# Documentation of Algorithms in AI Berkshire's `financial_rigor.py`: A Complete Technical Guide

> Explore algorithms in financial_rigor.py within the xbtlin/ai-berkshire repository. This guide details exact arithmetic for market-cap, valuation, fraud detection, and projections.

- Repository: [Xbt Lin/ai-berkshire](https://github.com/xbtlin/ai-berkshire)
- Tags: deep-dive
- Published: 2026-07-04

---

**The [`financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/financial_rigor.py) module in the `xbtlin/ai-berkshire` repository implements six production-grade financial algorithms built on Python's `decimal` module, providing exact arithmetic for market-cap verification, valuation metrics calculation, cross-source validation, Benford's law fraud detection, exact arithmetic evaluation, and multi-scenario valuation projection.**

The AI Berkshire project provides a self-contained "Financial Rigor Toolkit" within [`tools/financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/tools/financial_rigor.py) designed to eliminate floating-point drift in financial calculations. This module serves as the computational backbone for AI-driven investment research, ensuring reproducible, audit-ready results through high-precision decimal arithmetic and standardized validation patterns.

## The Exact Decimal Foundation

Before examining the algorithms, understand the underlying infrastructure. The module establishes a high-precision `Decimal` context at line 28 (`_CTX`) configured with 28-digit precision and `ROUND_HALF_EVEN` rounding. The `exact()` helper function (lines 28-38) converts any input—including floats, strings, or scientific notation—to `Decimal` without precision loss, serving as the mandatory gateway for all numeric operations in the toolkit.

## Six Core Algorithms in [`financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/financial_rigor.py)

### Market-Cap Verification (`verify_market_cap`)

Located at lines 61-90, this algorithm validates whether `price × shares` matches a reported market-cap value. It uses `exact()` to create `Decimal` values, multiplies them via `_CTX.multiply`, computes percentage deviation, and triggers color-coded warnings at 5% and 1% thresholds. The function returns a boolean indicating whether the calculated cap falls within acceptable tolerance of the reported value.

### Valuation Metrics Verification (`verify_valuation`)

Implemented at lines 98-160, this function derives PE, PB, ROE, P/FCF, dividend yield, and PS ratios from raw inputs. It computes ratios using `_CTX.divide` and scales percentages by 100 where required, returning results in a dictionary for downstream programmatic consumption. Each metric calculates only when its corresponding argument is supplied, making the function flexible for partial data scenarios.

### Cross-Source Data Validation (`cross_validate`)

Found at lines 67-104, this algorithm aggregates numeric fields from multiple data sources, compares each to a median reference, and flags outliers beyond a configurable tolerance (default 2%). It converts all source values via `exact()`, computes the median (lines 78-81), and returns a consensus value alongside a boolean consistency flag indicating overall data agreement.

### Benford's Law Fraud Detection (`benford_check`)

At lines 11-57, this statistical sanity-check detects possible data fabrication by comparing leading-digit distributions against expected Benford probabilities (`_BENFORD`). It requires at least 50 samples, computes observed frequencies, Mean Absolute Deviation (MAD), and Chi-square statistics, categorizing conformity into four levels to flag potentially manipulated datasets.

### Exact Arithmetic Calculator (`exact_calc`)

Located at lines 88-110, this safely evaluates expressions like `"510 * 9.11e9"` using exact decimal arithmetic rather than native floating-point. It whitelists safe characters, evaluates with an empty `__builtins__` namespace, converts results via `exact()`, and displays both formatted and raw decimal values for audit trails.

### Three-Scenario Valuation Modeling (`three_scenario_valuation`)

Implemented at lines 20-58, this projects target share prices under optimistic, neutral, and pessimistic growth assumptions. It iteratively compounds EPS using `_CTX.multiply` and `_CTX.add` over a user-defined forecast horizon, multiplies by target PE multiples, and calculates percentage change versus current price. The function prints a formatted table and returns `None`.

## Common Design Patterns in [`financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/financial_rigor.py)

All algorithms share four architectural patterns according to the source:

1. **Input sanitization** – Each public function receives primitive types (floats, strings, JSON) and immediately normalizes them using `exact()`.

2. **Exact arithmetic** – All mathematical operations are performed via the global `_CTX` context, guaranteeing reproducible results.

3. **Human-readable reporting** – The `fmt_number()` helper converts large numbers into culturally appropriate units (e.g., `"亿"` for Chinese-style reporting) before printing.

4. **Programmatic returns** – Besides printing, functions return plain Python structures (dicts, bools, floats) for downstream consumption.

## Practical Usage Examples

Below are practical invocations of the [`financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/financial_rigor.py) algorithms. All examples assume the repository root is on `PYTHONPATH`.

```python
from tools import financial_rigor as fr

# Market-cap verification (returns bool)

ok = fr.verify_market_cap(
    price=510, 
    shares=9.11e9,
    reported_cap=4.65e12, 
    currency="HKD"
)
print("Cap OK:", ok)

# Valuation ratios (returns dict)

ratios = fr.verify_valuation(
    price=510, 
    eps=23.5,
    bvps=120, 
    fcf_per_share=18,
    dividend=2.4
)
print(ratios)

# Cross-validation of revenue figures

consensus = fr.cross_validate(
    field_name="Revenue",
    source_values={
        "AnnualReport": 7518, 
        "Yahoo": 7500, 
        "StockAnalysis": 7520
    },
    unit="亿", 
    tolerance_pct=2.0
)
print(consensus)

# Benford's law sanity check

benford = fr.benford_check([
    1234, 2345, 3456, 4567, 5678,
    6789, 7890, 8901, 9012, 1023
] * 6)
print(benford)

# Exact arithmetic calculator

result = fr.exact_calc("510 * 9.11e9")
print("Exact result:", result)

# Three-scenario valuation (prints table, returns None)

fr.three_scenario_valuation(
    current_price=510, 
    current_eps=23.5, 
    shares_billion=9.11,
    growth_optimistic=0.15, 
    growth_neutral=0.08, 
    growth_pessimistic=0.0,
    pe_optimistic=25, 
    pe_neutral=20, 
    pe_pessimistic=15,
    years=3, 
    currency="HKD"
)

```

## Summary

- **[`tools/financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/tools/financial_rigor.py) implements six exact-decimal algorithms** for financial analysis in the AI Berkshire repository.
- **All calculations use Python's `decimal` module** with 28-digit precision and `ROUND_HALF_EVEN` rounding to prevent floating-point errors.
- **Key functions include `verify_market_cap`, `verify_valuation`, `cross_validate`, `benford_check`, `exact_calc`, and `three_scenario_valuation`.**
- **The toolkit follows consistent architectural patterns**: input sanitization via `exact()`, exact arithmetic via `_CTX`, formatted output via `fmt_number()`, and structured returns for programmatic use.

## Frequently Asked Questions

### What precision does [`financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/financial_rigor.py) use for calculations?

The module initializes a global `_CTX` context with 28-digit precision and `ROUND_HALF_EVEN` rounding at line 28. All numeric operations route through this context using the `exact()` helper function, ensuring no floating-point drift occurs in financial calculations.

### How does the Benford's Law check detect data fabrication?

The `benford_check` function compares the leading-digit distribution of a dataset against theoretical Benford probabilities. It computes Mean Absolute Deviation and Chi-square statistics, requiring at least 50 samples, and categorizes results into four conformity levels to flag potentially manipulated data.

### Can I use [`financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/financial_rigor.py) for real-time market data validation?

Yes. The `cross_validate` function accepts multiple data source values (e.g., from different APIs), computes a median consensus, and flags outliers beyond a configurable tolerance (default 2%). This makes it suitable for real-time validation of streaming financial data.

### Where is the exact decimal arithmetic implemented in the source code?

The foundation resides in lines 28-38 of [`tools/financial_rigor.py`](https://github.com/xbtlin/ai-berkshire/blob/main/tools/financial_rigor.py), where the `_CTX` context is defined. Individual algorithms like `verify_market_cap` (lines 61-90) and `verify_valuation` (lines 98-160) consume this infrastructure via the `exact()` function and `_CTX` operations.