SAE Power Theory Series · Paper 5: On the Development of Power · Shi
SAE 权力论系列 · Paper 5：论权力的发展 · Shi
Paper 5, Cultivation (育), is the fifth paper of the SAE Power Theory series. It belongs to the same one-directionally dependent conceptual system as the Prequel and Papers 1 through 4; it introduces no new theorem and re-establishes no proposition of Paper 1. Its single task is to unfold the developmental dynamics of power along T5, the power-right duality theorem.
The central claim is that any successfully operating structure of social power triggers, within the population in which it operates, pressure toward a migration of the DD distribution; power is therefore a driver of population-level development. This development proceeds along the T5 right-axis in three segments: a slow segment under a self-maintaining orientation, a middle segment in which the remainder of the one under power forces rights upward, and a cultivating segment under a releasing orientation. Cultivation is not one of two parallel directions standing alongside severing. In the directional grammar of T1 the two are dual; but within developmental dynamics, cultivation is the structural attractor at which this developmental logic, in the releasing orientation, runs to its end.
The paper establishes five criteria. C1 reads the dominant-layer migration proposition as a direction-neutral driver of development. C2 gives the three-segment structure and the coupling of rate to orientation along T5, and locates the transition from the middle to the cultivating segment as a bifurcation at structural overload. C3 defines cultivation as level-raising plus the dissolution of a local grid, not as a reduction of the remainder. C4 locates the propagation mechanism of cultivation as the transmission of a low-reflexive-binding-cost path across a population network. C5 lifts the ontological differential of L1 to the population level, yielding that difference expands under development and that ρ ≠ ∅ holds at all times in the upward direction.
Value attaches to direction, not to the remainder. This paper carries directional value, which is the ground on which cultivation is benign power; but the value attaches to the direction discriminated by T6, and the remainder itself remains without value. The internal mechanism of severing power is reserved for Paper 6, and resistance and dissolution for Paper 7.
Abstract
Paper 5, Cultivation (育), is the fifth paper of the SAE Power Theory series. It belongs to the same one-directionally dependent conceptual system as the Prequel and Papers 1 through 4; it introduces no new theorem and re-establishes no proposition of Paper 1. Its single task is to unfold the developmental dynamics of power along T5, the power-right duality theorem.
The central claim is that any successfully operating structure of social power triggers, within the population in which it operates, pressure toward a migration of the DD distribution; power is therefore a driver of population-level development. This development proceeds along the T5 right-axis in three segments: a slow segment under a self-maintaining orientation, a middle segment in which the remainder of the one under power forces rights upward, and a cultivating segment under a releasing orientation. Cultivation is not one of two parallel directions standing alongside severing. In the directional grammar of T1 the two are dual; but within developmental dynamics, cultivation is the structural attractor at which this developmental logic, in the releasing orientation, runs to its end.
The paper establishes five criteria. C1 reads the dominant-layer migration proposition as a direction-neutral driver of development. C2 gives the three-segment structure and the coupling of rate to orientation along T5, and locates the transition from the middle to the cultivating segment as a bifurcation at structural overload. C3 defines cultivation as level-raising plus the dissolution of a local grid, not as a reduction of the remainder. C4 locates the propagation mechanism of cultivation as the transmission of a low-reflexive-binding-cost path across a population network. C5 lifts the ontological differential of L1 to the population level, yielding that difference expands under development and that ρ ≠ ∅ holds at all times in the upward direction.
Value attaches to direction, not to the remainder. This paper carries directional value, which is the ground on which cultivation is benign power; but the value attaches to the direction discriminated by T6, and the remainder itself remains without value. The internal mechanism of severing power is reserved for Paper 6, and resistance and dissolution for Paper 7.
Keywords
SAE; Self-as-an-End; power theory; cultivating power; development; T5 power-right duality; reflexive-binding; remainder; structural attractor; dominant-layer migration; anti-teleology; Shi.
§I Introduction: Power as the Driver of Development
The Power Theory series is the dual of the SAE Moral Law series. The Moral Law treats, from the inside out, situations in which DD positions are symmetric or mutually maintained; Power Theory treats, from the outside in, situations in which DD positions are asymmetric and not mutually maintained. The Prequel cleared the referential space of power; Paper 1 established the 13DD point of origin and the three-layer source, made explicit the power-right duality, and established the three theorems of remainder, duality, and reflexive-binding. Paper 2 unfolded the geometry, phase, and dimension of power along the three morphological axes. Paper 3 separated the three persons of recognition and the state machine of operational-layer recognition. Paper 4 unfolded the limiting function of the remainder along T3 into a global property. On this foundation the task of Paper 5 is single and determinate: to unfold the developmental dynamics of power along T5, the power-right duality theorem.
This paper establishes no new theorem. T5 was set down in Paper 1; Paper 5 unfolds along T5, depends one-directionally on Papers 1 through 4, and does not redefine the earlier papers in turn. Paper 4, §IX, already reserved the directional dynamics of cultivating power for the present paper: the cultivating orientation of an elevated subject, the persistence of the absolute remainder ρ at the success of cultivation, and the amplification of inter-subject remainder difference at the population level are redeemed here and established as criteria.
The central claim, in one sentence: power is the driver of population-level development. Any successfully operating structure of social power triggers, within the population in which it operates, pressure toward a migration of the DD distribution. This development proceeds along the T5 right-axis: from a slow segment in which power presses the subject-position downward, through a middle segment in which the remainder of the one under power forces rights upward, to a cultivating segment in which power actively expands the subject-position; cultivation is the structural attractor at which this developmental logic, in the releasing orientation, runs to its end.
This claim carries directional value. The first four papers were strictly neutral; the present paper is the first in the series to carry directional value: cultivation is benign power, severing is not. But the value attaches to the direction discriminated by T6, not to the remainder; the remainder itself remains without value (Paper 4, L1). This separation runs through the whole paper.
Two words used here are especially liable to be misread as moral vocabulary, development and for, and must first be given their mechanical sense.
Development denotes the expansion of a population system's carrying capacity for higher-dimensional action options and for more complex asymmetric structures. It is a container whose internal tension rises continuously until phase transition; it carries no moral good. A population's development is a rise in the dimension of the action options it can bear and an increase in the complexity of the asymmetric structures it can maintain; it is not that its members are happier or freer.
For is not the psychological motive of the power-holder, nor a historical purpose, nor an intention of which the power-holder is aware; it is the automatic pathfinding vector of a mechanical system under a particular cost function. The recurring expressions power for power and power for rights denote the orientation of the power structure: a self-maintaining orientation, or a releasing orientation. Power for rights does not say that the power-holder has had a change of heart and wishes to grant rights; it says that the vector of the power system, under the weight of T6 reflexive-binding, is driven to point toward the maximal extension of subject-position retention along T5. Throughout the paper these expressions are read in this mechanical sense, not in the sense of intention.
Three clarifications follow.
First, development is a fact at the level of population structure, not a benefit to the individual under power. The dominant-layer migration proposition (Paper 1, §7) yields pressure toward a migration of the population's DD distribution, not a judgment about any individual's welfare. Severing power likewise drives development, because the operation of locking likewise triggers pressure toward a migration of the population's DD distribution and, by L3, provokes the accumulation, reshaping, and rebound of the remainder (Paper 4); but that severing drives development does not mean that severing is good for the locked individual, nor that the power is normatively endorsed. Micro-level coercion and macro-level phase transition are ontologically orthogonal.
Second, the three segments are not a doctrine of historical progress. The three segments are a structural gradient along the T5 right-axis, traversable in both directions: severing can re-lock and retreat toward the slow segment, and can be destroyed outright by the rebound of the remainder or by transgressive-state migration (Paper 4). The transition from the middle to the cultivating segment is not a one-way street but a bifurcation at structural overload, one branch running toward cultivating release and the other toward physical collapse (Paper 7); the two are exits of equal ontological standing, not a value-dichotomy of success and failure. Dominant-layer migration yields pressure toward development, that is, a directed drive, not a guarantee of development. Cultivation is the structural attractor at which this developmental logic runs to its end, that is, the drive points there; it is not a historical terminus, that is, it is not that power will in the end become benign. The ground of the tendency toward cultivation is the structural cost of continued locking at high DD (T6 reflexive-binding), not a moral arc of history.
Third, value attaches to direction, not to the remainder. The directional discrimination between severing and cultivation is given not by morphological position or operation type but by whether the T6 locking action is triggered (Paper 4). Direction carries value, the remainder does not; the benignity of cultivation is a directional property, not a result of the remainder's being healed. To move toward cultivation along the right-axis is the gradual withdrawal of T6 triggering.
This series does not predict, does not advocate, and does not evaluate any specific political event. The three segments, the transition, and self-reproduction, below, are mechanical descriptions at the structural level, not action prescriptions and not historical prophecy.
Proposition Preview
This paper establishes five criteria, unfolded along T5, with no new theorem. A one-sentence preview of each is given here, with the full statements distributed across §II through §VI, to give the reader a map of the criteria.
C1. Power as the driver of development. Any successfully operating structure of social power triggers pressure toward a migration of its population's DD distribution; this driver presupposes no direction, severing and cultivation are alike drivers of development, and they differ in rate and in mode of maintenance. Full statement in §II.
C2. The three segments and rate-orientation along the right-axis. Development proceeds along the T5 right-axis in three segments — self-maintaining orientation, rights forced upward, releasing orientation — with rate coupled to the degree of right-retention, and the transition from the middle to the cultivating segment is a bifurcation at structural overload. Full statement in §III.
C3. The ontological action of cultivation. Cultivation is level-raising plus the dissolution of a local grid, not a reduction or zeroing of the remainder; the absolute remainder ρ persists, and the decay of cultivating power is self-dissolution once the positional difference has discharged its function. Full statement in §IV.
C4. The self-reproduction cycle of cultivation. The product of cultivation carries a reproducible structural capacity; at high DD, severing exacts a heavier self-binding, so cultivation becomes the low-reflexive-binding-cost path, and self-reproduction is the physical transmission of this path across a population network. Full statement in §V.
C5. The population-level structure of the remainder in the upward direction. Level-raising expands the dimensional space of a subject's developable difference; at the population level overlap and difference grow together while difference grows the more, and ρ ≠ ∅ holds at all times in the upward direction and is structurally more pronounced than at the individual level. Full statement in §VI.
These five, together with the conceptual machinery established in Papers 1 through 4, constitute the entire toolkit of this paper. This paper establishes no further tools.
§II Power as the Driver of Development
Before unfolding the trajectory of development, one must establish whence the driver of development comes and why it presupposes no direction. This is given by C1.
> Criterion C1. Power as the driver of development. Any successfully operating structure of social power triggers pressure toward a migration of its population's DD distribution, and thereby an endogenous impetus to development (the dominant-layer migration proposition, Paper 1, §7). This driver presupposes no direction: severing power and cultivating power are alike drivers of development, differing in rate and in mode of maintenance, not in whether they drive. This development is a fact at the level of population structure, occurring by way of dominant-layer migration; it is not a benefit to the individual under power, nor a normative endorsement of the power.
The dominant-layer migration proposition of Paper 1, §7, is already established: when a structure of power operates successfully, it triggers in its population pressure toward a migration of the DD distribution. C1 reads this proposition as a driver of development; it does not re-establish it. For a structure of power to operate successfully, it must maintain the asymmetric structure it has arranged; maintenance requires that the one under power and the power-holder repeatedly register and operate their DD positions within the structure; and this repeated operation raises the population's capacity to bear higher DD positions, which is development as defined in §I. Wherever power operates, pressure toward development is pressed.
This driver presupposes no direction. Severing power maintains by locking; it likewise raises pressure on the population's DD distribution and, by L3, provokes the accumulation and rebound of the remainder (Paper 4); it drives development, only slowly, and with the power-holder continuously bearing the cost of reflexive-binding. Cultivating power maintains by release; it drives development faster. Both are drivers of development, differing in rate and in mode of maintenance, not in whether they drive. To read power as a driver of development closes off two symmetric intuitions at once: that power is only destruction, and that power is only static control. Power is neither pure destruction nor static control; it is the structural impetus that raises a population's capacity to bear DD.
This development is a fact at the level of population structure, not a benefit to the individual under power. Dominant-layer migration yields pressure on the population's DD distribution, and at that level both severing and cultivation are drivers. But an individual who has been locked has had their subject-position pressed down and their remainder pressed into the latent state; to say that severing has driven development at the population level, to say that this locked individual fares well, and to say that this power is legitimate, are three different things. Development holds at the level of population structure; it does not sink into individual welfare, nor rise into normative endorsement. Wherever this paper speaks of development hereafter, it speaks of it at the level of population structure.
§III Rate and Orientation of Development along the Right-Axis
Development is driven by C1. The axis along which it unfolds, the rate at which it proceeds, and the orientation toward which it tends are given by C2. This is the principal axis of the paper.
> Criterion C2. The three segments and rate-orientation along the right-axis. Development proceeds along the T5 right-axis (a right being the degree to which a subject-position is retained, Paper 1, §3) in three segments, distinguished by the orientation of power toward the subject-position of the one under power. First segment, self-maintaining orientation: power maintains the asymmetric structure itself, and the subject-position of the one under power is pressed toward the lower bound of T5 (not to zero; at zero, power withdraws, Paper 1, §6); development is slow. Second segment, orientation unchanged while rights are forced upward: the orientation of power remains self-maintaining, but the manifest and transgressive states of the remainder of the one under power (Paper 4, L2) force the subject-position upward, the lower bound of T5 is lifted, and development accelerates. Third segment, releasing orientation: the orientation of power turns to expanding the subject-position of the one under power until the positional difference dissolves of itself; development is fastest. Rate is coupled to the degree of right-retention: the lower the subject-position, the more the remainder is pressed into the latent state and the slower the development, and the higher the cost of reflexive-binding on the power-holder's side; the higher the retention, the more the manifest and transgressive states can force the rate upward. The transition from the second to the third segment is not an active turn by the system but a death-cross, at high DD, between the cost of reflexive-binding and the extractable resource: the T6 reflexive-binding cost of continued locking accumulates and accelerates, more so under high DD density and apparatus-based maintenance, and the present paper does not adjudicate it to be exponential or of any particular functional form, nor does it quantify it; when the system's bearable upper bound is exceeded, the structure bifurcates. One branch holds fast to locking and runs toward physical collapse (entering the dissolution of Paper 7); the other yields its hard locking at the weakest point of stress, the local grid is thereby dissolved, and nodes already raised to high DD fall into the releasing orientation (the third segment). The releasing orientation is not a moral awakening, nor a clever bid for survival; it is, in the branch that does not run toward physical collapse, the discharge path of least reflexive-binding dissipation. The transition runs in the same direction as the necessary triggering of T6 in Paper 1, §8 (at the refusal to ascend, T6 passes from optional to necessary triggering).
Development proceeds along the T5 right-axis. T5 is already established: the standing of power requires that the subject-position of the one under power be retained, and at extreme deprivation power withdraws (Paper 1, §6, the tyranny limit). A right, in this series, denotes the degree to which a subject-position is retained (Paper 1, §3, defined independently and prior to law), not a right in the legal sense. One end of this axis is the subject-position pressed toward the lower bound of T5; the other is the subject-position expanded until the positional difference dissolves; development is displacement along this axis.
The three segments are distinguished by the orientation of power toward the subject-position of the one under power, not by the intention of the power-holder. In the first segment, the orientation of power is to maintain the asymmetric structure itself, and it presses the subject-position of the one under power toward the lower bound of T5; the one under power is granted virtually no rights, the remainder is pressed into the latent state, and development in this segment is slow. In the second segment, the orientation of power remains self-maintaining, unchanged; what changes is on the side of the one under power, whose remainder, in its manifest and transgressive states (Paper 4, L2), forces the subject-position upward, the lower bound of T5 is raised, and rights are wrested out; development in this segment accelerates. It must be stressed that the expansion of rights in the second segment does not come from a change in the orientation of power but from the upward force of the remainder of the one under power; power remains self-maintaining, and rights are forced up, not granted. In the third segment, the orientation of power itself turns to release, that is, to expanding the subject-position of the one under power until the positional difference dissolves of itself; development in this segment is fastest.
Rate is coupled to the degree of right-retention. The lower the subject-position is pressed, the more the remainder of the one under power is pressed into the latent state (Paper 4, drift and misreading), the less it can act upon the structure, and the slower the development; at the same time, the cost to the power-holder of maintaining the locking is higher. The higher the degree of right-retention, the more the manifest state of the remainder (resistance and backlash) and its transgressive state (escape and migration) can force the subject-position upward, and the faster the development. The three states of the remainder are therefore the engine of the rate of development: the slow segment is the low-speed region in which the remainder is pressed into the latent state, the middle segment is the accelerating region in which the manifest and transgressive states force rights upward, and the cultivating segment is the highest-speed region in which the positional difference moves toward dissolving of itself.
The transition from the second to the third segment, the point most liable to be read as a doctrine of historical progress, must be written mechanically. The transition is not the system suddenly becoming clever, becoming benevolent, or progressing of its own accord. At high DD, the T6 reflexive-binding cost of continued locking accumulates and accelerates (the present paper does not adjudicate it to be exponential or of any particular functional form, nor does it quantify it), while the resource the structure can extract from the one under power is finite; the cost of reflexive-binding and the extractable resource cross at some point in a death-cross. When the system's bearable upper bound is exceeded, the structure bifurcates. One branch holds fast to locking, reflexive-binding crushes the structure, and it runs toward physical collapse, that is, the dissolution of Paper 7. The other yields its hard locking at the weakest point of stress: the local grid is forced open, and because the nodes there have already been raised to high DD — and severing exacts too heavy a self-binding at high DD, which is the mechanism of C4 — the only low-resistance configuration that maintains the residual connection without total collapse is the releasing orientation, and the system falls into the third segment. Cultivation is not the random product of rupture; it is the only configuration that, when hard locking fails, can contain the high-dimensional nodes without total implosion. The releasing orientation is not because power wishes to do good; it is, in the branch that does not run toward physical collapse, the discharge path of least reflexive-binding dissipation. These two branches are exits of equal ontological standing; cultivating release is not higher than physical collapse, it is merely the other path. This transition runs in the same direction as the necessary triggering of T6 in Paper 1, §8: at the refusal to ascend, T6 passes from optional to necessary triggering.
§IV The Ontological Action of Cultivation
Once power has fallen into the releasing orientation, what it does ontologically is given by C3. From this section, the paper enters the detailed dynamics of the cultivating endpoint.
> Criterion C3. The ontological action of cultivation. The ontological action of cultivating power in the releasing orientation is level-raising plus the dissolution of a local grid, not a reduction or zeroing of the remainder. Cultivation raises the one under power to a higher DD level and dissolves the particular option grid that the power-holder has imposed on them within that relation; the local relation of entrapment thereby loses its definition, rather than some differential being computed to zero. The absolute remainder ρ of the one under power as a 13DD subject is given by L1, ρ ≠ ∅ holds universally, and cultivation does not heal, fill, or erase it. On the power-holder's side: A does not lock, A's remainder is not compressed (no T6 reflexive-binding), and the orientation is toward releasing the one under power. The decay of cultivating power manifests as self-dissolution once the positional difference has discharged its function, and this dissolution is the mark of cultivation's success, not its failure (Paper 2, §IV.4, §IX.2).
What cultivation does is fundamentally not to reduce the remainder. Two things must be kept apart. One is the local relational grid: the finite option grid that the power-holder has marked out for the one under power within this relation. Cultivation raises the one under power to a higher DD level and dissolves this grid; the local relation of entrapment thereby loses its definition, rather than some differential being computed to zero. The other is the absolute remainder ρ: the remainder between the possibilities of the one under power as a 13DD subject and any finite structure, given by L1, with ρ ≠ ∅ holding universally. Cultivation does not heal, fill, or erase this absolute remainder. This is the dividing line between cultivation and every narrative of redemption or assimilation: a narrative of redemption promises to fill the remainder level; cultivation only dissolves one local grid, and the remainder persists undiminished as the subject rises into a higher level.
The power-holder's side is not compressed under cultivation. Under severing, A executes the locking, and A's subject-remainder is compressed into reflexive-binding (Paper 4, L4; T6). Under cultivation, A does not lock, A's remainder is not compressed, and A's orientation is toward releasing the one under power. This runs opposite to the dynamics of reflexive-binding on the power-holder's side under severing, whose full anatomy is reserved for Paper 6.
The decay of cultivating power manifests as self-dissolution once the positional difference has discharged its function. When a cultivating relation succeeds, the one under power rises into a higher level, the positional difference dissolves, and the relation dissolves with it: the student no longer needs the teacher, the recovered no longer need the physician, the editor withdraws behind the finished work. This dissolution is not the failure of cultivation but the mark of its success. Paper 2, §IV.4, already recorded this self-dissolution as the form of cultivating decay, and Paper 2, §IX.2, reserved its unfolding for the present paper, which takes it up here: cultivating power is completed in its own dissolution, whereas severing power maintains itself by continuous investment; the two part ways here in the form of their decay.
§V The Self-Reproduction Cycle of Cultivation
The ontological action of cultivation is toward self-dissolution. How a power oriented toward dissolution spreads across a population is given by C4. The answer is that the product of cultivation carries the capacity for cultivation, and that the mechanism of spread is the transmission of a low-reflexive-binding-cost path across a network.
> Criterion C4. The self-reproduction cycle of cultivation. The product of cultivation carries a reproducible structural capacity. A subject raised to a higher DD level has a thickened capacity to recognize the other as also a self (the core capacity of the 13DD point of origin, thickening as the DD level rises), that is, a raised structural resolution. This raising has two mechanical consequences. First, should the subject invoke severing in a new asymmetric relation, locking an other recognized as also a self is a heavier self-binding, and T6 reflexive-binding is heavier as structural resolution rises, so cultivation becomes the subject's low-reflexive-binding-cost path. Second, the same resolution is the structural capacity that cultivation requires (to keep or restore the other in the position of an end, §VII). On the power-holder's side, the most that is held toward the one being raised is hope for their development, not a will that they become some determinate thing: to will a determinate outcome for the other is to impose a grid on them again, which is a severing action and runs counter to the releasing orientation; hope imposes no grid, and is the only stance compatible with the releasing orientation. That the cultivated becomes one who can cultivate is therefore not out of will or gratitude; it is that the low-reflexive-binding-cost path is open to them at higher DD. The self-reproduction of cultivation is the physical transmission of this low-cost path across a population network, not a moral contagion of goodwill; severing maintains itself by the continuous investment of locking, cultivation spreads by the network transmission of a low-cost path. What the cultivated acquires is the possibility and the higher probability of a capacity to cultivate, not an obligation to become a cultivator; whether they in fact enter into a cultivating operation still depends on their 14DD and 15DD position and on conditions in the field. Self-reproduction is structural dynamics; it entails no historical necessity.
A subject raised to a higher DD level has a thickened capacity to recognize the other as also a self. This capacity is the core capacity of the 13DD point of origin (Paper 1); it thickens as the DD level rises, that is, the structural resolution is raised: the higher the subject, the more it can resolve the other not merely as a means but as a being that is also a self.
This raising of structural resolution has two mechanical consequences, and together they account for why cultivation reproduces, without appeal to any psychological motive. First, should the subject invoke severing in a new asymmetric relation, what it locks is an other it recognizes as also a self; to lock one recognized as also a self is a heavier self-binding, and T6 reflexive-binding is heavier as structural resolution rises. A high-DD subject that severs must bear a heavier self-binding than a low-DD one. Cultivation therefore becomes its low-reflexive-binding-cost path. Second, the same structural resolution is also the capacity that cultivation requires: only by resolving the other as an end can one keep or restore the other in the position of an end (§VII). Resolution is both the reason severing is costlier and the condition under which cultivation is possible.
On the power-holder's side, the most that is held toward the one being raised is hope for their development, not a will that they become some determinate thing. To will a determinate outcome for the other is to impose a grid on them again, to mold them toward a predetermined shape; that is a severing action and runs counter to the releasing orientation. A power that wills to mold its counterpart into some shape is already not cultivation but severing. Hope imposes no grid: to hope that the other develops, without prescribing what the other develops into, is the only stance compatible with the releasing orientation. That the cultivated becomes one who can cultivate is therefore not out of will or gratitude, but because the low-reflexive-binding-cost path is open to them at higher DD.
The self-reproduction of cultivation is the physical transmission of this low-cost path across a population network, not a moral contagion of goodwill. Severing maintains itself by the continuous investment of locking; once investment stops, the locking loosens. Cultivation spreads by the network transmission of a low-cost path: when the one who has been raised builds, at a higher level, a new asymmetric relation, the same low-reflexive-binding-cost path is open to them, and cultivation extends along the network. This is a structural difference between the two powers in their mechanism of propagation, not a good use set against a bad one. It must be stressed that what the cultivated acquires is the possibility and the higher probability of a capacity to cultivate, not an obligation to become a cultivator; whether they in fact enter into a cultivating operation still depends on their 14DD and 15DD position and on conditions in the field. Self-reproduction is structural dynamics; it entails no historical necessity, and is not a claim that cultivation will in the end prevail.
§VI The Population-Level Structure of the Remainder in the Upward Direction
As cultivation is transmitted across a population, the population's remainder structure changes with it. How level-raising reshapes the remainder at the population level is given by C5.
> Criterion C5. The population-level structure of the remainder in the upward direction. Level-raising does not reduce the remainder; it expands the dimensional space of a subject's developable difference. This expansion occurs at two levels, the individual and the population, the latter amplifying the former. At the individual level: the overflow of a subject raised to a higher DD level, of its infinite possibility against the higher-level grid, increases (L1), that is, the inexhaustible space of difference it can bear expands as the level rises; the increase of the total remainder here is a structural statement, not a measurable numerical index. At the population level: the overlap of mutually registrable and mutually maintained content, and the inter-subject difference, grow together, while difference grows the more. The structural ground is the extension of the ontological differential of L1 to the population level. L1 already established that the dimension of difference a single 13DD subject can unfold is infinite, whereas the overlap — the mutually registrable and mutually maintained content — is of finite dimension: mutual registration and maintenance can unfold along only finitely many dimensions, and overlap can itself be infinitely large but lies within a finite-dimensional subspace. Level-raising unfolds each subject's infinite-dimensional space of difference more fully, and difference lies along the infinitely many dimensions outside the finite dimension of overlap; infinite dimension against finite dimension, however large overlap grows within its own dimensions, it cannot absorb the difference that lies outside them. Therefore ρ ≠ ∅ holds at all times in the upward direction at the population level and is structurally more pronounced than at the individual level: however much mutual maintenance deepens, this residue of difference is not absorbed but expands.
Consider first the individual level. The overflow of a subject raised to a higher DD level, of its infinite possibility against the higher-level grid, increases (L1). This is not a reduction of the remainder; it is an expansion of the inexhaustible space of difference the subject can bear as the level rises. It must be noted that the increase of the total remainder here is a structural statement, not a measurable numerical index; it says that the space of difference the subject can bear expands in dimension, not that some quantity grows in number.
Consider next the population level, where this expansion is further amplified. At the population level, level-raising has two concurrent tendencies: the overlap of mutually registrable and mutually maintained content grows, that is, absolute consensus increases; and the inter-subject difference of the remainder grows. The two grow together, and difference grows the more. The structural ground is the extension of the ontological differential of L1 to the population level. L1 already established that the dimension of difference a single 13DD subject can unfold is infinite; whereas the overlap — the content two subjects can mutually register and mutually maintain — is of finite dimension: mutual registration and maintenance can unfold along only finitely many dimensions. Overlap can itself be infinitely large, but it lies within a finite-dimensional subspace. Level-raising unfolds each subject's infinite-dimensional space of difference more fully, and difference lies along the infinitely many dimensions outside the finite dimension of overlap; however large overlap grows within its finitely many dimensions, it cannot absorb the difference that lies outside them.
Therefore, however much mutual maintenance deepens, the residue of difference is not absorbed but expands; ρ ≠ ∅ holds at all times in the upward direction at the population level, and is structurally more pronounced than at the individual level. This overturns a common intuition: that an increase of consensus grinds people toward sameness. Consensus does indeed rise, but because each subject's infinite-dimensional space of difference is unfolded more fully, people become more unlike one another. A more developed population is not more homogeneous; rather, absolute consensus and incommensurable difference increase together, the latter lying along dimensions the former cannot reach, and growing the faster.
§VII The Dynamics of Cultivation across Morphologies
§IV through §VI unfolded cultivation along its ontological action, its reproduction, and its population structure. Cultivation may also be cut along the morphology of Paper 2. Paper 2, §IX.2, assigned to the present paper the morphological points of cultivating power in its various forms, and this section redeems them and connects with the cultivating forms of operational-layer recognition in Paper 3, §VIII.2 and §VIII.3.
Morphology does not determine the direction of cultivation. The discrimination is still given by T6: whether a form is cultivation or severing is read not from its morphological position but from whether it locks. What follows samples a few of Paper 2's positions to show what cultivation looks like in various forms, without an exhaustive correlation of form with direction.
Along the geometric axis, cultivation is not confined to the direct, face-to-face form. Cultivation can be indirect, raising a person by way of an environmental structure; it can be apparatus-based, a good educational structure that raises a person to a higher level even when the one under power and the power-holder are not in direct contact; it can be covert, a background structure that raises a person without the one being raised being aware of it. Covert cultivation and covert severing are alike in form and opposite in direction: the former dissolves a grid, the latter tightens one; the discrimination lies in T6, not in covertness.
At the interface with the Kingdom of Ends and the Kingdom of Means of Paper 2, §VIII, cultivation keeps or restores the one under power in the position of an end, whereas severing moves the one under power from the position of an end to that of a means (the latter reserved for Paper 6). This accords with the structural resolution of §V: to resolve the other as an end is the condition of cultivation; to reduce the other to a means is the mark of severing.
Cultivation also occurs by way of the four operations of operational-layer recognition (Paper 3, §VIII.2, §VIII.3). Cultivating power constructs a recognition structure oriented toward independence, such as the public recognition of the growth of the one being raised; maintains it; guides it; and withdraws its support when the one being raised no longer needs it. These four operations are oriented toward the dissolution of the positional difference, whereas the same four operations of severing power are oriented toward locking. The operations are the same, the orientations opposite, and the discrimination still lies in T6.
§VIII Series Interfaces
This paper unfolds the developmental trajectory and the cultivating endpoint of power along T5; it does not unfold the internal mechanism of severing, nor dissolution. The interfaces are given here.
The interface with Paper 6, Severing, lies in the internal mechanism of severing. The present paper treats severing only at the level of the trajectory, that is, the right-orientation and rate of development in the slow and middle segments. The internal anatomy of severing power — how the locking action is executed, how T6 reflexive-binding accumulates with locking, how the one under power is moved from the position of an end to that of a means, and the equivalence between severingness (the M5 candidate) and the triggering of T6 — is reserved for Paper 6, Severing. The present paper comes first; Paper 6 takes up the trajectory established here and then descends to the locking mechanism; Paper 6 invokes the trajectory of the present paper and does not redefine it.
The interface with Paper 7, Dissolution, lies in dissolution. The overload bifurcation of §III has two branches, cultivating release being one and physical collapse the other. The collapse branch — how a structure that holds fast to locking runs toward dissolution along the accumulation of reflexive-binding, and the dissolution dynamics of developmental regression and stagnation — is reserved for Paper 7, Dissolution. It must be stressed that the self-dissolution of cultivation is not dissolution: cultivation is the voluntary dissolution of a local grid, oriented toward the dissolution of the positional difference; dissolution is the structural collapse driven by severing. The two run opposite. The dissolution of Paper 7 and the release of the present paper are the two branches of the overload bifurcation, of equal ontological standing, not a value-dichotomy of failure and success.
The interface with the Kingdom of Ends of the Moral Law theory is tightest at cultivation. Power for rights, that is, the turn of the orientation of power to expanding the subject-position of the one under power, approaches in structure the mutual recognition and Kingdom of Ends of the first theorem of the Moral Law theory (recognizing the concrete other as an end). Cultivation keeping or restoring the one under power in the position of an end runs in the same direction as the Kingdom of Ends. But the present paper proceeds in the mechanical language of Power Theory, treating situations that are asymmetric and not mutually maintained; the full duality between Power Theory and the Moral Law theory is reserved for a crossing paper, and the present paper only marks the interface here, without merging into the Moral Law theory.
The interface with 16DD lies in the tendency of self-reproduction. The self-reproduction cycle of cultivation (C4) pushes a population toward deepening mutual maintenance, whose limit is the mutual non-doubt of 16DD, at which the concept of power itself dissolves. But this series stops at 15DD, and 16DD is excluded; the present paper stops at cultivation, that is, power still standing while its orientation is toward self-dissolution, and does not reach the dissolution of power. The situation at 16DD is reserved for a crossing paper.
§IX Conclusion
This paper has unfolded the developmental dynamics of power along T5, the power-right duality theorem, with no new theorem. The conceptual machinery established in Paper 1 is here unfolded in the dimension of development.
The results of this paper may be gathered into five. First, any successfully operating structure of social power triggers pressure toward a migration of its population's DD distribution, and power is therefore a driver of population-level development; this driver presupposes no direction, severing and cultivation are alike drivers, differing in rate and in mode of maintenance (C1). Second, development proceeds along the T5 right-axis in three segments — self-maintaining orientation, rights forced upward by the remainder, releasing orientation — with rate coupled to the degree of right-retention, and the transition from the middle to the cultivating segment is a bifurcation at structural overload, not an active progress (C2). Third, the ontological action of cultivation is level-raising plus the dissolution of a local grid, not a reduction or zeroing of the remainder; the absolute remainder ρ persists, and the decay of cultivating power is self-dissolution once the positional difference has discharged its function (C3). Fourth, the product of cultivation carries a reproducible structural capacity, severing exacts a heavier self-binding at high DD so that cultivation becomes the low-reflexive-binding-cost path, and the self-reproduction of cultivation is the physical transmission of this path across a population network, not a moral contagion (C4). Fifth, level-raising expands the dimensional space of a subject's developable difference, at the population level difference lies along the infinitely many dimensions outside the finite dimension of overlap, and ρ ≠ ∅ holds at all times in the upward direction at the population level and is structurally more pronounced than at the individual level (C5).
Thus power is the driver of population-level development, development proceeds along the T5 right-axis in three segments, and cultivation is the structural attractor at which this developmental logic, in the releasing orientation, runs to its end. Cultivation is not a good use of power but the low-reflexive-binding-dissipation configuration into which high-DD nodes fall at the overload bifurcation; it is oriented toward self-dissolution and transmits its own structural capacity across a network.
Value attaches to direction, not to the remainder. The benignity of cultivation is a directional property, discriminated by T6, not a result of the remainder's being healed; the remainder itself remains without value, and in the upward direction it does not diminish but increases at the population level. The internal mechanism of severing power is reserved for Paper 6, Severing, and resistance and dissolution for Paper 7, Dissolution. The work of the present paper is complete; Paper 6, Severing, takes up the internal anatomy of severing power.
Acknowledgments
This series is the dual of the SAE Moral Law series, the latter developed jointly by the author and Zesi Chen (陈则思). The present paper benefited from the outline and body review of a four-AI collaborative research methodology (Zilu, Zigong, Zixia, Gongxihua). At the outline stage, the four reviewers' revisions were incorporated, among them the rewriting of the self-reproduction cycle of cultivation from will to the transmission of a low-reflexive-binding-cost path across a network, the rewriting of the transition from the middle to the cultivating segment from an active turn to a bifurcation at structural overload, and the tightening of the argument for the population-level structure of the remainder into the extension of the ontological differential of L1 to the population level (the dimension of developable difference being infinite, the dimension of overlap finite). At the body stage, the transition was further written as the low-reflexive-binding-dissipation configuration into which high-DD nodes fall after hard locking yields at overload, and the load-bearing sentence was unified as triggering pressure toward a migration of the DD distribution. Gongxihua gave the final sign-off on both the outline and the body.
References
The following works of the SAE series are cited. All are archived on Zenodo, with the Chinese and English versions in the same record. The cited DOIs are concept DOIs, always pointing to the latest version.
Qin, H. (2026). What Power Is Not (SAE Power Theory Series, Prequel). Zenodo. https://doi.org/10.5281/zenodo.20368867
Qin, H. (2026). On the Origin of Power (SAE Power Theory Series, Paper 1). Zenodo. https://doi.org/10.5281/zenodo.20370225
Qin, H. (2026). On the Morphology of Power (SAE Power Theory Series, Paper 2). Zenodo. https://doi.org/10.5281/zenodo.20455221
Qin, H. (2026). On the Recognition of Power (SAE Power Theory Series, Paper 3). Zenodo. https://doi.org/10.5281/zenodo.20480135
Qin, H. (2026). On the Limits of Power (SAE Power Theory Series, Paper 4). Zenodo. https://doi.org/10.5281/zenodo.20532999
Qin, H. (2026). 非 · Negativa: On Negation Prior to Being (SAE Methodology, Paper 0). Zenodo. https://doi.org/10.5281/zenodo.19544619
Qin, H. (2026). Via Rho: The Way of the Remainder (SAE Methodology, Paper 00). Zenodo. https://doi.org/10.5281/zenodo.19657439
Qin, H. (2026). Four Foundational Theorems of the Moral Law · Dao (SAE Moral Law Series, Paper 1). Zenodo. https://doi.org/10.5281/zenodo.20011019
Qin, H. (2026). The Institutional Architecture of Mixed Reality (SAE Moral Law Series, Paper 9). Zenodo. https://doi.org/10.5281/zenodo.20262737
The subsequent papers of the series, Paper 6 (Severing) and Paper 7 (Dissolution), will appear in turn, sharing T5 and T6 as interfaces with the present paper.
(The Chinese version is the authoritative version; this English version is an independent rewrite, not a translation. Han Qin, 2026.)