“Is there a fundamentally irreducible rūpa—one entirely incapable of further division—even whilst possessing spatial extension?” and “Why does rūpa have to ultimately reduce to a minimum, indivisible unit ..?"
I am not sure the texts will address the ‘why’ it is necessary, to my view, they are describing the nature of reality (the ‘how’ not really the ‘why’).
That said, I am still trying to find a clear answer to your question about the ‘fundamentally irreducible rūpa’ that is backed up by the texts–have not managed to get my head around it as yet. Because ‘spatial extension’ is the earth element (and that has to be present in every rūpa-kalāpa) the mutual inseparability of the four mahā-bhūtas in the rūpa-kalāpas is relevant to your question as is how these relate to the space element (akāsa).
I am looking into these two soundly-based books which should have the answer somewhere, but I have not found it yet (maybe someone else can help):
- Y. Karunadasa Buddhist analysis of matter (Colombo: Dept of Cultural Affairs, 1967) (reprint Wisdom Publications, 2020)
- Y. Karunadasa, The Theravāda Abhidhamma: an inquiry into the nature of conditioned reality’ (Hong Kong: University of Hong Kong Press, pages 205-223; reprint Wisdom Publications, 2019).
Chapter 15 of this second book is ‘The material clusters (rūpa-kalāpa)’ and includes discussions not easily summarised for here, e.g., a quotation from page 208 (with references inserted in square brackets where needed):
“Thus for the Theravāda Abhidhamma, the ultimate unit of matter is not a unitary dhamma but a collection of unitary dhammas. In the Visuddhimagga where we find the theory introduced for the first time, it is called paramāņu (atom) [Vism 365]. Whereas in the sub-commentaries and Abhidhamma compendiums where we get the theory in its fully fledged version, the term used is kalāpa (cluster). [Vism-mhṭ 453 and others] The first term shows that it is the smallest unit of matter. The second term shows that although it is the smallest unit of matter, in the final analysis, it is a group of material dhammas, all having a simultaneous origination (ekuppāda) and a simultaneous cessation (eka-nirodha) and thus all forming a unity. [Ven. Bhikkhu Bodhi, Comprehensive manual of Abhidhamma, 352] Two other terms used to describe the smallest unit of matter are piņda (lump) and rūpa-samudāya (compound of material dhammas). They also show that the smallest unit of matter is a plurality.
“The basic principle behind the conception is this: What are called dependent material dhammas are always dependent on the great material dhammas. Hence the former do not arise independently of the latter. Nor can a single great material dhamma arise independently of the other three, and at least four of the dependent, namely colour, smell, taste, and nutritive essence. Thus none of the eight material dhammas, whether they are the four great elements or what is dependent on them, can have an independent, isolated existence. They always and necessarily arise by way of groups. [Abhidhammattha-Vibhāvinī-Tikā 58 : .. . etāni rūpāni kammādito uppajjamānāni’pi ekekaṃ vā samuṭṭhahanti, atha kho piṇḍato’va samuṭṭhahanti ….] Consequently when a given instance of matter, say, a piece of stone, is reduced to smaller pieces — whatever be the number of pieces and whatever be the size of each piece — the fact remains that each of them is a group of material dhammas. The smallest unit of matter, whether we calI it paramāņu (atom), piņda (lump), kalāpa (cluster) or rūpa-samudāya (compound of material dhammas), is no exception to this fundamental law.”
