Qwen3-1.7B · the 60 workspace states H[country, case] (5 relational operators × 12 countries), read live from the model. Three views of one claim: the operator is a manipulable direction that factorizes from the operand.
Many languages mark a noun's role in a sentence by changing its form, not its meaning. The noun (its stem) stays; a case-ending or particle — the role marker — says what job it is doing. That is declension.
| stem (the thing) | role marker | reads as | |
|---|---|---|---|
| Latin | ros- (rose) | -a / -am / -ae | rose as subject / object / possessor |
| German | der Hund (the dog) | der → den / dem | dog as subject / object / recipient |
| Japanese | inu (dog) | particle は / を / に | dog as topic / object / goal |
Two more terms this work borrows: syncretism — two roles that happen to share one form (Latin -ae is both genitive and dative singular; here language and demonym both surface as “Italian”). And fusion — the ending isn't cleanly detachable from the stem; they blend phonologically.
The finding: an LLM does the same. The country is the stem (operand); the relation — currency-of, capital-of, language-of… — is the case (operator): an addable direction that factorizes from the country, with its own syncretism and fusion. Below, watch it happen.
Colors encode the operator (case); identity is also carried by position and direct labels. Numbers are the measured logit differences from op_core.measure_swaps / pure_desinence. Source: scripts/op_geometry_dump.py.