Boundaries

Internal references

We have mentions of the Véda in the context of the ŕ̥c, sā́man, and yájus (AV 7.54.2, 15.3.6–8; ŞB 5.5.5.9–10; AB 5.32.1), or generally three-fold (TB 3.10.11.4), or alongside also the áṅgiras (i.e. átharvan, TS 7.5.11.2).

sUtra-kAra views

Mántra–Brā́hmaṇayor Veda-nāma-dheyám.
“The name ‘Véda’ is given to the Mántra and the Brā́hmaṇa.”
—Āpastamba-şrāuta-sūtrá 24.1.31

Ádhi-Dāivam áth’ ā́dhy-ātmam
ádhi-yajñam íti trayám
Mántreṣu Brā́hmaṇe c’ āivá
Şrutám íty ábhi dhīyate.

“The three-fold knowledge pertaining to the Gods, the soul, and the sacrifice, found in the Mántra-s and in the Brā́hmaṇa, is considered the Şrutá (Véda).”

—Şāṅkhāyana-gr̥hya-sūtrá 1.2.5

First, one has to understand what the terms “mantra” and “brAhmaNa” mean. brAhmaNa here does not mean the brAhmaNa-texts (as in shatapatha-brAhmaNa or taittirIya-brAhmaNa), but statements (which were already canonical by the time these definitions were made) which prescribe actions (vidhi) or praise/deplore actions, or are philosophical in nature.

तत्र धर्मब्रह्मप्रतिपादकमपौरुषेयं प्रमाणवाक्यं वेदः । स च मन्त्रब्राह्मणात्मकः । तत्र मन्त्रा अनुष्ठानकारकभूतद्रव्यदेवताप्रकाशकाः । तेऽपि त्रिविधा ऋग्यजुःसामभेदात् । … ब्राह्मणम् अपि त्रिविधम्,
विधिरूपम्, अर्थवादरूपं, तद्-उभय-विलक्षण-रूपं च । … विध्यर्थवादोभय-विलक्षणं तु वेदान्त-वाक्यम् ।

says prasthANa-bheda of madhusUdana-sarasvatI.

One must understand that vedic compilations (saMhitAs, brAhmaNa-s etc..) usually contain both these types of statements (unusual for them to have only mantra-s or only brAhmaNa-s - as in the case of shakala-saMhitA or ekAgni-kANDa..) .

As, such, Apastamba’s quote do not perclude AraNyaka-s from being considered part of the veda-s. Indeed, they are traditionally considered to be part of the veda-s, since they often share many traits with saMhitA and brAhmaNa compilations.

(As a matter of fact, for example, bRhadAraNyakopanIShat is part of shatapata-brAhmaNa; and AraNyaka-s are in a sense considered part of brAhmaNa-s.)

Closedness

A and S did not have some “open” definition in mind - they were obviously referring to mantra-s and brAhmaNa-s which were already canonical by the time they wrote; and which are relevant to the rites and thoughts they describe. They did not cherry pick either - “This is Original Vedic Religion TM. That is not.”

Linguistic view

“Vedic Sanskrit” is a modern western concept. I think, and many academicians would agree, that the linguistic intelligibility gap between the early Rigvedic language and the late Brāhmaṇa texts is bigger than that between the Brāhmaṇas and the earliest Upaniṣads (or even Mahābhārata). The chandas of Pāṇini does not include Brāhmaṇas (as is clear from छन्दोब्राह्मणानि च तद्विषयाणि, 4.2.66).

• उज्ज्वलः

Sectarian views

“चार वेद संहिता अपौरुषेय हैं
और ब्राह्मण,आरण्यक, षड्दर्शन,उपनिषद् और अष्टाध्यायी वगैरह ऋषियों के बनाये ग्रन्थ हैं।”
Arya-samAja founder dayAnanda-sarasvatI paraphrased

• Certain sects consider a few other works as equal to the veda-s.