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the alaya is standardly defined as the momentary basis of imputation of the person.
the better question is what rational source suggests that the alaya is not changing and not individual?
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Re. the momentariness of the Alayavijnana, the Lankavatara Sutra says: “Mahāmati, the ālaya-consciousness, which is known as “the tathāgata heart,” is momentary in its being associated with mentation as well as the latent tendencies of the active consciousnesses [but] it is nonmomentary [in its being associated] with the uncontaminated latent tendencies.”
In verse Stiramathi's commentary to I.16 the Mahayanasamgraha, he says that the Alayavijnana is momentary - else the latent tendecies would not be momentary.
In note 144 of Volume Two of A Compendium of the Mahayana, Karl Brunnhölzl writes: “The Pañcaskandhabhāṣya (D4068, fols. 100b.3–101a.3) comments on Saṃdhinirmocanasūtra V.7 as follows. Since the ālaya-consciousness appropriates bodies in one life after another and knows its own object, it is given the name “appropriating consciousness.” It is profound because ordinary beings do not understand it, and it is subtle because noble śrāvakas and pratyekabuddhas do not understand it. Or, it is profound because it is the sphere of buddhas and bodhisattvas, and it is subtle because it is not the sphere of śrāvakas and pratyekabuddhas. Since it functions as the support of the seeds of all afflicted phenomena, the verse says, “with all [its] seeds.” In answer to wondering whether this ālaya-consciousness is permanent or impermanent, the verse says, “flows like the stream of a river.” A river flows as a momentary stream by carrying wood, stones, and so on, with it. Likewise, the ālaya-consciousness operates uninterruptedly in saṃsāra as a momentary stream by being associated with the five omnipresent mental factors. Therefore, since it is impermanent, the verse says, “flows like a river.”
Vasubandhu utilizes the river metaphor again in the Trimsatika, when he says in verse 4 that the alaya consciousness "always evolves like a flowing stream, And is abandoned in the state of arhat."
As for whether the ground consciousness is 'shared' Maitreya/Asanga (and their commentators) deal with that question in the Dharmadharmatavibanga:
What appear to be outer, perceivable in common, Are perceiving awareness; they are not referents Existing as something extrinsic to consciousness, Because they are only experienced as common.
The counterpart is the one in which what is perceived Is not shared in common. Here awareness’ referent Is the minds and so on associated with others. These do not comprise an object of mutual exchange For perceiving awareness not resting nor resting poised, Because, for those not resting in equipoise, It is but their own conceptions that appear; And because, for those who are resting in equipoise, It is its faithful reflection that appears As the object encountered during samadhi absorption.
Finally, both Dharmakirti and Ratnakirti also address the iussue of other minds. You can read their views here -- Buddhist idealism and the problem of other minds by Roy Perret
This essay is concerned with Indian Yogācāra philosophers’ treatment of the problem of other minds in the face of a threatened collapse into solipsism suggested by Vasubandhu’s epistemological argument for idealism.