The ternary foundation

Phi counts in threes, with exactly three digit words:

That is the entire inventory of digits. Everything larger is built from these plus the scale units, countable nouns that name groups:

The scale units are nouns, not particles: they are groups you can have one or two of, the way English has a dozen. Because they are nouns, the modifier-first principle already tells you how numbers are built: the digit stands before the unit it counts, like every modifier before every thing.

These seven forms are the complete canonical inventory. Exact numerals use ta or wi before each named scale, omit scales whose coefficient is zero, and end with ta or wi when units remain. With rei as the highest scale, canonical exact Phi numerals run from mu (zero) through wi rei wi lau wi phoi wi shao wi (242). Values above 242 have no internal Phi numeral; an exact larger value remains in source material outside the Phi passage, while Phi can state the magnitude its discussion needs.

Why base three? Three is within the small range adults can commonly recognize without serial counting. Nine and twenty-seven are not directly visible as exact quantities, but regular arrangements of triads and triads of triads can make their grouping easier to inspect. That grouping remains a learned skill. Phi accepts the learning cost in exchange for a small digit inventory and conspicuous large exact forms; "human scale" is the project's value judgment, not a scientific boundary in perception. The design argument and its evidence limits are in documents/design/psychological_violence_of_measurement.md.

Ordinary competence does not require rapid conversion of arbitrary decimal numbers. A practical sequence starts with the forms through eight, continues through exact forms to twenty-six, and reaches the larger scales when conversation requires them. Extended exact counting and spoken arithmetic are later skills, not tests of whether someone can speak Phi.