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How can the integrity of a Vedic verse be verified?

A Vedic verse is revealed to rishi, and the rishi orally transmits that revelation to his students.

Now suppose two of his students learn correctly the same verse from the rishi. They go their own ways and return to meet each other 50 years later. They both recite the same verse and find out there are slight differences in word choice and swaras, but they both claim that that is how they remembered the verse was taught to them.

How does one go about reconciling this discrepancy? Does any Hindu text talk about reconciling transmission errors?

In my other question I talked about how one can verify the integrity of a verse through supernatural means.

But short of supernatural means, is there a way to verify the integrity through normal means?

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    ask vedic scholars about 'gana' parayana.. they have a specific numbering of x syllables forward and y syllables backward. it's a simple formula easy to remember. so, if on application of that forumla, the result doesn't match the chant, it's an error. just like error correcting codes to capture 1-bit parity error or 2-bit parity error.
    – ram
    Commented Feb 23, 2020 at 23:48
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    @ram Oh ok, I've heard about that but do not know details.
    – Ikshvaku
    Commented Feb 24, 2020 at 2:57

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It can be restored through secular scholarship. I don't know if there are are modern rishis who can "see" the original. Here is how RigVeda was restored to a more faithful form by scholarship.

https://liberalarts.utexas.edu/lrc/rigveda/index.ph

The approach taken by van Nooten and Holland to restore the original form of the poems was exclusively systematic. A precise set of procedures was applied, which owed their origin to suggestions made by a number of nineteenth-century Rigvedic scholars, among them Kuhn, Bollensen, Oldenberg, Grassmann, and E. Vernon Arnold. These procedures were:

Restoration of lost syllables. A large number of inappropriate vowel combinations are resolved, both within and between words. For example, the vocative "índraagnī" is restored for "índrāgnī" at 6.059.2b, where the metre clearly shows that the compounded name of the two deities retained the original four syllables. (Note: an alternative restoration, "índrāagnī", with dual ending to both members, is preferred by others, including Grassmann.)

Vocalization of the semivowel. There are innumerable instances where the semivowels y and v in the ancient editions clearly have syllabic value, and were originally vowels. The corresponding vowel (i before y, u before v) has been inserted. This single procedure alone restores the correct syllable count to a large number of verse lines. Where the semivowel resulted from an ancient internal sandhi convention it has simply been removed and the original vowel restored: vyáñjana and abhyáñjana at 8.078.02 are restored to viáñjana and abhiáñjana.

Marking of disyllabic long vowels. A number of long vowels, including the diphthongs e and o, in some words always have disyllabic value. Where the origin of the dissyllable remains uncertain this is indicated by use of a tilde over the vowel. Where the origin of the dissyllable is clear the original form has been restored.

Vowel insertion. The metre can frequently be restored by inserting a dropped vowel into some word forms. For example, the genitive/locative form "pitrós" should always be read "pitarós", and neuter nouns in "-man" and "-van" regularly had later syncopation applied to oblique cases by the ancient editors which is here restored. The name "índra", similarly, is often trisyllabic, "índara".

Correction of representation of "iva". This is consistently given as disyllabic by the ancient editors, but frequently should read "va" in the Rigveda (see section 41.1 of Ancient Sanskrit Online).

Quantitative restoration. Where metrical irregularity was consistently found in the representation of the same word or morphological form, it was clear that that word or form had suffered in the transmission of the text. For example, the word "pāvaká" is always metrically to be read "pavāká". Long vowels occurring in a number of dual forms have been revised for the same reason: "āśate" is given for "āśāte", "rāsathām" for "rāsāthām".

Use of the rest sign (midline dot). This editorial sign was adopted to mark a pause equivalent to the length of a syllable.

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    I don't think it's an approved way. Every field will have its own way to rectify mistake, if they occur. Why are you bringing in Secular scholarship into the issue? When scholars Yaska, could not understand the Veda in a comprehensive manner, what is the standing of modern day scholars? Commented Feb 24, 2020 at 0:44

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