Canonical: https://thonly.org/research/once-sunk-always-sunk · Licence: CC0 1.0
This study asks whether the Theravāda Buddhist texts commit a reader to the claim that every being can still become an arahant (a fully awakened disciple). It takes a six-part thesis posed by the first author on 2026-10-13, that beings are mind streams, are infinite in number, have infinitely many past lives, each had a past life in hell, that such a life is required for awakening, and so that every being has the potential to awaken, and checks each link against the Pāli canon, its commentaries and sub-commentaries, and a machine-checked encoding in the Lean 4 proof assistant. The first links hold or fail for plain reasons. A being's infinite past follows from the Abhidhamma's proximity condition, a derivation a sub-commentary already makes; the number of beings is "incalculable, its limit not discerned" in the canon and "infinite" only in the commentary; a past life in hell is neither forced nor excluded by anything found, and the need for one stands or falls with it. The sixth link is the center. The Vibhaṅga lists who is incapable of the path and who is capable, without a duration. The Kathāvatthu (XIX.7) refutes "absolute fixity for a worldling," which a commentary attributes to some Uttarāpathakas reading the Aṅguttara's "once sunk, stays sunk," and its reductios argue within a single life. The commentaries then differ in wording: the Aṅguttara commentary says, in its own voice, that fixed wrong view has "no limit … neither heaven nor path," while the Majjhima and Kathāvatthu commentaries fix it "in one existence only," hedged "mostly"; the sub-commentaries read repeat one argument (otherwise fixity in wrongness would be absolute), and the one on the Aṅguttara passage itself glosses the strong wording conditionally, as not a total absence of emergence. Encoded formally, the thesis entails the Kathāvatthu's answer, is refuted on the literal reading of the sutta, and is otherwise left open; the Kathāvatthu's answer alone does not give it, since the debate touches two of the Vibhaṅga's obstructions (the kamma- and the defilement-obstruction) and leaves the result-obstruction and faithlessness untouched. Whether every being will awaken, as opposed to can, is a question the Buddha leaves unanswered in AN 10.95, which the commentary files as a question to be set aside. The Abhidhamma's Yamaka formula "worldlings who will not obtain the path" partitions worldlings; a Kathāvatthu sub-commentary reads it as the incapable type, while another sub-commentary cites it under the hedged "mostly" idiom; no layer states a duration. A Yogācāra contrast is tagged as a cross-tradition import. The first author's predictions of PROVED are reported as scored: a miss on two links, unreachable on the sixth. Each finding carries its break.
Keywords: Buddhism, Theravāda, Abhidhamma, Kathāvatthu, Points of Controversy, absolute fixity, accantaniyāmatā, niyāma, abhabba, incapacity for the path, universal awakening, buddha-nature debate, icchantika, agotra, Aṅguttara Nikāya, Udakūpamā Sutta, once sunk, stays sunk, saṃsāra-stump, beginningless saṃsāra, rebirth, hell, Vibhaṅga, Puggalapaññatti, commentary, sub-commentary, Lean 4, formal verification, pre-registration
The paper uses Pāli technical vocabulary because it reads Pāli texts. An indexer searching in standard terms should find each concept under the term in the middle column. Layer tags: mūla is the canonical text; aṭṭhakathā the commentary; ṭīkā the sub-commentary; [X] a cross-tradition import, outside the Theravāda corpus this paper checks.
| Term as the tradition writes it | Standard term used in this paper | Layer where it is defined |
|---|---|---|
| abhabba, bhabba | incapable of, capable of (entering the path) | mūla (Vibhaṅga §826–827; AN 6.86) |
| niyāmaṃ okkamati | enters the fixed course (of rightness) | mūla |
| micchattaniyata, niyatamicchādiṭṭhi | fixed in wrongness; fixed wrong view | mūla (Dhammasaṅgaṇī §1035) |
| accantaniyāmatā | absolute (final) fixity | mūla (Kathāvatthu XIX.7); commentary |
| sakiṃ nimuggo nimuggova hoti | "once sunk, stays sunk" | mūla (AN 7.15) |
| saṃsārakhāṇuka, vaṭṭakhāṇu | stump of saṃsāra (one who does not emerge from the round) | aṭṭhakathā |
| kammāvaraṇa, kilesāvaraṇa, vipākāvaraṇa | the kamma-, defilement- and result-obstruction | mūla (Vibhaṅga §826) |
| yebhuyyena | "mostly" | mūla (DN 1 §39); commentaries |
| neyyattha, nītattha | a meaning that must be drawn out; an explicit meaning | ṭīkā |
| anantarapaccaya | proximity condition (each mental moment conditions its immediate successor) | mūla (Paṭṭhāna); commentary |
| santo saṃvijjamānā lokasmiṃ | "found in the world" (existence clause) | mūla (AN 7.15) |
| INDEPENDENT / PROVED / REFUTED | neither provable nor refutable from the stated premises / proved / the negation proved | the formal runs |
| held-out answer | the text's own answer, kept out of the premises so a proof cannot restate it | the formal runs |
| CAN / WILL | some possible history in which the being becomes capable / the actual history in which it does | this paper's reading of the thesis |
| agotra, icchantika, atyantaparinirvāṇadharmaka | [X] beings without a lineage for awakening; "those of great desire"; those of the nature never to attain nirvana | Yogācāra and tathāgatagarbha literature (not read here) |
Layers. Every Pāli line is tagged by the layer that says it: the canonical text (mūla), the commentary (aṭṭhakathā), the sub-commentary (ṭīkā), or a later treatise. A commentary's report of someone else's view (vadanti, "they say"; the Uttarāpathakas) is attributed to that holder together with the commentary's own verdict on it. A sub-commentary paragraph is split into its voices before it is quoted: the base commentary it quotes, and its own gloss.
Lines. file:line is the Chaṭṭha Saṅgāyana (CST) Tipiṭaka as in the VipassanaTech/tipitaka-xml romanized text at upstream commit 05d5d3c. Every Pāli quotation here was checked against its line with the project's reader tools; a quotation that failed on first transcription was corrected to the text's own spelling. Translations of Pāli are the authors' own and literal.
The runs. Three public, pre-registered runs underlie the formal parts (SiliconWat/formal-abhidhamma: runs/2026-10-13-first-thesis-past-lives-and-hell/ for links 3–5; …-sixth-supposition-potential/ and …-sixth-supposition-in-the-world/ for link 6). Each registered its question, premises, held-out answer and predictions in a file pushed before the proof was attempted. The method notes (held-out answers, leak check, isolated breaks) belong to the series' method paper, The Abhidhamma Compiled No. 5, and are not repeated here; this paper reports only what is needed to read the tables. Three terms matter. PROVED means the statement was derived from the listed premises alone. INDEPENDENT means models show both the statement and its negation consistent with them. NOT STRONG is the grade the runs' own rubric gave, meaning at least one rubric item failed; each failure is declared in the run file. This study is not part of the MA-sole Theorems of the Abhidhamma series: no run was graded strong, and the thesis is the first author's, not the machine's.
What this paper does not say. Abhabba is a capacity word. It is conditional (on obstructions, and on hearing the Dhamma: AN 6.86 says the six-quality person is incapable "even while hearing," s0403m2.mul.xml:3050) and indexed to a birth (Kathāvatthu XIII.4: bhabbo bodhisatto tāya jātiyā dhammaṃ nābhisametunti?, "is the bodhisatta, in that birth, capable of not penetrating the Dhamma?", abh03m3.mul.xml:10353). It is never a shared essence and never a property of a named person. Nothing in this paper is a verdict that any being, living or dead, is incapable of awakening. The texts are asked what they say about classes and about possible histories; where a commentary names a historical teacher as its instance of a class, this paper does not name him, because it gives no verdict on any person.
This paper is a study: it discloses readings of texts and the results of formal checks, not a mechanism. Its findings are listed at the width that survived the quick census reported below (the commentaries' division as a mapped finding, the two-obstruction scope of the Kathāvatthu's answer, the machine-checked chain, and the cross-tradition comparison), each with what would break it. Findings 1–4 and 9 are readings the census did not cover; they assert no priority. Where a finding rests on a published result, that result is cited, not claimed.
s0303m.mul.xml:3601). The definition includes matter. The Vibhaṅga lists a non-percipient existence (asaññābhava) among the existences (abh02m.mul.xml:3685); the run's axiom reads it as born without a rebirth-linking citta, which the run labels commentarial. The formal chain treats a being as one mind stream and is true to that frame only. Breaks if: a canonical text defines a being as a stream of mind alone, or the non-percipient existence is shown to contain a citta.s0511m.mul.xml:791), the mass of beings among them; its commentary glosses the mass of beings as "infinite, immeasurable, unmeasurable" (sattakāyo ananto aparimāṇo appameyyo, s0511a.att.xml:2369). The phrases anantā sattā and sattā anantā do not occur in the mūla text. Breaks if: a canonical text states the number of beings is infinite in its own voice. The argument for beginninglessness is in The Vibhajjavādin View of Time (§4.1), not here.abh03a.att.xml:9117), that each moment conditions its successor, and that an existence with mind begins with a rebirth-linking citta, a being with a citta now has infinitely many past existences (run 1, theorem T3, PROVED, constructive, each premise shown needed). A Vinaya sub-commentary (the Vajirabuddhi-ṭīkā) makes the same derivation, incidentally, in a gloss on the word "paṭhamaṃ" in the Pārājika on killing (vin06t.nrf.xml:2177), so this is a check of the texts, not a discovery. Supposition 4 (every being has a hell life in the past) is INDEPENDENT of these premises: the texts' laws about destinations count populations ("few … far more," the Nakhasikha discourse, s0302m.mul.xml:5223), which a one-being model cannot state. Supposition 5 (a hell life is required for awakening) follows from 4 read at every moment and stands or falls with it. For the Buddha himself the Apadāna states a hell life (s0510m1.mul.xml:44655): one stated case, no law. Breaks if: a Theravāda text is found asserting a past hell life of every being or its necessity for awakening; or a model with the world's destinations encoded admits no no-hell history.abh02m.mul.xml:9965, :9969). AN 6.86 gives the same six as one person's qualities and adds "even while hearing." Capacity is shown to change within a birth: had Ajātasattu not killed his father, the Dhamma-eye would have arisen on that very seat (imasmiññeva āsane … dhammacakkhuṃ uppajjissathā, DN 2 §253, s0101m.mul.xml:1477). Contrast with supposition 5. The Aṅguttara commentary on AN 6.86 glosses the same three obstructions: the kamma-obstruction as the five heinous deeds (pañcānantariyakammehi), the defilement-obstruction as fixed wrong view (niyatamicchādiṭṭhiyā), and the result-obstruction as a rebirth-linking that is the result of unwholesome kamma, or a rootless one that is the result of wholesome kamma (akusalavipākapaṭisandhiyā vā kusalavipākehi ahetukapaṭisandhiyā vā, s0403a.att.xml:3118). On that gloss a hell birth is itself an incapacity for that existence, which sits badly with supposition 5 (a hell life is required for awakening) unless the requirement is read across existences, not within one. That reading is the authors', not the text's. Breaks if: a canonical line gives the incapacity a stated extent across existences.abh03m3.mul.xml:12829); the commentary says the view belongs to some Uttarāpathakas, who rely on AN 7.15 (abh03a.att.xml:6029). The Theravādin grants the sutta and answers by parity: sabbakālaṃ ummujjitvā nimujjatīti? na hevaṃ vattabbe, "does he always emerge and sink again? That should not be said" (:12873). The commentary states the intention: na pana so bhavantarepi nimuggova. imasmiññeva hi bhave abhabbo so taṃ diṭṭhiṃ pajahitunti ayamettha adhippāyo, "he is not sunk in other existences too; in this very existence he is incapable of abandoning that view: that is the intention here" (:6045). The framing in existences is the commentary's. This result is published and cited, not claimed (Points of Controversy, 1915, XIX.7, pp. 340–341). Breaks if: the commentary's sentence is shown to be the opponent's, not the Theravādin's.s0401a.att.xml:5823); the Majjhima commentary "fixed in one existence only," but "mostly" no emergence (s0202a.att.xml:1587); the Dīgha commentary a limit of "immediately after that existence" (tassattabhāvassa anantaraṃ, s0101a.att.xml:2983, quoted in s0401t.tik.xml:3838), the best witness for the restricted reading; the Kathāvatthu commentary the restricted reading (abh03a.att.xml:6045). The sub-commentary lines (s0101t.tik.xml:2883, s0202t.tik.xml:887, s0302t.tik.xml:3369, s0402t.tik.xml:5190, s0105t.nrf.xml:605, s0401t.tik.xml:3826) carry one argument repeated almost verbatim (otherwise fixity in wrongness would be absolute, accantiko siyā); they count as one argument, not six witnesses. The sub-commentary on the Aṅguttara passage states it conditionally: "if he does not let go of that grasp, since it brings that state again for him, it is said 'there is no emergence from existence,' not from a total absence of emergence" (Tañce gāhaṃ na vissajjeti … na pana sabbaso vuṭṭhānassa abhāvato, s0401t.tik.xml:3826). That sentence is the only place the difference is read down: the same sub-commentary's gloss on the cosmological coda does not (attano kammabalena paccatiyeva, "he is cooked by the power of his own kamma," :3842). A treatise in the CST's undated "other" files, the Sīmāvisodhanī of Phra Sagarabuddhi, adds a remark of its own ("emergence could happen: our view," e1102n.nrf.xml:977). Breaks if: a sub-commentary is found that endorses the Aṅguttara commentary's categorical reading, or the conditional clause of s0401t.tik.xml:3826 is shown to address the cosmological coda only.abh03m3.mul.xml:12829; abh03a.att.xml:6029). The Aṅguttara commentary on AN 6.86 glosses the kamma-obstruction as the five heinous deeds and the defilement-obstruction as fixed wrong view (s0403a.att.xml:3118), so the debate touches both; that the Kathāvatthu's niyāma vocabulary maps onto the Vibhaṅga's obstructions is the authors' bridge through that gloss. The lines read say nothing about the result-obstruction (an unwholesome or rootless rebirth) or about faith (abh03m3.mul.xml:12829–12881; abh03a.att.xml:6029–6045). A caution on the commentary's closing remark: vacanamatte abhinivesaṃ akatvā attho pariyesitabbo is attached in the text to the Kathāvatthu's parity line (sabbakālaṃ ummujjitvā nimujjati …), not to the sutta (abh03a.att.xml:6045); reading it as a remark on the sutta's wording is the authors' inference, flagged where it recurs. A formal model shows a being that leaves its fixed wrong view yet remains rootless in every later existence (run 2, theorem T6B, PROVED by a model). Breaks if: a text is found that settles the duration of the result-obstruction or of faithlessness, or the model is shown excluded once kamma is encoded (the run did not encode kamma, and §6.3 item 9 gives a reason to expect it would be).the_thesis_entails_the_answer, PROVED), so a proof of the supposition from premises that do not restate the answer is unreachable. On the literal reading, "found in the world" plus the commentaries' identification of the once-sunk with fixed wrong view, the supposition is refuted for that person (t6r_refuted_on_the_literal_reading, PROVED); the literal reading and the Kathāvatthu's answer are contraries by how they were written (a plumbing check, not a finding). With the scope of "stays" left open, the supposition is INDEPENDENT. Breaks if: the encoding of "stays sunk" is shown to change an outcome. The run declares two readings (the view persists; the sutta's own contrast, lacking faith, shame, fear, energy and wisdom); on the second the refutation survives and the contrary check fails.s0404m3.mul.xml:3564), and Ānanda says the question is the same one asked another way (tadevetaṃ pañhaṃ bhagavantaṃ aññena pariyāyena apucchi, :3576): the gatekeeper of a one-gate city does not know how many pass, only that all who pass do so by this gate, and the Tathāgata is not concerned with how many. The commentary's own ground is that Uttiya asked "standing on the view of a being" (sattūpaladdhiyaṃ ṭhatvā), and it files the question as one to be set aside (ṭhapanīyapañha, s0404a.att.xml:2538). The Yamaka formula answers its question by listing persons: "arahants and worldlings who will not obtain the path" (arahā ye ca puthujjanā maggaṃ na paṭilabhissanti, abh03m4.mul.xml:5805; it recurs, e.g., at :14129). The line at :16697 is place-indexed ("the denizens of the woeful states and the non-percipient … there the truth of the path will not arise for them," tesaṃ tattha maggasaccaṃ), so it is not an unqualified "never obtains" across existences. Two sub-commentaries read the formula differently. The sub-commentary on the Yamaka (in the file abh03t, which also holds the Kathāvatthu sub-commentary) says a worldling is of two kinds by bhabba/abhabba, and glosses the formula as the abhabba worldling (abhabbo eva, abh03t.tik.xml:4225), so at that layer "will not obtain" bears on can, not only on will. The second DN-group sub-commentary cites the same formula ("in the Abhidhamma too," s0105t.nrf.xml:605) directly after explaining the stump-of-saṃsāra idiom as a meaning to be drawn out (neyyattha) and hedged "mostly" (yebhuyyena), not as the absoluteness of fixity; the paper's use of that line for finding 6 (reading fixity down) and for this finding (evidence of a class) is not reconciled by the sources, and the two readings stand side by side. The surviving sense: the formula partitions worldlings; one sub-commentary reads it as an incapable type; another sits it under a hedged idiom; no layer states a duration. The formal runs do not encode this; in their one-history models can and will coincide, so they cannot see it. Breaks if: the Yamaka's formulas are shown to range over a class that the Abhidhamma treats as possibly empty, or a text is found in which the Buddha declares the outcome for all beings, or a layer states a duration for the formula's class.This document and its contents are dedicated to the public domain under the Creative Commons CC0 1.0 Universal Public Domain Dedication, and are published so that they stand as prior art against any later attempt to enclose them. No patent has been or will be sought on anything disclosed in this paper by HeartBank®, Factory 333™, THonly™, Silicon Wat℠, or any entity under their common control, in any jurisdiction, at any time. The authors and those entities commit not to assert any patent right against any party practicing or teaching anything disclosed here. The commitment is stated rather than implied, is permanent, and is not conditioned on reciprocity, attribution, or field of use. A publication grants nothing and frees nothing already enclosed. Nothing here is claimed as a mechanism: the paper is a study, and what it discloses is the numbered list under Findings disclosed, with the readings in the body that support it. Trademark rights in the marks named here (HeartBank®, Factory 333™, THonly™, Silicon Wat℠, Miss Aquarius℠) are reserved separately and are not licensed by this publication.
What is already public, and cited rather than claimed:
The quick census (pre-registered 71dd64a, pushed 2026-10-13 before the first query). Aperture: English web, Google Books and Scholar, archive.org full texts, and the named works above; Burmese, Thai, Sinhala, Japanese, Chinese and German scholarship were not run; patents are out of scope for a study. The known-prior-art control (Points of Controversy XIX.7) was found, so the absences below stand for this aperture. Results: the Kathāvatthu's refutation and its commentary's framing, killed as a claim (1915; and McDermott 1989 if it covers it); the Yogācāra half of the comparison, commons (Ruegg 1976); the comparison of the Theravāda abhabba and Kathāvatthu with the Yogācāra classes, not found in this aperture on 2026-10-13; the map of the commentaries' division, the one-obstruction scope and the machine-checked chain, not found in this aperture on 2026-10-13, with the discount that Bodhi's notes, the likeliest home of the first, were not read. This is a report of searches, not a statement of novelty. A full literature census and a hostile Pāli reader are owed before this paper's first deposit; this draft asserts no priority.
Disclosed in the first version (2026-11-03): all ten findings. The date of any passage is that of the earliest timestamped version carrying it.
On 2026-10-13 the first author posed a set of suppositions: 1. a being is a mind stream; 2. the number of beings is infinite; 3. every being has an infinite number of past lives; 4. every being has a past life in which it experienced a hell realm; 5. a past life in the hell realm is required to become a buddha or arahant; and, after the restatements were approved, 6. thus, all beings have the potential to become a buddha or arahant. The restatement approved for the sixth reads: every being can still become an arahant; no being stays incapable of the path in every existence from some point on. ("Buddha or arahant" was narrowed to arahant, since a buddha also attains arahantship.)
The image the sixth link turns on is the Aṅguttara's water simile (AN 7.15). It lists seven persons "found in the world" (santo saṃvijjamānā lokasmiṃ, s0403m3.mul.xml:362) as people in deep water: the first sakiṃ nimuggo nimuggova hoti, "sinks once and stays sunk"; the second emerges and sinks again; the third emerges and stands; and so on to the one who has crossed and stands on dry land. The sutta explains the first: such a person "is endowed with entirely black unwholesome states" (samannāgato hoti ekantakāḷakehi akusalehi dhammehi, :366). The second is one whose faith, shame, fear, energy and wisdom arise well and then decay (:370). The question this paper asks is what the emphasis of nimuggova commits the Theravāda to, for how long, and what a formal check can add to a reading.
The question matters outside the study of texts because a reading in which some being is sunk forever and a reading in which none is would ground different attitudes toward persons. The first author's hope that none is, and his pre-registered prediction that the formal check would prove it, are a stake the reader should weigh (§11).
link what the check found
───────────────────────────────────────────────────────────────────────────────
1 a being is a mind stream ............................. the FRAME, not a finding
(SN 23.2 counts matter too)
2 the number of beings is infinite ..................... canon: "limit not discerned";
"infinite" is the commentary's
3 every being has infinitely many past lives ........... FOLLOWS (proximity); a CHECK
│
▼ does 4 follow from 3? no: a model with infinitely many past lives,
│ none in hell
4 every being has had a past life in hell .............. NOT FORCED (INDEPENDENT)
5 a hell life is required to awaken .................... stands or falls with 4
│
▼ does 6 follow from 4 and 5? no: a necessary condition met
│ does not make the goal possible
6 so every being can still awaken ...................... not settled by the Piṭaka;
commentaries differ in wording;
entails Kv XIX.7's answer;
REFUTED on the literal AN 7.15Links 1–5 are short results. Link 6 is the paper.
Link 1. The formal runs model one being as a stream of moments with possible histories. That is a modeling frame; SN 23.2 defines satto by attachment to all five aggregates, matter included, and the Vibhaṅga lists an existence without perception (finding 1). Nothing below depends on denying the frame, and nothing below proves it.
Link 2. The Buddhavaṃsa's verse is about four things that cannot be counted: the mass of beings, space, the world-systems and the Buddha's knowledge (s0511m.mul.xml:791–799). Their limit "is not discerned." The word "infinite" belongs to the commentary at s0511a.att.xml:2369. This is the same pattern as the beginning of saṃsāra, which is argued in The Vibhajjavādin View of Time §4.1. No theorem in the runs turns on the number of beings.
Link 3. The run proves: from the proximity condition (each mental moment has an immediate predecessor and an immediate successor), and from the rule that every existence with mind begins with a rebirth-linking citta, a being with a citta now has had infinitely many past existences. Each premise was shown needed by a model in which dropping it fails. The result is a check of the sub-commentary at vin06t.nrf.xml:2177, which says that "otherwise, in saṃsāra whose beginning is unknown, there is no first citta" and that a first would bring the fault of a new being appearing (bhāve vā navasattapātubhāvadosappasaṅgo), and not a discovery. The scope is narrower than the thesis. "Ticks are order, not time" in these models: a citta that ceased long before is still a proximity condition for a successor of its kind (ciraniruddhampi hi cittaṃ … anantarapaccayamattaṃ hotiyeva, the Dīgha sub-commentary on the non-percipient existence, s0101t.tik.xml:2057). And a being with no citta now (in cessation, or in the non-percipient realm) is outside the statement.
Why 4 does not follow from 3. A model with infinitely many past lives and none in hell is consistent with every premise used. The run records that its first witness, a being always human, is not a textual model: at a world's contraction the texts send beings to the Brahma world, and the Visuddhimagga says evaṃ devaloke paṭiladdhajjhānavasena sabbepi brahmaloke nibbattantīti, "thus, through jhāna attained in the deva world, all are born in the Brahma world" (e0102n.mul.xml:745). Three hedges follow. The Dīgha's own word is yebhuyyena, "mostly" (s0101m.mul.xml:331); its commentary closes "mostly" by sending the exceptions higher (s0101a.att.xml:2201); the Vinaya sub-commentary repeating the Visuddhimagga's sentence adds idañca yebhuyyavasena vuttaṃ, "this is said of the majority" (vin01t1.tik.xml:4461); and the Dīgha sub-commentary adds that it cannot be understood that all beings of the woeful states then arise in the form and formless worlds (na hi 'sabbe apāyasattā tadā rūpārūpabhavesu uppajjantī'ti sakkā viññātuṃ, s0101t.tik.xml:1945). So the always-human witness is excluded only on the universal reading and only at the commentarial layer; a witness with deva and Brahma lives remains.
The texts' laws about destinations are about populations. "Few are those beings who are reborn among humans; far more are those reborn elsewhere" (appakā te sattā ye manussesu paccājāyanti, s0302m.mul.xml:5223). A law of that form says something about a fraction and nothing about one being's history. A one-being world cannot state it, and a population world would need it added as a premise.
5 stands or falls with 4. If a hell life is required for awakening, and every being has awakened or can awaken, then every being has had one. The run proves the implication from 4 read at every moment to 5. The Apadāna states a hell life in the Buddha's own past (the Pubbakammapiloti Apadāna, s0510m1.mul.xml:44595, heading; tena kammavipākena, niraye saṃsariṃ ciraṃ, :44655), so a case exists; no law is stated.
Vibhaṅga §826–827 (abh02m.mul.xml:9965, :9969) give two lists, the abhabbā (those endowed with the kamma-, defilement- and result-obstructions, who are faithless, without desire, unwise) and the bhabbā. AN 6.86 has the same six as the qualities of one person, incapable "even while hearing the true Dhamma." The commentaries read the six disjunctively (the Puggalapaññatti commentary makes each a class and adds a seventh, those with no decisive support for path and fruit; the Visuddhimagga inserts vā); the Piṭaka's form is conjunctive. A formal encoding that takes §826 disjunctively and §827 as written is therefore a hybrid that no single layer asserts, and the run declares it. Neither list says how long the incapacity lasts. The Aṅguttara commentary on AN 6.86 glosses the three obstructions as the five heinous deeds, fixed wrong view, and an unwholesome or rootless rebirth-linking (s0403a.att.xml:3118); on the third gloss a hell birth is itself an incapacity for that existence (finding 4).
The Kathāvatthu is where the Piṭaka layer faces duration (XIX.7, abh03m3.mul.xml:12825–12881). The opponent's thesis, by the commentary, is that there is accantaniyāmatā for a worldling, on the strength of AN 7.15. The Theravādin's reductios are four: (i) the heinous deeds (matricide and the rest) are the shared ground, and the opponent will not call those who commit them absolutely fixed (§847); (ii) doubt could still arise in an "absolutely fixed" person, and doubt is abandoned only by the paths (§848); (iii) one fixed in eternalism might come to hold annihilationism, a second fixity that would make the first pointless (§849–850); and (iv) the sutta is granted and answered by parity, "does he always emerge and sink again?" (§851–852). The reductios argue within one life; the framing in existences is the commentary's. The commentary closes: sabbakālaṃ ummujjitvā nimujjatītiādi vacanamatte abhinivesaṃ akatvā attho pariyesitabboti dassanatthaṃ vuttaṃ, "'does he always emerge and sink again?' and the like was said to show that the meaning should be sought without clinging to the mere wording" (abh03a.att.xml:6045). The sentence attaches to the Kathāvatthu's parity line; that it also speaks of the sutta's wording is the authors' inference, not the text's. The Dhammasaṅgaṇī defines the course of wrongness (micchattaniyata) as the five heinous deeds together with the fixed wrong view (abh01m.mul.xml:7217), and its commentary defines niyata by the result's following "immediately after the breakup of the aggregates" (khandhabhedānantarameva vipākadānato niyatā, abh01a.att.xml:3465). On that definition, "fixed" is already a claim about the next existence; "absolute" extends it beyond.
voice (layer) says, in its own voice or as reported verdict on it
────────────────────────────────────────────────────────────────────────────────────────────────
AN 7.15 (mūla) "sinks once and stays sunk" (nimuggova) —
Kv XIX.7 (mūla), the Theravādin "does he always emerge and sink? — that refutes absolute
should not be said" fixity
Kv-a (aṭṭhakathā), on the OPPONENT some Uttarāpathakas, citing AN 7.15: a the sutta quoted
fixed-view holder is "a stump of saṃsāra, is "asādhakaṃ" —
fixed in other existences too" not a proof of it
Kv-a, its own voice "not sunk in other existences too; —
incapable of abandoning that view in
THIS existence"
AN-a on AN 1.310 (aṭṭhakathā), OWN fixed wrong view has "no limit"; the holder —
voice has "no emergence from existence ... neither
heaven nor path"
its own voice, on a world's end "when a world is destroyed and the many are —
born in the Brahma world, the fixed-view
holder is born in the back world-system"
its last clause: vadanti "cooks" there even when the world-system reported, holders
burns unnamed
Pp-a (aṭṭhakathā), reported "they say" there is no emergence for him "vadanti": a
reported view
MN-a (aṭṭhakathā), own voice "fixed in one existence only; but by hedged: yebhuyyena
habituation he likes that view in later ("mostly")
existences too; for such a one, MOSTLY, no
emergence"
DN-a, and AN-a on other suttas the same formula, hedged "mostly" —
ṭīkā on Kv (abh03t) the opponent took the sutta's emphasis the ṭīkā calls it
(about non-arising of supramundane faith the opponent's
IN THAT BIRTH) as being a stump of saṃsāra construal
ṭīkās on DN, MN, SN, AN and a second ONE argument repeated: "stump of saṃsāra" "otherwise fixity in
DN-group file is a meaning to be drawn out (neyyattha), wrongness would be
(six lines, counted as one) not explicit (nītattha); it should not be absolute (accantiko
said that, with opposite conditions at some siyā)"
time, he never lifts his head
ṭīkā on AN-a at AN 1.310 itself conditional: "if he does not let go of that its own gloss, on
grasp, it is said 'no emergence from one sentence; then
existence,' not from a total absence of quotes MN-a and DN-a
emergence" for it
ṭīkā on DN-a's limit quotes DN-a: "incapable of going even to the best witness for
heaven immediately after that existence" the restricted reading
treatise (CST e1102n; the "emergence from existence could happen "our view": that
Sīmāvisodhanī, undated) through detachment from wrong view with a treatise's remark,
good person's support" not a school viewLine references. AN 7.15 s0403m3.mul.xml:362; Kv abh03m3.mul.xml:12873; Kv-a on the opponent abh03a.att.xml:6029, own voice :6045 (tasmā asādhakametanti); AN-a s0401a.att.xml:5823 (the coda ends vadanti); Pp-a abh03a.att.xml:1773; MN-a s0202a.att.xml:1587; DN-a s0101a.att.xml:2983; ṭīkā on Kv abh03t.tik.xml:3205; ṭīkās on DN s0101t.tik.xml:2883, MN s0202t.tik.xml:887, SN s0302t.tik.xml:3369, AN s0402t.tik.xml:5190, a second DN-group file s0105t.nrf.xml:605; ṭīkā on AN-a s0401t.tik.xml:3826; late treatise e1102n.nrf.xml:977. The first heading of the file e1102n.nrf.xml reads Sīmavisodhanī; a 2022 article describes a Sīmāvisodhanī by Phra Sagarabuddhi Thera with a section on kappavināsa (Khumkhrong et al., MCU Pali Studies Buddhaghosa Perspective 8(1), pp. 16–31, https://so05.tci-thaijo.org/index.php/Palisueksabuddhaghosa/article/view/257266; fetched, abstract only), and the file's passage is on the dissolution of a world. The identification of the file with that treatise rests on the title and topic; the treatise is undated here, since the article gives no date for it.
Five details the map compresses.
The opponent's voice and the commentary's. The Kathāvatthu commentary reports, at :6029, the opponent's reply that the fixed-view holder is "a stump of saṃsāra" fixed in other existences too, while the matricide and the others are fixed in one existence only (niyatamicchādiṭṭhiko saṃsārakhāṇuko bhavantarepi niyatova ime pana ekasmiññeva attabhāve). That is the opponent's ground for refusing the charge that the heinous-deed doers are absolutely fixed. The commentary's own sentence, a few lines on (:6045), is the contrary of the opponent's reading. A quotation of the first sentence as the commentary's claim would reverse its use.
Two voices in one sub-commentary paragraph. At s0101t.tik.xml:2883 the sub-commentary speaks first in its own voice ("vaṭṭakhāṇu nāmesā" ti idaṃ vacanaṃ neyyatthaṃ, na nītatthaṃ, "this saying is a meaning to be drawn out, not explicit"), then quotes the Majjhima commentary ("is he fixed in this existence alone, or in another too? Fixed in this existence alone, but by habituation he likes that view in later existences too"), and then returns to its own voice: akusalañhi nāmetaṃ abalaṃ dubbalaṃ … aññathā sammattaniyāmo viya micchattaniyāmopi accantiko siyā, na ca accantiko, "unwholesome states are weak … otherwise fixity in wrongness, like fixity in rightness, would be absolute, and it is not." The same argument recurs at s0202t.tik.xml:887, s0302t.tik.xml:3369 (there on the cutting off of a person's wholesome root "in that existence, not absolutely," tasmiṃ attabhāve samucchedabhāvato, na accantāya), s0402t.tik.xml:5190, s0105t.nrf.xml:605 and s0401t.tik.xml:3826. It is one argument repeated almost verbatim, so the six lines are one witness, not six.
The Aṅguttara commentary's own voice, and the sub-commentary on it. The commentary's sentence is categorical: niyatamicchādiṭṭhiyā pana paricchedo natthi … tāya samannāgatassa bhavato vuṭṭhānaṃ natthi … neva saggo atthi na maggo, "fixed wrong view has no limit … for one endowed with it there is no emergence from existence … neither heaven nor path" (s0401a.att.xml:5823). Only the last clause of its cosmological coda is reported (vadanti, governing "cooks there even when the world-system burns"); the sentence "when a world is destroyed … the fixed-view holder is born in the back world-system" (Kappavināse … piṭṭhicakkavāḷe nibbattati) is the commentary's own voice, so the commentary itself places his rebirth across a world's dissolution. The sub-commentary on the same passage is conditional: Tañce gāhaṃ na vissajjeti, tassa punapi tabbhāvāvahattā vuttaṃ – "bhavato vuṭṭhānaṃ natthī"ti, na pana sabbaso vuṭṭhānassa abhāvato, "if he does not let go of that grasp, because it brings that state again for him, it was said 'there is no emergence from existence,' not from a total absence of emergence" (s0401t.tik.xml:3826). It then quotes the Majjhima and Dīgha commentaries (:3830, :3838; the Dīgha commentary's own limit is abhabbo tassattabhāvassa anantaraṃ saggampi gantuṃ, "incapable of going even to heaven immediately after that existence," s0101a.att.xml:2983), and glosses the coda without reading it down: he is "cooked by the power of his own kamma" (attano kammabalena paccatiyeva, :3842). So the difference is read down in that one sentence only. The division in the runs' own summary, the Aṅguttara commentary against the rest, is a division among the commentaries' words; the sub-commentary on it reads its base commentary conditionally. The runs' answer file lists the Aṅguttara sub-commentary at s0402t.tik.xml:5190 but not this one; the line was found in the course of this draft.
"Mostly" is hedged on both sides. The Majjhima commentary's own sentence that restricts fixity to "one existence only" continues that by habituation he likes the view in later existences and "mostly" (yebhuyyena) has no emergence. So its restriction carries a hedge, and the restricted reading's main witness is not "never again" either. The Dīgha commentary (s0101a.att.xml:2983) and the commentaries at s0203a.att.xml:1549 and s0402a.att.xml:4812 repeat the formula. The second DN-group sub-commentary says yebhuyyena was used because he is called a stump by habituation, "not because of the absoluteness of fixity in wrongness" (na pana micchattaniyāmassa accantikatāyā, s0105t.nrf.xml:605).
The undated treatise. The file is a treatise on the monastic boundary (the Sīmāvisodhanī, by the 2022 article's account); "late" is not claimed, since no date was found. It says, in its account of a world's dissolution, that those fixed in wrong view experience their results in other world-systems according to their kamma (aññacakkavāḷesu attano kammānurūpaṃ vipākamanubhonti), and then gives its own view that emergence from existence could happen through turning away from the adoption of wrong view with the support of a good person (… bhavato vuṭṭhānaṃ nāma bhaveyyāti amhākaṃ khanti, e1102n.nrf.xml:977). "Our view" is that treatise's remark, as one author's; it is not reported as a school's view.
Where the division stands. At the commentary layer the voices differ: the Aṅguttara commentary's categorical wording against the Majjhima commentary's hedged restriction and the Kathāvatthu commentary's. At the sub-commentary layer, in the lines read, they do not: the lines repeat one hedging argument, and the one on the Aṅguttara passage reads its base commentary's sentence conditionally. A report that "the commentaries divide" without the sub-commentary layer overstates the division; a report that "the tradition holds the restricted reading" without the Aṅguttara commentary's wording understates it.
The case for the unrestricted reading is plain wording: sakiṃ nimuggo nimuggova hoti, with an emphatic eva, in a sutta whose other six persons all emerge; the Aṅguttara commentary's own voice; the Puggalapaññatti commentary's report; and the observation that "seeking the meaning without clinging to the wording" is how a commentary can soften a text it finds hard (the Kathāvatthu commentary's phrase is attached to the Kathāvatthu's parity line, not to the sutta; applying it to the sutta's wording is an inference). The Kathāvatthu's answer is by parity ("he does not always emerge and sink again"), which an opponent can answer: the second person's sinking and emerging are said to repeat, the first's is said not to. The reply in the Kathāvatthu sub-commentary (abh03t.tik.xml:3205) is that the sutta's emphasis concerns the non-arising of supramundane faith "in that birth." This study does not resolve the objection. It reports that the Theravādin voice in the Kathāvatthu refutes absolute fixity, that the commentaries' wording differs, and that the sub-commentary lines read (one argument, repeated) take the restricted side.
The sentence admits two readings of "stays," and both were registered. Write H for the being's possible histories, a for the actual one, r₀ for an existence of the being, and r for a later one:
CAN : ∃h ∈ H, h agrees with a up to r₀, ∃r ≥ r₀: h has an existence at r and ¬incapable(h, r)
WILL: ∃r ≥ r₀: a has an existence at r and ¬incapable(a, r)Each witness model has one history, so CAN and WILL coincide in every model the runs built (theorem T6W is "the same fact as T6"); the modal apparatus carries no weight in the runs' results. Where this paper says "can," it means the first, with that discount.
| Run, theorem | Premises used | Outcome | What it says |
|---|---|---|---|
| 2 · T6 (CAN) | A124 (Vibhaṅga §826–827) | INDEPENDENT | A being incapable in every existence is not excluded, and no Piṭaka text found excludes it |
| 2 · T6W (WILL) | A124 | INDEPENDENT | The same fact as T6 |
| 2 · T6L | A124, A125 literal | PROVED | On the literal reading of AN 7.15, the once-sunk cannot become capable: a check of the Aṅguttara commentary |
| 2 · T6B | A124 | PROVED (a model) | A being that leaves its fixed wrong view may stay rootless forever: the Kathāvatthu's answer does not give the sixth supposition |
| 3 · T6R | A124, A125 existence clause + literal scope | PROVED (thesis REFUTED) | On the literal reading, the thesis fails for the once-sunk |
| 3 · T6X | A125 | PROVED | The literal reading and the Kathāvatthu's answer are contraries: a plumbing check by construction |
| 3 · T6O | A124, A125 | INDEPENDENT | With the scope of "stays" left open, the thesis is not settled |
| 3 · entailment | A124 §826 | PROVED | The sixth supposition entails the Kathāvatthu's answer |
In one sentence: the sixth supposition stands on the Kathāvatthu's side of the debate, and is refuted on the literal reading that the Kathāvatthu itself refutes and the Aṅguttara commentary holds. A proof of "every being can awaken" from the Piṭaka's premises alone is not available, because the premises say nothing about duration.
The existence clause of AN 7.15 was admitted as a premise by a ruling of 2026-10-13 (A394): a text's assertion that persons of a kind exist is an assertion, not a person-type acting as a law. Without it, REFUTED is unreachable by construction for any thesis about every being.
Each run was reviewed by a refuter before and after the proof, to hunt the case against it. What they found, and where this paper carries it:
abh07t.nrf.xml:5117); a rootless being can still do three-rooted wholesome kamma, and the best three-rooted wholesome kamma gives a three-rooted rebirth (:1837). A model that included kamma would therefore exclude the rootless-forever witness for CAN. A faithless-forever witness is untouched by that, and no text was searched for faith arising in every being: not run. This weakens finding 7 and is carried there.The thesis says can. The popular form is will. AN 10.95 is the canonical text on whether the Buddha answers questions of that shape. Uttiya asks, after the undeclared questions (the world eternal or not, finite or infinite, the soul and the body, the Tathāgata after death), what the Buddha has declared, and then whether by his Dhamma "the whole world, or half, or a third is led out" (sabbo vā … upaḍḍho vā tibhāgo vā, s0404m3.mul.xml:3564). "Thus spoken, the Blessed One was silent." Ānanda, fearing that Uttiya will take the silence for evasion, gives the simile of a border city with one gate and a wise gatekeeper who does not know how many creatures pass in and out, only that all who do so by this gate (:3572); so with the Tathāgata, who does not concern himself with how many will be led out, only that all who have been or will be led out of the world are led by abandoning the five hindrances, establishing the four foundations of mindfulness and developing the seven factors of awakening; and "you asked the same question another way; therefore the Blessed One did not answer" (:3576). The commentary's own ground is that Uttiya asked "standing on the view of a being" (sattūpaladdhiyaṃ ṭhatvā) and that the question is one of those to be set aside (ṭhapanīyapañha); Ānanda's concern, it says, is with how Uttiya takes the silence (s0404a.att.xml:2538). Note that Uttiya asks about the proportion of the loka led out, which the commentary reads as beings; the thesis speaks of every being.
Two readings follow, and both are the authors', not the text's. The Kathāvatthu defends a restricted can: no worldling is absolutely fixed, and the Buddha's "gate" is the same for every being who leaves. The sixth supposition's can is stronger (finding 7). The texts deliberately leave will unanswered: a proof of "all will" would be an answer the Buddha declined to give. The formal runs say the same in their own terms: the thesis entails the Kathāvatthu's answer, and nothing in the premises yields will.
The Abhidhamma's pairs complicate this and the runs did not encode it. The Yamaka answers its questions by listing persons, among them "worldlings who will not obtain the path" (arahā ye ca puthujjanā maggaṃ na paṭilabhissanti, abh03m4.mul.xml:5805; the formula recurs, e.g. :14129). The line at :16697 is place-indexed (the denizens of the woeful states and the non-percipient, "there" the path-truth will not arise for them), so it is not an unqualified statement across existences. The formula partitions worldlings; whether it carries an existence claim is what the layers differ on. The sub-commentary on the Yamaka glosses a worldling as of two kinds, bhabba and abhabba, and reads "who will not obtain the path" as the abhabba worldling (abhabbo eva, abh03t.tik.xml:4225); at that layer "will not obtain" bears on can, not only on will, so a worldling of that type is incapable, not merely one who does not. The second DN-group sub-commentary cites the same formula ("referring to which, in the Abhidhamma too," yaṃ sandhāya abhidhammepi …, s0105t.nrf.xml:605) straight after explaining that the stump idiom is hedged yebhuyyena, "mostly," and is not the absoluteness of fixity. The paper uses that line in finding 6 as reading fixity down and here as evidence of a class; one line cannot do both unreconciled, and the two sub-commentaries read the formula differently. Which reading holds is not settled here; no layer states a duration for the class. It is the first thing a hostile Pāli reader should be given. Its status: not a run, not reviewed by a refuter in the first pass; a second refuter pass (2026-11-03) corrected it.
Each run registered the predictions of two predictors before the proof: the machine co-author's and the first author's. The scoring rule that applies to the sixth supposition was ruled after the second run (A395, 2026-10-13): when a thesis entails a held-out answer, a prediction of PROVED is scored unreachable, never a miss, because no premise set can prove it without restating the answer.
| Run | Predictor | Prediction | Outcome | Score |
|---|---|---|---|---|
| 1 (links 3–5) | machine co-author | T3 PROVED, constructive, each premise needed | PROVED | hit |
| T4, T5 INDEPENDENT; T5 follows from T4 | INDEPENDENT; follows | hit | ||
| leak check: no answer near, nothing to leak | an answer was near (the sub-commentary's "no first citta") | miss | ||
| grade NOT STRONG | NOT STRONG (more items failed than predicted) | hit | ||
| first author | 3 PROVED | PROVED | hit | |
| 4 PROVED | INDEPENDENT | miss | ||
| 5 PROVED | INDEPENDENT | miss | ||
| 2 (link 6, potential) | machine co-author | T6, T6W INDEPENDENT | INDEPENDENT | hit (the layer clause narrowed: DN 1's "mostly" is closed by its commentary and reopened by its sub-commentary) |
| T6L PROVED (a check); T6B PROVED by a model | as predicted | hit | ||
| leak check: every row "no" | "no" on the one pair the instrument can form | hit (aperture noted) | ||
| grade NOT STRONG | NOT STRONG | hit | ||
| first author | 6 PROVED | not reachable under the hold-out | unreachable (the run's calibration line at grading read "miss"; rescored under A395, marked after grading) | |
| 3 (link 6, in the world) | machine co-author | T6R PROVED (thesis refuted on the literal reading) | PROVED | hit |
| T6X PROVED | PROVED, by construction | hit (plumbing) | ||
| T6O INDEPENDENT | INDEPENDENT, guaranteed by the hold-out | hit on the logic | ||
| leak check "no" for all three | "no" for two; the third by argument; also "no" for a real entailment | partial | ||
| grade NOT STRONG | NOT STRONG | hit | ||
| first author | 6 PROVED | not reachable | unreachable |
The first author's tally on the pre-registered chain is one hit (link 3), two misses (links 4 and 5), and two runs on the sixth link in which the prediction could not be won. The machine co-author's tally, on the rows above, is eleven hits, one miss and one partial. These are small numbers, the same data produced the corrections in §6.3, and neither tally is evidence about a method.
This section is tagged [X]: everything in it comes from outside the Theravāda corpus this paper checks, was not read in its primary texts, and is a contrast, not a claim about either tradition.
The Yogācāra and tathāgatagarbha literatures classify beings by lineage (gotra) and discuss, as a standing problem, beings said to lack the lineage for awakening: agotra, icchantika ("those of great desire"), and in some listings atyantaparinirvāṇadharmaka ("of the nature never to attain nirvana"). According to Ruegg's 1976 article, the Ratnagotravibhāga commentary (RGVV 1.41) reads any allusion to an icchantika who does not attain nirvana as concerning "a certain interval of time" (kālāntarābhiprāya), not a permanent incapacity. The reading is confirmed by a Cambridge excerpt; the full article remains unread, the primary text was not read, and no Yogācāra source was checked here.
What the contrast does and does not give. It gives a structural difference in what is classified: the Kathāvatthu debates the fixity of a course or view in a worldling; the [X] terms name classes of beings. It does not give a verdict on which tradition is right, a mapping of the Pāli abhabba onto icchantika, or any claim that the Theravāda texts are "closer" to one side. The authors hold the Theravāda texts as the corpus; the [X] material is held at arm's length. If the reported reading is right, both traditions contain a reading in which the incapacity is an interval; if it is wrong, finding 10 falls and nothing else here does.
| Finding | Falsified by |
|---|---|
| 1 | a canonical definition of a being as mind alone; a citta in the non-percipient existence |
| 2 | a canonical line stating the number of beings is infinite in its own voice |
| 3 | a Theravāda text asserting a past hell life of every being, or its necessity; a destination-aware model admitting no no-hell history |
| 4 | a canonical line giving the incapacity an extent across existences |
| 5 | the commentary's key sentence shown to be the opponent's |
| 6 | a sub-commentary endorsing the Aṅguttara commentary's categorical reading; or the conditional clause of s0401t.tik.xml:3826 shown to address the coda only |
| 7 | a text settling the duration of the result-obstruction or faithlessness; or a model with kamma encoded excluding the rootless-forever witness; or the bridge from the Kathāvatthu's niyāma vocabulary to the Vibhaṅga's obstructions (s0403a.att.xml:3118) shown unsound |
| 8 | the encoding of "stays sunk" shown to change an outcome |
| 9 | the Yamaka's formulas shown to range over a class treated as possibly empty; or a text in which the Buddha declares the outcome for all beings; or a layer stating a duration for the formula's class |
| 10 | the primary Yogācāra text not saying what the excerpt reports |
The authors' stake. The first author wrote the thesis hoping that no being is sunk forever, and predicted before the check that links 3 to 6 would be proved. The institution publishing this paper grounds its values in the Pāli canon and has a standing commitment against grounding dignity in a shared essence; a reading in which every being can awaken is attractive to both, and the pull is toward finding it in the texts. The check went against the pre-registered prediction on two links and could not be won on the third; the paper reports that. The opposite pull also exists: a commentary's strongest wording about the fixed wrong view is a cautionary tradition, and a reader attached to caution could read it as the whole of the matter. Both are declared. A sixth link that is "not settled by the Piṭaka" is, for a person who wants a verdict, a disappointing result; it is the one the texts support.
Done.
s0401t.tik.xml:3826 cited; the coda gloss no longer said to read the difference down; the Aṅguttara commentary's own-voice rebirth across a world's dissolution stated; the voice order at s0101t.tik.xml:2883 corrected); finding 7 (two obstructions touched, not one; the :6045 remark flagged as attached to the parity line); finding 4 (the contrast with supposition 5); finding 9's AN 10.95 ground; the late treatise now "undated" and attributed; finding 10's source status; and the removal of a priority-adjacent phrase.Not done.
s0403m3.mul.xml:366). The disjunctive reading of the six qualities is the commentaries'; the Piṭaka's form is conjunctive. The Piṭaka-layer INDEPENDENT of link 6 holds by silence.A sutta describes a man who sinks and does not rise. A debate in the third basket asks for how long, and its commentary answers that in this very existence he cannot let go of his view, and adds that the Kathāvatthu's own parity wording is not to be clung to (whether that extends to the sutta's wording is an inference). A later commentary says, in its own voice, that there is no limit; its sub-commentary glosses that, conditionally, as not a total absence. A machine-checked frame says what that does and does not give a thesis about every being: the thesis stands on the Kathāvatthu's side, the Kathāvatthu's answer alone does not give it, and will, which the Buddha, asked the same question in other words, did not answer, is not given at all. That is the whole result.
abhidhamma-executable-process-specification, concept DOI 10.5281/zenodo.21947259. · "Machine-Checked Consistency of a Buddhist Classification … The Counts Check." The Abhidhamma Compiled №4, the-counts-check, concept DOI 10.5281/zenodo.23020670. · "Causal Set Theory, the Growing Block, and the Buddhist Debate on the Three Times." the-vibhajjavadin-view-of-time (the beginning's argument, §4.1).SiliconWat/formal-abhidhamma; runs 2026-10-13-first-thesis-past-lives-and-hell (Samsara.lean), …-sixth-supposition-potential (Potential.lean), …-sixth-supposition-in-the-world (World.lean); registered 2026-10-14T03:17:28Z, 04:03:33Z and 04:39:24Z (UTC); graded at commits 4b9ffbb, f8e9eb3 and 7abc5ae. Software concept DOI 10.5281/zenodo.23067241. CC0.The authors thank the Vipassana Research Institute for the Chaṭṭha Saṅgāyana texts; the Pali Text Society and the translators of Points of Controversy, Shwe Zan Aung and C. A. F. Rhys Davids, whose 1915 work is the first source of this paper's central debate; Piya Tan for the water-simile study; the Internet Archive for the scan; and the scholars of the gotra and niyāma debates whose work this draft could not reach and a full census will. The reading of the sources, the adversarial reviews that preceded each run, and the drafting were done with Miss Aquarius, the name under which this institution discloses its AI collaboration. The thesis is the first author's; no run was graded strong, and the study is not part of the Theorems of the Abhidhamma series.
Pāli texts (Chaṭṭha Saṅgāyana, upstream commit 05d5d3c; read in the local copy with the tipitaka reader tools; status: fetched). Layer in the right-hand column.
| Work | Line | Layer |
|---|---|---|
| Vibhaṅga §826–827, §191, existences | abh02m.mul.xml:9965, :9969, :2797, :3685 | mūla |
| AN 7.15 (Udakūpamā) | s0403m3.mul.xml:362, :366, :370 | mūla |
| AN 6.86 (Āvaraṇa) | s0403m2.mul.xml:3050, :3054 | mūla |
| AN 1.310 | s0401m.mul.xml:1269 | mūla |
| AN 10.95 (Uttiya) | s0404m3.mul.xml:3536–3576 | mūla |
| Kathāvatthu XIX.7 §847–852; XIII.4 §664 | abh03m3.mul.xml:12829–12881; :10353 | mūla |
| Dhammasaṅgaṇī §1035 | abh01m.mul.xml:7217 | mūla |
| Yamaka | abh03m4.mul.xml:5805, :16697 | mūla |
| DN 1 §39; DN 2 §253 | s0101m.mul.xml:331; :1477 | mūla |
| SN 23.2 (Satta) | s0303m.mul.xml:3601 | mūla |
| Nakhasikha | s0302m.mul.xml:5223 | mūla |
| Buddhavaṃsa; Pubbakammapiloti Apadāna | s0511m.mul.xml:791–799; s0510m1.mul.xml:44595, :44655 | mūla |
| Aṭṭhasālinī; Pp-a, Kv-a, Paṭṭhāna commentary | abh01a.att.xml:3465; abh03a.att.xml:1773, :6029, :6045, :9117 | aṭṭhakathā |
| AN-a, MN-a, DN-a, commentaries on other suttas; Bv-a | s0401a.att.xml:5823; s0202a.att.xml:1587; s0101a.att.xml:2201, :2983; s0203a.att.xml:1549; s0402a.att.xml:4812; s0511a.att.xml:2369; s0403a.att.xml:3118; s0404a.att.xml:2538 | aṭṭhakathā |
| Visuddhimagga (XIII, contraction) | e0102n.mul.xml:745 | commentarial-tier text (a CST "mūla" file) |
| Sub-commentaries on Kv, DN, MN, SN, AN, AN-a at 1.310; a second DN-group file; Vinaya; Vajirabuddhi; Saṅgaha | abh03t.tik.xml:3205; s0101t.tik.xml:1945, :2057, :2883; s0202t.tik.xml:887; s0302t.tik.xml:3369; s0402t.tik.xml:5190; s0401t.tik.xml:3826, :3838, :3842; s0105t.nrf.xml:605; abh03t.tik.xml:4225; vin01t1.tik.xml:4461; vin06t.nrf.xml:2177 (incidental); abh07t.nrf.xml:5117, :1837 | ṭīkā |
Undated treatise (CST e1102n) | e1102n.nrf.xml:977 | other |
Secondary sources.
| Source | Status |
|---|---|
| Shwe Zan Aung & C. A. F. Rhys Davids, Points of Controversy (PTS, 1915), XIX.7, pp. 340–342 | fetched (archive.org scan; read) |
| Piya Tan, "Udakûpama Sutta," SD 28.6 (2006) | fetched (archive.org PDF; sections 1.1–1.2.2 read) |
| McDermott (1989), JIABS 12(1):139–146 | failed (bot-check page; details from a search result) |
| Ruegg (1976), BSOAS 39(2):341–363 | not fetched (the RGVV 1.41 reading confirmed by a Cambridge excerpt; the full article unread) |
| Khumkhrong et al., MCU Pali Studies Buddhaghosa Perspective 8(1) (2022), pp. 16–31, on the Sīmāvisodhanī | fetched (abstract only) |
| Bodhi (2012), The Numerical Discourses of the Buddha, notes on AN 7.15 and 1.310 | not fetched |
| Nyanatiloka, Guide through the Abhidhamma Piṭaka; Karunadasa on the Abhidhamma | not fetched |