# How a common-reference comparison works

A common reference lets two instruments be compared on one scale. The arithmetic is simple; the meaning of the inputs deserves just as much attention.

## Start with units, not just numbers

Suppose the supplied teaching values are 0.50 reference units per source unit and 6.00 reference units per target unit. Begin with a source amount of 120.00.

Multiplying 120.00 by 0.50 expresses the amount as 60.00 reference units. Dividing 60.00 by 6.00 expresses those same reference units as 10.00 target units.

```text
target amount = source amount × source reference value ÷ target reference value
120.00 × 0.50 ÷ 6.00 = 10.00
```

These are illustrative reference inputs. Use an authorized publication for operational values. The [published GHS–USD example](?page=seed-content/simulations/ghs-usd-example) gives the same calculation with instrument labels and dimensional reasoning.

## Separate three questions

| Question | What answers it |
| --- | --- |
| What reference value should one unit have? | A stated valuation methodology and its observations |
| What target amount follows from the supplied values? | The calculation and numeric policy |
| Can someone exchange or settle that amount? | An operating service with its own terms and capacity |

A calculation answers the middle question. The [TVX Formula reference](?page=seed-content/tvx-formula/1.0.0) and [oracle reference](?page=seed-content/oracle-system/index) explain the surrounding evidence requirements.

## Try a controlled change

Open the [learning lab](?page=lab). Keep the source amount and source reference value fixed, then change the target reference value from 6.00 to 8.00. The output changes from 10.00 to 7.50 target units.

This happens because each target unit now represents more of the shared reference. Try doubling the source amount next. Record which inputs changed before comparing the two results.

## Understand rounding

The SDK calculates with decimal strings and applies the selected rounding rule at the final output. Half up rounds an exact tie upward. Half even rounds an exact tie to an even final digit. Down discards the remaining fractional part for these nonnegative inputs.

For example, 1 × 1 ÷ 8 is exactly 0.125. At two decimal places, half up produces 0.13 while half even and down produce 0.12. A displayed result is not a promise that the reverse calculation will recover every original digit.

## Keep the context with the result

Record the source amount, both reference values, common unit, methodology, observation times, and rounding policy. The lab can export the arithmetic inputs and exact rational result. The export records whether inputs came from an illustrative preset or were entered by the user; source verification remains explicit.

Continue with the [learning lab](?page=lab) or the [evidence review guide](?page=seed-content/guides/review-evidence).


## Source references

The [SDK API contracts](?page=developer/toolkit-contracts) define numeric inputs, output precision, rounding, and error behavior. The [implementation provenance](?page=developer/toolkit-provenance) records the origin and scope of the software. These are project implementation sources; synthetic arithmetic is not independent validation of a valuation methodology.