Say it out loud and there is no difference: in Welsh, ei "his" and ei "her" are the same spoken word. What tells a listener which one you mean is not the little word at all — it is what happens to the first consonant of the next word. ei gath is his cat. ei chath is her cat. The gender of the owner has been moved out of the pronoun and into a consonant. Pick a noun and watch all three possessives fall out of one root.
Welsh has nine consonants that change their opening sound depending on the word in front of them. The same noun therefore appears with different first letters in different company. Here is one root in three hands. Every form below is generated by the mutation rules in your browser — the page cannot show you a form the rules do not produce.
A mutation is just a lookup: a trigger word forces one of three changes on the consonant that follows it. Choose any noun and any trigger and read the result, the rule that fired, and why that trigger fires it. The "why" is the deep part — held until §IV — but the surface is mechanical, and that is exactly the point: a sound law is a function you can run.
The whole system is three small tables. Soft mutation (treiglad meddal) is ordinary lenition and touches all nine consonants — it is by far the commonest. Nasal mutation (treiglad trwynol) turns the six stops into nasals. Aspirate mutation (treiglad llaes) turns voiceless stops into fricatives, and touches only three letters. A dash means the consonant is left alone; ∅ means it is deleted outright.
Here is the result, stated exactly. His softens; her spirantises. Whenever a noun begins with one of the nine mutable consonants — or with a vowel (where "her" prefixes an h-: ei henw "her name" vs ei enw "his name") — the two diverge, and the listener knows. This is provable, and the verifier proves it over the whole inventory.
But the trick has a hole, and the honest thing is to show it. When a noun already begins with a sound that neither mutation touches — f, ff, th, dd, ch, s, h, l, n, r, ng… — then his and her come out identical. ei nos is his night and her night; nothing in the sound decides. Welsh resolves this residue the blunt way: an echo pronoun after the noun — ei nos ef "his", ei nos hi "her". The mutation does the elegant work where it can, and grammar mops up where it can't.
Why should "her" spirantise and "his" soften? Because these mutations are fossils of ordinary junction-sandhi — the way sounds at the seam between two words used to rub off on each other — frozen after the conditioning sound itself wore away. (Wikipedia, "Consonant mutation"; the broad picture is consensus.)
The clearest case is the very one this page turns on. The feminine "her" descends from a form that ended in -s: *esjās. Before a following word, that -s spirantised the next consonant, and the documented Proto-Brythonic chain runs *esyās tegos > *esyāh tegoh > *esyāh θegoh — "her house", the t- already become θ-. Then the trigger word eroded to a bare ei, the -s gone — but the mutation it had caused stayed behind, reanalysed as the marker of "her". The masculine "his" descends instead from a vowel-final form *esjo; a word that ended in a vowel lenited the next consonant instead. Same little surviving syllable today; opposite lost endings.
The pattern generalises. Nasal-mutating triggers are the ones that once ended in a nasal — fy "my" (*mene), yn "in" (*en), whose -n nasalised the following stop. Aspirate-mutating triggers are the ones that ended in a consonant — a "and" (*ak), the numerals tri "three" and chwe "six" (*trīs, *swexs). The grammar of modern Welsh is, in part, a museum of consonants that no longer exist — a thing that happened to the sound long ago, kept working as a thing that now happens to the meaning.
Two layers, kept apart on purpose. The living system — the three tables and which words trigger which mutation — is standard, stable, descriptive Modern Welsh, and it is machine-checked: the verifier applies the rules and confirms every form on this page is exactly what they generate, anchored to attested forms (ei gath, ei chath, fy nghath, yng Nghymru…), and proves the his/her result across the entire consonant inventory. 136 checks pass offline.
The history in §V is a different kind of claim — cited, not re-derived. Forms carrying the linguist's asterisk are reconstructions; the general account (mutations from lost word-final sounds) is consensus, but the precise protoforms of individual triggers and the relative chronology of the spirant mutation are genuinely debated in the literature, and some scholars derive the aspirate mutation from earlier geminate consonants rather than a simple -s. The verifier checks the system; it does not and cannot adjudicate the reconstruction. And one living-language honesty note: the nasal mutation is receding in everyday speech — many fluent speakers say fy nghath only in careful registers and lenite or drop it otherwise; the tables describe the standard, not a tape recording of any one street.