A root cannot keep two breaths in a row. In Greek and Sanskrit — twice over, and on their own — the first one gives way. That is why the Buddha’s name begins with a soft B.
Say p, t, k with a little puff of air after them and you get the aspirated stops the ancients wrote φ θ χ and the Indians wrote भ ध घ — a stop carrying a breath. Two languages, far apart, made the same quiet rule about that breath: a word may not keep two of them in successive syllables — so the front one is dropped. It is the most elegant little law in historical linguistics, and the strange part is that Greek and Sanskrit arrived at it separately. Here it is, made runnable: a single Greek word that switches it on and off, an engine you can drive, and one inherited root that splits three ways.
Each row is a real form whose first breath has stepped aside, leaving the second standing. Touch one to see the underlying shape and which breath yielded.
A note on the letters: when this law operated, Greek φ θ χ were aspirated stops /pʰ tʰ kʰ/ — p, t, k plus a puff — not today’s /f θ x/. So θρίξ was /tʰríks/, with a breathy t, not an English “th”.
The whole law is a counting rule. Take two stops in successive syllables. If both carry a breath, the front one drops it. Toggle the breaths and watch the rule decide. The third toggle reproduces the famous blocker: an aspirate loses its breath before -s, which can leave the front one with no partner.
Greek “hair” keeps a stem with two breaths, /tʰrikʰ/. Add the nominative ending and add the genitive ending, and the very same stem comes out with a θ at the front in one case and a τ in the other. Step both derivations and watch why.
The same inherited word can lose its breaths in different branches for different reasons. Sanskrit and Greek drop the front breath by Grassmann’s law — independently. Germanic drops both by a different change, Grimm’s law, which shifted the whole consonant series. So the soft start of the Buddha’s name and the soft start of English bid are cousins by two unrelated routes.
Reconstructed Proto-Indo-European roots carry the asterisk (*); they are standard but unattested by definition. The deep Greek etymology marked * (πενθερός) is the received one, given for the parallel, not leant on.
Given a form, decide whether Grassmann’s law fires — i.e. whether two breaths actually meet in successive syllables.
An offline verifier (research/grassmann/verify.mjs) confirms the dataset is internally consistent: every wall item really deaspirates its first stop and keeps its second; the θρίξ derivation’s breath-count falls exactly where the rule says; the dissimilation engine on this page reproduces the nominative, genitive and reduplication outcomes; and the data embedded here is byte-identical to the source of truth. It does not re-prove Greek or Indo-Iranian philology — the forms are standard reference material; reconstructions carry the asterisk.