DOI: https://doi.org/10.5281/zenodo.23020020
Canonical: https://thonly.org/research/abhidhamma-and-discrete-quantum-gravity · Licence: CC0 1.0
This paper compares, as structures, three things in two discrete theories of spacetime with three things in the Theravāda Abhidhamma. The theories are causal set theory and loop quantum gravity. The three things are order, adjacency and ratio. It is a lens and not a physics claim. No row predicts anything, and none says that a Buddhist text anticipated a theory of quantum gravity. For each row, a plain primer of the physics comes first, then the Abhidhamma material with its textual layer named in words, then the correspondence, and then the point where it breaks.
Four rows survive an adversarial review run before drafting. A fifth was cut.
The dropped row, saṅkhāra (the conditioned as a whole) against quantum causal histories, is reported along with the reason it was dropped.
Keywords: causal set theory, loop quantum gravity, spin networks, area spectrum, quanta of space, partial order, Hasse diagram, discrete spacetime, relational space, Buddhist philosophy of space, Abhidhamma, Paṭṭhāna, kalāpa, paricchedarūpa, ākāsadhātu, Theravāda, Abhidharmakośa, momentariness, asaññasatta, time dilation, muon lifetime, cosmic time, preorder, Lean 4, formal verification.
This paper is written so that a reader who knows calculus, but no linear algebra, quantum mechanics or general relativity, can follow every step. Each physics section opens with a subsection marked Physics primer, which builds the idea from nothing. A reader who already knows the physics can skip those subsections. Everything else is written for the exhaustive reader: the Pāli is quoted, the textual layer of every Abhidhamma claim is named in words, and every correspondence ends with the place where it fails.
Formulas are written in plain Unicode. Display formulas sit in monospace blocks. Where a formula is quoted, the source that derives it is cited.
Four textual layers are kept apart throughout, with a grammar and a modern exegete used for single points. They are named in words at each use, and every Pāli passage added in the 2026-09-30 revision is cited by its Chaṭṭha Saṅgāyana file and line (for example abh07t.nrf.xml:1485) in the VRI tipitaka-xml text at commit 05d5d3c:
| Layer | Texts used here | Date (traditional or scholarly) |
|---|---|---|
| canon | Dhammasaṅgaṇī, Vibhaṅga, Dhātukathā, Kathāvatthu, Paṭṭhāna (Abhidhamma Piṭaka); for §5 also the Brahmajāla Sutta (DN 1), the Saṃyutta's chapter on the beginningless round (SN 15), and the Milindapañha, canonical in this edition only | compiled over the last centuries BCE; the Kathāvatthu is traditionally dated to the Third Council |
| commentary | Visuddhimagga, Sammohavinodanī (Vibhaṅga commentary), Atthasālinī (Dhammasaṅgaṇī commentary), the Kathāvatthu and Paṭṭhāna commentaries; for §5 also the commentaries on the Dīgha, Saṃyutta, Aṅguttara and Suttanipāta | c. 5th century CE |
| manual | Abhidhammatthasaṅgaha (Anuruddha) | variously dated; commonly c. 11th–12th century |
| sub-commentary | Abhidhammatthavibhāvinī-ṭīkā (Sumaṅgala); also the Mūlaṭīkā on the Vibhaṅga and on the Paṭṭhāna with their Anuṭīkās, the Dhammasaṅgaṇī Anuṭīkā, the Dīgha and Aṅguttara sub-commentaries and the Sāratthadīpanī (on the Vinaya) | c. 12th century for the Vibhāvinī; the Mūlaṭīkā is earlier, since the Vibhāvinī names its author (Mūlaṭīkākārādayo, abh07t.nrf.xml:5553) |
| grammar | Payogasiddhi, a Pāli grammar, used in §5.2 for one unit only | medieval |
| modern exegesis | Ledi Sayadaw, Paramatthadīpanī (on the manual) and Paṭṭhānuddesa-dīpanī | c. 1900 |
A claim that holds only at a later layer is not a claim about the canon. Several rows below live, or die, on exactly that distinction.
| Term as the tradition writes it | Standard term used in this paper | Layer where it is defined |
|---|---|---|
| paccaya; Paṭṭhāna | condition; the canonical treatise on the 24 conditioning relations | canon (summarised in the manual, ch. 8) |
| anantara, samanantara | proximity, contiguity (immediate succession of mind-moments) | canon |
| āsevana | repetition | canon |
| natthi, vigata | absence, disappearance | canon |
| sahajāta | co-nascence (arising together) | canon |
| aññamañña | mutuality | canon |
| purejāta | pre-nascence (the condition arose earlier and still exists) | canon |
| pacchājāta | post-nascence (the condition arises later than what it supports) | canon |
| sahajāta-, purejāta-, pacchājāta- modes of nissaya, indriya, vippayutta, atthi, avigata | the co-nascent, pre-nascent and post-nascent modes (sub-types) of support, faculty, dissociation, presence and non-disappearance | canon (e.g. Paṭṭhāna: atthipaccayena paccayo – sahajātaṃ, purejātaṃ …); grouped in the manual, ch. 8 |
| kamma (nānākkhaṇika) | volitional action (across different moments) | canon (Paṭṭhāna, e.g. Kusalattika §427: nānākkhaṇikā – kusalā cetanā vipākānaṃ khandhānaṃ …); the time classification is sub-commentarial |
| ārammaṇa | object condition | canon |
| upanissaya, pakatūpanissaya | decisive support; natural decisive support | canon |
| citta, cittakkhaṇa | a moment of consciousness; a mind-moment | canon; the durations are commentarial |
| uppāda, ṭhiti, bhaṅga | arising, presence, dissolution (the three sub-moments) | commentary and manual |
| rūpa-kalāpa | smallest material cluster | commentary; systematised in the manual |
| suddhaṭṭhaka | the "pure octad" (four great elements, colour, odour, taste, nutritive essence) | commentary and manual |
| ākāsadhātu | the space element | canon |
| paricchedarūpa | delimiting matter (space as the delimitation of material clusters) | manual and sub-commentary |
| anipphanna | not concretely produced; having no intrinsic nature of its own | commentary (Visuddhimagga, Sammohavinodanī); manual |
| padaṭṭhāna | proximate cause | commentary |
| paramāṇu | the smallest unit on the commentarial size ladder | commentary |
| kālavimutta | free of time (said of nibbāna and concepts) | manual; glossed in the sub-commentary |
| saṅkhāra, saṅkhata, asaṅkhata | the conditioned; conditioned; unconditioned | canon |
| sampayutta; ekuppādanirodha | conjoined (mind with its mental factors); one in arising and ceasing | canon; the formula is the manual's (ch. 2 §1) |
| asaññasatta, asaññābhava | non-percipient (mindless) beings; non-percipient existence, of one aggregate (matter) only | canon (DN 1; Vibhaṅga; Dhātukathā; Kathāvatthu III.11); commentary; manual |
| indriyabaddha, anindriyabaddha | bound to faculties (in a living body); bound to no being | commentary (Atthasālinī) |
| utusamuṭṭhāna rūpa | temperature-born matter, produced by the fire element inside and outside beings | manual (ch. 6) |
| kappa | aeon, world-cycle | canon (SN 15) |
| accharāsaṅghāta; mattā | a finger-snap; a mora (the time of a short vowel) | commentary; grammar |
| santati, santāna | series, continuity (of material or mental phenomena) | commentary |
| saṇṭhāna | shape (had by matter, lacked by mind) | commentary (Paṭṭhāna); sub-commentary |
This paper is a study. It discloses no mechanism, so it carries findings and not claims. Each finding is stated in its surviving form, after the scope repairs of the 2026-09-28 and 2026-09-30 revisions, with its break beside it. The falsifiers are collected in §10.
This document is dedicated to the public domain under CC0 1.0. The authors and HeartBank® will not seek patent on anything herein. Nothing here is a mechanism. The paper is a study, and its disclosures are the numbered findings under Findings disclosed above, each with its break stated beside it.
What is already public, and cited rather than claimed:
SiliconWat/formal-abhidhamma (CC0; software concept DOI 10.5281/zenodo.23067241) holds the machine check cited in §4.5 and the run that supplied three of §5.2's four lower bounds.The census. A quick novelty census ran on 2026-09-27. Its pre-registration was pushed publicly before any query was made: thonly/publications commit 7348ba2, timestamps/census/physics-lens-prereg.md. The search covered the English web (including dharma sites and popular Buddhism-and-physics writing), and arXiv, Google Scholar, PhilPapers, GitHub and Google Patents by keyword. Thai, Burmese, Sinhala, Chinese, Japanese and Khmer sources were not run, and no books were read. The pre-registered control, the known comparison The Ephemeral Projector, was found.
| Conjunct | Found | Verdict |
|---|---|---|
| (a) the Paṭṭhāna's typed conditions against causal-set order | a general causal-set–Abhidhamma resonance (the AI-generated post; names no Paṭṭhāna condition) | narrowed at general width; the typed-relation comparison was not found |
| (b) kalāpa against spin-network nodes | kalāpas compared with atoms, quanta and the Planck length in popular writing | narrowed at "smallest unit" width; the spin-network-specific comparison was not found |
| (c) paricchedarūpa (space as the between) against area on spin-network links | the commentarial reading of space as delimitation is public; no comparison with loop quantum gravity | not found in that aperture on that date |
| (d) saṅkhāra against quantum causal histories | — | not found; dropped before drafting (§6) |
| (e) the 17-moment lifetime as a discrete-time ratio | Sorkin and Dowker link causal-set becoming to Buddhist momentariness | narrowed at general width; the chain-length reading of the ratio was not found |
| the composition of rows in one structural map | — | not found in that aperture on that date |
⛔ "Not found in that aperture on that date" is a statement about a search. It is not a claim of priority, and nothing in this paper is offered as new. As a study that makes no priority claim, this paper owes no further census before deposit (ruled 2026-09-28); a literature census could narrow or kill the rows above, and would be reported here as a revision.
Physics has two great theories that do not fit together. General relativity describes gravity as the smooth geometry of spacetime. Quantum theory describes everything else as discrete, probabilistic excitations. A theory of quantum gravity would describe what spacetime is at the smallest scale, where both matter. Two of the candidate programmes make spacetime itself discrete:
The Theravāda Abhidhamma is also a discrete analysis. It resolves experience and matter into momentary phenomena (dhamma), connected by twenty-four typed conditioning relations. It gives matter a smallest cluster, and it gives space a definition.
It is therefore tempting to line the two up. That temptation has a long and mostly poor history, from The Tao of Physics onward, and this paper is built to resist it. Every row below is a structural comparison: it asks whether two frameworks share a shape (an order, an adjacency, a ratio), and it names exactly where the shape stops being shared. The Abhidhamma is an analysis of what can be known in experience. Quantum gravity is a theory of what spacetime is. Whether the two can be compared at all is the strongest objection to this paper, and §8 carries it rather than answering it.
The map, in one table:
ROW PHYSICS SIDE ABHIDHAMMA SIDE SURVIVING FORM
─────────── ──────────────────────────────────── ───────────────────────────────────── ──────────────────────────────────
1 ORDER causal set: a locally finite the Paṭṭhāna's 24 typed conditions only the earlier→later MODES (S) are
partial order ("before") (classified by manual + sub-comm.) acyclic, by selection: a strict order,
not yet a causal set; S also orders
across streams (kamma-born colour);
the rest is typing a causal set lacks
2 GRAIN spin-network node: a quantum OF rūpa-kalāpa: smallest material survives only as what row 3
space, with a volume cluster (matter IN space) presupposes; matter ≠ geometry
3 BOUNDARY spin-network link: the face two paricchedarūpa: the non-mixing of both put the unit of spatial
grains share; carries quantised area touching neighbours; "limit of matter" boundary at the ADJACENCY, not in
a unit (strongest row; the shared
part is generic; seven breaks)
4 RATIO proper time ∝ length of the longest most matter lasts 17 mind-moments dated on a stream's own moments where
chain between two events (51 sub-moments) there is one, a UNIT where there is
none; only the generic part survives:
a duration as a count
─ DROPPED ─ quantum causal histories saṅkhāra (the conditioned as a whole) category error; added no structureRows 2 and 3 are one argument told from two ends, so they share one section (§4).
Two different things are called discrete in this paper, and they must not be confused.
The Abhidhamma has object discreteness in abundance: moments, clusters, sub-moments. Its quantities are restricted only as counts of discrete units: a duration is a whole number of sub-moments, and a size is a step on a ladder of powers of thirty-six (§4.2). It never quantises a magnitude that is not a count, and that is what spectral discreteness is. In particular, its delimiting space (manual and sub-commentary) is assigned no magnitude at all (§4.6). This single fact limits every row below.
A relation is a rule that says, for any two things x and y, whether x stands in it to y. "Is an ancestor of" is a relation on people. Write it x ≺ y.
A partial order is a relation with two properties:
irreflexive: never x ≺ x (nothing precedes itself)
transitive: if x ≺ y and y ≺ z, then x ≺ z (ancestors of ancestors are ancestors)Together these make it acyclic: you can never follow the arrows and return to where you started. It is called partial because some pairs are not related either way. Two cousins are neither ancestor of the other.
A causal set is a partial order on a set of events, with one more property, local finiteness: between any two related events, only finitely many events lie. The relation means "can causally influence". In relativity, two events are either causally related (one is in the other's past light cone) or spacelike: too far apart in space, for the time between them, for any signal to connect them. In a causal set, spacelike simply means unrelated.
Links and the Hasse diagram. If x ≺ y and nothing lies between them, the pair is a link (mathematicians say covering relation). Drawing only the links, with later events higher, gives the Hasse diagram. Every other relation can be recovered by following links upward, since the order is transitive.
e f later events higher
\ /
\ /
d only LINKS are drawn;
/ \ a ≺ d, a ≺ e, a ≺ f, b ≺ e … follow by transitivity
b c
\ / b and c are UNRELATED (spacelike):
a neither can influence the otherOrder plus number. Sorkin's slogan for the programme is order + number = geometry. Two classical theorems (Hawking, King and McCarthy 1976; Malament 1977) show that, for spacetimes that are past- and future-distinguishing, the causal order fixes the geometry up to a conformal factor, that is, up to a local scale. Causal set theory supplies the missing scale by counting. Events are scattered at random (a "sprinkling") with, on average, one event per unit of spacetime volume in Planck units, so the number of events in a region measures its volume.
Time as chain length. A chain is a sequence x₁ ≺ x₂ ≺ … ≺ xₙ. Between two related events, the length of the longest chain grows in proportion to the proper time between them: the time a clock carried from one to the other would read. The result holds asymptotically and in expectation, for random sprinklings into Minkowski space (Brightwell and Gregory 1991). In a causal set, a duration is a count of steps. §5 uses exactly this.
Growth. In Rideout and Sorkin's sequential-growth models, the causal set is not given all at once. It grows, one element at a time, each new element born to the future of some existing ones. What is born stays. Sorkin reads this as a real becoming, a growing block: a past that accumulates and a future that does not yet exist.
The Paṭṭhāna, the last book of the Abhidhamma Piṭaka (canon), analyses how phenomena condition one another under twenty-four named conditions (paccaya). The manual (Abhidhammatthasaṅgaha, ch. 8) summarises them, and the sub-commentary (the Vibhāvinī) classifies each by the time its conditioning reaches. On the manual's ch. 8 it states:
… anantarasamanantaraāsevananatthivigatavasena pañcannaṃ atītakālikānaṃ, kammapaccayassa atītavattamānavasena dvikālikassa, ārammaṇaadhipatiupanissayapaccayānaṃ tikālikānaṃ, itaresaṃ pannarasannaṃ paccuppannakālikānañca vasena kālattayavanto, nibbānapaññattivasena kālavimuttā ca …
… [things are] possessed of the three times by way of the five belonging to the past (proximity, contiguity, repetition, absence, disappearance), the kamma condition belonging to two times (past and present), the object, predominance and decisive-support conditions belonging to three times, and the remaining fifteen belonging to the present; and free of time, by way of nibbāna and concepts …
The count checks: 5 + 1 + 3 + 15 = 24. The tetrad sorts the conditions by the time their conditioning state may have, and the same sentence then sets the time-free (nibbāna and concepts) beside the three times. So the classification is not exhaustive of what can condition: the object condition, placed among the three-time conditions, also reaches the time-free.
The remaining fifteen are root (hetu), co-nascence, mutuality, support (nissaya), pre-nascence, post-nascence, result (vipāka), nutriment (āhāra), faculty (indriya), jhāna, path (magga), association (sampayutta), dissociation (vippayutta), presence (atthi) and non-disappearance (avigata). "Belonging to the present" means the conditioning state exists when the conditioned one does. It does not mean that the two arose together. Pre-nascence belongs to the present because its condition arose earlier and still stands. So "present" is not "co-nascent", and several of the fifteen have modes, which the canon itself names. The Paṭṭhāna gives the presence condition as sahajātaṃ, purejātaṃ, pacchājātaṃ, āhāraṃ, indriyaṃ (co-nascent, pre-nascent, post-nascent, nutriment, faculty), and the dissociation condition as sahajātaṃ, purejātaṃ, pacchājātaṃ. The manual groups the modes (ch. 8, CST §30–§34):
| Condition | Co-nascent mode | Pre-nascent mode (condition arose earlier) | Post-nascent mode |
|---|---|---|---|
| support (nissaya) | mind with mind, the great elements with derived matter | the six bases for the seven consciousness elements, during the course of existence | — |
| faculty (indriya) | the immaterial faculties for co-nascent mind and matter | the five sensitivities for the five kinds of sense consciousness | — (the material life faculty, for the matter of its own cluster, is a third, separate mode) |
| dissociation (vippayutta) | mind for co-nascent matter; the base at rebirth-linking | the six bases, during the course of existence, purejātavasena | later mind for the earlier-arisen body |
| presence, non-disappearance (atthi, avigata) | sahajātaṃ | purejātaṃ | pacchājātaṃ (edible food and material life are two further, separate modes) |
The manual names the pre-nascent mode in words for dissociation, presence and non-disappearance. For support and faculty the pre-nascent reading is the one the canon gives for the base (vatthu kusalānaṃ khandhānaṃ nissayapaccayena paccayo) and the one the standard modern exposition gives for the sensitivities (Bodhi 1993, ch. VIII: "prenascence faculty"). At rebirth-linking the base arises together with the mind and is co-nascent, which is why the manual limits the pre-nascent mode to the course of existence.
A condition in the Abhidhamma is typed. The relation is not just "x conditions y", but "x conditions y as object", "as kamma", "as co-nascent", and so on. One pair can stand in several types at once.
The whole is not a partial order. Four features break it:
| Feature | Text (layer) | Why it is not a partial order |
|---|---|---|
| Mutuality (aññamañña) | canon; manual ch. 8 | x conditions y and y conditions x: a 2-cycle. A partial order forbids cycles. |
| Co-nascence (sahajāta) | canon; manual ch. 8 | relates what arises together. A causal order leaves simultaneous, unlinked events unrelated (spacelike). |
| Post-nascence (pacchājāta) | manual ch. 8: "pacchājātā cittacetasikā dhammā purejātassa imassa kāyassa pacchājātavasena" — "later-arisen consciousness and its concomitants [condition] this body, arisen earlier, by way of post-nascence" | the condition arises after what it supports: ordered by arising, the arrow runs backward. |
| Object (ārammaṇa) | manual ch. 3: mind-door objects may be "paccuppannamatītaṃ anāgataṃ kālavimuttañca" (present, past, future, and free of time); the sub-commentary glosses the time-free as "nibbānaṃ, paññatti ca" (nibbāna and concepts) | a future object conditions a present mind, and a time-free object is in no order at all. |
The surviving form. Because several conditions have modes, the surviving relation is defined over condition-modes, not over whole conditions. Some modes always run from what arose earlier to what arises later:
the ACYCLIC SUB-RELATION S (defined over MODES)
──────────────────────────────────────────────────────────────────────────────
anantara, samanantara the moment just ceased → the next moment
āsevana a moment → the next, as repetition
natthi, vigata the moment just ceased → the next (by its absence)
purejāta an earlier-arisen, still-present base or object → a later-arising mind
kamma (nānākkhaṇika) a past volition → its later result, across many moments
pre-nascent MODES of the same earlier-arisen bases (and, for faculty, the five
nissaya, indriya, sensitivities) → the later-arising consciousness, during the
vippayutta, atthi, course of existence
avigataThe co-nascent and post-nascent modes of those five conditions stay out of S, and so does kamma's co-nascent mode.
Every one of the twenty-four, assigned:
| Where it goes | Conditions (or modes) |
|---|---|
| in S (whole condition) | proximity, contiguity, repetition, absence, disappearance, pre-nascence |
| in S (one mode only) | kamma (across moments); support, faculty, dissociation, presence, non-disappearance (pre-nascent modes) |
| out: co-nascent only | root, co-nascence, mutuality, result, jhāna, path, association; the co-nascent modes of kamma, support, faculty, dissociation, presence, non-disappearance, predominance and nutriment |
| out: runs backward | post-nascence; the post-nascent modes of dissociation, presence and non-disappearance |
| out: reaches three times, or the time-free | object, predominance (object mode), decisive support |
| out: not sorted by arising here | nutriment (edible food); faculty and presence (material life), whose relata co-exist in one body without a stated arising order |
Why S is acyclic (a one-line proof). Let t(x) be the moment at which phenomenon x arises. For every mode in S, x S y implies t(x) < t(y). Along any chain x₁ S x₂ S … S xₙ, the arising times strictly increase, so the chain can never return to x₁. ⚠️ This proof shows less than it seems to. S was selected by the condition t(x) < t(y), so its acyclicity follows from the selection and is not a finding about the text. A strict order can be read over S, and its transitive closure is a partial order. But the closure is the reader's construction (see the next paragraph), and whether S meets the rest of §3.1's definition is taken up in §3.4.
⚠️ One condition was removed from S by the adversarial review. The original list included pakatūpanissaya (natural decisive support). The sub-commentary classes decisive support as tikālika, reaching all three times (quoted above), and the manual's list of natural decisive supports includes present things (a person, climate, food, lodging). It is therefore not guaranteed to run earlier-to-later, and it is out.
A second, smaller correspondence: generators, not closure. The manual and the sub-commentary present the conditions as primitive. Neither says that because x conditions y and y conditions z, x conditions z. Whether the Paṭṭhāna itself anywhere composes two conditions into a third is part of the canonical check this paper owes (§11); U Nārada's translation (1969), which works through the Paṭṭhāna's own permutations, is the route for it. On the manual's presentation, the relations are primitive, like a causal set presented by its links rather than by its full transitive order. The likeness is partial. Proximity (anantara) holds only between immediate successors, so it is link-like in the strict Hasse sense. Kamma across moments, however, spans many intermediate moments and is still primitive, so S is a set of generating relations that is neither the Hasse diagram nor the full order.
The surviving form of the row, stated once:
As the manual and the Vibhāvinī classify the Paṭṭhāna's conditions, the condition-modes that always run from earlier-arising to later-arising (proximity, contiguity, repetition, absence, disappearance, pre-nascence, kamma across moments, and the pre-nascent modes of support, faculty, dissociation, presence and non-disappearance) form an acyclic typed relation over which a strict order, but not yet a causal set in §3.1's sense, can be read. The remaining conditions and modes (the co-nascent ones, the post-nascent ones, and the object, predominance and decisive-support conditions that reach all three times) are typed structure that a causal set does not have.
abh01a.att.xml:3721), used "only on the occurrence of phenomena" (dhammānaṃ pavattimeva ca upādāya kālavohāro, Paṭṭhāna Mūlaṭīkā, abh03t.tik.xml:4309), and define no index across streams. In a causal set there is no time apart from the order. Whether a stream's succession stands to its time in that way, or presupposes one, this paper leaves open; its proof needs t either way.Order between streams. The sibling paper Twenty-Four Kinds of Because (§4.7) finds that no condition joins two mental continua and that two people have no shared clock. No shared clock is not no order, and S itself carries some. Kamma across moments runs from a past volition to its results, and the canon counts matter among them (nānākkhaṇikā – kusalā cetanā vipākānaṃ khandhānaṃ kaṭattā ca rūpānaṃ kammapaccayena paccayo, Paṭṭhāna, abh03m7.mul.xml:6065; manual ch. 8 §17, abh07t.nrf.xml:2865). Kamma-produced matter includes visible form (rūpaṃ kammassa katattā rūpāyatanaṃ, Dhammasaṅgaṇī §652, abh01m.mul.xml:5549), and every kamma-born cluster carries the inseparable eight, colour (vaṇṇa) among them (manual ch. 6 §46, §27, abh07t.nrf.xml:2273, :2169). Colour is a pre-nascent object for the five-door process of whoever sees it (pañcārammaṇāni ca pañcaviññāṇavīthiyā purejātavasena, manual ch. 8 §19, abh07t.nrf.xml:2873). Both edges are in S. A second route runs through mind-born matter: a mind originates matter by co-nascence (cittacetasikā dhammā aññamaññaṃ sahajātarūpānañca, ch. 8 §28, abh07t.nrf.xml:2909), at its own arising sub-moment (Sammohavinodanī, abh02a.att.xml:409), and mind-born octads carry colour too (ch. 6 §47, abh07t.nrf.xml:2277).
stream A … a₀ ·········· a₁ ──── a₂ ──── a₃ … proximity (in S)
│ kamma, across │ co-nascent: arises WITH a₂
▼ moments (in S) ▼ (NOT in S)
matter kamma-born colour mind-born colour each lasts 17 mind-moments
│ │
│ pre-nascent object: arose EARLIER, still present (in S)
▼ ▼
stream B … b₁ ──────────────────── b₂ … eye-consciousnesses that see them
t(a₀) < t(colour) < t(b₁): an order ACROSS streams, carried by S alone
t(a₂) = t(colour) < t(b₂): the same kind of order, through one edge S excludesThe carrier is the colour, never the bodily intimation, which lasts one mind-moment (§5.2) and is not visible. Three limits apply. (1) Each route is the reader's composition of two edges the texts state separately. (2) The mind-born route lives only in the larger relation of S with the co-nascent modes, whose reflexive-transitive closure is a preorder, not a partial order: mutuality relates co-nascent phenomena both ways (ch. 8 §29, including the base and the resultant mind at rebirth-linking, paṭisandhikkhaṇe vatthuvipākā aññamaññaṃ, abh07t.nrf.xml:2913). But its cycles all lie inside co-nascent clusters (a mind with its factors, the great elements of one cluster, the base with the resultant mind), none of which spans two streams, and every S edge raises the arising time, so the order it gives between streams is strict. "Preorder" describes the whole relation, not its cross-stream part. (3) Neither route makes S a causal set. As a lens only, this is relativity's shape rather than a causal set's: no global clock, yet a causal order between separate places, carried here by matter as there by signals. Nothing here bounds a speed, and the co-nascent cycles have no light-cone counterpart.
Co-nascence also presupposes a simultaneity, of a mind and the matter it originates, that a causal set lacks; a claim that one mind-moment occurs everywhere at once was checked and found no textual basis. For §3.5's third falsifier the result is mixed. S connects the kamma route, but the mind-born pair (a₂ before b₂) is an order the texts' own definitions imply and S alone cannot connect, so the falsifier is engaged in a narrowed form: S carries part of the order between streams, not all of it.
Geometry is a field. In general relativity, the gravitational field is the geometry of spacetime: it decides lengths, areas and volumes. There is no stage apart from it. If the gravitational field is quantised, then lengths, areas and volumes become quantum quantities, and quantum quantities typically come in steps.
What "spectrum" means. In quantum theory, each measurable quantity is represented by an operator: a rule which, given the state of a system, yields the possible results of measuring it. The list of possible results is the quantity's spectrum. A spectrum is discrete if the possible results are separated by gaps. Think of a function that can only take values on the rungs of a ladder. An electron's energy in an atom has a discrete spectrum, and that is why atoms emit light at sharp colours. Loop quantum gravity finds that area and volume have discrete spectra (Rovelli and Smolin 1995; Ashtekar and Lewandowski 1997).
A spin network. A quantum state of space in loop quantum gravity is described by a graph: points (nodes) joined by lines (links). Each link carries a label j called a spin, taking values j = ½, 1, 3/2, 2, …. Each node carries a second label, the intertwiner, which records how the links meeting there fit together.
j₁
│
j₄ ─────●───── j₂ ● a NODE: a grain ("quantum") of space
│n each line: a LINK, labelled by a spin j
j₃ the node's volume depends on j₁…j₄ and the intertwinerArea lives on links. Take any surface. Its area is a sum over the links that pierce it:
A = 8πγ ℓ_P² Σ √( j (j + 1) ) sum over the links crossing the surface
ℓ_P = √(ħG / c³) ≈ 1.6 × 10⁻³⁵ m the Planck length
γ = the Barbero–Immirzi parameter, a dimensionless constant of the theory
(γ ≈ 0.2375 from black-hole entropy counting, Domagala–Lewandowski
and Meissner 2004; ≈ 0.274 under the later Ghosh–Mitra counting;
the value depends on the state-counting convention)This is the formula for links that cross the surface transversally. When a node lies on the surface itself, the general formula adds further terms (Ashtekar and Lewandowski 1997). The smallest non-zero area is one link with j = ½:
A_min = 8πγ ℓ_P² √(3/4) = 4√3 π γ ℓ_P² ≈ 21.8 γ ℓ_P²There is nothing between zero and this value. That gap is what "area has a discrete spectrum" means.
Volume lives at nodes. Each node has a volume, but volume is not an independent label. It is computed from the spins of the links meeting there and from the intertwiner, and it takes discrete values. A node where only three links meet has zero volume: the volume operator vanishes on gauge-invariant two- and three-valent nodes (Loll 1996, who also computed the four-valent spectrum). In the geometric picture below, the same fact reads simply: three faces whose area-vectors sum to zero must lie in one plane, and a flat shape has no volume. Volume needs at least four links.
Nodes are quanta of space, not things in space. Rovelli (Zakopane lectures, §I.A): the quanta of gravity "do not live in space, but give rise to space themselves." There is no background in which the network sits. "Where" means "which node, adjacent to which".
Grains and faces. Bianchi, Doná and Speziale (2011) showed that a node can be read as a small polyhedron, a quantum polyhedron, whose faces are its links. The reading is semiclassical: coherent spin-network states represent semiclassical polyhedra, which is most reliable at large spins and least trustworthy at small spins, including the j = ½ where the smallest area sits. Adjacency is also definite only for a spin-network basis state on a fixed graph; a general quantum state of space is a superposition of graphs. Rovelli states the consequence plainly (Zakopane lectures, §II.F): "Two grains n and n′ are adjacent if there is a link l connecting the two, and in this case the area of the elementary surface separating the two grains is determined by the spin of the link joining n and n′."
┌───────────────┐┌───────────────┐
│ grain n ││ grain n′ │ the face they share IS the link l;
│ (volume) ││ (volume) │ its area = 8πγℓ_P² √(j_l (j_l + 1))
└───────────────┘└───────────────┘
the same thing as a graph: n ●────────── j_l ──────────● n′In one sentence: in loop quantum gravity, the boundary between two neighbouring grains of space is the adjacency itself, and it carries a quantised area.
The kalāpa is matter. The smallest material cluster (rūpa-kalāpa) is not in the canonical Abhidhamma books. The Dhammasaṅgaṇī has no kalāpa vocabulary. The clusters appear in the commentary (the Visuddhimagga names the "pure octad", suddhaṭṭhaka, and the decads), and the manual systematises them into twenty-one kinds (Abhidhammatthasaṅgaha ch. 6: "kalāpā ekavīsati"). The simplest, the pure octad, is eight inseparable material phenomena: the four great elements (extension, cohesion, heat, motion) together with colour, odour, taste and nutritive essence.
The commentarial size ladder. The Vibhaṅga commentary (Sammohavinodanī), in a passage teaching a monk to see small faults as large, gives a ladder of sizes:
chattiṃsa paramāṇavo ekassa aṇuno pamāṇaṃ. Chattiṃsa aṇū ekāya tajjāriyā pamāṇaṃ. Chattiṃsa tajjāriyo eko rathareṇu.
Thirty-six paramāṇu make the measure of one aṇu; thirty-six aṇu, one tajjārī; thirty-six tajjārī, one rathareṇu [a mote of chariot dust].
So one paramāṇu is 1/36³ = 1/46,656 of a chariot-dust mote. The commentary describes the paramāṇu as ākāsakoṭṭhāsika, of the order of a portion of space, and says it is visible only to the divine eye. ⚠️ The ladder is for the paramāṇu, not the kalāpa. The commentary does not use the word kalāpa there. The identification of the two, common in modern summaries (including both encyclopedia articles cited above), is later exegesis.
Canon — a cavity. The Dhammasaṅgaṇī (§637) defines the space element:
Katamaṃ taṃ rūpaṃ ākāsadhātu? Yo ākāso ākāsagataṃ aghaṃ aghagataṃ vivaro vivaragataṃ asamphuṭṭhaṃ catūhi mahābhūtehi — idaṃ taṃ rūpaṃ ākāsadhātu.
What is the material phenomenon that is the space element? That which is space, belonging to space, void, belonging to the void, an opening, belonging to an opening, untouched by the four great elements — this is the space element.
The Vibhaṅga, also canon, gives examples of the internal space element: the ear-holes, the nostrils, the mouth, the passage by which food is swallowed, where it rests and where it leaves. At the canonical layer, space is a cavity with extent: a gap in matter, the kind of thing that has room in it.
Canon — not unconditioned. The Kathāvatthu (VI.6, §460–462, verified in the Chaṭṭha Saṅgāyana text) refutes the thesis "ākāso asaṅkhato", that space is unconditioned. One of its arguments is homely: "Udapāne khaññamāne anākāso ākāso hotīti? Āmantā." When a well is dug, does what was not space become space? Yes. And when an empty jar is filled, space disappears. Something that can be made and unmade is not unconditioned. The commentary attributes the rejected thesis to the Uttarāpathakas and the Mahisāsakas (so spelled there). The Mahiṃsāsakas are one of the four Vibhajjavādin branches in Cousins's account (Cousins 2001), which the sibling paper uses. Once again, the branch that kept the Pāli canon argues against a sibling branch.
Commentary — three spaces, and a characterisation. The Kathāvatthu commentary distinguishes three spaces:
tividho ākāso — paricchedākāso, kasiṇugghāṭimākāso, ajaṭākāso … Tesu paricchedākāso saṅkhato, itare dve paññattimattā.
Space is threefold: delimiting space, the space left by removing a meditation disk, and unentangled [open] space … Of these, delimiting space is conditioned; the other two are mere concepts.
The Visuddhimagga (ch. XIV, CST ¶442) characterises the space element in its fourfold formula:
Rūpaparicchedalakkhaṇā ākāsadhātu, rūpapariyantappakāsanarasā, rūpamariyādapaccupaṭṭhānā, asamphuṭṭhabhāvacchiddavivarabhāvapaccupaṭṭhānā vā, paricchinnarūpapadaṭṭhānā. Yāya paricchinnesu rūpesu idamito uddhamadho tiriyanti ca hoti.
The space element has the characteristic of delimiting matter; its function is to display the boundaries of matter; it is manifested as the confines of matter, or as the state of being untouched, as holes and openings; its proximate cause is the matter delimited. It is that by which one can say of delimited material things, "this is above, below, around that."
The last sentence matters for §4.5. Direction and position are defined only relative to delimited matter.
Manual — not a constituent. The Abhidhammatthasaṅgaha (ch. 6, the verse closing the section on kalāpas):
Kalāpānaṃ pariccheda-lakkhaṇattā vicakkhaṇā; Na kalāpaṅgamiccāhu, ākāsaṃ lakkhaṇāni ca.
Because space has the characteristic of delimiting the kalāpas, and because of the nature of the characteristics, the wise do not call space, nor the characteristics, a constituent of a kalāpa.
Space is between kalāpas, never in one. The manual also classes this delimiting matter (paricchedarūpa) as anipphanna: not concretely produced, with no intrinsic nature of its own. The term is older than the manual; the Visuddhimagga and the Sammohavinodanī already use it. It is counted as one of the twenty-eight material phenomena, but the standard expositions do not count it among the ultimate realities (Bodhi 1993, ch. VI), and one reads it as "nothing but the mere limitation of matter" (Karunadasa 1967, ch. 5).
Sub-commentary — the non-mixing of touching neighbours. The Vibhāvinī, on the same chapter:
Cakkhudasakādiekekakalāpagatarūpānaṃ kalāpantarehi asaṃkiṇṇabhāvāpādanavasena paricchedakaṃ, tehi vā paricchijjamānaṃ, tesaṃ paricchedamattaṃ vā rūpaṃ paricchedarūpaṃ … Vijjamānepi ca kalāpantarabhūtehi kalāpantarabhūtānaṃ samphuṭṭhabhāve taṃtaṃrūpavivittatā rūpapariyanto ākāso. Yesañca so paricchedo, tehi sayaṃ asamphuṭṭhoyeva. Aññathā paricchinnatā na siyā tesaṃ rūpānaṃ byāpībhāvāpattito. Abyāpitā hi asamphuṭṭhatā.
Delimiting matter is what delimits the matter in each kalāpa (the eye-decad and the rest) by making it unmixed with neighbouring kalāpas; or what is delimited by them; or their mere delimitation … Even where neighbouring kalāpas touch one another, space is the separateness of each one's matter, the limit of matter. And it is itself untouched by the things it delimits. Otherwise those material things would not be delimited, since they would come to pervade one another. For non-pervasion is non-touching.
┌────────────┐ ┊ ┌────────────┐
│ kalāpa K₁ │ ┊ │ kalāpa K₂ │ K₁ and K₂ may TOUCH;
│ (8+ rūpas) │ ┊ │ (8+ rūpas) │ space is the ┊ : their non-mixing,
└────────────┘ ┊ └────────────┘ "the limit of matter"
↑
paricchedarūpa — not a constituent of either (manual);
untouched by what it bounds (sub-commentary);
no nature of its own; no magnitude assigned (anipphanna);
its proximate cause is the matter it delimits (commentary)The Vibhāvinī's wording answers a question the Indian schools had argued for centuries. The Abhidharmakośabhāṣya (ad I.43, Pradhan ed., pp. 32–33) asks it directly:
kiṃ punaḥ paramāṇavaḥ spṛśanty anyonyam āhosvin na / na spṛśantīti kāśmīrakāḥ / … yadi tāvat sarvātmanā spṛśeyur miśrībhaveyur dravyāṇi / athaikadeśena sāvayavāḥ prasajyeran / niravayavāś ca paramāṇavaḥ
Do atoms touch one another, or not? The Kashmiri masters say they do not touch. … If they touched with their whole selves, the substances would mix. If they touched with a part, they would have parts. But atoms are partless.
The same passage adds that contact means only arising without interval, and that "their being without interval is just that there is nothing between them" (tad evaiṣāṃ nirantaratvaṃ yan madhye nāsti kiñcit). ⚠️ nirantaratvaṃ is this paper's emendation: the GRETIL e-text reads niruttaratvaṃ [032|20]. The emendation follows the passage's own nirantara in the line before, and Pradhan's printed page was not checked. Bhadanta Vasumitra holds that they do not touch, and that we call it touching when there is no interval.
Two cautions before the comparison. First, the Kośa's contact debate concerns partless atoms (paramāṇu). Its functional counterpart of the kalāpa is a different item, the smallest aggregate of eight substances (aṣṭadravyaka, ad II.22), the counterpart of the pure octad. So the comparison below is of the role of minimal units, and it does not identify the Kośa's atom with the Sammohavinodanī's paramāṇu (which §4.2 already keeps apart from the kalāpa). Second, the Kośa also has a conditioned space element. Besides unconditioned ākāśa (I.5), it names the cavity: dvāravātāyanamukhanāsikādiṣu chidram ākāśadhātvākhyam (I.28, [018|13]), "the hole in a door, a window, the mouth, the nose and so on is called the space element", which it says is light and darkness (ālokatamasī kila). That is a close parallel to the Vibhaṅga's ear-holes and nostrils (§4.3).
The two traditions share the premise: if minimal units truly touched, they would mix. The Vibhāvinī keeps the premise by making touching conventional only: "non-pervasion is non-touching" (abyāpitā hi asamphuṭṭhatā). They draw different conclusions:
| Do the units touch? | What is between them? | |
|---|---|---|
| Kashmiri Sarvāstivāda (Kośa ad I.43) | no | nothing ("nothing between them") |
| Theravāda sub-commentary (Vibhāvinī) | conventionally yes; strictly no (non-pervasion is non-touching) | something: delimiting matter, the non-mixing — counted among the material phenomena, though anipphanna and not an ultimate reality |
| Loop quantum gravity | grains share a face | something: the link, which carries area |
On this one question, the Theravāda answer and loop quantum gravity have the same shape: the between is not nothing. It is a named, counted item of the list (one of the twenty-eight material phenomena in one, a link in the other), and it is not itself one of the minimal units: not a kalāpa, not a node. The Kashmiri answer makes the between empty. ⚠️ Two limits on that shape. The Theravāda item is counted but is not an ultimate reality, and Karunadasa (1967) reads it as the mere limitation of matter, which moves it toward the Kashmiri nothing: what separates the two answers on that reading is that one names and counts the between and the other does not. And the two "neither" relations are opposite in incidence (§4.6, break 6). The Sarvāstivāda counts ākāśa among the unconditioned (I.5), which is the thesis the Kathāvatthu refutes, and separately names the conditioned cavity (I.28).
Both frameworks put the unit of spatial boundary at the adjacency between minimal units. In loop quantum gravity, a spin-network link is the face that two neighbouring grains of space share. In the Vibhāvinī, space is the non-mixing of touching neighbouring kalāpas, "the limit of matter", untouched by what it bounds and a constituent of neither. In neither framework is the boundary itself one of the minimal units. In both, "where" is defined by adjacency and not by a background: Rovelli's quanta "do not live in space", and the Visuddhimagga's space is "that by which one can say of delimited material things, 'this is above, below, around that'".
That is the whole of the claim. The next paragraphs give the tradition's reason for it; everything else in this section limits it.
Why the between is matter's, and never mind's. The tradition gives the reason, from the commentary on. The Paṭṭhāna commentary calls successive mind-moments contiguous "thoroughly without interval, because of the absence of shape" (saṇṭhānābhāvato suṭṭhu anantarāti samanantarā, abh03a.att.xml:7697). Its Mūlaṭīkā spells this out: mental phenomena, lacking shape as material phenomena have it, and with condition and conditioned never standing together, admit no division "this is below, above, across from that" (rūpadhammānaṃ viya saṇṭhānābhāvato paccayapaccayuppannānaṃ sahāvaṭṭhānābhāvato ca "idamito heṭṭhā uddhaṃ tiriya"nti vibhāgābhāvā, abh03t.tik.xml:4305), which is the Visuddhimagga's formula for what space does for matter (§4.3). Its Anuṭīkā ties the absence of division to shapelessness (abh05t.nrf.xml:4637), and the Vibhāvinī defines contiguity by it (saṇṭhānābhāvena suṭṭhu anantarapaccayo samanantarapaccayo, abh07t.nrf.xml:6653). Ledi Sayadaw draws the contrast in so many words: between two material clusters, even bound together in a stone pillar, "there is an interval, an opening; not so between the earlier and later two groups of mind and mental factors", which, having no shape, have no delimiter and no interval at all (dvinnaṃ rūpakalāpānaṃ majjhe antaraṃ nāma vivaraṃ nāma atthiyeva. Na tathā purimapacchimānaṃ dvinnaṃ cittacetasika kalāpānaṃ majjhe, Paṭṭhānuddesa-dīpanī, e0501n.nrf.xml:229).
The two reasons reach differently. Within one stream both hold: no two moments are present at once ("even for Buddhas, two minds do not occur together", buddhānampi hi dve cittāni ekato nappavattanti, Suttanipāta commentary, s0505a.att.xml:685), and what is present together in one moment, consciousness with its factors, is conjoined, "one in arising and ceasing, one in object and base" (ekuppādanirodhā ca, ekālambaṇavatthukā, manual ch. 2 §1, abh07t.nrf.xml:329), the opposite of the non-mixing that defines the delimiter. Across streams, where moments of two minds can be present at once, the second reason does not apply and shapelessness must do the work; these passages speak of succession within a stream and do not discuss that case.
Only the within-stream precondition has been checked by machine, in Lean 4, in the public repository SiliconWat/formal-abhidhamma (CC0; software concept DOI 10.5281/zenodo.23067241), file kala/Time.lean with the definitions in kala/Axioms.lean (commit deb9dec):
a stream s: moments, a successor map, and a clock tick : Moment → ℤ
one_at_a_time : tick a = tick b → a = b (A1: tick is injective)
a kalāpa k: birth : ℤ ; k present at t := birth ≤ t < birth + 17
between k₁ k₂ t := k₁ present at t ∧ k₂ present at t (co-presence only)
theorem mind_has_no_between (s) (t) : ¬ ∃ a b, a ≠ b ∧ tick a = t ∧ tick b = t
theorem matter_can_have_a_between : ∃ k₁ k₂, k₁ ≠ k₂ ∧ between k₁ k₂ 5 (a witness)What the check reaches is small. mind_has_no_between is the one-at-a-time axiom restated as the injectivity of tick; it never mentions between, which is defined only on kalāpas and only as co-presence. Kalāpas carry a birth on an integer line in mind-moment units and are attached to no stream. Nothing in the model touches, adjoins or has a shape, so neither the row's adjacency nor the shapelessness reason is formalised. The run script, re-run for this revision, checks these two and five more theorems in the file, and each of six deliberate breaks of the axioms (among them dropping the one-at-a-time axiom) makes the build fail. The file is exploratory, outside the repository's pre-registration, and its model is the authors'. The asymmetry is also a known shape: a stream is a chain (§3.1), and kalāpas present together play the part of an antichain, a set of elements none of which precedes another; that the between belongs to the antichain adds nothing specific to loop quantum gravity (§9).
The grain row survives only through the boundary row. Kalāpa against node, taken alone, is a comparison of a smallest-unit-of-matter with a smallest-unit-of-space. That is the general "smallest unit" comparison the census found common, and it fails on the matter/geometry distinction below. It earns a line in the table only because the boundary row presupposes minimal units with neighbours.
Recall from §3.1 that in a causal set the proper time between two related events is proportional to the length of the longest chain between them. There is no clock apart from counting. Two durations can be compared by comparing chain lengths, and the ratio is meaningful even though no unit of time is ever introduced. (Converting to seconds needs the sprinkling density, one element per Planck volume. The ratio does not need it.)
Three sub-moments per mind-moment. The manual (ch. 4 §8, abh07t.nrf.xml:1229): "Uppādaṭhitibhaṅgavasena khaṇattayaṃ ekacittakkhaṇaṃ nāma" — a mind-moment consists of three sub-moments: arising, presence, dissolution.
Seventeen mind-moments per material phenomenon. The next line: "Tāni pana sattarasa cittakkhaṇāni rūpadhammānamāyū" — seventeen such mind-moments are the lifespan of material phenomena. The manual then shows where seventeen comes from. It is the length of the longest process by which a sense object is known: one past life-continuum moment, two vibrations of the life-continuum, and fourteen moments of the process itself: "cuddasa vīthicittuppādā, dve bhavaṅgacalanāni, pubbevātītakamekacittakkhaṇanti katvā sattarasa cittakkhaṇāni paripūrenti" (§11, :1241). Seventeen is a consistency condition. A physical object must last as long as the longest process that cognises it.
The commentary gives the same figure in its own words: while matter persists, sixteen minds arise and cease, and it ceases with the seventeenth (rūpe dharanteyeva soḷasa cittāni uppajjitvā nirujjhanti. Taṃ pana sattarasamena cittena saddhiṃ nirujjhati, Sammohavinodanī, abh02a.att.xml:413). Its simile has a short-legged and a long-legged man walking together, sixteen steps to one, and its lesson is stated first: "matter cannot go on leaving mind behind, nor mind leaving matter; the going of both is of one measure" (rūpaṃ pana arūpaṃ arūpaṃ vā rūpaṃ ohāya pavattituṃ na sakkonti. Dvinnampi ekappamāṇāva pavatti, abh02a.att.xml:417).
Fifty-one sub-moments, with exceptions. The sub-commentary: "Visuṃ visuṃ pana ekapaññāsa cittakkhaṇāni honti. Rūpadhammānanti viññattilakkhaṇarūpavajjānaṃ rūpadhammānaṃ" — counted separately, they are fifty-one; "material phenomena" means those other than the intimations and the characteristic phenomena (abh07t.nrf.xml:4837). It then states the exceptions. The two intimations (bodily and vocal) last one mind-moment. Of the characteristics, arising and impermanence match the mind-moment's arising and dissolution sub-moments, and decay lasts forty-nine sub-moments. There is no single material clock.
Seventeen, sixteen and a third, or sixteen: the count is disputed. The Sammohavinodanī holds two rules. It first dates kamma-born matter by one stated "because it came in the [older] commentary" (aṭṭhakathāyaṃ āgatattā vuttaṃ): matter arisen at one mind's arising sub-moment ceases at another's (abh02a.att.xml:421), sixteen mind-moments and a third. It then rejects that rule as conflicting with the canonical Yamaka (imāya pāḷiyā virujjhati, :429) and replaces it with seventeen: matter arisen with the rebirth-linking mind ceases with the seventeenth, and matter arisen at that mind's presence sub-moment ceases at the arising of the eighteenth (:433). The Vibhaṅga Mūlaṭīkā reads the passage so (abh02t.tik.xml:305), and finds both the seventeen and the older "sixteen and a third" (yā ca aṭṭhakathāyaṃ tatiyabhāgādhikasoḷasacittakkhaṇāyukatā, :309) at odds with the commentary's own account of death and rebirth-linking, in which eleven mind-moments of an object's life have passed and five remain (abh02a.att.xml:2889; e0102n.mul.xml:4045). Its Anuṭīkā concludes "sixteen only" (abh02t.tik.xml:4933), and four lines later speaks of "sixteen or seventeen" (soḷasahi sattarasahi vā cittakkhaṇehi, :4937). The Vibhāvinī reports the sixteen as the view of "some" (keci) and rejects it as without substance (tayidamasāraṃ), citing the replacement rule, and reads any sixteen as a count of the moments fit to condition mind (abh07t.nrf.xml:4845); Ledi Sayadaw finds that rejection "not good" (taṃ na sundaraṃ, e0301n.nrf.xml:2745). Seventeen is the manual's figure and the Vibhāvinī's, not a settled one.
The presence sub-moment is disputed too. The Vibhāvinī reports that "some reject the presence moment of consciousness" (keci pana cittassa ṭhitikkhaṇaṃ paṭisedhenti), because the canonical Yamaka names only arising and dissolution (bhaṅguppādāva kathitā, na ṭhitikkhaṇo, abh07t.nrf.xml:4833). It names no one; the cross-reference to the Vibhaṅga Mūlaṭīkā beside the passage is the edition's. The Mūlaṭīkā does raise the question in its own voice, on the same ground: "whether it exists or not is to be examined" (so ca atthi natthīti vicāretabbo, abh02t.tik.xml:313). Sumaṅgala rejects the dissent, citing the commentary's three sub-moments. Without presence, this paper's arithmetic gives 17 × 2 = 34 in place of 51 (the dissent states no count), and decay's forty-nine sub-moments would be undefined.
An absolute scale, named but not timed. The Vibhaṅga commentary says of feeling, a mental factor present in every consciousness, that "in the moment of a finger-snap it arises and ceases a hundred thousand koṭi times" (ekaccharakkhaṇe koṭisatasahassasaṅkhyā uppajjitvā nirujjhati, abh02a.att.xml:533). The texts say what a finger-snap is without giving it a duration. The Aṅguttara commentary names it by a gesture, "the mere making of a sound by striking two fingers" (dve aṅguliyo paharitvā saddakaraṇamattanti attho, s0401a.att.xml:1119). A Pāli grammar, the Payogasiddhi, makes it the unit of vowel length: "the short time is the time called a finger-snap or an eye-blink; by it the short vowel has one measure" (rassakālo nāma accharāsaṅghāto akkhinimmilanasaṅkhāto vā kālo, tena ekamatto rasso, e0807n.nrf.xml:205). Each fixes a unit of reckoning, not a number of seconds. This paper takes a finger-snap as about a tenth of a second, and that assumption is its own.
The texts state the rate of mind itself as round lower bounds in four works, not as one number:
| Work (layer) | Locus | Words | Reading |
|---|---|---|---|
| Saṃyutta commentary, on SN 12.61 (commentary) | s0302a.att.xml:1463 | ekasmiñhi accharākkhaṇe anekāni cittakoṭisatasahassāni uppajjanti | many × 10¹² mind-moments per snap |
| Milindapañha, quoted on the next line of the same commentary | s0518m.nrf.xml:2838; s0302a.att.xml:1467 | ekaccharākkhaṇe pavattacittassa ettakā vīhī lakkhaṃ ṭhapīyamānā … parikkhayaṃ pariyādānaṃ gaccheyyuṃ | more minds in a snap than grains in over a hundred cartloads of rice |
| Sāratthadīpanī, on the Vinaya (sub-commentary) | vin01t2.tik.xml:341 | accharāsaṅghātamatte khaṇe anekakoṭisahassacittappavattisambhavato | many × 10¹⁰ per snap |
| Dhammasaṅgaṇī Anuṭīkā (sub-commentary) | abh04t.nrf.xml:821 | accharāsaṅghātakkhaṇena anekakoṭisaṅkhāya cittuppattiyā | many × 10⁷ per snap |
The readings take koṭi as 10⁷, satasahassa as 10⁵ and sahassa as 10³; aneka, "not one", makes each a floor. Read strictly as "at least two", it would put the first floor at 2 × 10¹², above the commentary's own flat 10¹² for feeling, which arises and ceases with its mind; so either aneka is not a strict floor of two, or two of Buddhaghosa's commentaries differ by a factor of two. This paper reads the figures as round orders of magnitude. None of the four works states a ceiling. On the tenth-of-a-second assumption, the floors put a mind-moment at or below about 10⁻¹³ to 10⁻⁸ seconds, far below any timescale on which perception is measured.
The texts deny that this succession is seen by the reasoner and by "others", not by everyone. The Dīgha commentary says the speculative reasoner of DN 1 "does not see the breaking up of mind" (cittassa bhedaṃ na passati), because each mind-moment ceases only after conditioning the next, and so takes mind to fly on elsewhere like a bird (s0101a.att.xml:2245): a diagnosis of his error. The Sāratthadīpanī says the order of a Buddha's teaching "is not discerned by others", while the order of several monks' questions "is discerned by one so wise" (pucchanavāro tādisassa paññavato paññāyati … Buddhānaṃ pana desanāvāro aññesaṃ na paññāyateva, vin01t2.tik.xml:341), and the Vibhaṅga Anuṭīkā reserves true knowledge of the elements to the Tathāgata (nānādhātūsu tathāgatasseva yathābhūtañāṇaṃ, abh02t.tik.xml:4937). So the tradition does give the mind-moment an outside scale, the snap, and the offer cannot be taken as a measurement. (Three of the four floors were supplied by the refuter of the formal-abhidhamma run rate-of-mind control, 2026-09-30, runs/2026-09-30-rate-of-mind-control/RUN.md.)
The Abhidhamma measures the lifetime of matter in mind-moments. This paper counts the lifetime by its elements, as the manual does (sattarasa cittakkhaṇāni, seventeen moments), because each mind-moment is itself a stretch of time. A causal-set chain is conventionally counted by its links, since its elements are points; the difference of one does not matter at large counts, but it does at seventeen.
Two cases, which the texts treat differently. An earlier version of this paper had matter "timed by the mind's chain". The texts support that where a stream exists, and not where none does.
abh02a.att.xml:421), dates mind-born and kamma-born matter from the mind it arises with to the seventeenth (:429–:433, §5.2), and ends the kamma-born series with the death-mind (tato paṭṭhāya kammajarūpapaveṇī na pavattati, :425). Mind dates this matter without conditioning it: after rebirth-linking, kamma-born matter goes on "without mind, from kamma alone" (vinā cittena kammatova kaṭattārūpānaṃ pavatti hotīti, Paṭṭhāna commentary, abh03a.att.xml:7857).abh03m1.mul.xml:421; the Vibhaṅga lists it, abh02m.mul.xml:3685), and the Kathāvatthu (III.11) refutes an opponent who read DN 1's line that these deities fall away "when perception arises" (saññuppādā ca pana te devā tamhā kāyā cavanti, s0101m.mul.xml:487) as proof of perception among them (abh03m3.mul.xml:5797). The Paṭṭhāna commentary calls it the place of matter, where "material phenomena arise without even a rebirth-linking mind as a mental condition" (paṭisandhicittamattampi arūpapaccayaṃ vinā rūpadhammāva uppajjanti, abh03a.att.xml:7861). The manual gives them no occurrence of mind at all (sabbathāpi cittappavatti natthevāti, abh07t.nrf.xml:1485; also :1957, :2349) and a lifespan of five hundred aeons (:1693), and the Dīgha sub-commentary answers "for how long?" in aeons: "at most five hundred great aeons", by the momentum of the kamma, like an arrow from a bow (ukkaṃsato pañca mahākappasatānipi tiṭṭhanti asaññasattā. Jhānavegeti asaññasamāpattiparikkhate kammavege, s0101t.tik.xml:2053). Matter outside every being is the same case: temperature produces matter "internally and externally" (ajjhattañca bahiddhā ca, manual ch. 6 §35, abh07t.nrf.xml:2213), and what lies outside one's continuum is external "whether bound to faculties or not" (indriyabaddhā vā anindriyabaddhā vā, Atthasālinī, abh01a.att.xml:3485), like the two trees of §13.So the general statement of seventeen is not tied to a present mind. The Vibhāvinī glosses the manual's "seventeen mind-moments" as "moments like the moments of seventeen minds" (sattarasannaṃ cittānaṃ khaṇāni viya khaṇāni, abh07t.nrf.xml:4837; likewise "one mind-moment", :4849), and Ledi Sayadaw calls the division of one moment into mind's and matter's a conceptual construction (kappanāvasena, e0301n.nrf.xml:2749). That is the reading of the seventeen as a unit of reckoning, a duration counted in mind-moment lengths. It is not the only reading open: the Vibhaṅga Anuṭīkā derives matter's longer life from its being made known by mind, in sixteen or seventeen mind-moments (abh02t.tik.xml:4937), which leaves the reading that the count describes matter as cognised, and says nothing of matter no mind cognises.
Where a stream exists, the texts date its mind-born and kamma-born matter on its own mind-moments, sub-moment by sub-moment, without making mind that matter's condition. Where none exists, no text counts matter in mind-moments: the mindless beings' material series is timed by kamma's momentum in aeons, and a sub-commentary makes the mind-moment a unit. What survives of the causal-set comparison is generic: a duration stated as a count of steps (§9).
The row's name, ratio, needs one correction. The ratio is 17 : 1, a material lifetime against one mind-moment, but both terms are measured in the same unit. Matter has no chain of its own in S, so the row gives a ratio of durations, not a ratio of two chain lengths.
A second reckoning, and how the texts relate it. Asked how long an aeon (kappa) is, the Buddha answers that it is not easy to count in "so many years, or so many hundreds of years …" (so na sukaro saṅkhātuṃ ettakāni vassāni iti vā, ettakāni vassasatāni iti vā) and gives the simile of a mountain a league on each side, wiped with a cloth once a century, which would wear away before the aeon ends (SN 15.5, s0302m.mul.xml:3529–:3533; past aeons are "not easy to count", SN 15.8, :3565). The aeon is not counted in years; the simile sets it against a process timed in centuries. The texts do relate it to the mind-moment, in the mindless beings' case, and the relation is divergence. Since "the usage 'time' rests only on the occurrence of phenomena", the Paṭṭhāna Mūlaṭīkā finds "no time-interval" between the death before that existence and the rebirth-linking after it, for "the occurrence of matter makes no interval in the occurrence of mind, because it is another series" (kālantaratā natthi … na ca rūpadhammappavatti arūpadhammappavattiyā antaraṃ karoti aññasantānattā, abh03t.tik.xml:4309); its Anuṭīkā names the objection this answers, "how then is it said, 'having passed five hundred aeons'?" (abh05t.nrf.xml:4641). The Paṭṭhāna commentary had already rejected a view of "the teachers" that contiguity means nearness in time, because the attainment before cessation is still the contiguity condition of the fruition after it, and granted that "there is no nearness in time there" (kālānantaratā natthi, abh03a.att.xml:7697); the Vibhāvinī follows it and counts the rebirth-linking that arises "even after a time-interval" from the mindless existence the same way (kālantarepi, abh07t.nrf.xml:6653). Ledi Sayadaw: "between two minds, in the non-percipient existence, the person stands without mind for five hundred aeons" (dvinnaṃ cittānaṃ antare asaññasattabhave pañcakappasatāni puggalo acittako tiṭṭhati, e0501n.nrf.xml:233). The two reckonings meet and do not agree: five hundred aeons in one, no interval in the other. As a lens only, the pair recalls relativity's proper time along a worldline and the cosmic time of the expanding (FLRW) cosmologies; nothing in the likeness is a prediction. For this row the divergence settles one point: the aeon is not a second chain for the seventeen to be compared with.
s0401t.tik.xml:1666). The Milindapañha grades seven kinds of mind, from those that "arise heavily and go on slowly" (garukaṃ uppajjati dandhaṃ pavattati) to a Buddha's, quicker "by an incalculable degree" (s0518m.nrf.xml:2842–:2870), without saying whether the moment or the process is quicker; the Sāratthadīpanī reads a Buddha's speed as a brief dwelling in the life-continuum (bhavaṅgaparivāso lahuko, vin01t2.tik.xml:341), not a shorter moment. On those readings "longest" selects nothing; read as moment lengths, the Milinda's grades would narrow this break.abh07t.nrf.xml:1237), but the Vibhāvinī glosses that count as a unit (abh07t.nrf.xml:4849, §5.3). A muon, moreover, is a series (santati), not a kalāpa, and the texts let a series' duration vary: "as series, phenomena are short-lived or long-lived as opposing or favourable conditions meet; by their own characteristic they are of one measure" (pabandhavasena hi … parittakālā dīghakālā ca honti, sabhāvalakkhaṇavasena pana ekaparicchedā, Dhammasaṅgaṇī Anuṭīkā, abh04t.nrf.xml:821). They also make an interval only within its own series (abh03t.tik.xml:4309). So the measured muon meets no textual claim directly: what conflicts with dilation is an unmeasured, frame-independent per-kalāpa count; the place of a duration within its series is textual; physics adds the Lorentz factor. The verdict is a collision with a reading, never agreement.The first version of this lens had a fifth row: saṅkhāra, the conditioned as a whole (sabbe saṅkhārā, "all conditioned things"), against Fotini Markopoulou's quantum causal histories. That framework puts quantum state spaces on a causal set, and so joins causal order to quantum structure.
It was cut before drafting, for two reasons.
The neighbour, stated accurately. Markopoulou's 2000 paper assigns a finite-dimensional Hilbert space (a quantum state space) to each event and evolution operators between sets of events. The same paper already notes a problem: the evolution does not see the individual causal relations. It proposes, as an alternative, attaching the Hilbert spaces to the edges (the covering relations) and the operators to the events. On that reading, the state space on an edge from p to q is "the state space of p as seen by q". Hawkins, Markopoulou and Sahlmann (2003) then revised the definition. They put operator algebras on the events and made each causal relation carry a completely positive map, the most general quantum transformation, so that the evolution respects every individual relation.
There is an irony here, and it is recorded rather than used. Both moves make the relation a carrier of structure. That fits the Paṭṭhāna's relation-first typing better than the original event-first definition did, but it does not rescue the row. A typed relation carrying a completely positive map is still not a relation of object, predominance or kamma.
The best-known meeting of Buddhist thought and physics is Carlo Rovelli's reading of Nāgārjuna (cross-tradition: Madhyamaka) beside relational quantum mechanics, in Helgoland. On the relational view, a system has properties only relative to another system. On Nāgārjuna's, nothing has own-being (svabhāva): everything is empty of intrinsic existence. Rovelli finds the two congenial.
This paper does not use that pairing, for a reason of structure and not of loyalty. Madhyamaka denies own-being (svabhāva) to every dharma, so it admits no ultimately real units to put in adjacency. The Theravāda Abhidhamma is realist about dharmas: its moments, its material phenomena and its conditions are real events. A discrete theory needs discrete units and relations among them. The Theravāda supplies both, so it is the Buddhist framework that can be compared structurally with causal sets and spin networks. It is also the framework whose space can be put beside a link: space as the delimitation between real units. One point weakens the contrast and should be stated. The boundary at the centre of the adjacency row is the one Theravāda item defined as lacking own-nature (anipphanna). The units are real (nipphanna, concretely produced); their delimitation is not a unit. So the argument for the Theravāda over Madhyamaka rests on the units, not on the boundary: a discrete comparison needs real units, and only the Theravāda supplies them. The Madhyamaka comparison is a comparison of attitudes toward relation. It is real, but it is a different comparison.
The institution's ruling, stated plainly. The institution publishing this paper has ruled, for its own purposes, that delimiting space (paricchedākāsa) is conditioned; open space and the space of a removed meditation disk (kasiṇa) are concepts (paññatti); and only nibbāna is unconditioned. The ruling follows the Theravāda reading of the space element as delimiting matter, and it declines the Sarvāstivāda reading of ākāśa as unconditioned. It follows the texts at each point. The canon's Kathāvatthu refutes "space is unconditioned" (VI.6). At the close of the same debate (§462) the Theravādin also declines to call space conditioned without qualification, and the commentary supplies the qualification: it is delimiting space that is conditioned, while open space and meditative space are mere concepts. A concept is not an unconditioned phenomenon, so nothing is left unconditioned but nibbāna. The Sarvāstivāda draws a comparable line: beside its unconditioned ākāśa (Kośa I.5), it names a conditioned space element, the cavity (I.28), as §4.4 records.
Objection. "The Abhidhamma is a phenomenology: an analysis of what appears in experience, made for the purpose of liberation. Quantum gravity is a theory of what spacetime is. The kalāpa contains colour, odour and taste, which are qualities of matter as sensed. The Kathāvatthu commentary says that space between two trees is known by the mind, from the absence of visible matter, not seen by the eye. A comparison of the two frameworks compares an account of knowing with an account of being. Any shared shape is a coincidence of two different questions."
What survives it. Most of the objection stands, and the paper does not answer it away. Every row compares formal shape: an acyclic relation, a boundary located at an adjacency, a duration expressed as a count. Shape is the only thing two frameworks with different subject matter can share, and it is all this paper claims they share. The objection does not show that the shapes differ. It shows that shared shape proves nothing about shared subject matter, and the paper agrees. What the objection does remove is any reading of the lens as evidence that the Abhidhamma knew physics, or that physics vindicates the Abhidhamma. Neither reading was offered, and the objection makes sure neither can be taken.
The strongest claim is the adjacency row (§4.5). Against it: the idea that a boundary lives at the adjacency is not specific to loop quantum gravity. It holds in any cellular picture of extended stuff: a cell complex, a Voronoi tessellation, a chessboard, and Regge calculus (Regge 1961), in which curved spacetime is approximated by flat simplices glued along shared faces, and the geometry is fixed by the edge lengths of neighbouring cells. The Western literature on boundaries has argued the ownership question directly. When two bodies touch, does the boundary belong to one of them (Bolzano), to neither (a view the literature traces to Leonardo), or is it two coincident boundaries, one belonging to each (Brentano)? (Varzi's survey; Casati and Varzi 1999, ch. 5.) The "neither" view is the nearest Western neighbour of the manual's "a constituent of neither". Brentano's is a contrast: his coincident boundaries are dependent parts of the bodies they bound, which is the opposite of the Vibhāvinī's delimiter, untouched by both. Aristotle defined place as the innermost boundary of the containing body (Physics IV.4), a boundary account of where that is two millennia old and owes nothing to quanta. The Kośa's debate (§4.4) shows the Indian schools arguing the same question in the first millennium. If the shared shape is generic, then the match with loop quantum gravity specifically is weaker than the table makes it look.
What loop quantum gravity adds to the generic picture is that the adjacency carries a quantised magnitude, and that volume is derived from it. Those are exactly the two features the Abhidhamma lacks (§4.6, breaks 1 and 2). So the part of the row that is loop-quantum-gravity-specific is the part that fails, and the part that holds is generic. The row survives only in this form: the Theravāda sub-commentary's answer to "what is between minimal units?" has the shape of the answer loop quantum gravity gives, and not the shape of the answer an earlier Indian school gave. The paper does not refute the generic reading. It claims no more than that.
The same counter-argument, run on the ratio row (§5.3). Against it: every discrete clock counts steps, so "a duration is a count" is not specific to causal sets. The causal-set-specific features are three: proper time is the length of the longest chain, whichever chain that is; the relation between chain length and proper time is statistical, holding on average over a random sprinkling; and there is no time apart from the order. The first two are among §5.4's breaks, and the third is left open (§3.4). So, as with the adjacency row, what holds for certain is generic: a duration stated as a count of steps (§5.3).
| Row | The finding | Falsified by |
|---|---|---|
| 1 Order | the earlier→later sub-relation S, over condition-modes, is acyclic (by selection); a strict order, not yet a causal set, can be read over it; S also orders moments of different streams; the rest is extra typing | a member of S with the conditioned arising at or before the condition, in any layer; cross-moment kamma with a present or future relatum; an implied temporal order S cannot connect (engaged in a narrowed form between streams, §3.4; open within a stream) |
| 2–3 Adjacency | both put the unit of spatial boundary at the adjacency between minimal units, and neither makes it a unit; the shared part is generic; the between is matter's and never mind's, for the tradition's own reason | a text making delimiting matter a kalāpa constituent, or placing space inside a cluster; a text with two moments of one stream present at once, with mind given shape, or with space delimiting mental phenomena; a formulation of loop quantum gravity in which area between adjacent grains is not carried by their adjacency; a reading of the Vibhāvinī's space as mere absence (partly engaged, §4.7) |
| 4 Ratio | matter dated on a stream's own moments where there is one, a unit where there is none; only the generic part survives, a duration as a count of steps; the aeon meets the mind-moment only as divergence | a text timing matter independently of mind-moments; a text counting the mindless beings' matter, or external matter, in some present mind's moments; a text counting the aeon in mind-moments; seventeen shown to be observed rather than derived |
| The scale (§5.2) | the snap is named, not timed; the rate is round lower bounds in four works, with no ceiling | a text giving the finger-snap a duration, or the rate an upper bound |
| The dropped row | saṅkhāra ↔ quantum causal histories adds no structure | a structural feature of quantum causal histories with a Paṭṭhāna counterpart not already in rows 1–4 |
The authors' stake. The authors write from within the Theravāda. The institution publishing this paper grounds its values in the Pāli canon, has ruled the Theravāda reading of space over the Sarvāstivāda one, and uses the word space on an organisational map of its own. Nothing in this paper bears on that map, and the ruling was made so that the map would not borrow a predicate it should not have. There is a pull, for authors in this position, to see the tradition anticipate frontier physics; the founder's own question began as a hope that the Abhidhamma might hold the bridge between the discrete and the smooth. The pull was acted on, and caught. An adversarial review before any prose dropped a row, merged two and narrowed the order row; outside review caught summaries that outran their own sections; and the 2026-09-30 revision withdrew three statements of the deposited text: that matter is "timed by the mind's chain" (§5.3), that nothing in S orders moments of different streams (§3.4), and that the finger-snap figure is one rhetorical number (§5.2). The sibling paper's first framing made the same kind of error in the other direction. The reversals are part of the result.
Done:
tipitaka-xml commit 05d5d3c, with fifteen lines of context and a mechanical check of each quotation; kala/Time.lean and kala/Axioms.lean (commit deb9dec) read and their run script re-run (seven theorems check, six breaks fail); the run rate-of-mind control read for its three floors only; Rossi and Hall (1941) read in a scanned copy; and the revision's draft put through an adversarial review, whose corrections it carries.Not done:
The Kathāvatthu commentary gives a small example. A person looks at two trees. The eye sees the trees. The mind, finding no matter between them, knows "space". Loop quantum gravity, asked where the space is between two grains, also answers between, and puts a number on it, which the text does not. The shared part is the generic one (§9). The two answers share that shape and have two subjects. This paper records the shape and marks the boundary between the subjects, which, as in the text it reads, belongs to neither side.
| Venue | Identifier |
|---|---|
| Primary canonical | <https://thonly.org/research/abhidhamma-and-discrete-quantum-gravity> |
| GitHub | <https://github.com/thonly/publications/blob/main/defensive-publications/abhidhamma-and-discrete-quantum-gravity.md> |
| Sibling paper | <https://thonly.org/research/the-vibhajjavadin-view-of-time> |
| Census pre-registration (public) | thonly/publications commit 7348ba2, timestamps/census/physics-lens-prereg.md |
| Sibling paper (the Paṭṭhāna's relations) | <https://thonly.org/research/patthana-typed-causation-vocabulary> |
| Lean 4 formalisation (public, CC0) | <https://github.com/SiliconWat/formal-abhidhamma> (kala/Time.lean, kala/Axioms.lean); software concept DOI 10.5281/zenodo.23067241 |
The authors thank the Vipassana Research Institute for the Chaṭṭha Saṅgāyana texts; the GRETIL project and the editors of its Abhidharmakośabhāṣya e-text; and the physicists whose lectures and primers are written to be read by people outside the field. The reading of the sources, the adversarial review and the drafting were done with Miss Aquarius, the name under which this institution discloses its AI collaboration.
Physics
Pāli and Sanskrit sources (Chaṭṭha Saṅgāyana edition, VRI tipitaka-xml, unless noted; file:line references are to the romn/ text at commit 05d5d3c)
abh01m.mul); §652, kamma-produced visible form (abh01m.mul.xml:5549).abh02m.mul.xml:3685).abh03m1.mul.xml:421).abh03m3.mul.xml:5797); VI.6 Ākāsakathā, §460–462; VI.7, §463 (abh03m3.mul).abh03a.att).abh03a.att.xml:7697); on the root condition, kamma-born matter going on without mind, and non-percipient existence as the place of matter (:7857, :7861).e0101n.mul, e0102n.mul; e0102n.mul.xml:4045).abh02a.att.xml:533); the lifetime of matter, the two walkers, and the older and replacement rules for dating kamma-born matter (abh02a.att.xml:409–:433); the death-and-rebirth passage (abh02a.att.xml:2889).abh01a.att.xml:3485, :3721).abh02t.tik.xml:305, :309, :313, :4933, :4937).abh03t.tik.xml:4305, :4309; abh05t.nrf.xml:4637, :4641).abh07t, bound with the sub-commentary): among others abh07t.nrf.xml:329, :1229–:1241, :1485, :1693, :1957, :2169, :2213, :2273, :2277, :2349, :2865, :2873, :2909, :2913.abh07t): among others abh07t.nrf.xml:4833–:4849, :5553, :6653.abh03m7.mul): §427 (kamma across moments, abh03m7.mul.xml:6065); the modes of the presence, dissociation and support conditions.s0101m.mul.xml:487).s0302m.mul.xml:3529–:3533, :3565).s0101a.att.xml:2245); and the Dīgha sub-commentary on DN 1, the mindless beings' material series (s0101t.tik.xml:2053).s0302a.att.xml:1463, :1467).s0401a.att.xml:1119); and the Aṅguttara sub-commentary on AN 1.48, every mind of the same moment (s0401t.tik.xml:1666).s0505a.att.xml:685).vin01t2.tik.xml:341).abh04t.nrf.xml:821).s0518m.nrf.xml:2838–:2870).e0807n.nrf.xml:205).e0301n.nrf.xml:2745, :2749); Paṭṭhānuddesa-dīpanī, on the between and on the mindless existence (e0501n.nrf.xml:229, :233).Other neighbours
kala/Time.lean, kala/Axioms.lean, and the run runs/2026-09-30-rate-of-mind-control/. <https://github.com/SiliconWat/formal-abhidhamma>; concept DOI 10.5281/zenodo.23067241.