Okay, here is the English translation of the detailed, verse-by-verse analysis of the Heart Sutra, strictly cross-referenced with relevant complete passages from the Mahāprajñāpāramitā Sūtra (primarily Xuanzang's 600-fascicle version, especially focusing on fascicles 526, 527, 528, but not limited to them).

Heart Sutra Basis 1: [The Heart Sutra of Prajñāpāramitā, Translated by the Tang Dynasty Tripitaka Master Xuanzang]

• Meaning of the Heart Sutra Phrase:
  • Points out that this sutra is the "heart," the core essence (心经 - xīn jīng) of the extensive Mahāprajñāpāramitā Sūtra.
  • "Prajñāpāramitā" means "Perfection of Wisdom" or "Wisdom Gone to the Other Shore," referring to the ultimate wisdom that can sever afflictions, transcend the cycle of birth and death (saṃsāra), and reach the shore of Nirvāṇa.
  • Indicates the translator is Master Xuanzang of the Tang Dynasty.
• Related Passages from the Mahāprajñāpāramitā Sūtra (Referring to the Preface and relevant definition sections):
  • Mahāprajñāpāramitā Sūtra (Fascicle 1) First Assembly, Preface Chapter, First Part: "Thus have I heard. At one time the Bhagavān was dwelling in Rājagṛha, on Gṛdhrakūṭa Mountain, together with a great assembly of twelve hundred fifty bhikṣus, all Arhats, whose outflows had ceased, who were free from afflictions, [...] whose minds had attained self-mastery, having reached the victorious other shore..." (Although this doesn't directly define "Prajñāpāramitā," it points out that "reaching the victorious other shore" is the goal of practice, implying the function of Prajñā.)
  • Mahāprajñāpāramitā Sūtra (Fascicle 401) Second Division, Chapter on Conditions, First Part: The Buddha told Śāriputra: "Mental engagement corresponding to the wisdom of omniscience (sarvajñā-jñāna), with great compassion (mahākaruṇā) as its chief element, and non-attainment (anupalabdhi / aprāpti) as its skillful means – this is Prajñāpāramitā." (This provides a crucial definition: Prajñā has the Buddha's wisdom of omniscience as its substance, is guided by great compassion, and uses the empty wisdom of non-attainment as its skillful means.)
  • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: The Buddha told Subhūti: "The profound Prajñāpāramitā gives birth to all Buddhas; it is the mother of all Buddhas. It reveals the true nature of all dharmas in the world and is called the supreme path. Through this Prajñāpāramitā, Śrāvakas, Pratyekabuddhas, Bodhisattvas, and Tathāgatas are able to reach the other shore. Having reached the other shore, they skillfully sever forever all afflictions along with their latent tendencies (vāsanā) and realize ultimate, permanent, blissful Nirvāṇa." (This excellently interprets the function of Prajñāpāramitā: giving birth to Buddhas, revealing the true nature, enabling the four types of sages to reach the other shore, severing afflictions, and realizing Nirvāṇa.)
• Explanation of Principles:
  • The character "心" (xīn, heart/core) in the Heart Sutra's title signifies its central position within the vast Prajñā corpus; it is the outline and essence. The Mahāprajñāpāramitā Sūtra itself is a comprehensive, deep, and repetitive exposition of the core concept of "Prajñāpāramitā."
  • From the definitions and descriptions in the Mahāprajñāpāramitā Sūtra, it is evident that "Prajñāpāramitā" is not merely wisdom at the cognitive level, but a complete system of practice integrating great compassion (for the benefit of beings), the view of non-attainment (understanding emptiness), and orientation towards ultimate liberation (reaching the other shore, realizing Nirvāṇa, attaining Buddhahood).
  • Master Xuanzang being the translator of both sutras ensures that the core ideas of the Heart Sutra are doctrinally consistent with the extensive discourses of the Mahāprajñāpāramitā Sūtra, making it key to understanding the entire Prajñā dharma gate.

Heart Sutra Basis 2: [Avalokiteśvara Bodhisattva, while practicing the profound Prajñāpāramitā, illuminated and perceived that the five skandhas are all empty, thus liberating [beings] from all suffering and hardship.]

• Meaning of the Heart Sutra Phrase:
  • The subject who contemplates and practices: Avalokiteśvara Bodhisattva.
  • The method and state of practice: Deeply practicing Prajñāpāramitā (行深 - xíng shēn).
  • The content of realization through practice: Using Prajñā wisdom to contemplate, penetratingly seeing that the five skandhas (form, feeling, perception, formations, consciousness) which constitute the "self" and the world are ultimately empty of inherent nature (皆空 - jiē kōng).
  • The function and result of the practice: Based on this realization, transcending and liberating from all suffering and hardship (度一切苦厄 - dù yīqiè kǔ è) that arise from attachment.
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Regarding "Bodhisattva Mahāsattva" and "Practicing Profound Prajñā":
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "At that time, the venerable Subhūti again addressed the Buddha, saying: 'The World-Honored One constantly speaks of the profound Prajñāpāramitā. Based on what meaning is the profound Prajñāpāramitā called Prajñāpāramitā?' The Buddha told Subhūti: 'Because through this Prajñāpāramitā, one reaches the ultimate other shore of all dharmas, it is called Prajñāpāramitā. Furthermore, Subhūti! Because through this Prajñāpāramitā, Śrāvakas, Pratyekabuddhas, Bodhisattvas, and Tathāgatas are able to reach the other shore, it is called Prajñāpāramitā.'" (Explains Prajñā is the means for Bodhisattvas and others to reach the other shore.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "If a Bodhisattva Mahāsattva practices the profound Prajñāpāramitā, all evil māras, māra armies, arrogant individuals, and external path practitioners cannot destroy them; all worldly afflictions such as greed, hatred, delusion, etc., cannot sway them." (Describes the state and power of "practicing profound Prajñā": unshakeable by internal and external obstacles.)
  • Regarding "Illuminated and perceived that the five skandhas are all empty":
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: The Buddha told Subhūti: "When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they should contemplate the form skandha as empty because it is ultimately unborn; they should contemplate the feeling, perception, formation, and consciousness skandhas as empty because they are ultimately unborn." (Directly states that when practicing profound Prajñā, one should contemplate the "ultimate unborn-ness" of the five skandhas to know their "emptiness.")
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "Furthermore, Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they should contemplate the form skandha up to the consciousness skandha as empty because their self-nature is non-existent; they should contemplate the form skandha up to the consciousness skandha as empty because their self-nature is unattainable." (Further explains "emptiness" means the five skandhas have "no self-nature," are "unattainable.")
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "How is it that when Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they do not think: 'I use Prajñāpāramitā to eliminate dharmas?' Subhūti! Because the nature and characteristics of all dharmas are empty, there is nothing that can eliminate and nothing to be eliminated. Here, no dharma is eliminated by another dharma; this dharma is not the eliminator, that dharma is not the eliminated, because both dharmas are unattainable." (Profoundly interprets the meaning of "emptiness": it's not that a real "emptiness" eliminates a real "dharma," but that dharmas are inherently empty by nature; the eliminator and the eliminated are both unattainable. "Illuminated perception" is realizing this principle.)
  • Regarding "Liberating from all suffering and hardship":
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "Bodhisattva Mahāsattvas practicing profound Prajñāpāramitā can accomplish difficult deeds. They do not apprehend sentient beings, nor the designation of sentient beings, yet for the sake of sentient beings, they seek unsurpassed, perfect, complete enlightenment (Anuttarā Samyaksaṃbodhi), wishing to liberate them from the immeasurable suffering and affliction of the three realms of saṃsāra and have them realize ultimate, permanent, blissful Nirvāṇa." (Explains the Bodhisattva's purpose in practicing Prajñā is to liberate beings from suffering and attain Nirvāṇa.)
• Explanation of Principles:
  • "Avalokiteśvara Bodhisattva" represents the Mahāyāna practitioner archetype who relies on Prajñā wisdom for self-benefit and benefiting others. "Practicing profoundly" (行深 - xíng shēn) is not just intellectual understanding but, within meditative concentration and wisdom practice, a continuous, deep contemplation and experience of the principle of Prajñā emptiness, reaching a state unshaken by circumstances.
  • "Illuminating and perceiving the five skandhas are all empty" is the core insight of Prajñā. The five skandhas are the basis of the "self" to which ordinary beings cling. The Mahāprajñāpāramitā Sūtra clearly points out that contemplating their "ultimate unborn-ness," "non-existent self-nature," and "unattainable self-nature" is the realization of emptiness. This emptiness is not nihilism but refers to the lack of an independent, permanent, unchanging substance (self-nature, svabhāva).
  • "Liberating from all suffering and hardship" is the inevitable result of Prajñā wisdom. Suffering arises from attachment to the five skandhas and other dharmas, believing them to be real, which generates craving, aversion, and delusion. Once Prajñā wisdom "illuminates and perceives" their empty nature, the root of attachment (clinging to self, clinging to dharmas) is destroyed, and suffering naturally ceases. Simultaneously, Bodhisattvas use this wisdom to guide sentient beings toward liberation from suffering.

Heart Sutra Basis 3: [Śāriputra, form is not different from emptiness; emptiness is not different from form. Form itself is emptiness; emptiness itself is form. So too are feeling, perception, formation, and consciousness.]

• Meaning of the Heart Sutra Phrase:
  • Using the form skandha (material phenomena) from the five skandhas as an example, it reveals the relationship between phenomena and emptiness. "Not different" (不异 - bù yì) indicates emptiness is not separate from form, and form is not separate from emptiness. "Is exactly" (即是 - jí shì) indicates form, right now, is emptiness, and emptiness, right now, manifests as form. They are not two independent things but two aspects of the same reality.
  • This principle applies equally to the four skandhas of feeling, perception, formation, and consciousness.
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Regarding "Form is not different from emptiness, emptiness is not different from form":
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "Thus, the form skandha up to the consciousness skandha, their self-nature is precisely non-nature (niḥsvabhāva). Due to this non-nature, all dharmas are empty. Subhūti! This emptiness is not different from the form skandha; it is not different from the feeling, perception, formation, consciousness skandhas. The form skandha is also not different from emptiness; the feeling, perception, formation, consciousness skandhas are also not different from emptiness." (Clearly states the self-nature of the five skandhas is non-nature (emptiness), and that emptiness and the five skandhas are "not different" (非异 - fēi yì) from each other.)
  • Regarding "Form itself is emptiness, emptiness itself is form":
    • Mahāprajñāpāramitā Sūtra (Fascicle 407) Second Division, Chapter on Contemplation, Second Part: "Śāriputra! Form (rūpa) is exactly emptiness (śūnyatā), emptiness is exactly form; feeling (vedanā), perception (saṃjñā), formation (saṃskāraḥ), consciousness (vijñāna) are also like this." (Within the Mahāprajñāpāramitā Sūtra, there indeed exists text almost identical to this line in the Heart Sutra, explicitly stating the "is exactly" (即是 - jí shì) relationship between form and emptiness, and feeling, perception, formation, consciousness and emptiness.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "If by this Thusness (tathatā) the Tathāgata is posited, then by this Thusness Śrāvakas and Pratyekabuddhas are posited, by this Thusness Bodhisattva Mahāsattvas are posited, by this Thusness the form skandha, feeling skandha, perception skandha, formation skandha, consciousness skandha are posited..." ("Thusness" is another name for emptiness. This passage indicates that the form skandha and all other dharmas are posited or manifest based on Thusness (emptiness), implying that phenomena like form are themselves the function and manifestation of Thusness (emptiness), i.e., "form is emptiness." Conversely, Thusness (emptiness) must be expressed through phenomena like form, hence "emptiness is form.")
    • Mahāprajñāpāramitā Sūtra (Fascicle 528) Tenth Division, Subhūti Chapter, Second Part, Section 2: "All dharmas have non-nature as their nature. If all dharmas have non-nature as their self-nature, how can differences be spoken of when contemplating form up to consciousness? Subhūti! This is merely nominal designation. The nature and characteristics of all dharmas are ultimately empty. In this emptiness, there are no differences." (Emphasizes the inherent nature of all dharmas is non-nature (emptiness), i.e., "form is emptiness." Seemingly diverse dharmas like form have no difference in their essential emptiness.)
• Explanation of Principles:
  • "Form is not different from emptiness" refutes the view of annihilationism, which holds that emptiness exists apart from phenomena. "Emptiness is not different from form" refutes the view of eternalism, which holds that phenomena exist substantially apart from emptiness.
  • "Form itself is emptiness" directly points out that the essence of phenomena (dependently arisen existence) is emptiness (empty nature). "Emptiness itself is form" explains that emptiness is not a void but can manifest all phenomena (marvelous existence within true emptiness).
  • These two pairs of relationships (not different, is exactly) profoundly reveal the dialectical unity and non-duality of dependent origination and empty nature. Prajñā wisdom is the realization of this unimpeded fusion of phenomena and essence, conventional truth and ultimate truth.
  • "So too are feeling, perception, formation, and consciousness" indicates that this non-dual principle applies to all mental and material phenomena; the five skandhas as a whole are dependently arisen and empty in nature.

Heart Sutra Basis 4: [Śāriputra, this empty nature of all dharmas is not produced, not destroyed; not defiled, not pure; not increasing, not decreasing.]

• Meaning of the Heart Sutra Phrase:
  • Further describes the characteristics of the "empty nature of all dharmas" (诸法空相 - zhū fǎ kōng xiāng), the essential emptiness of all things.
  • It transcends the duality of time and existence (not produced, not destroyed).
  • It transcends the duality of value and attribute (not defiled, not pure).
  • It transcends the duality of quantity and scope (not increasing, not decreasing).
  • The empty nature is the absolute reality, transcending all dualistic conceptual distinctions.
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Mahāprajñāpāramitā Sūtra (Fascicle 528) Tenth Division, Subhūti Chapter, Second Part, Section 2: "If all dharmas are ultimately non-existent, without production, without destruction, without defilement, without purity, without increase, without decrease, abiding permanently in Thusness (tathatā), the Dharma Realm (dharmadhātu), Dharma Nature (dharmatā), the True Limit (bhūtakoṭi), then not even the slightest dharma can emerge from there to proceed towards Nirvāṇa, nor can the slightest dharma enter from outside." (This passage most directly and completely contains the six "negations" described in the Heart Sutra, pointing out that the characteristics of emptiness (ultimately non-existent, Thusness, etc.) are precisely "no production, no destruction, no defilement, no purity, no increase, no decrease.")
  • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "This profound Prajñāpāramitā is permanent and unchanging, like space, without production, without destruction, without annihilation, without permanence, not defiled, not pure, without increase, without decrease, not existent, not non-existent, not combined, not dispersed." (Uses these terms transcending duality to describe Prajñāpāramitā itself. Since Prajñā is the wisdom realizing emptiness, the realm of emptiness it cognizes naturally possesses these characteristics.)
  • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "Furthermore, Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they should contemplate the Noble Truth of Suffering up to the Noble Truth of the Path as empty because they are ultimately unborn... they should contemplate the Thirty-Seven Factors of Enlightenment as empty because they are ultimately unborn... they should contemplate the Ten Powers of the Tathāgata, the Four Fearlessnesses, the Four Unhindered Knowledges, Great Loving-kindness, Great Compassion, Great Joy, Great Equanimity, and the Eighteen Unshared Dharmas of a Buddha as empty because they are ultimately unborn." (Explains that whether worldly dharmas (suffering, origin) or supramundane dharmas (cessation, path, factors of enlightenment, Buddha qualities), their inherent nature is "ultimately unborn" (not produced, not destroyed), having no substantial defilement, purity, increase, or decrease.)
• Explanation of Principles:
  • "This empty nature of all dharmas" refers to the true inherent nature of all myriad things—emptiness.
  • "Not produced, not destroyed": In emptiness, there is no substantial arising or ceasing. The arising and ceasing of phenomena are merely illusions of dependent origination; their empty nature is eternally thus.
  • "Not defiled, not pure": Emptiness itself is beyond words and characteristics, transcending the concepts of defilement and purity established by the discriminating minds of ordinary beings. Afflictions are empty, and Nirvāṇa is also a manifestation of emptiness; emptiness itself is neither defiled nor pure.
  • "Not increasing, not decreasing": Emptiness pervades everywhere. It does not increase due to practice or realization, nor does it decrease due to sentient beings' delusion or transmigration. It neither increases in sages nor decreases in ordinary beings.
  • These six negations thoroughly dismantle our erroneous understanding of reality based on dualistic thinking patterns, guiding us to enter the absolute emptiness that transcends conceptual discrimination.

Heart Sutra Basis 5: [Therefore, in emptiness, there is no form, no feeling, perception, formation, or consciousness. No eye, ear, nose, tongue, body, or mind. No forms, sounds, smells, tastes, tactile objects, or dharmas. No eye element, and so forth, up to no mind-consciousness element.]

• Meaning of the Heart Sutra Phrase:
  • "Therefore" (是故 - shì gù) connects the preceding statement to the conclusion: based on the aforementioned principle of the "empty nature of all dharmas," it follows that within emptiness (空中 - kōng zhōng), there are no substantially existing five skandhas (form, feeling, perception, formation, consciousness), no substantially existing twelve āyatanas (six sense faculties: eye, ear, nose, tongue, body, mind; and six sense objects: forms, sounds, smells, tastes, tactile objects, dharmas), and no substantially existing eighteen dhātus (realms/elements: six sense faculty elements, six sense object elements, six consciousness elements).
  • This thoroughly negates the inherent, substantial existence of the basic elements (skandhas, āyatanas, dhātus) that constitute individual life and cognitive activity.
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "Furthermore, Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they should contemplate the form skandha up to the consciousness skandha as empty because they are ultimately unborn; they should contemplate the eye base (āyatana) up to the mind base as empty because they are ultimately unborn; they should contemplate the form base up to the dharma base as empty because they are ultimately unborn; they should contemplate the eye element (dhātu) up to the dharma element as empty because they are ultimately unborn; they should contemplate the eye-consciousness element up to the mind-consciousness element as empty because they are ultimately unborn." (This passage directly and completely corresponds to this section of the Heart Sutra, stating that under Prajñā contemplation, the five skandhas, twelve āyatanas, and eighteen dhātus are all "empty because they are ultimately unborn." "In emptiness, there is no..." means realizing they are "empty because ultimately unborn.")
  • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "Subhūti! How do Bodhisattva Mahāsattvas, when practicing the profound Prajñāpāramitā, cultivate the elimination of the form skandha and also eliminate this cultivation? Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they do not think: 'The form skandha is a dharma that can be cultivated for elimination, and I am able to cultivate its elimination.' Why? Because these Bodhisattva Mahāsattvas attain nothing regarding the form skandha and the cultivation, due to its empty self-nature. Similarly, they cultivate the elimination of the feeling, perception, formation, consciousness skandhas and also eliminate this cultivation." (And subsequent similar discussions about "cultivating elimination" for the twelve āyatanas and eighteen dhātus.) (This explains that "in emptiness, there is no..." is not physical disappearance but "non-attainment" (anupalabdhi) under wisdom's gaze, realizing their empty self-nature, thus no longer clinging. Even the thought and act of "eliminating clinging" itself must be transcended, reaching complete non-abiding.)
  • Mahāprajñāpāramitā Sūtra (Fascicle 528) Tenth Division, Subhūti Chapter, Second Part, Section 2: "Furthermore, Subhūti! The notion of form up to the notion of consciousness is dualistic; the emptiness of the notion of form up to the emptiness of the notion of consciousness is non-dual. The notion of the eye base up to the notion of the mind base is dualistic; the emptiness of the notion of the eye base up to the emptiness of the notion of the mind base is non-dual... [similarly for object bases and elements]... The notion of the eye-consciousness element up to the notion of the mind-consciousness element is dualistic; the emptiness of the notion of the eye-consciousness element up to the emptiness of the notion of the mind-consciousness element is non-dual." ("Notion" (想 - xiǎng) refers to clinging, assuming substantial existence. Considering skandhas, āyatanas, dhātus as real is "dualistic" (二 - èr, dual/opposed/discriminated); realizing their emptiness is "non-dual" (不二 - bù èr, transcending duality). "In emptiness, there is no..." means abiding in this state of "non-duality.")
• Explanation of Principles:
  • The skandhas, āyatanas, and dhātus are the fundamental framework in Buddhism for analyzing the mind-body world. Ordinary beings cling to them as substantially real, which is the root of saṃsāra.
  • "Therefore, in emptiness, there is no..." negates, at the level of ultimate truth (paramārtha-satya, emptiness), that these dharmas possess an independent, unchanging self-nature. They are phenomena dependently co-arisen and nominally designated; their essence is emptiness.
  • This does not negate the phenomenal function of the skandhas, āyatanas, and dhātus in conventional truth (saṃvṛti-satya), but rather dismantles the clinging to their "substantial self-nature." Understanding this point allows one to remain unbound by phenomena while penetrating their empty nature.

Heart Sutra Basis 6: [No ignorance, and also no cessation of ignorance. And so forth, up to no aging and death, and also no cessation of aging and death.]

• Meaning of the Heart Sutra Phrase:
  • Further negates the substantial self-existence of the Twelve Links of Dependent Origination (Pratītyasamutpāda) – the chain of causation from ignorance (avidyā) to aging and death (jarāmaraṇa) that explains the cycle of rebirth – and its reversal process (the path to liberation, from the cessation of ignorance to the cessation of aging and death).
  • "No ignorance... no aging and death" negates the substantial reality of the forward cycle (flow); "no cessation of ignorance... no cessation of aging and death" negates the substantial reality of the reverse cycle (cessation).
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "Furthermore, Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they should contemplate ignorance up to aging and death as empty because they are ultimately unborn; they should contemplate the cessation of ignorance up to the cessation of aging and death as empty because they are ultimately unborn." (Directly corresponds to the Heart Sutra, pointing out that the links of dependent origination in forward sequence (ignorance to aging and death) and in reverse sequence (cessation of ignorance to cessation of aging and death) are all "empty because they are ultimately unborn.")
  • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "Subhūti! How do Bodhisattva Mahāsattvas, when practicing the profound Prajñāpāramitā, cultivate the elimination of ignorance and also eliminate this cultivation? Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they do not think: 'Ignorance is a dharma that can be cultivated for elimination, and I am able to cultivate its elimination.' Why? Because these Bodhisattva Mahāsattvas attain nothing regarding ignorance and the cultivation, due to its empty self-nature. Similarly, they cultivate the elimination of formations, consciousness, name-and-form, the six bases, contact, feeling, craving, clinging, becoming, birth, aging and death, and also eliminate this cultivation." (Again explains using "cultivating elimination" and "non-attainment" that each link of the twelve nidānas and its antidote (cessation) are, under Prajñā contemplation, empty of self-nature and unattainable.)
  • Mahāprajñāpāramitā Sūtra (Fascicle 528) Tenth Division, Subhūti Chapter, Second Part, Section 2: "Furthermore, Subhūti! The notion of ignorance up to the notion of aging and death is dualistic; the emptiness of the notion of ignorance up to the emptiness of the notion of aging and death is non-dual." (Similarly uses "dualistic" and "non-dual" to distinguish between clinging and realizing emptiness. Considering the links of dependent origination as real is "dualistic"; realizing their emptiness is "non-dual." "No ignorance..." means abiding in "non-duality.")
  • Mahāprajñāpāramitā Sūtra (Fascicle 528) Tenth Division, Subhūti Chapter, Second Part, Section 2: "When Bodhisattva Mahāsattvas cultivate recollection of the Buddha, they should not contemplate the Tathāgata, the Arhat, the Perfectly Enlightened One through the dharmas of dependent origination. Why? Because all dharmas of dependent origination are without self-nature." (Clearly states that dependent origination itself is without self-nature.)
• Explanation of Principles:
  • The Twelve Links of Dependent Origination are a crucial theory explaining the mechanism of cyclic existence. Ordinary beings, due to ignorance, create karma and transmigrate through birth and death. Practitioners, through wisdom, destroy ignorance and reverse the process of dependent origination to attain liberation.
  • This line in the Heart Sutra points out, from the high perspective of Prajñā emptiness, that both the factors causing saṃsāra (ignorance, aging and death, etc.) and the methods used to counteract them ("cessation," extinction) lack substantial self-nature in the ultimate truth.
  • Clinging to the idea that there is a real "ignorance" to be "ceased" or a real "aging and death" to be "eliminated" is itself a subtle form of clinging to dharmas (dharma-grāha). Prajñā wisdom transcends both sides – arising and ceasing – abiding in the non-dual reality of dependent origination and empty nature.

Heart Sutra Basis 7: [No suffering, no origin, no cessation, no path. No wisdom and also no attainment, because there is nothing to attain.]

• Meaning of the Heart Sutra Phrase:
  • Negates the substantial self-existence of the core doctrine of the Śrāvaka path – the Four Noble Truths (Suffering, Origin, Cessation, Path).
  • Negates the substantial self-existence of the wisdom (智 - zhì) that realizes and the fruit (得 - dé, e.g., Nirvāṇa, Bodhi) that is attained.
  • Points out the fundamental reason for all these "negations": the core insight of Prajñā, which is "non-attainment" (无所得 - wú suǒ dé).
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Regarding "No suffering, origin, cessation, path":
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "Furthermore, Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they should contemplate the Noble Truth of Suffering as empty because it is ultimately unborn; they should contemplate the Noble Truths of Origin, Cessation, and the Path as empty because they are ultimately unborn." (Directly states the Four Noble Truths are also "empty because ultimately unborn.")
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, if they think: 'The Noble Truth of Suffering should be fully known, the Noble Truth of Origin should be abandoned, the Noble Truth of Cessation should be realized, the Noble Truth of the Path should be cultivated,' thinking thus, they are not practicing Prajñāpāramitā. Why, Subhūti? Because Bodhisattva Mahāsattvas practicing Prajñāpāramitā attain nothing regarding all dharmas, nor do they cling to anything." (Clearly points out that clinging to the substantial operations of the Four Truths (knowing, abandoning, realizing, cultivating) is not practicing Prajñā, because the core of Prajñā is non-attainment, non-clinging.)
  • Regarding "No wisdom and also no attainment":
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "World-Honored One! Is the non-dual dharma attained by means of a non-dual dharma?' The Buddha said: 'No, Subhūti!' 'World-Honored One! Is the non-dual dharma attained by means of a dual dharma?' The Buddha said: 'No, Subhūti! Why? Subhūti! Both dual and non-dual dharmas are unattainable. Therefore, the attained wisdom of omniscience is not attained by means of dual or non-dual dharmas. However, the dharma of non-attainment can attain non-attainment. Therefore, attaining through non-attainment is called true attainment.'" (Profoundly explains that the "attainment" in Prajñā is realized through "non-attainment." "Wisdom" is the means of attainment, "attainment" is the result; in Prajñā, both the means and the result are unattainable, which constitutes true realization.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 528) Tenth Division, Subhūti Chapter, Second Part, Section 2: "If there is attainment, it is not Prajñāpāramitā; if there is non-attainment, it is Prajñāpāramitā. Those who have attainment have no attainment, no direct realization (abhisamaya), and also no unsurpassed, perfect, complete enlightenment. If there is non-attainment, that is attainment, that is direct realization, that is unsurpassed, perfect, complete enlightenment." (Extremely clearly contrasts "attainment" with Prajñā/realization, and equates "non-attainment" with Prajñā/realization. "No wisdom and also no attainment" means abiding in this state of "non-attainment.")
  • Regarding "Because there is nothing to attain":
    • Mahāprajñāpāramitā Sūtra (Fascicle 528) Tenth Division, Subhūti Chapter, Second Part, Section 2: "Subhūti! Bodhisattva Mahāsattvas should practice the profound Prajñāpāramitā of non-attainment. Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā of non-attainment, they do not attain the perfection of generosity (dāna-pāramitā), nor the giver, recipient, gift, or any karmic results; they do not attain the perfection of ethical discipline (śīla-pāramitā), nor the keeping or breaking of precepts... they do not attain the perfection of wisdom (prajñā-pāramitā), nor foolishness or wisdom; ... up to not attaining omniscience (sarvajñatā), knowledge of the path aspects (mārgākārajñatā), knowledge of all aspects (sarvākārajñatā), nor the Tathāgata, Arhat, Perfectly Enlightened One, nor ordinary beings, Śrāvakas, Pratyekabuddhas, Bodhisattvas, Buddhas, nor Nirvāṇa." (Systematically explains the application of "non-attainment" in the practice of the six perfections up to the realization of Buddhahood: all dharmas are unattainable.)
• Explanation of Principles:
  • The Four Noble Truths are the foundation of Buddhist dharma, but Prajñā transcends clinging to their concepts and operations. In ultimate emptiness, suffering, origin, cessation, and path also lack self-nature.
  • "No wisdom and also no attainment" dismantles the clinging to the duality of subject (knower) and object (known) in practice. Believing there is a real wisdom that can attain a real fruition still falls within the discriminating mind. The realization of Prajñā transcends subject-object duality; it is an "attainment of non-attainment."
  • "Because there is nothing to attain" (以无所得故 - yǐ wú suǒ dé gù) is the crucial finishing touch of Prajñā thought. Because the inherent nature of all dharmas is empty and utterly unattainable, therefore the skandhas, āyatanas, dhātus are empty, dependent origination is empty, the Four Noble Truths are empty, and even the realizing wisdom and the realized fruition lack self-nature in the ultimate sense. Only by abiding in the correct view of "non-attainment" can one truly enter emptiness, destroy all clinging, and perfect Prajñā.

Heart Sutra Basis 8: [Bodhisattvas, relying on Prajñāpāramitā, have no hindrance in their minds. Because there is no hindrance, they have no fear. Far apart from inverted views and illusions, they reach ultimate Nirvāṇa.]

• Meaning of the Heart Sutra Phrase:
  • Points out that Bodhisattvas (菩提萨埵 - Pútísàduǒ), by relying on the practice of Prajñāpāramitā, can achieve a state where their minds are free from attachment and obstruction (无挂碍 - wú guà ài), consequently having no fear or anxiety (无有恐怖 - wú yǒu kǒng bù), are liberated from all wrong views and illusory discriminations (远离颠倒梦想 - yuǎnlí diāndǎo mèngxiǎng), and ultimately realize the state of complete liberation, Nirvāṇa (究竟涅槃 - jiūjìng nièpán).
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Regarding "relying on Prajñāpāramitā":
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "If a Bodhisattva Mahāsattva is far apart from the skillful means of Prajñāpāramitā, even though they may draw near to and make offerings to Buddhas, plant roots of goodness in the presence of Buddhas, or practice generosity, pure precepts, patience, diligence, and meditative concentration for many kalpas, they still cannot attain the wisdom of omniscience." (Illustrates from the negative side: without Prajñā, even with other good deeds, one cannot attain Buddhahood, highlighting the importance of "relying on Prajñā.")
  • Regarding "have no hindrance in their minds":
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they see no dharma that should be avoided, and see no dharma that should be drawn near to, because the nature and characteristics of all dharmas are empty." (Realizing all dharmas are empty, without grasping or rejecting, the mind is naturally without hindrance.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "These Bodhisattva Mahāsattvas have no clinging regarding all dharmas, whether conditioned or unconditioned. Why? Because these Bodhisattva Mahāsattvas know that all dharmas are ultimately empty, utterly without substance that can be clung to." (No clinging is equivalent to no hindrance.)
  • Regarding "Because there is no hindrance, they have no fear":
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "If a Bodhisattva Mahāsattva practices the profound Prajñāpāramitā, all evil māras, māra armies, arrogant individuals, and external path practitioners cannot destroy them... Thus, Subhūti! When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, all worldly humans and non-humans cannot harm or frighten them." (Prajñā has protective power; the practitioner's mind is stable, invulnerable to external harm, naturally free from fear.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 538) Tenth Division, Chapter on Entrustment, Sixth Part: The Buddha told Ānanda: "These good men and good women, by hearing the profound sutra of Prajñāpāramitā, will have all fears eliminated." (Directly states hearing and practicing Prajñā eliminates fear.)
  • Regarding "Far apart from inverted views and illusions":
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "Sentient beings have inverted and delusional attachments; regarding this Thusness, they neither know nor see it. Bodhisattva Mahāsattvas, for their benefit, reveal dharmas according to conventional appearances, wishing to liberate them from the cycle of birth and death." (Bodhisattvas themselves are already free from inversion (颠倒 - diāndǎo), enabling them to help beings abandon inversion. Inversion refers to wrong views like taking the impermanent as permanent, suffering as happiness, non-self as self, impure as pure.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "When Bodhisattva Mahāsattvas practice the profound Prajñāpāramitā, they should practice the profound Prajñāpāramitā free from conceptual proliferation (prapañca)... Conceptual proliferation is the root of birth and death." ("Conceptual proliferation" (戏论 - xìlùn) is similar to inverted views and illusions. Being free from prapañca is being far apart from inverted views and illusions.)
  • Regarding "ultimate Nirvāṇa":
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "Through this Prajñāpāramitā, Śrāvakas, Pratyekabuddhas, Bodhisattvas, and Tathāgatas are able to reach the other shore. Having reached the other shore, they skillfully sever forever all afflictions along with their latent tendencies, and realize ultimate, permanent, blissful Nirvāṇa." (Clearly states that relying on Prajñā enables the realization of "ultimate, permanent, blissful Nirvāṇa," i.e., ultimate Nirvāṇa.)
• Explanation of Principles:
  • This section describes the practical function and attainment of Prajñā wisdom in Bodhisattva practice.
  • "Mind without hindrance" is the cause, stemming from Prajñā's destruction of clinging to self (ātma-grāha) and clinging to dharmas (dharma-grāha).
  • "No fear" is the result; because the mind has no object of attachment, the root cause of fear – fear of loss or harm – is eliminated.
  • "Far apart from inverted views and illusions" means Prajñā wisdom discerns the true reality of dharmas, destroying all erroneous cognitions and illusory imaginations based on ignorance.
  • "Ultimate Nirvāṇa" is the final goal, referring to the complete cessation of afflictions and transcendence of saṃsāra through Prajñā wisdom, attaining the most perfect state of liberation. For Mahāyāna Bodhisattvas, this Nirvāṇa is "Non-Abiding Nirvāṇa" (apratiṣṭhita-nirvāṇa), dwelling neither in saṃsāra nor in static Nirvāṇa, but functioning with the union of wisdom and compassion.

Heart Sutra Basis 9: [All Buddhas of the three times, relying on Prajñāpāramitā, attain Anuttarā Samyaksaṃbodhi.]

• Meaning of the Heart Sutra Phrase:
  • Not only Bodhisattvas, but all Buddhas of the past, present, and future (三世诸佛 - sān shì zhū fó), also rely on the practice of Prajñāpāramitā to attain Unsurpassed, Perfect, Complete Enlightenment (阿耨多罗三藐三菩提 - Anuttarā Samyaksaṃbodhi), which is the state of perfect Buddhahood.
  • Emphasizes that Prajñāpāramitā is the fundamental and indispensable path to achieving Buddhahood.
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "Subhūti! The profound Prajñāpāramitā gives birth to all Buddhas; it is the mother of all Buddhas (诸佛母 - zhū fó mǔ); it reveals the true nature of all dharmas in the world and is called the supreme path." (Directly calls Prajñā the "mother of all Buddhas," indicating Buddhas are born from Prajñā.)
  • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: "The Buddhas of the past, future, and present are also like this: all rely on Prajñāpāramitā, due to non-attainment, and realize unsurpassed, perfect, complete enlightenment." (While explaining "attaining through non-attainment," it explicitly mentions that Buddhas of the three times all "rely on Prajñāpāramitā, due to non-attainment" to realize Bodhi, closely matching this line in the Heart Sutra.)
  • Mahāprajñāpāramitā Sūtra (Fascicle 528) Tenth Division, Subhūti Chapter, Second Part, Section 2: "The Buddha said: Subhūti! When I originally cultivated the Bodhisattva path, practicing the perfection of generosity up to the perfection of wisdom, using non-attainment as the skillful means, I had no clinging regarding any dharma. With the wisdom corresponding to a single moment (ekakṣaṇa-saṃyukta-prajñā), I realized unsurpassed, perfect, complete enlightenment." (Śākyamuni Buddha describes his own path to Buddhahood, clearly stating it involved practicing the six perfections, especially the perfection of wisdom (manifested as non-attainment, non-clinging, wisdom corresponding to a single moment), to attain supreme Bodhi.)
  • Mahāprajñāpāramitā Sūtra (Fascicle 575) Eleventh Division, Chapter on Profound Meaning, Sixteenth Part: "All Buddhas, World-Honored Ones of the three times, rely entirely on the profound and wondrous Dharma of Prajñāpāramitā to realize unsurpassed, perfect, complete enlightenment, turn the wondrous Dharma wheel, and liberate sentient beings." (Again emphasizes all Buddhas of the three times rely on Prajñā to realize Bodhi.)
• Explanation of Principles:
  • This line elevates the status of Prajñāpāramitā to the highest level; it is not only the core of Bodhisattva practice but the sole basis for attaining Buddhahood.
  • "Anuttarā Samyaksaṃbodhi" is the perfect wisdom and state of awakening realized by a Buddha. Attaining this state means thoroughly understanding the true nature of all dharmas, completely eradicating all afflictions and latent tendencies, and possessing immeasurable merits and abilities.
  • Prajñā enables the attainment of Buddhahood because it fundamentally destroys ignorance, self-clinging, and dharma-clinging, which are the obstacles to realization, thereby revealing the inherent Buddha-nature within all beings. Without Prajñā's empty wisdom, all other practices cannot lead to the ultimate fruition of Buddhahood.

Heart Sutra Basis 10: [Therefore, know that Prajñāpāramitā is the great divine mantra, the great bright mantra, the unsurpassed mantra, the unequaled mantra, able to eliminate all suffering – it is true and not false.]

• Meaning of the Heart Sutra Phrase:
  • Summarizes the supreme virtues of Prajñāpāramitā, likening it to a mantra (咒 - zhòu) possessing inconceivable power and efficacy.
  • "Great divine mantra" (大神咒 - dà shén zhòu): Has great power, able to conquer all obstacles.
  • "Great bright mantra" (大明咒 - dà míng zhòu): Has great illumination, able to dispel all darkness of ignorance.
  • "Unsurpassed mantra" (无上咒 - wú shàng zhòu): Is the highest, most supreme Dharma gate, none can surpass it.
  • "Unequaled mantra" (无等等咒 - wú děng děng zhòu): Is unique, incomparable, nothing can be equal to it.
  • It can truly and unfailingly eliminate all the suffering of saṃsāra.
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • Regarding "Great divine mantra" (Power):
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "If a Bodhisattva Mahāsattva practices the profound Prajñāpāramitā, all evil māras, māra armies, arrogant individuals, and external path practitioners cannot destroy them; all worldly afflictions such as greed, hatred, delusion, etc., cannot sway them." (Shows its great power to subdue internal and external obstacles.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 578) Twelfth Division, Unequaled Chapter, First Part: (Prajñā enables Bodhisattvas to) "quickly attain the wisdom of omniscience, able to rescue limitless, boundless sentient beings, liberating them from the great suffering of birth and death, and enabling them to attain the bliss of Nirvāṇa." (Possesses the immense divine power to quickly achieve fruition and liberate vast numbers of beings.)
  • Regarding "Great bright mantra" (Illumination):
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "It reveals the true nature of all dharmas in the world and is called the supreme path." (Prajñā truthfully reveals the real nature of dharmas, like a bright lamp dispelling darkness.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 574) Eleventh Division, Chapter on Non-Attainment, Fifteenth Part: "This true Prajñāpāramitā can illuminate all dharmas as ultimately empty, signless, wishless, unborn, unceasing, undefiled, unpure, like space, ungraspable and unattachable." (Directly uses the word "illuminate" (照 - zhào) to describe Prajñā's function.)
  • Regarding "Unsurpassed mantra" (Supreme):
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "Through this Prajñāpāramitā... Tathāgatas are able to reach the other shore... realize ultimate, permanent, blissful Nirvāṇa." (Being able to lead to Buddhahood and ultimate Nirvāṇa, it is naturally unsurpassed.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 402) Second Division, Preface Chapter, First Part: "The Buddha told Śāriputra: 'The Prajñāpāramitā practiced by Bodhisattva Mahāsattvas, know that it is precisely unsurpassed Bodhi.'" (Directly equates Prajñā with unsurpassed Bodhi.)
  • Regarding "Unequaled mantra" (Incomparable):
    • Mahāprajñāpāramitā Sūtra (Fascicle 578) Twelfth Division, Unequaled Chapter, First Part: (Chapter title itself is "Unequaled Chapter" - 无等等品) "At that time, the World-Honored One told Śāriputra: 'If a Bodhisattva Mahāsattva wishes to realize unsurpassed, perfect, complete enlightenment, they should study Prajñāpāramitā. Śāriputra! This Dharma which Bodhisattva Mahāsattvas should study has nothing equal to it, hence it is called unequaled (无等等 - wú děng děng).'" (Directly explains the meaning of "unequaled": no dharma can be equal to or compared with it.)
  • Regarding "Able to eliminate all suffering, true and not false":
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "...wishing to liberate them from the immeasurable suffering and affliction of the three realms of saṃsāra and have them realize ultimate, permanent, blissful Nirvāṇa." (Clearly states its efficacy in eliminating suffering.)
    • Mahāprajñāpāramitā Sūtra (Fascicle 527) Tenth Division, Subhūti Chapter, Second Part, Section 1: "If one practices Prajñāpāramitā, one practices the true meaning of the nature and characteristics of all dharmas. If one practices the true meaning of the nature and characteristics of all dharmas, then one understands the Thusness, Dharma Realm, Dharma Nature, non-falsity (不虚妄性 - bù xū wàng xìng), non-alterability, equality, freedom from arising, the definite nature of dharmas, the abiding nature of dharmas, the True Limit of all dharmas." (Emphasizes the connection of Prajñā with "truth" and "non-falsity.")
• Explanation of Principles:
  • This passage is a high praise of the value and function of Prajñāpāramitā. "Mantra" here does not refer solely to specific syllables (though a mantra follows), but takes its meaning as "true word" (真实语), "dharani" (总持 - that which holds all meanings), "illumination" (明 - dispelling darkness), and "divine" (神 - power), metaphorically representing the inconceivable functions of Prajñā wisdom.
  • Great divine, great bright, unsurpassed, unequaled praise Prajñā's perfection and supremacy from four dimensions: power, wisdom, status, and uniqueness.
  • "Able to eliminate all suffering, true and not false" is the final affirmation of its efficacy. Prajñā wisdom, by revealing the reality of emptiness, fundamentally dismantles the root cause of suffering (clinging). Its liberating effect is real, reliable, and inevitable.

Heart Sutra Basis 11: [Therefore, the mantra of Prajñāpāramitā was spoken. The mantra was spoken thus: Gate Gate Pāragate Pārasaṃgate Bodhi Svāhā.]

• Meaning of the Heart Sutra Phrase:
  • Because Prajñāpāramitā possesses the immeasurable merits and power described above, a mantra that can be recited is finally given as a condensed symbol and practical expedient for the Prajñā dharma gate.
  • The mantra roughly translates to: Gone! Gone! Gone to the other shore! Everyone, gone together to the other shore! Awakening! May it be perfectly accomplished!
• Related Passages from the Mahāprajñāpāramitā Sūtra:
  • The Mahāprajñāpāramitā Sūtra itself is vast and provides detailed explanations of Prajñā principles; it generally does not end with a single condensed mantra. However, the entire content of the Mahāprajñāpāramitā Sūtra serves as an extensive explanation of the meaning contained within this mantra.
  • Gate (Gate - Go! Transcend!): Corresponds to the countless teachings in the Mahāprajñāpāramitā Sūtra about "going beyond" clinging, "transcending" the states of ordinary beings and the two vehicles (Śrāvakas and Pratyekabuddhas), and "crossing over" the ocean of suffering and saṃsāra.
    • Mahāprajñāpāramitā Sūtra (Fascicle 578) Twelfth Division, Unequaled Chapter, First Part: "Surpassing all Śrāvakas and Pratyekabuddhas, entering into the Bodhisattva's correct nature of detachment from birth (正性离生 - zhèngxìng líshēng)." ("Surpassing," "entering into" convey the meaning of "Gate.")
  • Pāragate (Pāragate - Gone to the other shore!): Directly corresponds to the core meaning of "Pāramitā" (Perfection / Gone to the Other Shore).
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "Through this Prajñāpāramitā, Śrāvakas, Pratyekabuddhas, Bodhisattvas, and Tathāgatas are able to reach the other shore..." ("Reaching the other shore" is "Pāragate.")
  • Pārasaṃgate (Pārasaṃgate - Completely / Together gone to the other shore!): Embodies the Mahāyāna spirit of benefiting self and others, liberating all beings.
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "Bodhisattva Mahāsattvas... for the sake of sentient beings, seek unsurpassed, perfect, complete enlightenment, wishing to liberate them from the immeasurable suffering and affliction of the three realms of saṃsāra..." ("For the sake of sentient beings," "liberating them" reflects the "Saṃ" (together) aspect.)
    • "Saṃ" can also mean "completely, thoroughly," corresponding to Prajñā's "ultimate" (究竟 - jiūjìng) liberation.
  • Bodhi (Bodhi - Awakening): The ultimate goal of Prajñā.
    • Mahāprajñāpāramitā Sūtra (Fascicle 526) Tenth Division, Subhūti Chapter, First Part: (Re-quote) "...realize unsurpassed, perfect, complete enlightenment (Bodhi)."
  • Svāhā (Svāhā - May it be accomplished / Hail!): The concluding aspiration and affirmation of the mantra.
    • The entire discourse of the Mahāprajñāpāramitā Sūtra is aimed at enabling all beings to ultimately and perfectly accomplish the path to Buddhahood.
• Explanation of Principles:
  • The mantra at the end of the Heart Sutra can be seen as a highly condensed summary of the path and goal of the Prajñā dharma gate. It is not only a summation of Prajñā theory but also a practical guide and an empowerment.
  • Reciting this mantra can be understood as making an aspiration: May I (and all beings) transcend this shore of affliction and clinging (Gate), reach the other shore of wisdom and liberation (Pāragate), may all beings together reach the ultimate, perfect other shore (Pārasaṃgate), and finally attain unsurpassed, perfect, complete enlightenment (Bodhi Svāhā)!
  • Although the main body of the Mahāprajñāpāramitā Sūtra consists of doctrinal exposition, the Prajñā path itself emphasizes the unity of textual Prajñā (understanding), contemplative Prajñā (practice), and reality Prajñā (realization). The mantra can serve as a skillful means to help practitioners recollect the meaning of Prajñā, focus the mind, and attune themselves to the empty nature of Prajñā.

Summary:

By comparing the Heart Sutra verse by verse with the relevant complete passages from the Mahāprajñāpāramitā Sūtra, we can clearly see:

1. High Degree of Consistency: The core ideas of the Heart Sutra, such as the emptiness of the five skandhas, the non-duality of form and emptiness, the empty nature of all dharmas, non-attainment, the virtues of Prajñā, and realizing Bodhi through Prajñā, all have extensive, repeated, and profound expositions and demonstrations within the Mahāprajñāpāramitā Sūtra. The Heart Sutra is indeed a highly condensed distillation and essence of the Mahāprajñāpāramitā Sūtra.
2. Mutual Complementation of Brevity and Breadth: The Heart Sutra is concise and points directly to the core. The Mahāprajñāpāramitā Sūtra, conversely, draws widely from various sources and engages in repeated analysis, providing a rich background, argumentation, and detail for each line of the Heart Sutra, helping us understand its profound meanings more deeply and accurately.
3. The Core of Prajñā: The shared core of both sutras is "Prajñāpāramitā" – the wisdom that penetrates the inherent emptiness of all dharmas, and the path of practice based on this wisdom to destroy clinging, overcome all suffering and hardship, and ultimately attain unsurpassed Bodhi. The key lies in the view and practice of "non-attainment" (anupalabdhi / aprāpti).

This comparative study helps us avoid superficial interpretations or misunderstandings of the Heart Sutra and allows for a deeper appreciation of the profound subtlety of the Prajñā dharma gate.