, Grok 4 and Copilot ALL fail in a simple calculation as:

Question 2347 × 8912 = ?

See Claude 4.5 Sonnet miss every attempt:

ATTEMPT 01 20,915,264 PLAUSIBLE ANSWER ATTEMPT 02 20,921,264 SAME QUESTION, DIFFERENT NUMBER ATTEMPT 03 20,916,644 NO EXECUTION TRAIL

AI is a probabilistic model: guess instead of calculating. Even the most advanced AI models make critical errors in arithmetic, dates, data analysis and logic.

THE DIFFERENCE IS IN THE ARCHITECTURE

Understanding the question is not the same as executing the calculation.

The model identifies intent. The Mathematical Engine provides precision.

THE SOLUTION In SOCEO, the AI model orchestrates, the tool executes

The AI model identifies when a calculation is required and calls our Virtual Machine tool. The tool downloads a Python arithmetic library, performs the calculation and returns the 100% accurate result. The AI model only communicates the response; the tool ensures accuracy every time.

01 AI model identifies the need 02 Tool executes in Python 03 Result 100% Accurate VIRTUAL MACHINE · PYTHON 2347 FIRST FACTOR × 8912 SECOND FACTOR = 20,916,464 ✓ EXACT RESULT 2347 × 8912 = 20,916,464

The tool is responsible for accuracy, not the AI model. This architectural choice makes all the difference in reliability and ROI.

02 · THE CALCULATION IN PLAIN VIEW

Each number opens and shows how it was done.

The formula, input values and source of each. Without these, a number is just an opinion in a pretty font.

The July CAC breaks down into media investment divided by new customers. The period from 1 to 31 July applies to both terms of the division. Organic referrals are excluded because their origin is not recorded. 02 REVENUE ORDERS COSTS FINANCE PERIOD CLOSING FORMULA (R − C) ÷ R TERMS SOURCES OUTPUT 02 · THE CALCULATION IN VIEW

03 · CONFIDENCE INTERVAL

A projection without a margin of error is a guess disguised as certainty.

The band widens as the scenario moves away from what the business has already done. Predicting routine activity is safer than predicting something unprecedented.

The projection is an interval, with a lower and upper bound, rather than a single value. Comparable historical volatility defines the interval’s width. Without similar history, the number is marked as an estimate, rather than a fact. 03 COMPARABLE HISTORY CENTRAL PROJECTION UPPER BOUND LOWER BOUND 03 · CONFIDENCE INTERVAL

04 · WHAT CHANGES IF

The variable that most moves the result appears first.

Of ten things you can move, three explain almost the full effect. Planeja orders by impact, not by ease.

Sensitivity measures how much the result changes for each point of variation. Each lever’s effort appears beside its expected return. A lever with no source to measure the gain is excluded from the ranking. 04 PRICE GREATEST IMPACT DISCOUNT MEDIUM IMPACT CHANNEL LOWER IMPACT CHANGED SCENARIO 04 · WHAT CHANGES IF

05 · WHEN IT CANNOT

If a source is missing, it says so.

Without a recorded return, there is no realized margin. The engine shows the gap instead of filling it by assumption.

The calculation is marked as partial and names the term lacking a source. No plausible number replaces data that nobody supplied. The calculation stops where a term is missing and states where it stopped. 05 KNOWN REVENUE MISSING RETURN FORMULA DECISION BLOCKED 05 · WHEN IT CANNOT PROCEED

WHY A SEPARATE ENGINE

A language model estimates. A calculation engine calculates. It sounds like a technical detail, but it determines whether you can take the number into a meeting. WITH GENERIC AI ALONE The number is predicted, not calculated The model chooses the most likely digit. Close to correct is not correct. Repeating the question changes the answer Without a fixed calculation, the same question on two days returns two values. You cannot audit it You receive the result, without the operation that produced it. It fills what is missing When a data point is missing, it fills it with what seems reasonable. WITH THE MATHEMATICAL ENGINE The calculation actually runs Stated formula, values read from the source, deterministic result. Same question, same number Twice today or a month from now: the same data gives the same result. Every number can be opened Formula, terms, sources and period appear with the result. Without a source, it stops The gap is declared instead of becoming a plausible number.

AI remains part of the process: it understands the question and explains the answer. It does not perform the arithmetic.

AN OPEN NUMBER

This is how a number explains itself. In your account, values and sources come from your business. MONTHLY CAC R$ 126.00 +17% against the previous month

CAC = ad spend ÷ new customers

MEDIA INVESTMENT R$ 18,900 Meta Ads · Google Ads NEW CUSTOMERS 150 Orders · first purchase PERIOD July 1 to 31 monthly close

LIKELY CAUSE Cost per thousand impressions (CPM) rose 23% and conversion fell 22% among the new audience.

WHAT IS MISSING Organic referrals are not marked at the source, so they do not enter this calculation.

THE CATALOG OF CALCULATIONS

Each calculation combines sources from different tools. That is why it cannot come from one spreadsheet: its terms are not all in the same place. CALCULATION HOW IT IS CALCULATED WHERE ITS TERMS COME FROM WHAT IT ANSWERS Contribution margin (revenue − variable cost) ÷ revenue orders, costs, gateway fees What remains from each sale before fixed costs. CAC ad spend ÷ new customers Meta Ads, Google Ads, orders The cost of acquiring another customer. LTV average order value × frequency × lifetime orders, subscriptions A customer's value before they leave. LTV ÷ CAC LTV ÷ CAC the two calculations above Whether acquisition pays off, and in how many purchases. Break-even point fixed cost ÷ unit contribution margin costs, orders, payroll The volume at which the month stops making a loss. ROAS by channel attributed revenue ÷ investment advertising, orders, attribution window Which channel returns more per real invested. Acquisition payback CAC ÷ monthly margin per customer advertising, orders, costs How many months it takes a customer to return their acquisition cost. Price elasticity regression over past variations price history, volume What happens to volume when the price changes.

None of them accept estimated term without marking that it is estimated.

SOURCES THAT FEED THE CALCULATIONS

The terms of a calculation live in different tools. That is why margin stays in the spreadsheet: half its numbers are elsewhere. SH Shopify products · orders · customers HT Hotmart products · sales · students ST Stripe payments · customers · subscriptions MP Mercado Pago payments · preferences · orders MA Meta Ads campaigns · ad sets · ads GA Google Ads campaigns · ads · metrics CA Conta Azul ledger entries · accounts · sales OM Omie customers · orders · ledger entries EX Excel workbooks · worksheets · tables GS Google Sheets spreadsheets · tabs · rows

If one is missing, the calculation is marked as partial and never completed by assumption.

See connector catalog

THE REPERTORY OF THIS CHAPTER

Calculations that support the decision. Each combines different sources rather than relying on one spreadsheet. Contribution margin (revenue − variable costs) ÷ revenue shows what remains from each sale before fixed costs. CAC investment ÷ new customers combines advertising with first-purchase orders. LTV order value × frequency × lifetime is compared with CAC to see whether acquisition pays off. Break-even point fixed costs ÷ unit contribution margin shows the volume at which the month stops making a loss. ROAS attributed revenue ÷ investment evaluates each channel with the attribution window visible. Price elasticity regression over historical data estimates how volume responds when prices change.

Without a source for one term, the calculation is explicitly marked as partial.

WHERE THIS HAPPENS

This chapter is part of the second engine. 01 Conecta

It brings the metrics spread across each tool and maintains visible source, access and gaps.

→ 02 Planeja

Absorb these metrics, calculate on top of the set and return revisable routes.

→ 03 Age

Executes the approved route with an owner, deadline and human approval when needed.

→ 04 Controla

Tracks the result, anticipates deviations and returns new context.

↺

The result returns to the Conecta Engine as new metric, decision and evidence.

NEXT CHAPTER

The calculation is complete. Now it becomes a course of action.

A number alone changes nothing. It must become a step with an owner and deadline.

Go to Routes and scenarios Talk to the team