Vedārambha
The popular claimThis is the saṁskāra that is in every list of sixteen and in almost nobody's life, because the rite before it swallowed it.
There is a question worth asking before anything else on this page: if Upanayana already initiates a student and hands him the Gāyatrī, what is left for a separate rite to begin?
The honest answer is: very little, and that is why this saṁskāra has the thinnest independent life of the sixteen.
The distinction, while it lasted
The intended difference is one of eligibility versus commencement. Upanayana makes a person a student — it confers the status, the girdle, the staff, the teacher, the Gāyatrī. Vedārambha is the first study itself: the opening of the text, the first recitation of the saṁhitā the student's family line is attached to.
Stated that way the two are clearly separable, and the later digests that enumerate sixteen saṁskāras separate them. But the Gṛhya Sūtras themselves do not treat the start of study as a distinct ceremony with its own name. In Āśvalāyana and Pāraskara the teaching of the Sāvitrī and the beginning of instruction sit inside the Upanayana sequence. Vedārambha is a category the list-makers needed more than the ritual manuals did.
This is not a criticism of the list. Sixteen is a shapely number and the enumerations that reach it are doing something legitimate — naming every distinguishable transition in a life. It does mean that a reader looking for a separate ceremony with its own procedure will find the sources oddly quiet.
What is actually done, where it is done
Where Vedārambha is observed as its own moment it is short. The student sits facing the teacher, the fire is kindled or the lamp lit, the appropriate opening formula of the śākhā is pronounced, and the first lines are recited after the teacher and repeated. Offerings are made to the ṛṣis of the line. In many households it happens the same morning as the Upanayana, an hour or two later, and no one present would describe it as a second ceremony.
Upākarma and Utsarjana
The reason Vedārambha never needed to be a large rite is that the tradition already had a mechanism for beginning study, and it repeats every year.
Upākarma, at the full moon of Śrāvaṇa, opens the year's study; Utsarjana closes it. The sacred thread is renewed at Upākarma, which is why that day is still observed widely under the name of the thread rather than the study. Between them lies the reading season. A student's first year simply begins at the next Upākarma after his initiation.
So the calendar carried the function. A once-in-a-life rite marking the same thing was always going to be redundant, and it became so.
What survived
As a named separate saṁskāra: very little. As a practice: more than the name suggests. Upanayana is still performed in many communities, and the teaching of the first verses is inside it. Upākarma is observed annually by large numbers of people. The function of Vedārambha — the moment a student is first put in front of the text — persists without the label.
There is also a modern echo worth naming without overstating it: the schools and pāṭhaśālās that begin a term with a formal first recitation are doing the same thing under a different arrangement.
What this page does not say
It does not manufacture a ceremony to fill the entry. Several popular accounts of the sixteen give Vedārambha a full procedure with a list of steps; we have not been able to trace those steps to a Gṛhya Sūtra, and where we cannot trace something we say so rather than repeat it confidently.
It does not say that anyone has missed something by not performing it separately, and it does not treat the collapse of the rite into Upanayana as a decline. Two ceremonies becoming one because they always described one act is tidying, not loss.
Source — Ashvalayana Grhya Sutra and Paraskara Grhya Sutra on Upanayana and the commencement of study; the Upakarma and Utsarjana rites of the annual study year; the later nibandha lists that enumerate Vedarambha as a separate samskara
Every claim on this site names its source, and every calculator shows its arithmetic.