Does any shastras mention shortening vedas with yugas? Like satyug having full version, then treta yuga having abridged and then dwapar having further abridged version and kali having the same.
Or anything related to this in shastras about vedas?
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No. We have less than a dozen shakhas of the Vedas that started out to be over 1000 at the beginning of the Yuga. For details, see this Wikipedia entry.
Even this is just the portion revealed to Rishis in the current Chaturyuga. Vedas are infinite in size. This is illustrated by the following story.
The Kathaka Shruti (Taittirya Brahmana 3.10.11) has the story of Bharadvaja who was given 3 lifetimes by Indra as he was pursuing to learn the entire Vedas.
bharadvājo hi tribhirāyurbhiḥ brahmacaryamuvāsa।
To preempt Bharadvaja from asking for a 4th lifetime, Indra appeared in front of him and asked him what would he do if he got a 4th life.
tam ha jīrṇim sthaviraṃ śayānam indra upavrajyovāca - ''bharadvāja! yatte caturtham āyur dadyām, kimenaina kuryā?" iti।
Bharadvaja replied that he would spend the next life as a student in pursuit of learning the remaining Vedas.
brahmacaryamevainena careyamiti hovāca
Indra then showed him the entire Vedic corpus in the form of 3 mountains. Bharadvaja was thrilled as he thought that he has learnt so much in his three lifetimes.
tam ha trīn girirūpān avijñātān iva darśayāṃ cakāra
To show him how much he had learnt in the 3 lifetimes, Indra took a handful of earth from each of the 3 mountains and.put it down on the ground.
teṣāṃ haikaikasmān muṣṭhinā ādade
"These three fistfuls represent what you have learnt. The mountains represent what you are yet to learn. The Vedas are infinite" said Indra.
sa hovāca bharadvājetyāmantrya, "vedā vā ete। anantā vai vedāḥ"।