Practice · DānaVolume TwoPart II · Āgama ViewPaper 5 of 31

The Velāma Sūtra

中文主題：鞞羅摩經

Author: Shi Huijing 釋慧鏡

Date: Spring 2026

Version: 1.0

ID: DANA-P05

Abstract

Contemporary Effective Altruism (EA), taking Peter Singer's 1972 "Famine, Affluence, and Morality," William MacAskill's 2015 Doing Good Better, and GiveWell's cost-effectiveness analyses as its principal coordinates, has built a refined ranking system for "which kind of giving is most effective" — a system achieving high quantification along the axis of effect magnitude, but whose utility scale structurally cannot accommodate "structural release from the welfare system itself" as a class of effect; early Buddhism, in the Velāma case of the fifth century BCE, placed precisely this class at the apex of a single ladder running from material giving to the perception of impermanence. This paper argues that AN 9.20 Velāmasutta and its three Chinese parallels — T0073 Fo shuo Xuda jing (佛說須達經) with 鞞藍 (Bilan), T0026/155 Xudaduo jing (須達哆經) with 隨藍 (Suilan), and Ekottara Āgama juan 19 "Chapter on Equal Approach to the Four Truths" sūtra 3 with 毘羅摩 (Biluomo) — are not four translation versions of a single narrative, but four independent-lineage crystallizations of the same jātaka-case; the four versions jointly preserve the structural skeleton "material giving → recipient rank → sangha-field → triple refuge → precepts → loving-kindness → vipassanā apex," while at the apex saññā they display four different liberation-directed configurations — the perception of impermanence (aniccasaññā, Pāli prototype), impermanence-suffering-emptiness-non-self (T0073's complete four-mark formula), impermanence-suffering-emptiness-non-soul (T0026/155's four-mark variant), and the perception of non-delight in the world (anabhiratasaññā, T0125's apex substitution). These four apex configurations are not translation drift; they are four lineages' independent answers to the question "how vipassanā is to be concretized at the apex of the ladder." Nor is the Velāma ladder isolated within the Pāli: SN 55.31–33 Puññābhisanda forms its structural twin (triple refuge + the fourth position cycling through sīla / cāga / paññā), and Vinaya Cūḷavagga VI.4 Anupubbikathā (graduated teaching) supplies its pedagogical blueprint (dāna → sīla → sagga → ādīnava → nekkhamma → the four noble truths). The argument proceeds in three layers: the four-way synoptic reading version by version (§III 3.1–3.4), the structural convergence and the "not-an-isolate" argument (§III 3.5), and the structural isomorphism with contemporary Effective Altruism across the first seven rungs and the categorical break at the apex (§IV). Once the ladder's structure is read clearly, both the condescension misreading in the Chinese tradition ("merit ranking among donors") and the projection misreading in the West ("early Buddhism looks down on secular generosity") can be refuted: the "eighty-four thousand great-giver" whom the Velāma ladder transcends is the Buddha's own past life — this is not condescension, but a self-redrawing at the level of jātaka narrative. The paper opens the recipient axis as the core chapter of Part II The Āgama View, taking up the dual-axis analysis (motivation / quality) from P04 and handing off to P06 Sīha sutta on present-life benefits.

I. Problem Consciousness

Move the scene from the year-end donation dialogue of the previous paper into a more structural contemporary Western intellectual setting. Since the late 2010s, Effective Altruism (EA) has expanded from a small academic circle at Oxford into a mainstream discussion framework that spans Oxford, Harvard, and Silicon Valley. Its core claim is compact: charitable effects differ by orders of magnitude, and orders of magnitude can be measured. Peter Singer's 1972 "Famine, Affluence, and Morality," with its thought experiment of "the drowning child in the pond," made explicit the asymmetry between moral distance and moral obligation, setting the ethical starting point for the entire movement; GiveWell, since 2007, has been openly comparing global charities by rigorous cost-effectiveness analysis, producing verifiable calculations such as "five thousand dollars saves one life"; MacAskill's 2015 Doing Good Better operationalized the order-of-magnitude difference into a practical tool for career choice and donation decisions. By the mid-2020s, it is nearly impossible for a Western reader attentive to philanthropy not to have encountered the question "which kind of giving is most effective" taken seriously and structurally.

EA's contribution is that it takes the ranking problem seriously — not all giving is equally effective, not all recipients convert resources into welfare equally. This seriousness is itself precisely what the Velāma case of early Buddhism did. AN 9.20 Velāmasutta¹ gives a ladder precise enough to be enumerated: the brahmin Velāma performs eighty-four thousand acts of great giving (gold bowls, silver bowls, copper bowls, elephants, carriages, cows, girls, seats, bolts of cloth — eighty-four thousand of each, along with food and drink "flooding like a long river"). The Buddha's "but" serves as the watershed: "but in that great giving there was no one worthy of offering, no one who could purify the gift" (tasmiṁ kho pana dāne na koci dakkhiṇeyyo ahosi, na taṁ koci dakkhiṇaṁ visodheti, translation mine). From this decisive watershed, the text ascends rung by rung: a gift to a single stream-enterer surpasses Velāma's eighty-four thousand; a gift to a hundred stream-enterers surpasses the former but cannot match a gift to one once-returner; and so on, up to the sangha headed by the Tathāgata, then to building a vihāra for the sangha of the four quarters, to the triple refuge, to the five precepts, to loving-kindness for the time it takes to milk a cow, and — the perception of impermanence for the time it takes to snap one's fingers. At the peak of the twelve rungs stands a thought whose duration is measured by a bodily gesture.

This structure itself produces a structural break within the EA coordinate system. The first seven rungs are largely containable within EA's scale of effect — "a gift to one stream-enterer surpasses a gift to a hundred ordinary persons" in EA grammar becomes "the effect multiplier of giving to a particular class of recipient is significant." But at the loving-kindness finger-snap and the impermanence-perception moment, the EA coordinate system fails — because EA's utility metric (lives saved, QALYs, welfare-weighted aggregates) structurally cannot accommodate structural release from the welfare system itself as a class of effect. This is not EA being insufficiently refined; it is its categorical boundary: the grammar of welfare optimization does not contain a slot for "outside the welfare frame."

The paper's thesis is this structural break. To let the thesis stand rigorously, three background facts that easily generate misreadings must first be clarified.

First: the "eighty-four thousand great-giver" who gets surpassed is the Buddha's own past life. All four versions state this explicitly: "Is the Velāma / Bilan / Suilan / Biluomo of that time someone else? Do not think so. I am he" (AN 9.20: Ahaṁ tena samayena velāmo brāhmaṇo ahosiṁ, translation mine). If the Western reader misses this, the whole ladder gets read as "Buddhism looks down on secular generosity" or "the saints are snobs"; once it is read clearly, the ladder's structural meaning completely shifts — the Buddha is not belittling anyone else's eighty-four thousand; he takes his own past-life greatest-giving as the coordinate origin, and sets out a ladder that even he had not yet climbed in that lifetime. This ladder is a self-redrawing, not a putting-down of others.

Second: the four versions are not four translations of a single narrative. What §III will dissect in detail is the crystallization of four independent lineages — AN 9.20 (Pāli prototype, twelve rungs, apex aniccasaññā), T0073 Fo shuo Xuda jing² (Bilan, eleven rungs, apex "all formations are impermanent, suffering, empty, non-self" in complete four-mark form), T0026/155 Xudaduo jing³ (Suilan, twelve rungs, apex "impermanent, suffering, empty, non-soul" in four-mark variant), and Ekottara Āgama juan 19 "Chapter on Equal Approach to the Four Truths" sūtra 3⁴ (Biluomo, compressed to six rungs, apex substituted by "the perception of non-delight in the world"). The four versions jointly preserve the same structural skeleton, but at the apex saññā they present four different configurations. To read the four as "four translations of one story" is to misread the apex-saññā divergence as translation drift and miss four lineages' independent answers to "how vipassanā concretizes at this position" — this is the key re-reading on which the whole of §III depends.

Third: Velāma is not an isolated narrative paradigm. Within the Pāli canon, the Velāma ladder has a full doctrinal twin in SN 55.31–33 Puññābhisanda⁵: all three sūtras take the triple refuge as the first three positions, and the fourth position cycles among sīla, cāga, and paññā; SN 55.33's fourth position, paññā udayatthagāminī (the knowledge of arising and passing), is precisely the liberation-directed equivalent of Velāma's apex aniccasaññā. Further down, Vinaya Cūḷavagga VI.4⁶ records the anupubbikathā (graduated teaching) the Buddha gave Anāthapiṇḍika at their first meeting — giving → virtue → heaven → the danger of sensual pleasures → the benefit of renunciation → the four noble truths. The Velāma ladder is precisely the jātaka-narrative version of this graduated teaching, and Anāthapiṇḍika, as Velāma's auditor, is himself the first recipient of the graduated teaching — the Buddha is using a teaching structure Anāthapiṇḍika has personally experienced to address him in the present moment. The Velāma ladder is therefore not an outlier of the Navaka-nipāta but a trope already structurally repeated within the Pāli itself.

With these three backgrounds in place, the paper's argumentative space becomes clear. First, the four versions are dissected one by one, displaying the skeleton-preservation alongside the apex-saññā divergence and its structural meaning (§III 3.1–3.4). Second, the four converge, and the argument is made that the four apex-saññā configurations are four independent lineage crystallizations, not translation drift, with SN 55.31–33 and Vin Cv VI.4 serving as Pāli-canonical anchors for Velāma's non-isolation (§III 3.5). Third, EA is used as a contemporary external mirror to show the structural isomorphism across the first seven rungs and the categorical break at the apex (§IV). Fourth, three misreadings — the condescension projection, the transactional reading, and the MBSR-style downgrade — are addressed in the middle-way corrections (§V). When the argument is complete, the reader should be able to see: the Velāma ladder is not the early canon's competitive alternative to contemporary philanthropic studies; it is a categorically different answer to the question "what is the apex of giving." Its contemporary relevance lies not in measuring more accurately than EA, but in measuring something different.

II. Canonical Foundation

This section's citations run along two axes. Axis A (sūtras) is organized into four groups: the four parallel versions of the primary source (Group 1), the Pāli structural twin and pedagogical template (Group 2), cross-orthogonal references (Group 3), and honest-absence markers (Group 4). Axis B (treatises) takes SN 55.31–33 and Vin Cv VI.4 as structural reference points. In keeping with NIAN-A dual-track discipline, Nikāya material is cited by PTS edition, Chinese material by Taishō volume and sūtra number.

2.1 A · Sūtra

Group 1: The four parallel versions

AN 9.20 Velāmasutta¹, in Aṅguttara Nikāya, Navaka-nipāta, Sīhanādavagga, tenth sūtra (PTS iv.392–396). The opening scene is Jeta's Grove of Anāthapiṇḍika in Sāvatthī, where the Buddha asks Anāthapiṇḍika whether his household gives; Anāthapiṇḍika answers, "there is giving in the household, but only coarse husked food." The Buddha first expounds the qualitative contrast between "giving with respect" and "giving without respect" (sakkacca / asakkacca dāna), then turns to the Velāma jātaka: eighty-four thousand golden bowls (filled with silver grain), eighty-four thousand silver bowls (filled with golden grain), eighty-four thousand copper bowls (filled with golden grain), eighty-four thousand elephants (with golden ornaments and banners), eighty-four thousand carriages (with leopard-tiger-skin cushions, golden ornaments, and banners), eighty-four thousand milch cows (with fine ropes and copper pails), eighty-four thousand maidens (with gem earrings), eighty-four thousand couches (with rugs, deer-skins, and red pillows), eighty-four thousand koṭi bolts of fine cloth (linen, cotton, silk, wool), plus food and drink "flooding like a long river." The giver's self-identification is revealed: "I was the Velāma of that time." Immediately the twelve-rung ladder unfolds, with "this is of greater fruit than that" (idaṁ tato mahapphalataraṁ) as the progressive clause, culminating in "the perception of impermanence for even the time of a finger-snap" (accharāsaṅghātamattampi aniccasaññaṁ bhāveyya).

T0073 Fo shuo Xuda jing², translated by Guṇavṛddhi of the Southern Qi (ca. 492 CE), Taishō vol. 1 No. 73. The sūtra opens with Anāthapiṇḍika's self-report that his household's giving is coarse, and the Buddha first lists the "five conditions of excellent giving" (miaoshi wuyuan: faith, timeliness, one's own hand, personal attendance, and awareness of causation) as quality preconditions — these five conditions are the Chinese parallel to AN 5.148 Sappurisadānasutta⁷, and have no corresponding preamble in the other three versions — before turning to the Bilan jātaka. 鞞藍 (Bilan) is the Chinese transliteration closest to the Pāli Velāma among all four versions (a two-character transcription). The eighty-four-thousand list has six named categories plus one summary category (food and assorted delicacies), for seven categories total — matching well the Pāli's eight major categories (with the three bowl-categories of gold, silver, and copper). The eleven-rung ladder uses "not as much as" as its progressive clause; its apex is "one who reflects on, even for the time of a finger-snap, that all formations are impermanent, suffering, empty, and non-self obtains greater merit" — a complete four-mark abhidharma formula. This version uniquely preserves the dual brevity-image: the loving-kindness rung uses "the time of milking a cow" (goubniu-qing, 搆牛頃)⁸, while the apex impermanence-perception uses "the time of a finger-snap" (tanzhi-qing, 彈指頃) — precisely matching the Pāli gandhohanamatta / accharāsaṅghātamatta dual image. The sūtra closes with a Tathāgata-appearance coda: "In that age, my teaching did not reach the ultimate, I was not free from birth, old age, sickness, and death; now the Tathāgata's teaching reaches the ultimate, free from suffering" — a liberation-directed gathering.

T0026/155 Xudaduo jing³, translated by Gautama Saṅghadeva of the Eastern Jin (ca. 398 CE), Taishō vol. 1 No. 26 (〈Chapter of Brahmins〉 sūtra 155, located in juan 39). This version opens with a four-cell matrix of "heartfelt / non-heartfelt × excellent giving / coarse giving" — the Buddha first expounds to Anāthapiṇḍika a fourfold matrix of "the fruits of desired and undesired states of mind," then turns to the Suilan jātaka. The eighty-four-thousand list has eight categories, uniquely including "golden bowls filled with golden grain / silver bowls filled with silver grain" to supplement the internal combinatorial symmetry beyond the "gold-silver interchange" — giving it two more items than AN 9.20. The twelve-rung ladder's structure is identical to the Pāli, except that the order of rungs 7–8 (sangha headed by the Buddha / vihāra for the sangha of the four quarters) is switched, and rungs 9–10 (refuge / five precepts) are merged into "going for refuge with joyful heart to the three jewels of Buddha, Dharma, and the community of monks, and undertaking the precepts." The apex reads "one who contemplates that all dharmas are impermanent, suffering, empty, and non-soul" — a four-mark variant, where "non-soul" (feishen, 非神) is an ancient rendering of anātman (rather than the later wuwo 無我) and is among the earliest translation strata in philological terms.

Ekottara Āgama juan 19 "Chapter on Equal Approach to the Four Truths" (〈等趣四諦品〉) sūtra 3⁴, translated by Gautama Saṅghadeva of the Eastern Jin (ca. 397 CE), Taishō vol. 2 No. 125. This is the Biluomo jātaka (a three-character transcription, looser than Bilan / Suilan). The eighty-four-thousand list reaches eleven categories (including water-vessels, houses, etc.), but the ladder is compressed to six rungs — from great giving it jumps directly to "building a vihāra for the sangha of all quarters," skipping the middle four fruitions (stream-enterer / once-returner / non-returner / arahant) and the paccekabuddha and Tathāgata rungs entirely. The six rungs are: great giving → vihāra → triple refuge → five precepts → loving-kindness for the time of a finger-snap → "the perception of non-delight in the world" for but a moment. The apex does not use the perception of impermanence; it uses the perception of non-delight (anabhiratasaññā, the non-delight-in-the-world saññā from the ten-saññā list of AN 10.60) — this substitution is a genuine liberation-directed divergence, not translation drift; see §III 3.4.

Group 2: Pāli structural twin and pedagogical blueprint

SN 55.31–33 Puññābhisandasutta I/II/III⁵, PTS v.391–392. The three sūtras share the same structure — "four streams of merit, streams of the wholesome, nutriments of happiness" (cattāro puññābhisandā kusalābhisandā sukhassāhārā), with the first three positions fixed as "confirmed faith" (aveccappasāda) in the Buddha, in the Dhamma, and in the Sangha, and the fourth position cycling: SN 55.31 takes the virtues dear to the noble ones (ariyakantehi sīlehi); SN 55.32 takes generosity (cāga, defined by the five markers muttacāga / payatapāṇi / vossaggarata / yācayoga / dānasaṁvibhāgarato); SN 55.33 takes the knowledge of arising and passing (paññā udayatthagāminī ariyā nibbedhikā sammā dukkhakkhayagāminī). The three in parallel show that the fourth position is structurally substitutable among sīla → cāga → paññā, with its peak at SN 55.33's knowledge of arising and passing — precisely the internal Pāli equivalent of Velāma's apex perception of impermanence.

Vinaya Cūḷavagga VI.4 Anāthapiṇḍika-vatthu⁶. This passage records the anupubbikathā (graduated teaching) Anāthapiṇḍika received at his first meeting with the Buddha: discourse on giving (dānakathā) → discourse on virtue (sīlakathā) → discourse on heaven (saggakathā) → the danger of sensual pleasures (kāmānaṁ ādīnava) → the benefit of renunciation (nekkhamme ānisaṁsa) → the four noble truths (suffering, origin, cessation, path). This sequence is the pedagogical compression of the Velāma ladder — giving as base, the noble truths as peak. Anāthapiṇḍika, as AN 9.20's listener, is himself the first recipient of this sequence, and his personal stream-entry history is a practice of this sequence.

Group 3: Cross-orthogonal references (≤1 sentence each)

It 98 Dānasutta⁹: "There are two gifts — the gift of material things and the gift of Dhamma. The gift of Dhamma is supreme" (dvemāni, bhikkhave, dānāni — āmisadānañca dhammadānañca. etadaggaṁ imesaṁ dvinnaṁ dānānaṁ yadidaṁ dhammadānaṁ, translation mine). This is the most compact hierarchical statement within the Pāli canon along the "content axis" of giving — orthogonal and complementary to the Velāma recipient axis: the recipient axis asks "to whom," the content axis asks "what." §III 3.5 will touch on this one line to mark the structural complementarity of the two axes without developing it further (the content axis is the main venue of P24 Samantabhadra's Practice of Extensive Offering).

SN 55.40 Nandiyasutta¹⁰: "If a noble disciple has confirmed faith in the Buddha... and is satisfied with this faith, and does not further strive day and night in solitude, he is called an abider in heedlessness" (pamādavihārī, translation mine). This line is Pāli-canonical evidence for "one must not stop at the middle of the Velāma ladder" — even when the four factors of unshakable faith are complete, stopping there without ascending falls into the abider-in-heedlessness condition. §V of this paper cites this for the structural rebuttal of "one well-fed saint surpasses Velāma's eighty-four thousand = transactional calculus."

T0073's opening "five conditions of excellent giving" passage: "Householder! An excellent giver is one who gives with faith, gives in season, gives with his own hand, goes in person to give, and gives in the conviction that good action has a fruit." These five conditions are the Chinese parallel to AN 5.148 Sappurisadānasutta⁷; their presence is flagged here but they do not enter the main argument (to avoid overlap with P04's quality axis). Still, in §V's middle-way corrections they serve as the rebuttal tool for "early Buddhism affirms the qualitative validity of secular giving."

Group 4: Honest-absence markers

It 27 / AN 11.16 Mettānisaṁsasutta: Per Bhikkhu Bodhi's AN translation index, this sūtra is the independent Pāli-canonical passage for "loving-kindness surpasses all merit-giving"; but the current collection does not include it. This paper does not cross-check online, does not reconstruct from memory — the "loving-kindness finger-snap surpasses the five precepts" passage within the Velāma sūtra already suffices as internal evidence, requiring no external Pāli reinforcement. Deferred to future vault remediation.

T0072 Xuda zhangzhe jing (alternate Guṇavṛddhi translation) / T0074 Fo shuo zhangzhe shibao jing (Faxian of Zhao Song translation): T0073's CBETA header cross-references itself as "No. 73 [No. 26(155), Nos. 72, 74, No. 125(27.3)]," flagging T0072 and T0074 as potential parallels in the Velāma cluster. These were not checked in the present cycle (the CBETA XML fallback has already been used for T0073; a second fallback exceeds this paper's scope). Flagged here for the future list.

2.2 B · Commentary

The commentarial layer is kept brief. Traditional commentaries on the Velāma ladder — scattered across Buddhaghosa's Samantapāsādikā and the Manorathapūraṇī (AN commentary) — are mostly rung-by-rung lexical glosses and defenses of the legitimacy of the eighty-four-thousand count, offering limited structural contribution to the main argument of "four-way synopsis" and "four-way apex-saññā crystallization." SN 55.31–33 and Vin Cv VI.4 serve as the internal Pāli "commentarial-functional substitute" — both are sūtras, yet they also serve structurally as doctrinal references for the Velāma ladder. The full two-voice commentarial dialogue (Buddhaghosa as lead voice, Yogācāra as counter-voice) continues the Part I convention and will be reactivated in Part IV at the Mahāyāna dāna-pāramitā stage.

Note on commentarial structure: As with Part I's three papers and P04, this paper preserves the two-voice commentarial structure. Because the argument relies on four-way synoptic canonical juxtaposition, the commentarial layer is deliberately compressed to let the sūtra layer speak.

III. Core Argument

This section has five layers of argument: the full unfolding of the AN 9.20 prototype and the structural meaning of the apex brevity-image (3.1); the philological pivot-position of the T0073 Bilan version (3.2); the four-mark variant in the T0026/155 Suilan version (3.3); the apex substitution in the T0125 Biluomo version (3.4); and the structural argument of the four-way convergence (3.5). The first four treat each version independently; the fifth integrates them into a dual conclusion: the four-way apex-saññā crystallization is four independent liberation-directed configurations rather than translation drift, and the Velāma ladder is a structural Pāli trope, not an isolate.

3.1 AN 9.20 prototype — twelve rungs and the structural significance of the apex accharāsaṅghātamatta

AN 9.20's ladder has twelve rungs, whose structure can be clearly divided into three segments. First segment · recipient rank (rungs 1–6): a gift to one possessed of right view (diṭṭhisampanna, the sūtra's synonym for stream-enterer) → a gift to one hundred possessed of right view cannot match a gift to one once-returner → and so on, up to a hundred paccekabuddhas cannot match a gift to one Tathāgata, the fully awakened one. This six-rung segment uses the "hundredfold quantity" as the bridging syntax for each step, making it clear that even with a hundredfold quantity increase, the rank differential still keeps a lower-rank aggregate short of a single higher-rank recipient. Second segment · sangha and precept (rungs 7–10): the sangha headed by the Buddha → building a vihāra for the sangha of the four quarters → going for refuge in the three jewels with a luminous mind → undertaking the five precepts. This segment moves from individual recipient to institutional and normative object. Third segment · inner cultivation apex (rungs 11–12): loving-kindness for the time of milking a cow → perception of impermanence for the time of a finger-snap.

The structural meaning of the three segments lies not in the escalation of magnitude but in the category switch. The first segment's recipient-rank is an externally identifiable person (some noble one); the second segment's sangha and precepts are institutional or normative objects (an institution, a set of rules); the third segment's loving-kindness and impermanence-perception are the practitioner's own inner cultivation — requiring no external recipient, no institutional object. This is the text's gradual inward contraction: from individual recipient → collective/institutional → personal inner cultivation. The apex is not an amplified version of "the biggest material gift"; it is a different class of object after the category has already switched.

The apex's two brevity-images (gandhohanamatta / accharāsaṅghātamatta) reveal the structural feature of this category switch. Gandhohanamatta (the cow-milking interval) and accharāsaṅghātamatta (the finger-snap moment), as time-quantifiers, both indicate extremely short durations — in sharp contrast with the first segment's hundredfold quantity escalation (hundreds, thousands, even sands of the Ganges). Why is the apex marked by such short times? The answer is: the effect of inner cultivation comes from qualitative, not quantitative, activation. The cow-milking interval of loving-kindness suffices to surpass Ganges-sand-many acts of precept-observance, because loving-kindness is the category switch from "following sīla" to "arising of the four divine abidings"; similarly, the finger-snap moment of impermanence-perception suffices to surpass Ganges-sand-many acts of loving-kindness, because the perception of impermanence is the category switch from "arising of the four divine abidings" to "emergence of the knowledge of arising and passing." Time shrinking to the limit is meant to mark the quality of this thought, not the quantity of its duration. Were the apex also to use hundredfold escalation ("a hundred cow-milking-intervals of loving-kindness surpass a hundred finger-snaps of impermanence-perception"), the structural meaning of the ladder would collapse — the ladder stands precisely because quantity and quality are orthogonal axes: quantitative escalation works within each segment, but cross-segment transition must depend on qualitative category switching.

This structure matters particularly for the contemporary reader. We tend to read "surpassing" as "quantity amplification" — donate more, save more, observe precepts longer, hold loving-kindness longer. AN 9.20's apex accharāsaṅghātamatta is a direct structural rebuttal to this reading: true surpassing lies not in amplifying quantity but in switching category. §IV will make this the structural ground for the EA-coordinate-system break.

3.2 The Fo shuo Xuda jing Bilan version — philological pivot and the dual brevity-image

T0073 plays a philological pivot-role among the four versions, for three reasons. First, 鞞藍 (Bilan) is the closest Chinese transliteration of the Pāli Velāma among all four versions — a two-character transcription (bǐ-lán) directly corresponding to Ve-lāma's two syllables, tighter than T0026/155's 隨藍 (Suilan, whose initial suí deviates from ve-) and T0125's 毘羅摩 (Biluomo, a three-character transcription adding a -ma tail). Second, T0073 is the only Chinese version that preserves the dual brevity-image — the loving-kindness rung uses "cow-milking interval" (搆牛頃; 搆 means to press, to milk; 搆牛頃 = the interval of milking a cow, precisely matching gandhohanamatta), and the apex rung uses "finger-snap moment" (彈指頃, precisely matching accharāsaṅghātamatta). T0026/155 uses the cow-milking interval at the apex (merging the two images into one), T0125 uses the finger-snap at the apex (also merging); only T0073 maintains the one-to-one correspondence with the Pāli dual imagery. Third, T0073's apex adopts the complete four-mark formula "all formations are impermanent, suffering, empty, non-self — one who reflects on this, even for the time of a finger-snap" — with the four marks (anicca / dukkha / suñña / anātman) in abhidharma formulaic parallel, a complete four-mark expression of Sarvāstivādin style.

T0073 thereby plays a triple philological bridging function: closest to the Pāli in transliteration, most complete in preserving the brevity-image, and expanding at the apex saññā from the single perception of impermanence to the complete four-mark formula. These three functions make T0073 the philological intermediary between the Pāli and later Chinese versions — preserving the oldest-stratum dual-image structure (demonstrating early Chinese translation's precision in rendering the Pāli), and providing the subsequent abhidharma-ized apex expansion (demonstrating that this expansion is not translation error but a lineage's deliberate choice to formulate the apex saññā doctrinally).

The difference between T0073's eleven-rung structure and AN 9.20's twelve-rung structure deserves precise handling. T0073 merges the Pāli's rungs 11 (loving-kindness) and 12 (impermanence-perception) into a single sentence — "as for extending loving-kindness to all beings, even for the cow-milking interval; as for reflecting with mindful thought that all formations are impermanent, suffering, empty, non-self, even for the finger-snap moment, this obtains the greater merit" — yielding an outward count of eleven (after merging) rather than twelve. But this merger is not a rung-omission; it is a syntactic merger; the structural function of each rung is fully preserved (loving-kindness stands alone, impermanence-perception stands alone, with two brevity-images marking their respective rungs). Readers counting by structural function will have twelve rungs; readers counting by syntactic sentences will have eleven. Both counts are valid, but one must not infer from the eleven/twelve syntactic difference that T0073 omits any rung — the fact is that every rung's content and function is fully preserved.

T0073's opening "five conditions of excellent giving" (faith, timeliness, one's own hand, personal attendance, awareness of causation) shares structural root with AN 5.148 Sappurisadānasutta, further consolidating T0073's status as "philological preserver" — it preserves not only the Velāma sūtra's own dual imagery but also the inter-sūtra link between the Velāma sūtra and other giving-sūtras (AN 5.148). This link has been broken in the other three versions (T0026/155 uses the four-cell "heartfelt / non-heartfelt × excellent / coarse" matrix; T0125 uses the simpler "desired / undesired state of mind" opening; AN 9.20 uses the binary "giving with respect / without respect"); only T0073 preserves the complete five-condition sequence.

3.3 The Xudaduo jing Suilan version — twelve-rung structure and the philological micro-difference of "non-soul"

T0026/155 is the version closest to AN 9.20 in structure — the twelve rungs are fully preserved, with rungs 7–8 (sangha headed by the Buddha / vihāra for the sangha of the four quarters) exchanged in order, and the rest strictly synchronous. The eighty-four-thousand list has eight categories (matching the Pāli's seven major categories plus food and drink), with two additional items ("gold bowls with gold grain / silver bowls with silver grain") supplementing the self-matching combinations beyond the "gold-silver interchange," giving slightly more total items than AN 9.20. This version's most philologically distinctive feature lies in the four-mark variant at the apex — "all dharmas are impermanent, suffering, empty, and non-soul."

"Non-soul" (feishen, 非神) is one of the ancient Chinese renderings of anātman (non-self). This rendering appears in the earliest Chinese translation strata (Eastern Han to Eastern Jin), reflecting the translation bureau's understanding of ātman at the time — ātman was often rendered as "soul/spirit" (神, i.e., the soul, the individual subject), so anātman was correspondingly rendered as "non-soul." By Xuanzang's translation era (early Tang), this rendering had been replaced by wuwo (無我, "non-self"). T0026/155, translated in 398 CE (Eastern Jin), stands precisely in the transition period when "non-soul" was still in use but "non-self" had begun to emerge — Gautama Saṅghadeva's choice of "non-soul" over "non-self" shows the translation bureau's deliberate continuation of the older translation tradition.

"Non-soul" and T0073's "non-self" point to the same concept philologically (anātman), but carry a doctrinal micro-difference. "Non-soul" emphasizes the negation of a substantial soul — directly refuting the Brahmanical ātman concept, pointing out that there is nothing in the dharmas that can be called a "soul" (a soul-substance). "Non-self" is broader, capable of negating simultaneously the individual soul and all the "mine" dependencies. T0073's "non-self" is the more mature abhidharma-ized expression (the four marks of impermanence/suffering/emptiness/non-self as a complete formula); T0026/155's "non-soul" preserves the earlier anti-Brahmanical debate context. This micro-difference does not affect the main argument (both are Chinese renderings of anātman, both maintain the four-mark structure), but it has independent significance for philological history — providing direct evidence of lexical-choice diversity at the apex saññā across different Chinese translation traditions.

T0026/155's preambular "heartfelt / non-heartfelt × excellent giving / coarse giving" four-cell matrix deserves a note in passing. These four cells establish at the opening four possible combinations of giving-mind and giving-object: heartfelt-excellent, heartfelt-coarse, non-heartfelt-excellent, non-heartfelt-coarse — indicating that "state of mind" determines the qualitative nature of the fruit (for instance, heartfelt giving yields the desired kind of excellent food). This four-cell is the Chinese translation's fused handling of motivation axis and quality axis — motivation (heartfelt / non-heartfelt) and quality (excellent / coarse) are cross-classified within a single matrix. This paper does not unfold the four-cell (to avoid overlap with P04's motivation / quality axes), but its existence must be flagged: T0026/155 establishes this matrix at the opening, showing the depth of the Chinese tradition's structural analysis of dāna. The relation between this four-cell and the Velāma ladder is a two-level "opening-frame / jātaka-story" structure — the opening frame supplies matrix-analysis for everyday giving, while the jātaka supplies ladder-analysis for extreme giving; together they constitute T0026/155's distinctive "complete picture of giving-doctrine."

3.4 The Ekottara Āgama Biluomo version — six-rung compression and the apex substitution by the perception of non-delight

T0125 is the most structurally divergent of the four versions. The most obvious difference is the compression of the ladder to six rungs: great giving → building a vihāra for the sangha of all quarters → triple refuge (Buddha, Dharma, noble ones) → undertaking the five precepts → loving-kindness toward beings for the time of a finger-snap → "the perception of non-delight in the world" for but a moment. Compared to AN 9.20's twelve rungs, T0125 has deleted the entire first segment "recipient rank" (the four fruitions plus paccekabuddha plus Tathāgata, seven rungs in total). This is a structurally major omission — from "great giving" the text jumps directly to "vihāra," with every individual noble-one recipient-rung in the middle gone.

Two possible reasons for this compression, not mutually exclusive. Reason one · editorial logic: T0125 belongs to the Ekottara structure (edited with numerical increments as its axis); this sūtra is placed in chapter 27 "Equal Approach to the Four Truths," whose theme is teachings related to the four noble truths. The editor may have deleted the individual-noble-one rungs (whose connection to the four truths is relatively indirect) to keep the sūtra tightly aligned with the "equal approach to the four truths" theme, retaining only the institutional / precept / inner-cultivation rungs (vihāra, triple refuge, five precepts, loving-kindness, perception) as a pointer to the four truths. Reason two · narrative simplification: the editor may have judged that the escalation of individual-noble-one rungs (hundredfold, thousandfold...) was difficult for ordinary readers to absorb, and compressed it to the four rungs of institution / precept / inner cultivation for a clearer delivery of the core message "the higher one ascends, the greater the fruit." Both reasons can explain the compression, and neither diminishes T0125's status as an "independent Velāma parallel" — compression is an editorial choice, not a translation error.

But the real structural significance lies in the apex substitution. T0125's apex does not use the perception of impermanence (aniccasaññā); it uses "the perception of non-delight in the world" (sabbaloke anabhiratasaññā). This substitution is the deepest liberation-directed divergence among the four versions. The perception of non-delight belongs to the ten saññā list in AN 10.60 Girimānandasutta¹¹ — the ten perceptions are "impermanence-perception, suffering-in-impermanence-perception, non-self-in-suffering-perception, perception of the foulness of food, perception of non-delight in the whole world, death-perception, foulness-perception, perception of danger, perception of abandonment, perception of detachment." The perception of non-delight and the perception of impermanence are adjacent in the ten-saññā system, but their functions differ: the perception of impermanence (aniccasaññā) emphasizes "the impermanent nature of dharmas," pointing toward the observation of impermanence; the perception of non-delight (anabhiratasaññā) emphasizes "non-attraction to the world," pointing toward the renunciation vector. The two have different liberation-directed orientations: the perception of impermanence points toward the arising of wisdom (paññā), the perception of non-delight points toward the arising of renunciation (nekkhamma).

Is this substitution translation drift or an independent liberation-directed configuration? The evidence strongly points to the latter. First, T0125 does not fail to recognize the perception of impermanence — the same Ekottara collection, juan 49 sūtra 3¹² treats the perception of impermanence independently and at length ("contemplate the perception of impermanence, diffuse the perception of impermanence..."), with a complete jātaka (King Pure-Sound) supporting it. This proves the translation bureau was fully familiar with the perception of impermanence as an independent meditative object and simply chose not to place it at the Velāma ladder's apex. Second, the perception of non-delight has its own independent structural position in AN 10.60 — it is not a subtype or variant of the perception of impermanence, but one independent perception in the ten-saññā list. Third, functionally, the perception of non-delight as the Velāma ladder's apex is internally consistent with the ladder's pedagogical goal (from material giving toward liberation) — it directly points to "non-delight in the world" (the renunciation vector) as the entry to liberation, forming a complete renunciation sequence with the earlier rungs of five precepts, loving-kindness, etc.

T0125's apex substitution is therefore the translation bureau's or editor's independent liberation-directed judgment on "how vipassanā concretizes at the apex of the ladder" — not a mistranslation, not drift, but the independent position of the Ekottara lineage at this position. This judgment stands in parallel with AN 9.20's perception of impermanence, T0073's complete four-mark formula, and T0026/155's four-mark variant as four independent liberation-directed configurations. The full structural significance of this thesis is integrated in §III 3.5.

3.5 Four-way convergence — skeleton-preservation, apex four-way crystallization, and Velāma as non-isolate

Laying the four versions side by side yields two simultaneously holding structural conclusions.

Conclusion one · structural skeleton preserved. The four versions jointly preserve the same structural skeleton: material giving → recipient rank (or its compressed replacement) → sangha-field → triple refuge → precepts → loving-kindness → vipassanā apex. Even in the extreme case of T0125's six-rung compression, the three core elements of this skeleton — institutional field (vihāra), precept-body (triple refuge + five precepts), and inner-cultivation apex (loving-kindness + perception) — are fully preserved. The consistency across the four versions in structural skeleton is not evidence of translation common ancestry but of four lineages' structural consensus on the same jātaka-case: no matter in what context this story is transmitted, all four traditions hold that "giving must shift from material to inner cultivation to reach the apex" is an unomittable core message.

Conclusion two · the apex crystallizes into four independent liberation-directed configurations, not translation drift. The four versions' apex saññā are, respectively: perception of impermanence (AN 9.20), impermanence-suffering-emptiness-non-self (T0073), impermanence-suffering-emptiness-non-soul (T0026/155), and perception of non-delight (T0125). The differences among the first three lie at the philological level (perception of impermanence → complete four-mark formula → four-mark variant) and can be viewed as "different lexical packagings of the same liberation-directed orientation"; but T0125's perception of non-delight is a liberation-directed substitution — it points to renunciation (nekkhamma) rather than wisdom (paññā). Thus the four versions display at the apex at least two independent liberation-directed configurations (three versions on the wisdom vector, one version on the renunciation vector), with three philological lexical choices inside the wisdom-vector group. Treating every philological micro-difference as an independent crystallization yields four crystallizations.

The significance of this conclusion is that the four early-Buddhist traditions did not arrive at a unified answer to the question "how vipassanā concretizes at the Velāma ladder's apex." Each lineage gave its own crystallization according to its internal vipassanā system (single perception of impermanence; complete four-mark observation; ten-saññā system). This plurality is not confusion; it is early Buddhism's systematic openness toward the depth of vipassanā — the apex permits coexistence of multiple vipassanā configurations, provided that the structural function of pointing toward liberation is intact.

Conclusion three · Velāma is not an isolate. §2.1 Group 2 has already laid out SN 55.31–33 Puññābhisanda and Vin Cv VI.4 Anupubbikathā as Pāli-internal structural references for the Velāma ladder. SN 55.33's fourth-position "knowledge of arising and passing" (paññā udayatthagāminī) and Velāma's apex "perception of impermanence" share liberation-directed orientation entirely — the former is the sudden insight into the arising-and-passing of the five aggregates, the latter is the finger-snap-moment observation of the impermanence of dharmas; both are vipassanā expressions in the stream-entry context. The three-sūtra parallel of SN 55.31–33 shows that the fourth position is structurally substitutable among sīla, cāga, and paññā — which directly answers the three-rung inner-cultivation contraction at the end of the Velāma ladder ("precept → loving-kindness → perception of impermanence"): Velāma's final three rungs are precisely the narrative unfolding of SN 55.31 → SN 55.32 → SN 55.33 (normative precept → cāga / loving-kindness → knowledge of arising and passing). The Velāma ladder is therefore not an isolated narrative but the jātaka-narrative version of an internal Pāli trope.

Vin Cv VI.4's anupubbikathā further consolidates this thesis. The Buddha's first teaching to Anāthapiṇḍika adopts the sequence dāna → sīla → sagga → ādīnava → nekkhamma → four noble truths; this sequence is the pedagogical compression of the Velāma ladder — giving as base, noble truths as peak. Worth noting: Anāthapiṇḍika, as AN 9.20's listener, is himself the first recipient of this graduated teaching — when the Buddha preaches the Velāma sūtra to him, he is effectively using the graduated-teaching structure Anāthapiṇḍika has already personally experienced to teach him in the present. This layer of narrative self-reference is not coincidence but the structural reason for the Velāma sūtra's placement in AN 9.20: the Buddha chooses the jātaka-compression of the graduated teaching to show Anāthapiṇḍika the topic of "the apex of the ladder of giving" that was not fully unfolded in his earlier graduated-teaching instruction. The Velāma ladder is therefore the structural mirror of Anāthapiṇḍika's own path — his anupubbikathā is narrativized at the jātaka level.

It 98 Dānasutta's "two gifts — material gift and Dhamma gift; the Dhamma gift is supreme" further reinforces this thesis as an orthogonal reference. The Velāma ladder treats the recipient axis (to whom), while It 98 treats the content axis (what); the two axes are orthogonal and complementary. None of the four Velāma versions handle the content axis (no discussion of "Dhamma gift vs. material gift"), and It 98 does not handle the recipient axis (no discussion of "noble one vs. ordinary person"); together the two constitute two independent dimensions of early Buddhism's structural analysis of dāna. The orthogonality of these two axes further confirms the structural completeness of the Velāma ladder — it is not the Pāli's only ladder-treatment of dāna but the specialized exposition along the recipient axis, parallel to the content axis.

Summary: The four-way synoptic view shows the four lineages' consensus on the structural skeleton and plurality at the apex saññā; the Pāli-internal references (SN 55.31–33 / Vin Cv VI.4 / It 98) show the Velāma ladder as a structural trope rather than an isolate. Taking the two layers together, the Velāma ladder secures its position: early Buddhism's structured answer to "the apex of giving" reaches a four-lineage consensus that "inner cultivation surpasses material giving," permits multiple vipassanā configurations at the apex, and forms a complete trope-network with the Pāli's other ladder-treatments.

IV. Interdisciplinary Interchange: Structural Isomorphism between the Velāma Ladder and Effective Altruism, and the Categorical Break at the Apex

The most serious contemporary intellectual movement engaging with "which kind of giving is most effective" is Effective Altruism (EA). Peter Singer's 1972 "Famine, Affluence, and Morality"¹³ argues through the thought experiment "you walk past a pond and see a drowning child" — if we can save someone at minor cost but do not, we are morally equivalent to standing by as they die — establishing the ethical foundation for the EA movement. Singer's argument has two structural consequences: first, geographic distance does not grant moral exemption (whether the child is in your backyard pond or across the world, the moral obligation is the same in strength); second, opportunity cost is moral cost (every dollar not used to save a life carries its own moral weight). William MacAskill's 2015 Doing Good Better¹⁴ operationalizes this ethical framework into a practical decision tool — career choice, donation targets, and charity-project comparisons can all be ranked by the principle of "maximum marginal effect." GiveWell (founded in 2007)¹⁵ openly compares global charity projects by rigorous cost-effectiveness analysis, producing verifiable calculations such as "five thousand dollars saves one life," becoming the empirical pillar of the EA movement.

EA and the Velāma ladder show precise structural isomorphism across the first seven rungs. Both hold that giving's effects differ by orders of magnitude and that the order of magnitude can be ranked. Velāma's "one hundred stream-enterers cannot match one once-returner" is structurally isomorphic with EA's "the marginal effect of preventing malaria in low-income countries is significantly higher than that of supporting a local hospital in a high-income country" — both take seriously "effect-differences produced by recipient-class differences." More finely: Velāma's first-segment recipient rank (ordinary → stream-enterer → once-returner → non-returner → arahant → paccekabuddha → Tathāgata) and EA's "direct-effect" hierarchy (general charity → charities with verification mechanisms → GiveWell top charities → high-marginal life-saving programs) both adopt the structure of "fine-grained grading + hundredfold quantification" — GiveWell publicly tags "program X saves a life per X dollars, program Y per 10X dollars," isomorphic with Velāma's "hundredfold sum cannot match a single higher rung." The second segment's sangha-field (institutional recipients) and the third segment's precept-body and loving-kindness (inner cultivation) have correspondents in EA grammar as well — institutional donations (long-term support for effectively-operated NGOs) and personal habit changes (vegetarianism, carbon reduction, altruistic habits) have already been operationalized in EA as "systemic impact" and "lifestyle impact."

But at the apex of the third segment — the loving-kindness finger-snap and the impermanence-perception moment — the EA coordinate system structurally fails. EA's utility scale is built within the category of welfare optimization — lives saved, QALYs improved, weighted welfare totals, expected welfare of potential future individuals. All these scales share one structural feature: they all measure effects within the system, under the premise that the welfare system continues to operate. Securing better welfare for more lives is optimizing welfare output within welfare logic.

The impermanence-perception moment is not on this scale. It points not to "greater welfare within the welfare system" but to structural release from the welfare system itself — all dharmas are impermanent; the intrinsic nature of all optimized welfare is empty, perishable, painful. This orientation does not aim to break EA's optimization work; it aims to point out: the optimization work has a structural boundary — it can only operate under the premise that the optimized subject continues to exist; the apex perception of impermanence points precisely to the deconstruction of this premise.

Three non-reducible differences:

Difference in ultimate end: EA's ultimate end is the maximization of welfare totals; the Velāma apex's ultimate end is the inflow of liberation (nibbāna-pavattana). Their guidance vectors differ — the former toward "optimization within the system," the latter toward "structural loosening of the system." This is not a "more refined vs. cruder" relation; it is a categorical difference between two teloi.
Difference in measurement scale: EA's measurement scale is publicly verifiable quantitative indicators (lives saved, QALYs, welfare scores); the Velāma apex's measurement scale is structural categorical judgment (whether vipassanā arises, whether a qualitative liberation-directed switch has occurred). The former is externally verifiable and cross-subject comparable; the latter is first-person qualitative judgment within meditative experience, not on a public measurement scale. This is not a "subjective vs. objective" opposition (both involve subjective aspects); it is a structural difference between publicly measurable vs. not publicly measurable.
Difference downstream: EA's downstream is the improvement of welfare indicators (more lives, better living, less suffering); the Velāma apex's downstream is the meditative progression from access concentration (upacāra) to absorption (appanā), and further to path-knowledge and fruition-knowledge in the liberation-directed progression. Both have describable downstreams, but their categorical natures are wholly different — the former is welfare-fact, the latter is meditative-fact.

⚠️ Unidirectional analogy caveat: The EA framework can help contemporary Western readers quickly identify contemporary scenes corresponding to the Velāma ladder's first seven rungs — GiveWell's cost-effectiveness analysis is the modern operationalization of "recipient-rank determines effect-magnitude," and MacAskill's career-choice tool is the contemporary guide for "structural maximization of giving." This direction of analogy is valid. The reverse does not hold: one cannot deploy the Velāma apex's vipassanā to "optimize" EA's ethical calculation — that is a problem within EA's own ethical-category, and the vipassanā apex was not designed to do that. The analogy is structurally isomorphic across the first seven rungs and categorically broken at the apex; the break-point is the categorical boundary between welfare-optimization and liberation-directed cultivation.

The analytical form of this section continues the syntax of P04 §IV — using a contemporary discipline as an "external mirror" to reflect the liberation-directed markers of the early Buddhist structure. P04 used Andreoni's warm glow + Bénabou–Tirole's identity signaling + Harbaugh fMRI to handle the contemporary counterpart of the motivation axis; this paper uses Singer + MacAskill + GiveWell to handle the contemporary counterpart of the recipient axis. The two §IV sections together constitute Part II's early "contemporary dual handles" — one paper mirrors the liberation-directed markers of cittālaṅkāra through motivation analysis, the other mirrors the categorical break of the vipassanā apex through cost-effectiveness analysis. The two papers share structural syntax — isomorphism across the first N rungs / positions, categorical break at the apex / topmost position — and this shared syntax is itself Part II's coherent signature for the structural analysis of dāna.

V. Middle-way Corrections

This section addresses two misreadings and two cautions, all relating to this paper's four-way synoptic architecture.

❌ Misreading 1: Early Buddhism looks down on secular generosity

A Western reader encountering Velāma's eighty-four-thousand great-giving being "surpassed" by a single well-fed stream-enterer can easily read this as "early Buddhism looks down on secular generosity" — reading the whole ladder as a devaluation of material giving. This reading errs on two levels.

First level · the text itself rebuts the reading. T0073's opening "five conditions of excellent giving" (faith, timeliness, one's own hand, personal attendance, awareness of causation) is the sūtra's own explicit affirmation of secular good giving — the sūtra opens by defining "excellent giving" (giving of quality) by five qualitative standards, and uses this as the premise for unfolding the Velāma jātaka. These five conditions do not require large giving, do not require giving to noble ones, only require giving with faith, in season, with one's own hand, in person, and with awareness of causation — qualitative conditions within reach of any ordinary householder. T0026/155's "heartfelt / non-heartfelt × excellent / coarse" four-cell preamble likewise affirms the qualitative possibility of secular good giving — "heartfelt excellent giving" is explicitly classified under the positive fruit category of "desiring excellent household, excellent five-pleasures." All four versions take "quality-laden secular giving" as the premise of the jātaka, not a devaluation of secular giving as the premise.

Second level · jātaka-narrative self-reference. All four versions state explicitly: the great giver whom Velāma's eighty-four-thousand great-giving "surpasses" is the Buddha's past life. The Buddha is not devaluing another's eighty-four thousand; he is taking his own past-life greatest giving as the coordinate origin of the ladder. If the Velāma ladder were an expression of "Buddhism looking down on secular generosity," that expression's first target would be the Buddha himself — which is logically impossible. The structural meaning of the Velāma ladder is therefore not comparative (the Buddha devaluing Velāma) but self-redrawing (the Buddha using his own past life to demonstrate that "even the greatest giving has its rank-limit"). Once this narrative self-reference is read clearly, the condescension-projection misreading automatically fails.

❌ Misreading 2: "One well-fed saint > Velāma's eighty-four thousand" = transactional calculus of merit

Another misreading reads the ladder as an "input-output optimization formula" — giving to a higher-ranked noble one is low input for high output; giving to ordinary persons is high input for low output; the whole ladder is a merit investment-return table. This reading mistakes recipient rank for a transactional coefficient.

This reading is explicitly rebutted within the Pāli canon at SN 55.40 Nandiyasutta. The sūtra says: if a noble disciple has confirmed faith in the Buddha, Dhamma, and Sangha, together with virtues dear to the noble ones, but "is satisfied with this faith and does not further strive day and night in solitude" — even with the four factors of unshakable faith complete (the first three stream-entry limbs plus the precept-body), stopping there without ascending falls into pamādavihārī (abider in heedlessness). If the transactional-merit formula held, "one well-fed stream-enterer already surpasses Velāma's eighty-four thousand" would imply that stopping at stream-entry suffices to secure the maximum merit-investment return — but SN 55.40 explicitly negates this conclusion: even when stream-entry is secured, ceasing to strive is heedlessness. The recipient-rank progression of the Velāma ladder is not a progression of transactional coefficients; it is a progression of path-direction. Each rung's "surpassing" lies not in a better transactional return but in the deeper path-direction the rung's recipient represents. A gift to a stream-enterer surpasses a gift to an ordinary person because the stream-enterer already carries the kindling of vipassanā, making the gift "an event linked to the liberation-directed vector" rather than "a transaction within the welfare cycle"; a gift paired with loving-kindness surpasses a gift to a stream-enterer because loving-kindness has become the practitioner's own inner cultivation, no longer resting on an external recipient. Every rung points to the internalization and deepening of path-direction, not to an upgrade of transactional efficiency. Read the structure clearly, and the transactional-merit misreading automatically fails.

⚠️ Caution 1: The ladder is not linear substitution but ladder-stacking

Contemporary readers encountering the Velāma ladder easily read it as "the later rung replaces the earlier" — since the moment of impermanence-perception surpasses Velāma's eighty-four thousand, one may simply cultivate the perception of impermanence and skip giving; since loving-kindness surpasses the five precepts, one may simply cultivate loving-kindness and skip the precepts. This reading mistakes a progressive structure for a substitutive one.

The sūtra's grammar directly rebuts this reading. All four versions present the progression with comparative phrases such as "this is of greater fruit than that" or "not as much as," but nowhere does the text say "once the upper rung is established, the lower rung can be discarded." SN 55.33's knowledge of arising and passing as the fourth position is an augmentation above the first three (triple refuge), not a replacement; SN 55.40's pamādavihārī caution demonstrates just this — after the four factors of unshakable faith are complete, the striving of impermanence-observation is "further ascent," but the lower foundation (four factors of unshakable faith) must still be maintained; one who discards the lower foundation is an abider in heedlessness. Vin Cv VI.4's anupubbikathā likewise — dāna → sīla → sagga → ādīnava → nekkhamma → four noble truths is a gradual unfolding, not "once one enters the four noble truths, giving can be discarded." The internal structure of the Velāma ladder is ladder-stacking — the upper rung rests on the lower rung as its base; one cannot omit the lower rung and ascend the upper alone. One who claims "I cultivate only the perception of impermanence, no longer giving, holding precepts, or cultivating loving-kindness" has not, in fact, ascended the apex of impermanence-perception — an apex without the lower foundation is a suspended conceptual game, not the practice the sūtra describes.

⚠️ Caution 2: The apex vipassanā is not to be downgraded into MBSR-style short meditation

A contemporary Western reader encountering the expression "a finger-snap of impermanence-perception surpasses a cow-milking interval of loving-kindness" is easily tempted to absorb this teaching into the contemporary MBSR (Mindfulness-Based Stress Reduction) tradition's "short-meditation effectiveness" — three-minute breathing space, five-minute impermanence-observation, ten-minute mindfulness meditation — reading accharāsaṅghātamatta (the finger-snap moment) as Pāli-canonical endorsement of "short meditation suffices."

This is a downgrade-error. The finger-snap is not "the minimum effective dose of short meditation"; it is the critical point where the category switch occurs. §III 3.1 has already argued that the structural meaning of the apex brevity-image is to mark the qualitative category switch (from precept-body to loving-kindness, from loving-kindness to impermanence-observation), not to mark "short meditation suffices." A finger-snap of impermanence-perception surpasses a cow-milking interval of loving-kindness not because "the finger-snap" is the shortest time needed for impermanence-perception, but because even when shortened to a finger-snap, as long as the qualitative insight into impermanence genuinely arises (the inner perception of the impermanence of dharmas genuinely surfaces), the category switch it accomplishes (from the four divine abidings to the knowledge of arising and passing) has already occurred. The structural function of this teaching is to guarantee that "once the qualitative category switch occurs, quantity of duration becomes secondary" — not to guarantee that "a finger-snap of meditation time suffices to accomplish the qualitative switch."

MBSR-style short meditation is a therapeutic practice whose purpose is emotional regulation and stress reduction; the perception of impermanence is a path-practice whose purpose is the arising of the knowledge of arising-and-passing and the unfolding of the liberation-directed vector. The two differ wholly in teleology and downstream structure — even where the surface behavior appears similar (both involve short concentration, both involve impermanence-related observation), the structural functions differ. Reading the finger-snap as MBSR-style short meditation amounts to downgrading the apex of the path of liberation into an emotional-management technique, an entirely opposite direction. This caution continues P04 §V's same-class caution against downgrading cittālaṅkāra into MBSR-style mindful charity — both cautions jointly mark: the inner-cultivation teachings of the Pāli canon have their own liberation-directed structure and are not to be appropriated as rhetorical assets of contemporary welfare-optimization frameworks.

VI. Conclusion

Essentials restated: The four versions of the Velāma sūtra (AN 9.20 / T0073 / T0026/155 / T0125 juan 19) are four independent lineages' parallel crystallizations of the same jātaka-case. Together they preserve the structural skeleton "material giving → recipient rank → sangha-field → triple refuge → precepts → loving-kindness → vipassanā apex," while at the apex saññā they present four liberation-directed configurations — the perception of impermanence, impermanence-suffering-emptiness-non-self, impermanence-suffering-emptiness-non-soul, and the perception of non-delight. These four crystallizations are not translation drift; they are four lineages' independent liberation-directed answers to "how vipassanā concretizes at the apex of the ladder." The Velāma ladder is not an isolate within the Pāli canon — SN 55.31–33 is its structural twin, Vin Cv VI.4's anupubbikathā is its pedagogical blueprint, and It 98's content axis is the orthogonal complement to its recipient axis. In contrast with contemporary Effective Altruism, the first seven rungs are structurally isomorphic (both take seriously "the ranking of giving's effects"), while at the apex there is a categorical break (EA's welfare-optimization scale structurally cannot accommodate "structural release from the welfare system" as a class of effect). This paper occupies the core recipient-axis analysis of Part II's early segment, and together with P04's motivation axis / quality axis constitutes the "three-axis parallel" picture of Part II's opening — motivation axis (giver's inner configuration), quality axis (giving-event structure), and recipient axis (recipient structure) — jointly completing the Pāli-Āgama-end laying of the internal structural analysis of dāna.

Practice guidance: For the contemporary reader, the practice significance of the Velāma ladder lies not in "finding the highest-ranked recipient to maximize merit" — that is the transactionalized misreading, refuted in §V — but in structural self-location. With each act of giving, the practitioner can locate themselves inwardly along this ladder: at this moment, on which rung am I? If at the recipient-rank rungs, do I recognize the recipient's quality rather than merely weigh the quantity of the gift? If at the institutional / precept rungs, do I see the institutional or normative structure behind this gift? If at the inner-cultivation rungs, do I see that this gift has activated my own loving-kindness or impermanence-observation? This locating is not to provoke anxiety over "not reaching the apex" — the apex is a rung the Buddha himself had not climbed in that life, so contemporary practitioners have certainly not reached it — but to honestly see this moment's gift in its structural position, making this gift a conscious step on the meditative trajectory, not an unconscious habitual motion. The ladder's function is a signpost, not a measuring stick; a direction-guide, not a performance score.

Open question: This paper treats the apex of giving — the Velāma ladder marks "where giving's ceiling is." The next paper, P06 Sīha sutta — Present-Life Benefits of Giving, treats the opposite-direction question — where giving's present-life floor is. AN 5.34 / AN 7.57 Sīhasenāpatisutta¹⁶ records the general Sīha asking the Buddha, "In this life, what visible benefits does giving have?" — the Buddha answers with five present-life benefits (loved by good people, approached by good people, a good reputation spreading, fearlessness in assembly, rebirth in a good destination after death). These five benefits lie not in the "further-ascent" of the Velāma ladder but in the "more-this-life" of the Velāma ladder — Velāma treats the structure of ascent; Sīha treats the structure of present-life feedback; read together, the two papers constitute Part II's dual-faceted analysis of "the height of giving vs. the thickness of giving." P06 will thereby open Part II's middle segment, handling present-life benefits and experiential structures, laying the ground for the integration of Part II's later segment (P07 on individual fields of giving, P08 on the three bases of meritorious action).

Closing structural observation: This paper treats the recipient axis; together with P04's motivation axis and quality axis, it forms Part II's early-segment internal structural analysis of dāna — giver's inner configuration, giving-event structure, and recipient structure. This trinity-analysis will, in Part II's later segment, stand in contrast with the external effect-structure of dāna (present-life benefits, karmic trajectory), eventually integrating in P08's three-bases-of-meritorious-action passage into a complete picture of early Buddhist giving-doctrine. As the opening paper of Part II's middle segment, this paper, with "the categorical switch at the apex," establishes the structural depth of giving, and for the volume's larger arc from the Pāli root toward the Dharmadhātu offering, it fixes the core coordinate of Part II — giving is not the accumulation of quantity; it is the ascent of category.

References

1. Primary Buddhist Sources

Pāli Canon

Aṅguttara Nikāya. Pali Text Society edition.
Saṃyutta Nikāya. Pali Text Society edition.
Itivuttaka. Pali Text Society edition.
Vinaya Piṭaka (Cūḷavagga). Pali Text Society edition.

Chinese Canonical Translations

Fo shuo Xuda jing （佛說須達經）， translated by Guṇavṛddhi of the Southern Qi, Taishō vol. 1, No. 73.
Madhyama Āgama （中阿含經）， translated by Gautama Saṅghadeva of the Eastern Jin, Taishō vol. 1, No. 26.
Ekottara Āgama （增一阿含經）， translated by Gautama Saṅghadeva of the Eastern Jin, Taishō vol. 2, No. 125.

2. Commentarial Literature

This paper's main argument rests on four-way synoptic sūtra juxtaposition and Pāli structural reference; the traditional commentarial layer is deliberately compressed to let the sūtra layer speak in parallel. The full two-voice commentarial dialogue (Buddhaghosa lead voice, Yogācāra counter-voice) continues the Part I convention and will be reactivated in Part IV at the Mahāyāna dāna-pāramitā stage.

3. Modern Scholarship

Bodhi, Bhikkhu, trans. The Numerical Discourses of the Buddha: A Translation of the Aṅguttara Nikāya. Boston: Wisdom Publications, 2012.
Bodhi, Bhikkhu, trans. The Connected Discourses of the Buddha: A Translation of the Saṃyutta Nikāya. Boston: Wisdom Publications, 2000.
GiveWell. Top Charities Research Process and Methodology. San Francisco: GiveWell.
MacAskill, William. Doing Good Better: How Effective Altruism Can Help You Make a Difference. New York: Gotham Books, 2015.
Singer, Peter. "Famine, Affluence, and Morality." Philosophy & Public Affairs 1, no. 3 (1972): 229–243.
Sujato, Bhikkhu, trans. Aṅguttara Nikāya, Saṃyutta Nikāya, Itivuttaka. SuttaCentral CC0 editions.

4. Sūtra & Śāstra Index

Abbreviation	Full Name	Taishō / PTS	Translator / Author
AN	Aṅguttara Nikāya	PTS edition	—
SN	Saṃyutta Nikāya	PTS edition	—
It	Itivuttaka	PTS edition	—
Vin	Vinaya Piṭaka	PTS edition	—
《佛說須達經》	Independent single-fascicle sūtra	T 01 No. 0073	Guṇavṛddhi of Southern Qi
《中阿含經》	Madhyama Āgama	T 01 No. 0026	Gautama Saṅghadeva of Eastern Jin
《增一阿含經》	Ekottara Āgama	T 02 No. 0125	Gautama Saṅghadeva of Eastern Jin

Cross-reference index to the series

This volume, P01 What Giving Ultimately Does: The paper continues the three-word semantic field established in P01 (dāna / cāga / yāga) — the four-version recipient-axis analysis takes dāna as the primary term for the outward-behavior layer (cāga appears within the Velāma ladder as the inward configuration of the eleventh-rung loving-kindness; yāga does not appear within the ladder), showing that the structural analysis along the recipient axis takes dāna's behavior-layer as its object, structurally distinct from cāga's inner layer and yāga's ritual layer.
This volume, P02 Cāga as a Faculty of Stream-Entry: §III 3.5's SN 55.31–33 is the structural twin of the Velāma ladder — SN 55.32's fourth-position cāga (defined by the muttacāga five markers) is P02's main venue. This paper borrows SN 55.31–33's three-sūtra cyclic-substitution structure to show the structural continuity between cāga as the fourth stream-entry limb and the eleventh rung (loving-kindness) of the Velāma ladder — cāga occupies the fourth position in SN 55.32 as a stream-entry limb, occupies the eleventh rung in Velāma as its external event, and ascends in SN 55.33 into paññā udayatthagāminī (equivalent to Velāma's twelfth-rung perception of impermanence).
This volume, P03 Cāga as an Object of Recollection: §I mentions the §IV syntactic correspondence with P04, but there is structural resonance with P03 as well — the Velāma ladder's apex of impermanence-perception is the subsequent stage of the cāgānussati object (with the cāga-event as anussati nimitta → loving-kindness [four divine abidings] → perception of impermanence [vipassanā]). The cāgānussati-object layer handled by P03 is the starting point from which this ladder ascends. P03 §VI's open question "how upacāra extends to appanā" is not directly answered here, but the Velāma ladder's apex perception of impermanence, as the entry to vipassanā, provides early Buddhism's narrative-layer answer: the structural switch at the inner-cultivation apex is precisely the categorical jump from upacāra (holding cāgānussati object) to appanā / vipassanā (perception of impermanence).
This volume, P04 Eight Bases of Giving: §IV of this paper corresponds in syntax exactly with §IV of P04 — P04 handles the contemporary counterpart of the motivation axis (Andreoni / Bénabou–Tirole / Harbaugh), while this paper handles the contemporary counterpart of the recipient axis (Singer / MacAskill / GiveWell); both papers take "structural isomorphism across the first N rungs / positions, categorical break at the apex / topmost position" as their argumentative signature. The two §IV sections together constitute Part II's opening "contemporary dual handles" — motivation analysis + cost-effectiveness analysis, each mirroring the liberation-directed markers of the early Buddhist structure. P04's motivation axis, quality axis, and this paper's recipient axis together constitute the "three-axis parallel" picture of Part II's early segment; see §VI's closing structural observation.
This volume, P06 Sīha Sutta — Present-Life Benefits of Giving: §VI's open question points explicitly here. This paper treats the apex of giving (ladder-ascent); P06 will treat the present-life floor (present-life benefits) — the five present-life benefits from the Sīhasenāpatisutta (AN 5.34 / AN 7.57) constitute Velāma's "more-this-life" counterpart. The two papers read together constitute Part II's dual analysis of "the height of giving vs. the thickness of giving."
This volume, P07 Fourteen Kinds of Personal Gift-Fields: §I of this paper indicates that "the Velāma ladder treats the ladder-type recipient axis; P07 MN 142 treats the taxonomic-type recipient axis" — the two papers share an axis but differ in structure: this paper treats the recipient axis with "ladder-progression"; P07 treats it with "fourteen taxonomic categories of personal giving." The two read together give the complete analysis of the recipient axis for Part II — ladder-depth (this paper) + taxonomic-breadth (P07). This paper's §III 3.5 treats It 98's content axis only as an orthogonal reference; P24 Samantabhadra's Practice of Extensive Offering is the main venue for the content axis.
This volume, P08 Three Bases of Meritorious Action as Container: §VI's closing structural observation points to P08. The recipient axis handled here, together with P04's motivation axis and quality axis, will be integrated into a complete picture of early Buddhist giving-doctrine in the AN 8.36 three-bases-of-meritorious-action container — Part II's early-segment three-axis parallel analysis finds its structural container in P08's three-bases × three-intensities matrix.
This volume, P11 From Dāna to Dāna-Pāramitā: The apex perception of impermanence as a "categorical switch of giving" has structural continuity with the "three-sphere purity" (三輪體空) of dāna-pāramitā to be handled in P11 — the Velāma ladder's apex vipassanā points toward the path of dāna being taken up into the paññā-pāramitā structure; P11 will use the early-Mahāyāna three-sphere-purity (emptiness of giver, recipient, and gift) to carry this structural turn to completion. This paper is the Pāli-end preparation for that structural turn.
This volume, P15 Vajracchedikā on Giving: The structural reason for §V's caution 2 ("the apex vipassanā must not be downgraded into MBSR") resonates methodologically with P15's Vajracchedikā "one should practice giving without abiding in anything" (應無所住行於布施) — both insist that the liberation-directed structure of vipassanā / prajñā cannot be absorbed as rhetorical asset by contemporary therapeutic practices.
NIAN volume Part I, P04 Recollection and Jhāna: The Velāma ladder's eleventh rung (loving-kindness for the cow-milking interval) and twelfth rung (perception of impermanence for the finger-snap) engage the structure argued in Visuddhimagga chapter 7 — loving-kindness, as a brahmavihāra bhāvanā, can reach appanā (the main venue of NIAN P04); the perception of impermanence, as a vipassanā bhāvanā, does not lie within the recollection system. The structural cross-reference between the two volumes at this point: this paper uses Buddhaghosa's stratification of "recollection reaches upacāra, four divine abidings reach appanā, vipassanā is a categorical switch," the complete unfolding of which is in NIAN P04.
Pointing at the Moon Part V Vajracchedikā series: §III 3.5's It 98 as an orthogonal reference of the content axis has a long-range resonance with the Dharmadhātu offering structure of S8 (Avataṃsaka) in the Eight-Volume series — Velāma's recipient axis unfolds in the Mahāyāna transmission as It 98's content axis (with Dhamma-giving as supreme), eventually completing the structural turn at the "supreme of all offerings is the Dhamma offering" section of Samantabhadra's Practice of Extensive Offering. P24 is the main venue of this long-range resonance.

Paper: DANA-P05 · The Velāma Case and the Apex of the Recipient Ladder · DĀNA · Part II · Āgama View Author: 釋慧鏡 (Shi Huijing) · Project: 指月 / Pointing-at-the-Moon · Series: The Six Practice Gates （六行門） License: CC BY-NC-SA 4.0 CBETA collation: Citations from Fo shuo Xuda jing T0073, Madhyama Āgama juan 39 sūtra 155, and Ekottara Āgama juan 19 sūtra 3 verified against CBETA Electronic Tripiṭaka 2024 edition. Pāli citations (AN 9.20, SN 55.31–33, SN 55.40, AN 5.148, AN 10.60, It 98, Vin Cv VI.4) follow SuttaCentral Mahāsaṅgīti Tipiṭaka Buddhavasse 2500 with PTS numbering. Repository: https://github.com/pointing-at-the-moon/six-practice-gates

Footnotes

AN 9.20 Velāmasutta, Aṅguttara Nikāya, Navaka-nipāta, Sīhanādavagga, tenth sūtra. PTS iv.392–396. Mahāsaṅgīti Tipiṭaka Buddhavasse 2500 edition; Bhikkhu Sujato's English translation is CC0-licensed. The opening scene is Jeta's Grove of Anāthapiṇḍika in Sāvatthī; after the Buddha expounds "giving with respect / giving without respect" (sakkacca / asakkacca) to Anāthapiṇḍika, he turns to the Velāma jātaka — an eighty-four-thousand list of eight major categories (gold bowls with silver grain, silver bowls with gold grain, copper bowls with gold grain, elephants, carriages, milch cows, maidens, couches) + eighty-four thousand koṭi of fine cloth + food and drink "flooding like a long river." The giver's self-identification: "I was the Velāma of that time" (ahaṁ tena samayena velāmo brāhmaṇo ahosiṁ). The twelve-rung ladder: a gift to one diṭṭhisampanna (the sūtra's synonym for stream-enterer) → a hundred stream-enterers + one once-returner → a hundred once-returners + one non-returner → a hundred non-returners + one arahant → a hundred arahants + one paccekabuddha → a hundred paccekabuddhas + one Tathāgata → the sangha headed by the Buddha → building a vihāra for the sangha of the four quarters → going for refuge in the three jewels with a luminous mind → undertaking the five precepts (not-killing / not-stealing / not-misconducting / not-false-speech / not-intoxicants) → loving-kindness for the time of milking a cow (gandhohanamattampi mettacittaṁ bhāveyya) → the perception of impermanence for the time of a finger-snap (accharāsaṅghātamattampi aniccasaññaṁ bhāveyya). Each rung uses idaṁ tato mahapphalataraṁ ("this is of greater fruit than that") as its progressive clause. This sūtra is the tenth (final) sūtra of Sīhanādavagga, structurally significant as the climax of the "Lion's Roar" chapter. ↩ ↩²
Fo shuo Xuda jing, translated by Guṇavṛddhi of the Southern Qi, Taishō vol. 1 No. 73. Ca. 492 CE. Single-juan sūtra, Taishō pp. T01.879a03–880a04; the Velāma jātaka main section at T01.879b08–c17. CBETA header self cross-reference: No. 73 [No. 26(155), Nos. 72, 74, No. 125(27.3)]. The opening "five conditions of excellent giving" (faith, timeliness, one's own hand, personal attendance, awareness of causation) is the Chinese parallel to AN 5.148 Sappurisadānasutta, with no corresponding preamble in the other three Velāma versions. The eighty-four-thousand list has six categories (gold bowls with silver grain, silver bowls with gold grain, elephants, horses, cows, jade maidens) plus one summary category (food and assorted delicacies). The Song, Yuan, and Ming editions add two further items at the gold/silver bowls position ("gold bowls filled with gold, silver bowls filled with silver," apparatus #0879006); the Taishō takes the shorter reading. Both readings leave the main argument unaffected. The ladder is eleven rungs in syntactic form (functionally twelve); the apex "one who reflects on, even for the time of a finger-snap, that all formations are impermanent, suffering, empty, and non-self" is a complete four-mark abhidharma formula. The sūtra closes with a Tathāgata-appearance coda ("in that age my teaching did not reach the ultimate; now the Tathāgata's teaching reaches the ultimate"). ↩ ↩²
Madhyama Āgama juan 39, 〈Chapter of Brahmins〉 sūtra 155, Xudaduo jing, translated by Gautama Saṅghadeva of the Eastern Jin, Taishō vol. 1 No. 26. Ca. 398 CE. The "heartfelt / non-heartfelt × excellent giving / coarse giving" four-cell frame serves as the opening preamble; the Suilan jātaka's eighty-four-thousand list has eight categories (gold bowls with silver grain, silver bowls with gold grain, gold bowls with gold grain, silver bowls with silver grain, elephants, horses, cows, maidens); the twelve-rung ladder is structurally synchronous with AN 9.20, except that rungs 7–8 (sangha headed by the Buddha / vihāra for the sangha of the four quarters) are switched in order, and rungs 9–10 (refuge / five precepts) are merged into "going for refuge with joyful heart to the three jewels of Buddha, Dharma, and the community of monks, and undertaking the precepts." The apex "all dharmas are impermanent, suffering, empty, and non-soul" is a four-mark variant — "non-soul" (非神) is the earlier Chinese form of anātman (predating Xuanzang-era "non-self"), reflecting the Eastern Jin translation bureau's anti-Brahmanical-ātman debate context. The Buddha's self-identification: "The brahmin great-householder called Suilan at that time... know that this is me." The sūtra closes with a Tathāgata-appearance coda ("in that time the teaching did not reach the ultimate... not free from birth, old age, sickness, death"), structurally cognate with T0073. ↩ ↩²
Ekottara Āgama juan 19, 〈Chapter on Equal Approach to the Four Truths〉 (chapter 27) sūtra 3, translated by Gautama Saṅghadeva of the Eastern Jin, Taishō vol. 2 No. 125. Ca. 397 CE. The Biluomo jātaka, scene at Jeta's Grove of Anāthapiṇḍika in Sāvatthī, with Anāthapiṇḍika (阿那邠邸 the householder) as the interlocutor. The eighty-four-thousand list has eleven categories (including silver bowls with gold grain, gold bowls with silver grain, gold and silver water-vessels, cows, jade maidens, bedding, clothing, elephants, horses, carriages, houses). The ladder is compressed to six rungs: great giving → building one vihāra for the sangha of all quarters → triple refuge (Buddha, Dharma, noble ones) → undertaking the five precepts → loving-kindness toward beings for the time of a finger-snap → "the perception of non-delight in the world" for but a moment. The apex does not use the perception of impermanence; it uses the perception of non-delight (anabhiratasaññā, the fifth saññā in the ten-saññā list of AN 10.60). This is the version with the greatest ladder-structural divergence from AN 9.20 among the Chinese — the middle seven rungs (four fruitions + paccekabuddha + Tathāgata) are entirely omitted. Ekottara Āgama juan 49 sūtra 3 treats the perception of impermanence with an independent jātaka (King Pure-Sound), demonstrating that the translation bureau was familiar with the perception of impermanence as an independent meditative object; the apex substitution is the editor's / bureau's conscious choice, not a mistranslation. ↩ ↩²
SN 55.31–33 Puññābhisandasutta I–III, Saṃyutta Nikāya, Mahāvagga, Sotāpattisaṁyutta. PTS v.391–392. The three sūtras share the structure "four streams of merit, streams of the wholesome, nutriments of happiness" (cattāro puññābhisandā kusalābhisandā sukhassāhārā), with the first three positions fixed as confirmed faith in the Buddha, Dhamma, and Sangha (aveccappasāda), and the fourth position cycling: SN 55.31 takes the virtues dear to the noble ones; SN 55.32 takes generosity (cāga, defined by the five markers muttacāga / payatapāṇi / vossaggarata / yācayoga / dānasaṁvibhāgarato); SN 55.33 takes the knowledge of arising and passing (paññā udayatthagāminī ariyā nibbedhikā sammā dukkhakkhayagāminī). The three-sūtra parallel's structural meaning: the fourth position is structurally substitutable among sīla / cāga / paññā, with its peak at SN 55.33's knowledge of arising and passing — the internal Pāli equivalent of Velāma's apex perception of impermanence. This sūtra is the Pāli-canonical anchor for this paper's "Velāma is not an isolate" argument. ↩ ↩²
Vinaya Cūḷavagga VI.4, Senāsanakkhandhaka, Anāthapiṇḍika-vatthu. PTS Vin ii.156–157 or thereabouts. Records the anupubbikathā (graduated teaching) Anāthapiṇḍika received at his first meeting with the Buddha (near Sītavana at Rājagaha): dānakathā (discourse on giving) → sīlakathā (discourse on virtue) → saggakathā (discourse on heaven) → kāmānaṁ ādīnava okāra saṅkilesa (the danger, degradation, and defilement of sensual pleasures) → nekkhamme ānisaṁsa (the benefit of renunciation) → dukkha / samudaya / nirodha / magga (the four noble truths). This sequence is the pedagogical compression of the Velāma ladder and the standard format of "the excellent teaching shared by all Buddhas" (buddhānaṁ sāmukkaṁsikā dhammadesanā). Anāthapiṇḍika, as AN 9.20's listener, is the first practitioner of this sequence; the Buddha's preaching of the Velāma sūtra to him effectively uses the graduated-teaching structure already familiar to him to display the jātaka narrative of the ladder's apex. ↩ ↩²
AN 5.148 Sappurisadānasutta, Aṅguttara Nikāya, Pañcaka-nipāta. PTS iii.172. Lists the five qualities of a good person's giving: giving with faith (saddhāya dānaṁ deti), giving with respect (sakkaccaṁ dānaṁ deti), giving in season (kālena dānaṁ deti), giving with a compassionate mind (anuggahitacitto dānaṁ deti), and giving without harming self or others (attānañca parañca anupahacca dānaṁ deti). T0073's opening "five conditions of excellent giving" (faith, timeliness, one's own hand, personal attendance, awareness of causation) is the Chinese parallel to this sūtra; though individual items differ slightly (with "one's own hand" corresponding to the tactile aspect of respect, "personal attendance" to the non-harming aspect of respect, and "awareness of causation" to the causal understanding within faith-giving), the overall five-item structure shares the same root. This paper flags the correspondence without full parallel listing (to avoid overlap with P04's quality axis); this correspondence is the philological basis for §V's middle-way-correction argument that "early Buddhism affirms secular generosity." ↩ ↩²
T0073's CBETA electronic edition reads 𤛓 at the position "cow-milking interval" (CJK Ext-B, Unicode U+24ED3, graphically ⿰牜冓, meaning "to press, to milk a cow"), precisely matching Pāli gandhohana (the act of milking a cow). Because this character lies outside the BMP, some fonts and e-readers cannot render it correctly (displaying as a blank square); this paper uses the widely available character 搆 throughout to ensure cross-device readability. For the precise philological form, consult the CBETA XML original (T01n0073). T0026/155 uses the same 𤛓 character at its apex (merging the two brevity-images at the apex); T0125 uses 彈指 (finger-snap) at the apex and does not involve this character. ↩
Itivuttaka 98 Dānasutta. PTS It 98. The full short passage: "Mendicants, there are two kinds of giving — the gift of material things and the gift of Dhamma. Of these two gifts, the gift of Dhamma is supreme" (dvemāni, bhikkhave, dānāni — āmisadānañca dhammadānañca. etadaggaṁ, bhikkhave, imesaṁ dvinnaṁ dānānaṁ yadidaṁ dhammadānaṁ, translation mine). This is the most compact hierarchical statement along the Pāli canon's "content axis of giving" (what to give), orthogonal and complementary to the Velāma ladder's recipient axis (to whom). This paper touches on it only at §2.1 Group 3 and §III 3.5, without development; the comprehensive treatment of the content axis is reserved for P24 Samantabhadra's Practice of Extensive Offering (the Avataṃsaka Dharmadhātu offering chapter, the main venue of Part VIII). ↩
SN 55.40 Nandiyasutta, Saṃyutta Nikāya, Mahāvagga, Sotāpattisaṁyutta. PTS v.396. The interlocutor is Nandiya the Sakyan. The Buddha says: "When a noble disciple has the four factors of unshakable faith, if he is satisfied with this faith, and does not further strive day and night in solitude..., because the dharmas have not yet been made manifest, he is called an abider in heedlessness" (pamādavihārī, translation mine). This sūtra is Pāli-canonical evidence for "one must not stop at the middle of the Velāma ladder" — even when the four factors of unshakable faith (the first three stream-entry limbs plus the precept-body) are complete, stopping there without ascending falls into the abider-in-heedlessness condition. §V of this paper uses this to rebut the misreading "one well-fed saint surpasses Velāma's eighty-four thousand = transactional calculus of merit" — if the transactional calculus held, stopping at stream-entry would constitute maximum investment return, but SN 55.40 explicitly negates this conclusion. ↩
AN 10.60 Girimānandasutta, Aṅguttara Nikāya, Dasaka-nipāta. PTS v.108–112. The Buddha teaches Ānanda ten saññā (dasa saññā) to cure Girimānanda's severe illness: aniccasaññā (perception of impermanence), anattasaññā (perception of non-self), asubhasaññā (perception of foulness), ādīnavasaññā (perception of danger), pahānasaññā (perception of abandonment), virāgasaññā (perception of detachment), nirodhasaññā (perception of cessation), sabbaloke anabhiratasaññā (perception of non-delight in the whole world), sabbasaṅkhāresu aniccasaññā (perception of impermanence in all formations), ānāpānasati (mindfulness of breathing). T0125 juan 19's Velāma-ladder apex "perception of non-delight in the world" corresponds to this sūtra's eighth perception, sabbaloke anabhiratasaññā. Within the ten-saññā list, the perception of impermanence and the perception of non-delight are adjacent but independent — the perception of impermanence points toward the arising of wisdom (paññā); the perception of non-delight points toward the arising of renunciation (nekkhamma) — proving that T0125's apex substitution is an independent liberation-directed configuration, not translation drift. ↩
Ekottara Āgama juan 49, sūtra 3, translated by Gautama Saṅghadeva of the Eastern Jin, Taishō vol. 2 No. 125. The sūtra opens with "one should contemplate the perception of impermanence, diffuse the perception of impermanence; by contemplating and diffusing the perception of impermanence, one completely severs sense-desire, form-desire, formless-desire, ignorance, and conceit," and unfolds the complete meditative teaching on the perception of impermanence around the jātaka of King Pure-Sound as its main axis. This sūtra proves that T0125's translation bureau was fully familiar with the perception of impermanence as an independent meditative object and carried it via an independent jātaka — T0125's choice of the perception of non-delight as apex substitute for the perception of impermanence in the Velāma ladder is a conscious liberation-directed choice by the editor / translation bureau, not ignorance of the perception of impermanence. ↩
Singer, Peter. "Famine, Affluence, and Morality." Philosophy & Public Affairs 1, no. 3 (1972): 229–243. The article argues via the thought experiment "you walk past a pond and see a drowning child": if one can save someone at minor cost but does not, one is morally equivalent to letting them die. Two structural consequences: geographic distance grants no moral exemption; opportunity cost is moral cost. Establishes the ethical foundation of the Effective Altruism movement. §IV of this paper uses this to correspond to Velāma's basic premise that "recipient-rank differences produce effect differences" — both take seriously "the ranking of giving's effects," structurally isomorphic. ↩
MacAskill, William. Doing Good Better: How Effective Altruism Can Help You Make a Difference. New York: Gotham Books, 2015. The book operationalizes Singer's ethical framework into a practical decision tool — career choice, donation targets, charity-project comparisons can all be ranked by the principle of "maximum marginal effect." Five framing questions: how big is the effect? is this the most important problem? is this field neglected? is this approach tractable? if I don't do it, what happens? §IV of this paper uses this to correspond to the Velāma ladder's "quantitative judgment of rung-progression" — MacAskill's marginal-effect ranking is structurally isomorphic with Velāma's "hundredfold sum cannot match a higher rung." ↩
GiveWell. Top Charities Research Process and Methodology. GiveWell has since 2007 been openly comparing global charity projects by rigorous cost-effectiveness analysis, producing verifiable calculations such as "X dollars saves one life." The top-charities list (e.g., Against Malaria Foundation, GiveDirectly, Malaria Consortium) is updated periodically, using life-saved per dollar and QALY gained per dollar as its main comparison metrics. §IV of this paper takes this as representative of EA's empirical pillar — the Velāma ladder's "a hundred stream-enterers cannot match one once-returner" corresponds in EA grammar to GiveWell's fine-grading of "program X saves one life per X dollars, program Y per 10X dollars." ↩
AN 5.34 Sīhasenāpatisutta / AN 7.57 Sīhasenāpatisutta, Aṅguttara Nikāya. PTS iii.39 / iv.79. General Sīha (Sīha senāpati) asks the Buddha, "In this very life, what directly visible benefit (sandiṭṭhika) does giving have?" — the Buddha answers with five present-life benefits: loved by good people, approached by good people, a good reputation spreading, fearlessness in assembly, rebirth in a good destination after death. This sūtra is the main venue of P06; §VI of this paper marks only its existence, leaving the unfolding to P06. ↩

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