SAE Power Series · Paper 2: On the Morphology of Power · Shi
SAE 权力论系列 · Paper 2：论权力的形态 · Shi
Paper 1 established eight propositions (T1–T6, the dominant-layer migration thesis, the 13DD uniqueness-of-origin thesis, and the three-source thesis) and developed the genetic dynamics of power. Paper 2 introduces no new theorem and re-derives nothing already established; it unfolds the conceptual machinery of P1 along the dimensions of morphology. The term morphology is used here in the strict mechanical and topological sense, not in the biological sense of classification. P2 establishes three morphological criteria—M1 three-axis decomposition, M2 apparatus non-subjecthood, M3 network conduction—and one phase-axis lemma (M4), which together support the entire paper. The central claim of P2 can be condensed into a single sentence: Apparatuses do not wield power; individuals invoke apparatuses to wield power. The topological legitimacy of an apparatus is borrowed, not native. This paper unfolds power morphology along three independent criteria axes—geometric, phase, and dimensional—and on this basis treats: phase structure (§IV); the topological legitimacy of abstract collective entities as so-called collective power-subjects (§V); algorithmic power as a modern special form (§VI); the bystander-C transfer effect in multi-agent networks (§VII); the Means-Kingdom vs Ends-Kingdom interface anchoring (§VIII); and the rigorous separation of morphology from directionality (severing-mode vs cultivating-mode) in §IX. The working premise of P2 is the full conceptual machinery of P1. P1 establishes; P2 attaches; the dependency is one-way. ---
Abstract
Paper 1 established eight propositions (T1–T6, the dominant-layer migration thesis, the 13DD uniqueness-of-origin thesis, and the three-source thesis) and developed the genetic dynamics of power. Paper 2 introduces no new theorem and re-derives nothing already established; it unfolds the conceptual machinery of P1 along the dimensions of morphology.
The term morphology is used here in the strict mechanical and topological sense, not in the biological sense of classification. P2 establishes three morphological criteria—M1 three-axis decomposition, M2 apparatus non-subjecthood, M3 network conduction—and one phase-axis lemma (M4), which together support the entire paper.
The central claim of P2 can be condensed into a single sentence: Apparatuses do not wield power; individuals invoke apparatuses to wield power. The topological legitimacy of an apparatus is borrowed, not native.
This paper unfolds power morphology along three independent criteria axes—geometric, phase, and dimensional—and on this basis treats: phase structure (§IV); the topological legitimacy of abstract collective entities as so-called collective power-subjects (§V); algorithmic power as a modern special form (§VI); the bystander-C transfer effect in multi-agent networks (§VII); the Means-Kingdom vs Ends-Kingdom interface anchoring (§VIII); and the rigorous separation of morphology from directionality (severing-mode vs cultivating-mode) in §IX.
The working premise of P2 is the full conceptual machinery of P1. P1 establishes; P2 attaches; the dependency is one-way.
§I Introduction: The Work of Morphology
P1 answers what power is and where power originates. P2 answers in what structural modes power can manifest. The two questions belong to different layers but share the same machinery: T1 (asymmetric severing operations), T2 (registration), T3 (remainder), T4 (source-displacement), T5 (power–rights duality), T6 (locking-action-triggered back-binding), together with the dominant-layer migration thesis, the 13DD uniqueness-of-origin thesis, and the three-source thesis.
The object of morphology is the geometry of severing. The word severing is used here first in the generic T1 sense—the asymmetric severing operation: A, through asymmetric operation, alters, restricts, or directs B's available DD-positions and movement paths. It is not the directional severing power of P6, which arises only when T6's locking action is triggered. P2 describes only the forms of asymmetric severing operations along the dimensions of geometry, phase, dimension, network, and apparatus; it does not adjudicate their direction.
The word severing has two legitimate positions in P2. First, as the generic verb in T1's sense; second, as the directional adjective in severing power (paired with cultivating power) in the sense of P6's locking. The bare term severing defaults to the generic; when directional pairing is invoked, the text explicitly writes severing-mode or cultivating-mode.
Terminological Ecology (fixed across the series)
| Chinese | English | Position in the Series | Note |
|---|---|---|---|
| 凿构 | chiseling-constructing | cross-series core operation | SAE Moral Law / Foundation concept; sculptural, not equivalent to Power Theory severing |
| 凿削 | severing | generic / directional dual role | generic = T1's asymmetric severing operation; directional = severing-mode power triggered by T6 |
| 涵育 | cultivating | directional | paired with directional severing; oriented toward the dissolution of the position-differential |
| 殖民 | colonizing | directional / institutional | 14DD substitution of one's own purpose for another's own law; see Moral Law P9 |
Propositional Roadmap
P2 establishes three morphological criteria and one phase-axis lemma. No new T-theorem is introduced.
> Criterion M1 (Three-Axis Decomposition). Any power form can be located simultaneously along three independent criteria axes: the geometric axis, the phase axis, and the dimensional axis (13/14/15DD).
> Criterion M2 (Apparatus Non-Subjecthood). Any abstract collective entity (state, juridical person, corporation, church) is not a 13DD subject; it is a 14DD narrative apparatus. Apparatuses do not wield power; key-node individuals invoke apparatuses to wield power.
> Criterion M3 (Network Conduction). In multi-agent networks, the conduction of power is determined by the registration structures of bystander nodes, not by the intention of the wielder.
> Lemma M4 (Phase Decay). Any complete and stable power structure necessarily enters a decay phase along the phase axis. Decay is driven by the joint action of three factors—T3 remainder persistence, T5 seam-thinning, and dominant-layer migration pressure—and cannot be structurally evaded. M4 is the joint corollary of T3, T5, and the dominant-layer migration thesis on the phase axis; it is not an independent T-theorem.
Three criteria plus one lemma support the whole paper.
§II The Three Criteria Axes of Morphology
P2 unfolds along three independent criteria axes. The independence of the three axes derives from the topological-stacking principle of the three-source thesis (P1 §III) and is invoked here rather than separately argued.
§II.1 The Geometric Axis
The geometric axis describes the structural relation between the locus of severing and the locus of its bearing. It admits three binary partitions.
Direct severing vs. indirect severing. Direct: there is no third party between A and B; A, as the severing party, directly registers B's DD-position and applies pressure. Indirect: A applies severing through a mediator (an apparatus, a third-party subject, the physical environment); A may not appear directly in B's registration structure.
Individual severing vs. apparatus severing. Individual: A as a single 13DD subject performs severing. Apparatus: A invokes a 14DD apparatus (institution, corporation, state, algorithmic system) to perform severing. The two differ in T6 back-binding bearing paths; see §V.5.
Open severing vs. concealed severing. Open: the severing operation registers visibly in both A's and B's registration structures. Concealed: the severing operation is invisible in B's registration structure or is misread as natural order, fate, or free choice. Concealed severing is structurally homologous with T4 source-displacement: both are displacements that power performs on itself in order to stabilize itself.
§II.2 The Phase Axis
The phase axis describes the phasic position of severing along the structural lifecycle. Four phases: establishment, maintenance, transmission, decay. Complete and stable power structures are analyzed along all four phases; short-lived power events may skip phases and need not pass through all four. Detailed treatment is in §IV.
§II.3 The Dimensional Axis
The dimensional axis describes the DD-level on which severing operates (13/14/15). The three sources (P1 §III) appear on the dimensional axis as three dominant-dimension forms: 13DD mechanical source (protection–response exchange), 14DD meaning source (narrative), 15DD recognition source (reputation). The three layers stand in topological stacking, not historical succession: the moment a new dimension is added to the load-bearing structure is not the moment the old dimension is abolished.
§II.4 The Independence of the Three Axes
The three criteria axes are independent. The same power form can be located simultaneously on all three, yielding a three-dimensional morphological coordinate. Example: modern algorithmic power has coordinates (indirect severing, apparatus severing, concealed severing) × (predominantly maintenance phase, intensified transmission phase) × (14DD narrative dominant, 13DD mechanics underlying). §VI develops this coordinate in detail.
§II.5 The Rigorous Separation of Morphology from Directionality
Morphology presupposes no directional severing-mode or cultivating-mode. All positions on the criteria axes can be occupied by severing-mode forms and cultivating-mode forms alike. Cultivating power can equally be indirect (a mentor lifting a student through environmental structures), apparatus-based (a good educational institution), or concealed (a background structure lifting without the lifted noticing). The criterion for severing-mode vs. cultivating-mode is given by T6's locking-action trigger, not by morphological coordinates.
This separation lets P2 hold its neutrality throughout: all positions on the three axes are mechanical facts, presupposing no moral evaluation and no direction. The question of direction belongs to P5 (cultivating power) and P6 (severing power).
§III Geometric Forms
This section unfolds the three binary partitions of §II.1 and describes the mechanics of each pair.
§III.1 Direct vs. Indirect Severing
Direct severing is the simplest power form: A registers B as the other end of an asymmetric structure and alters B's DD-positions through direct command, coercion, or pressure. The responsibility structure of direct severing is clear: A appears directly in B's registration structure as the wielder.
Indirect severing proceeds through a mediator. The mediator can be a physical environment (city walls, road layouts, segregation infrastructures), a 14DD apparatus (institutions, algorithms, corporate hierarchies), or a third-party subject (agents, intermediaries, executors). A does not appear directly in B's registration structure, but A's severing still operates on B's DD-positions. The responsibility structure of indirect severing is complex, but its ontological basis remains a 13DD subject: A wields through a mediator; A remains the source of severing; the mediator is only an amplifier or conduit.
The special brittleness of indirect severing: when the mediator itself is identified or replaced, A's severing chain breaks. A power structure dependent on intermediaries collapses immediately when the intermediary withdraws. This brittleness provides one concrete path to the decay analysis in §IV.
§III.2 Individual vs. Apparatus Severing
Individual severing: A as a single 13DD subject performs severing. The master–slave relation is the simplest individual severing form. An employer over a single employee, a father over a son, a teacher over a student—all are concrete individual severing forms.
Apparatus severing: A invokes a 14DD apparatus to perform severing. The peculiarity of apparatus severing is treated in §V. The key difference lies in T6 back-binding bearing paths. Individual severing's back-binding is 100% anchored to the invoker; apparatus severing's back-binding is also 100% anchored to the invoker, but the apparatus, as a construct, produces its own independent construct-level remainder, which is not back-binding but a different kind of cost; see §V.5.
§III.3 Open vs. Concealed Severing
Open severing registers visibly in both A's and B's registration structures. A father's parental power over a son operates openly; a court's judicial power over a defendant operates openly; an employer's employment power over an employee operates broadly openly (within a contractual framework). The stability of open severing comes from the very fact that both sides register.
Concealed severing is invisible or misread in B's registration structure. B does not know it is being severed, or misreads the severing's result as a natural law, a free choice, or fate. Concealed severing is structurally homologous with T4 source-displacement: both are displacements power performs on itself to stabilize itself. Open severing places itself on the table but performs displacement via claimed sources (divine, mandate, law); concealed severing erases its own existence altogether, leaving B unaware that severing is occurring.
A mechanical sharpening: the deeper the concealment, the lower the short-term maintenance cost (B does not resist), but the more severe the long-term back-binding. Once concealment is broken, B's registration structure abruptly re-registers all prior severing as illegitimate, and back-binding cost accumulates sharply. This is one internal driver of the decay analysis in §IV, and the fundamental reason why concealed power is not actually more stable than open power in the long run.
§III.4 Combinations of the Three Partitions
The three binary partitions yield 2³ = 8 geometric forms. The eight are not uniformly distributed. The master–slave relation is typically (direct, individual, open); modern algorithmic power is typically (indirect, apparatus, concealed); traditional bureaucracy is typically (indirect, apparatus, open); paternalism is typically (direct, individual, semi-open). Specific forms are more stable on some dimensional axes and more frequent in some phases. The empirical calibration of distributions is left as a gap and not closed within this series.
§IV Phase Forms
Complete and stable power structures are analyzed along four phases along the phase axis: establishment, maintenance, transmission, decay. Short-lived power events (a one-off coercion, a fleeting dominance) may skip phases and need not pass through all four; but any power structure that enters maintenance eventually faces decay or transformation. Lemma M4 addresses the phasic dynamics of stable structures, not the full course of every power event.
The four phases on the phase axis are structurally isomorphic with the four-phase generation order produced by Negativa's self-interrogation in SAE Methodology 0 (Via Negativa, DOI: 10.5281/zenodo.19544619). The phase axis is the manifestation of an SAE methodological structure within the morphology of Power Theory. P2 does not re-derive the structural origin of the four phases; it invokes Methodology 0.
§IV.1 Establishment Phase
Establishment is the first occurrence of a 13DD jump and the initial anchoring of a registrable structure. Its time constant is slow: both sides must mutually complete initial registration within a shared field. Establishment is the most fragile phase: the withdrawal of either side at this point can prevent the structure from forming.
The key mechanics of establishment is the initial completion of T2 registration. Without T2's completion, no power relation exists—only the output of force (see P1 §IV three-part table). Establishment's stability depends on the depth of the initial registration: if both sides register each other as the ends of an asymmetric structure, establishment completes; if only one side registers (e.g., A attempts to wield but B does not register), establishment fails and the relation falls back to the layer of mere force.
§IV.2 Maintenance Phase
Maintenance is the running state of an already established structure. Its core mechanics is T6's locking action. If maintenance does not invoke locking (i.e., does not attempt to fix B's DD-position downward), maintenance cost can remain low; once locking is invoked, T6 back-binding cost ceases to be a one-time cost and becomes ongoing maintenance cost, possibly accelerating under apparatus-amplification, network-amplification, or high-pressure maintenance conditions.
Maintenance is the phase in which the mechanical difference between severing-mode power and cultivating-mode power is most manifest. Severing-mode maintenance invokes locking and triggers T6 back-binding; cultivating-mode maintenance does not invoke locking, does not trigger T6, and orients toward the dissolution of the position-differential. The full directional dynamics are left to P5 and P6.
§IV.3 Transmission Phase
Transmission is transfer across generations and across personnel changes. The core function of a 14DD apparatus is the transmission phase: a power structure that cannot transmit lives only one generation; one that can transmit necessarily encodes itself into some 14DD apparatus. Institution is the materialization of the transmission phase.
A mechanical feature of transmission: transmission is not simple replication. Every transmission accompanies a redistribution of the remainder ρ. The transmitted structure, at the moment of transmission, is no longer the original; it is the structure re-registered by the new bearer according to that bearer's own DD-positions. The power structure a father transmits to a son is, in the son's hands, re-registered according to the son's DD-position—it is not the simple persistence of the original. The transmission phase accumulates the internal tensions described by the dominant-layer migration thesis.
§IV.4 Decay Phase
Any complete and stable power structure necessarily enters a decay phase. This is structural necessity, not empirical contingency. Decay is driven by the joint action of three factors.
First, the persistence of T3 remainder. Every severing operation leaves a remainder; the remainder is irreducible; long accumulation forms the energetic reservoir of drift, recoil, and migration.
Second, T5 seam-thinning. Every power, in order to stabilize itself, tends to press B's subject-position downward. The deeper the press, the thinner the T5 seam, and the closer the power-bearer comes to the boundary of erased from A's operational structure. Once that boundary is breached, power exits (P1 §VI).
Third, dominant-layer migration pressure. A power structure matches the population's DD-distribution at the initial moment, but successful operation triggers DD-ratio rise, and the upgraded population produces stress with the original structure.
The three factors superimpose: the decay phase cannot be evaded by any stable power structure. The only difference is in when the decay phase arrives, not whether it arrives. Hence Lemma M4:
> Lemma M4 (Phase Decay). Any complete and stable power structure necessarily enters a decay phase along the phase axis. Decay is driven by the joint action of T3 remainder persistence, T5 seam-thinning, and dominant-layer migration pressure, and cannot be structurally evaded. M4 is the joint corollary of T3, T5, and the dominant-layer migration thesis on the phase axis; it is not an independent T-theorem.
Directional Disambiguation of Decay
Decay is not an evaluative term; it merely indicates that the asymmetric structure no longer maintains itself in its original form. Under the two directional modes, decay manifests differently.
For severing-mode power, decay manifests as accumulated brittleness, rising back-binding cost, seam-breach, and final collapse. This is the mechanical object of P7 (resistance and dissolution).
For cultivating-mode power, decay can manifest as the self-dissolution of the position-differential once it has completed its purpose. The student a teacher has cultivated no longer needs the teacher; parents, physicians, editors, mentors—all benign powers orient toward their own self-dissolution. This kind of decay is not failure; it is the mark of successful cultivation. Cultivating power's decay is treated in P5.
Hence M4 connects cleanly with P5, P6, and P7, without internal conflict.
Defense statement: this series does not predict, advocate, or evaluate any specific political event. The decay phase here is a structural mechanical description, not a prescription for action and not a prediction of events.
§IV.5 Transitions Between the Four Phases
At the morphological level: establishment to maintenance is the normal transition; maintenance to transmission requires apparatus-encoding; transmission to decay is structurally necessary; after decay, the structure either dissolves (P7) or restarts (a new establishment phase, but not the continuation of the original—rather, a new structure anchored upon the ruins).
The Rigorous Separation between Physical Apparatus Persistence and Topological Power Continuity. The 14DD apparatus is most adept at borrowing a body to rebirth a soul: one dynasty ends, a new dynasty takes over the same offices, uses similar legal codes and institutional frameworks. On the surface, power continues; in fact it does not. The old power relation, in the decay phase, walks toward topological death: the T2 registration between the original A and B is wholly erased. Even if a new wielder A′ occupies the same physical apparatus and uses similar operational forms, this is a fresh T2 registration process, not a continuation of the old power. The 14DD apparatus can rebirth (physical persistence), but topological power cannot rebirth (T2 must be re-established).
Lemma M4 addresses the death of topological power, not the dissolution of the physical apparatus. This rupture is absolute; it is not a tautology of dynastic cycle. The restart therefore does not mean the old power revives; it only means a new power completes its own establishment phase upon the ruins. Once the old power relation walks through the decay phase, it dies finally and cannot be restored.
§V Construct as 14DD Apparatus: The Topological Legitimacy of So-Called Collective Power-Subjects
This section directly addresses the topological legitimacy of abstract collective entities (state, juridical person, corporation, church) as so-called collective power-subjects. It is the central chapter of P2.
§V.1 The State, Juridical Person, Corporation, Church Are Not 13DD Subjects
SAE's ontological stance: the criterion for a 13DD subject is ρ ≠ ∅ together with a self-conscious field. The state has no self-conscious field; the juridical person has no ρ; the corporation cannot register itself nor be registered by itself as a subject; the church, as a community of faith, does not possess a single self-conscious field. None of them passes the criterion for 13DD subjecthood.
This argument is structural, not empirical. It is not that a 13DD state has not yet been discovered; it is that the state cannot structurally be a 13DD subject, because it has no self-conscious field. Any attempt to elevate an abstract collective entity to subjecthood (Hegelian spirit of the state, strong-form readings of legal personality doctrine, theories of collective will) commits ontological-category misplacement.
§V.2 They Are 14DD Narrative Apparatuses
The condition of existence of these abstract entities is 14DD narrative bearing: the narratives about we, about the institution, about the legal person are borne stably by a sufficient number of 13DD subjects. Once the bearing dissolves (e.g., during state collapse, corporate bankruptcy and liquidation), the apparatus dissolves with it. The apparatus is not a 13DD subject; it has no subject-level ρ; the construct-level remainder it produces is treated separately (see §V.5).
The material forms of an apparatus (office buildings, file cabinets, legal texts, official seals, server farms) are necessary but not sufficient. The existence of material form does not constitute the existence of the apparatus. The apparatus exists insofar as a sufficient number of 13DD subjects register these material forms, together with abstract narrative, as our state, our company, our church. Without this registration, the material forms remain mere material.
§V.3 The Apparatus Does Not Wield Power; Individuals Invoke the Apparatus to Wield Power
This is the central proposition of §V. Every appearance of power exercised by the apparatus is, in fact, power exercised by one or more key-node 13DD subjects invoking that apparatus.
The state does not sign decrees; key-node officials sign decrees through the state apparatus. The corporation does not lay people off; key-node managers lay people off through the corporate apparatus. The algorithm does not recommend; key-node engineers and product leads direct recommendations through the algorithmic apparatus. The church does not excommunicate; key-node clergy excommunicate through the church apparatus.
Any expression of abstract entity wielding power can and must be reduced to key-node individual wielding power. This reduction is not a rhetorical simplification but an ontological fact: 13DD is the sole origin point of social power (P1 §III: 13DD uniqueness of origin); the 14DD apparatus, as narrative-bearing, has no power-wielding capacity in itself; it participates in the power chain only when invoked by a 13DD subject.
§V.4 The Topological Legitimacy of the Apparatus Is Borrowed
The topological legitimacy of an apparatus as a collective power-subject does not derive from the apparatus itself (the apparatus has no self-existence). It derives from the 13DD subjecthood of the key-node individuals who invoke it, together with the 14DD narrative network that bears it. The apparatus's subjecthood is borrowed, not native; superimposed, not foundational.
Concretely: when we say the state has power, we are in fact saying (i) the state—a 14DD apparatus—is sustained in the narrative bearing of a sufficient number of 13DD subjects, and (ii) key-node individuals can wield power through this apparatus because the apparatus has pre-encoded many asymmetric severing paths. The apparatus's legitimacy equals narrative bearing strength multiplied by the 13DD subjecthood density of key nodes. Neither factor is dispensable.
An apparatus with high narrative bearing but vacated key nodes (e.g., a government in exile) cannot wield: there are no invocable key nodes. An apparatus with full key nodes but collapsed narrative bearing (e.g., a regime that has lost its mandate—internal commands can still issue but are no longer registered externally as power) likewise cannot wield: there is no bearing narrative network. Both factors must be present for the apparatus to function as the amplifier projecting the key-node's severing across a wide field.
§V.5 Apparatus Back-Binding Bearing: Who Bears T6
This section performs a rigorous ontological cut, to prevent the shorthand apparatus bears back-binding from sliding into apparatus possesses quasi-subjecthood.
The ontological definition of T6 back-binding (P1 §VIII): a locking operation requires A to continuously invest DD operational space in maintaining the structure; the deeper the locking, the more compressed A's subjective remainder. The bearing of back-binding requires ρ; therefore, the bearer of back-binding can only be a 13DD subject. The apparatus, as a 14DD construct, has no subject-level ρ and cannot bear T6 back-binding in subject-fashion.
From this follows the rigorous ontological statement.
The T6 back-binding of individual severing is borne directly by the severing individual, 100% anchored.
The T6 back-binding of apparatus severing is 100% borne by the key-node individual who invokes the apparatus; it cannot be shared by the apparatus. An official wielding the state's coercive machinery bears back-binding anchored on his own ρ; an engineer directing users through algorithms bears back-binding anchored on his own ρ; a manager laying off through corporate hierarchies bears back-binding anchored on his own ρ.
But the apparatus, as a construct, by SAE's remainder discipline (Methodology 00 Via Rho, DOI: 10.5281/zenodo.19657439; ρ ≠ ∅; every construct produces remainder), still produces a construct-level remainder. The apparatus's remainder is not T6 back-binding; it is a cost of a different nature. The two are partitioned to their proper loci.
T6 back-binding is anchored in 13DD subjects (the invokers) and accumulates when the locking action is triggered.
Apparatus remainder, as the mediator cost at the 14DD construct level, manifests as brittleness accumulation, complexity rise, maintenance cost increase, interface failure, and decline in narrative-bearing capacity.
The two are not the same cost distributed across two loci; they are two costs of different natures, each depositing in its own place. This ontological cut keeps §V.5 consistent with SAE's remainder discipline (every construct has remainder; the apparatus is no exception) while preserving T6's subject-level boundary (back-binding 100% anchored to 13DD subjects).
Non-Dilutability of T6 Back-Binding. In modern large-scale apparatuses, severing chains are often partitioned across many key nodes (product managers set targets, engineers tune parameters, reviewers apply labels, executives sign off, operators execute). A naive misreading: since no single individual performs the complete locking action, perhaps each individual's borne back-binding tends toward zero, and T6 thereby fails at the apparatus level.
No. T6 back-binding is not physical weight; it cannot be averaged over headcount. Any 13DD subject participating in the core action of the severing chain—whose operation severs some movement-possibility of B—has completely triggered one T6 locking within his or her own 13DD field. The engineer's act of tuning parameters is, at the ontological level, an independent locking; the reviewer's act of labeling, likewise. Back-binding is not divided by N among N participants; it is borne 100% by each of the N subjects within their own interiors as subject-level remainder compression.
Hence, apparatus-level division of labor does not dilute T6; it only replicates T6. Each additional node participating in the core severing chain adds one full T6 back-binding to the system rather than dividing one. The 14DD bureaucracy cannot evade T6 through division of labor; nor can too many to blame cancel back-binding's bearing at the ontological level. The non-dilutability of back-binding is T6's precise apparatus-level expression, structurally precluding the illusion of distributing back-binding through the apparatus.
It follows that the deeper the severing a key-node individual performs through the apparatus, the less the individual's own T6 back-binding can be eliminated, and the faster the apparatus's remainder accumulates. The deeper the severing embedded within the apparatus, the shorter the apparatus's life as a transmission-phase carrier. This furnishes one concrete mechanical conduction path to the decay phase of §IV.4. The full dynamics of apparatus-level remainder are left to P7.
§V.6 The Pragmatic Layering of Strict Ontological Statement and Everyday Shorthand
In ordinary language, state power, corporate power, institutional violence function as shorthand: they denote the phenomenon of wielding through this apparatus. SAE Power Theory does not deny the practical usefulness of such shorthand; it insists, only at the level of strict ontological statement, that the apparatus is not a 13DD subject, the apparatus does not wield, and the apparatus is the 14DD amplifier of the key-node individual's wielding.
The two layers of language do not conflict, but in the ontological layer of Power Theory only the strict statement is admissible; shorthand must not seep into the propositional layer. This distinction allows Leviathan, will of the state, the company has decided, and similar grand expressions to continue in literary and everyday usage—but not in SAE Power Theory's ontology.
§VI The Three-Layer Severing Chain of Algorithmic Power
Algorithmic power is a special form of modern social power. It is not a new power source (the origin remains 13DD); it is the new concrete form of the 14DD apparatus in the age of algorithms.
Fixed statement (parallel to §V.3's apparatus does not wield): The algorithm does not wield power; designers, deployers, invokers, and maintainers wield power through the algorithmic apparatus. The peculiarity of algorithmic power lies not in the algorithm becoming a subject, but in 11DD/12DD capabilities (computation, prediction, classification) being invoked at scale by a 14DD apparatus and plugged into the power chain through 13DD+ key nodes. Any algorithmic power expression can and must be reduced to key-node individuals wielding through an algorithmic apparatus. This fixed statement closes the slide toward algorithm as power-subject and aligns with the Permission Asymmetry Theorem of SAE AI Paper 2 (DOI: 10.5281/zenodo.19671870).
§VI.1 First Layer: Data-Collection Severing
The user's DD-positions (behavior, preferences, location, relations) are sampled and recorded. This process is already a severing operation: registration between A (the platform operator) and B (the user) is asymmetric—A can observe B; B cannot equally observe A.
The first-layer severing cuts observational symmetry: B's DD-positions are exposed to A; A's DD-positions (especially the algorithm's internal parameters and data uses) are concealed from B. Collection itself is typically concealed within the user's registration structure (see §III.3, concealed severing). The user notionally accepts terms of service, but the actual content and depth of collection usually exceed the user's concrete understanding. T2 registration is completed here through the user's compliance with the restricted interaction space, without requiring the user's full cognition of the specific collection mechanism.
§VI.2 Second Layer: Model-Inference Severing
Based on the collected data, the model infers the user's unobserved DD-positions. The object of inference includes not only the user's manifested displacements but also displacements the user has not yet made which the model predicts. The inference result is fed back into A's operational structure as the content of asymmetric registration but does not enter B's registration structure: B typically does not know what he or she has been inferred to be.
The second-layer severing cuts representational privacy. The user's 13DD-level self-representation (I take myself to be such-and-such) and the user-representation within A's operational structure (the model infers the user to be such-and-such) may differ entirely, with the user unaware of this asymmetry. This is the special manifestation of T4 source-displacement in the age of algorithms: not A producing a false claim about its own source, but A producing a false representation of B, so that B in A's operational structure becomes another B′.
§VI.3 Third Layer: Action-Targeting Severing
Based on the inference, the user's available DD-positions and movement paths are structurally biased. The biasing occurs in the form of recommendation, ranking, suppression, priority adjustment—not direct coercion. The user, within the biased environment, exercises free choice, but the choice space has already been severed.
The third-layer severing cuts path accessibility. The choice space B sees is not the real choice space; it is the subset already severed by A. B freely chooses within the subset, but the subset's boundary is drawn by A. This is the extremal form of concealed severing: B not only does not know who A is; B easily misreads the post-targeted subset as the complete choice space.
§VI.4 Composite Mechanics of the Three-Layer Severing Chain
First, concealment (see §III.3) is fully loaded across all three layers, intensifying layer by layer. The first-layer concealment is the user does not know the depth of collection; the second-layer concealment is the user does not know what he or she has been inferred to be; the third-layer concealment is most severe—the user most easily reads the post-targeted result as his or her own free choice.
Second, apparatus-ness (see §III.2) fully dominates. The algorithmic system is the pure form of the 14DD apparatus; no link in the chain involves a direct interpersonal registration. The user never faces designer, deployer, invoker, or maintainer face-to-face; the entire power relation proceeds through the apparatus.
Third, large-scale parallelism. The algorithm can simultaneously sever the DD-positions of users at the scale of tens of millions. This is the physical feature of apparatus severing, not a new mechanical source. A single key node (a product lead) invoking a single apparatus (a recommendation system) can simultaneously wield power over millions of Bs. This is the special amplification of the borrowed-legitimacy formula of §V.4 (narrative bearing × key-node density) in the age of algorithms.
§VI.5 T2 Registration's Blind-Box Engagement: The Ontological Guarantee of Algorithmic Power
The three-layer severing chain of algorithmic power is highly concealed across all three layers. B (the user) may be entirely unaware of A (the platform / algorithm operator); B may even misread algorithmic behavior as natural law or as B's own free will. Does T2 registration still hold here? In the scenario where B does not know who A is, is this still power, or has it degenerated into 11DD/12DD physical manipulation?
Answer: the object of T2 registration is not A's face but the bent action-space. B has not seen A, but B has adapted his or her action to the option grid the algorithm has drawn; B's self-consciousness says, this is now the only reasonable / desirable option I have. Compliance with and registration of the restricted choice space is, at the topological level, T2 registration. The algorithm's concealment hides A's existence and A's wielding action, but does not hide the consequence of severing (the structural biasing of B's action space). As long as B's action space undergoes an asymmetric structural displacement, and B at the 13DD level executes that displacement for some reason (even a misread reason), T2 has engaged.
The criterion anchor between 11DD and 13DD+ concealed power: 11DD blocks you with a wall (physical coercion; no registration occurs; the action is independent of B's self-conscious field); 13DD+ concealed power lets you reach the conclusion I should go this way on your own (registration occurs; B's self-conscious field has incorporated the bent space into its action-space, even if B has misread the reason for registration). Algorithmic power is the latter, not the former.
T2 thus remains binding in the most concealed scenarios of algorithmic power. Algorithmic power, as the modern form of 13DD+ concealed power, fully engages T2's ontological boundary and does not fall out of the scope of SAE Power Theory.
Ontological Absoluteness of T3 Remainder (Non-Psychological). The deepest concealment of algorithmic power is when B perfectly internalizes the algorithmic targeting as B's own free will, with no subjective friction or sense of resistance. A naive question follows: if B subjectively complies entirely, where does T3 remainder (the energetic reservoir of recoil, drift, blow-back) come from? If remainder does not exist, does the driving mechanism of M4's phase decay not break?
Answer: remainder (ρ) is not B's psychological discomfort or consciousness of resistance. Remainder is the structural residue at the ontological level—the topological differential between the infinite DD-possibilities ontologically inherent to B as a 13DD subject and the finite option grid the 14DD apparatus supplies. This differential does not depend on whether B subjectively notices, on whether B experiences discomfort, on whether B is prepared to resist. Even if B complies perfectly, the ontological differential persists and continues to act.
Hence the driving mechanism of M4's decay phase does not depend on B's psychological state. Decay is not because B wakes up and rebels, but because the 14DD apparatus must continuously expend computation, energy, and maintenance to conceal this ontological differential—to smooth over the small incongruences the differential produces. The apparatus-level brittleness accumulation of §V.5 is, in essence, the cumulative cost of this concealment action. When the cost of concealment exceeds the apparatus's bearing threshold, the decay phase manifests.
Thus the T3 remainder discipline is fully stripped from the psychological layer and anchored in the ontological topological differential. Even under the most perfectly concealed form of algorithmic power (B subjectively unaware), ρ ≠ ∅ still holds, and the mechanical mechanism of M4's decay phase remains intact.
§VI.6 Interface with SAE AI Paper 2's Permission Asymmetry Theorem
The Permission Asymmetry Theorem of SAE AI Paper 2 (DOI: 10.5281/zenodo.19671870) is the mechanical anchor of the three-layer severing chain of algorithmic power. The asymmetry of permissions between algorithm operators and algorithm users is, at the level of P2's morphology, the asymmetric registration structure of the three-layer severing chain. This section invokes that theorem and does not re-derive it; it only identifies the interface position.
The full interface between Power Theory and SAE AI is left to a future cross-series paper; it is not closed within this series.
§VII Multi-Agent Networks and the Bystander-C Transfer Effect
The bystander-C transfer effect, foreshadowed at the end of P1 §VI, is unfolded here in full.
§VII.1 The Minimal Three-Agent Scenario
A wields power over B; C is present as bystander but does not participate directly. The question: what is C's mechanical position in this three-agent scenario?
§VII.2 C's Registration Determines the Direction of Network Conduction
If C registers the A–B relation as natural, legitimate, reasonable, C becomes a forward-bearing node of A's power. A's asymmetric severing acts not only on B but, through C's forward registration, propagates to other nodes in the network. C is an amplifier.
If C registers the A–B relation as illegitimate, abnormal, to be broken, C becomes a counter-amplifying node of T6 back-binding. Back-binding is borne not only by A; it propagates through C's counter registration to other nodes in the network, raising A's maintenance cost. C is a back-binding amplifier.
§VII.3 C Is Not a Neutral Bystander: The Topological Physics of Silence
At the morphological level: C's position continues to produce conduction effects within the network topology, whether or not C is aware of it.
In a 13DD multi-agent network, the moment asymmetric severing occurs, it creates a gradient field in what would otherwise be a flat network space. For a bystander C standing within this gradient field, the mechanical fact is binary.
If C outputs a counter-vector (15DD interrogation, 14DD resistance, 13DD refusal to respond), C, within the network topology, cancels or interferes with A's gradient field. This is the counter-amplifying channel of §VII.2.
If C remains silent, C, within the network topology, does not output a counter-vector and automatically becomes a zero-resistance conducting node of that gradient field. This is the forward-bearing node of §VII.2.
Hence, neutrality is a pseudo-concept of 14DD political language; it does not exist in 13DD network topology. Silence need not be presupposed to be read as forward registration in any specific content: in B's registration structure it may be read as tacit consent, abandonment, helplessness, absence, or unawareness, depending on C's position, visibility, capability, and risk structure. But the topological fact stands: a node that does not output a counter-vector is, in network structure, a zero-resistance conducting node, objectively amplifying the power gradient. This is the key mechanical fact of §VII.
Note: this section is a mechanical description, not bystander ethics. Morphology does not evaluate what C ought to do; it only describes C's objective position within the network topology. The question of bystander moral responsibility is not treated within this series.
§VII.4 The Topology of the n-Agent Network
The three-agent scenario extends to n agents. Network centrality acquires a concrete mechanical meaning: high-centrality C nodes affect power conduction far more than peripheral C nodes. This furnishes one network-topological reading of the apparatus's reified form (§V).
§VII.5 The Apparatus as the Crystallization of the C-Network
A stable power apparatus (state, corporation, church, school) is, from the perspective of §VII, the network-crystallization of a large number of C nodes organized to repeatedly perform forward registration. An apparatus is not a freestanding entity; it is the stabilized form of an organized C-network.
Hence §V's apparatus concept and §VII's network concept converge: the apparatus is the crystallized C-network. This convergence gives the borrowed-legitimacy formula of §V.4 (narrative bearing × key-node density) a concrete network-topological reading: narrative bearing strength corresponds to the density of C nodes performing forward registration; key-node density corresponds to the availability of high-centrality C nodes. The two simultaneously manifest in network topology, and the apparatus as the C-network crystallization is precisely what is made visible here.
§VII.6 Anchoring for P3
This section does not unfold the recognition dynamics in full. The dual aspect of forward registration vs. counter registration (ontological registration vs. operational recognition) is unfolded in P3 (the chapter on recognition). This section only sets the anchor.
§VIII Means-Kingdom vs Ends-Kingdom Interface Anchoring
This section anchors the Means-Kingdom vs Ends-Kingdom interface for P6 (severing power). The interface is P6's task; P2 only anchors it at the morphological level.
The distinction between Kingdom of Ends and Kingdom of Means is established in SAE Moral Law Paper 1 (DOI: 10.5281/zenodo.20011019). At the morphological level: every form of severing-mode power involves moving B, within A's operational structure, from end-position to means-position; every form of cultivating-mode power involves preserving or restoring B's end-position in A's operational structure.
A morphological candidate criterion (M5; not anchored in P2; left to P6):
> M5 (candidate, left to P6). A power form is severing-mode if and only if, within A's operational structure, it moves B's position from the Kingdom of Ends to the Kingdom of Means.
Note: M5 is only a candidate formulation of the interface position; it is not anchored in P2. P2 only indicates the interface position between three-axis morphology and the Kingdom distinction; P6 alone adjudicates whether a given form locks B into the means-position. P2 does not commit in advance to M5's strict equivalence with T6; that equivalence is fully argued in P6.
Interface position: T6's locking action (introduced in §IV.2's maintenance phase), in Kingdom language, is locking B into the means-position; T6 not triggered is B retains the end-position within A's operational structure. The two languages translate into one another but do not reduce to one another.
The Cross-Series Dual Interface. The Means-Kingdom vs Ends-Kingdom interface is simultaneously the interface of opposing forms with Moral Law Paper 1's First Theorem (must recognize the concrete other as end). Moral Law says one must recognize the concrete other as end (the affirmative form of inner legislation); P6, extending severing to morphology, says severing is precisely moving B from end-position toward means-position (the negative form of outer force). The two propositions form a precise duality in the language of the Means / Ends Kingdoms. T5's identity as the shared spine of the two series gains precise expression in Kingdom language; the dual coverage of the two series becomes complete.
§IX Morphological Boundaries and Series Interfaces
§IX.1 The Boundaries of Morphology
There is no formless power in this series. Every concrete power has a concrete position on the three criteria axes; every concrete power has a concrete phase among the four; every concrete power involves at least one of the three sources. Morphology covers fully; no residue of power without form remains.
§IX.2 Morphology Does Not Presuppose Direction
Morphology presupposes no moral judgment and no direction. Every position on the three criteria axes (direct/indirect, individual/apparatus, open/concealed, establishment/maintenance/transmission/decay, 13/14/15DD) is neutral with respect to directional severing-mode power and cultivating-mode power. Whether a given form is severing-mode depends on whether T6's locking action is triggered, not on its morphological coordinates. Form itself is not the object of evaluation; it is only a mechanical fact.
§IX.3 Interfaces with Other Papers in the Series
Interface with P3 (recognition): the dual aspect of bystander C's registration (ontological registration vs. operational recognition) of §VII is unfolded in P3.
Interface with P4 (the remainder): the remainder-driven mechanism of §IV.4's decay phase is directly furnished by T3's remainder persistence; P4 will fully describe the concrete dynamics of remainder across different forms.
Interface with P5 (cultivating power): the concrete forms of cultivating power along the three criteria axes (especially the cultivating-mode versions of concealed severing and apparatus severing) are given by P5.
Interface with P6 (severing power): the full dynamics of severing-mode power are given by P6; P2 §VIII only anchors the Means / Ends Kingdom interface for P6.
Interface with P7 (resistance and dissolution): the decay phase of §IV.4 together with the counter-amplification mechanism of §VII furnishes the morphological foundation for P7's treatment of resistance and dissolution; the full dynamics of apparatus-level remainder of §V.5 are also left to P7.
§X Closing
P2 establishes three morphological criteria (M1 three-axis decomposition, M2 apparatus non-subjecthood, M3 network conduction) and one phase-axis lemma (M4 phase decay). No new T-theorem. The full conceptual machinery of P1 obtains its concrete morphological unfolding in P2.
The core results of P2 are five.
One. The geometry of power unfolds along three independent axes—geometric, phase, dimensional (M1).
Two. Abstract collective entities (state, juridical person, corporation, church) are not 13DD subjects; they are 14DD narrative apparatuses. Apparatuses do not wield power; individuals invoke apparatuses to wield power. The topological legitimacy of an apparatus is borrowed, not native (M2).
Three. Algorithmic power is the modern special form of the 14DD apparatus, not a new power source. The three-layer severing chain (collection, inference, targeting) is the complete manifestation of apparatus severing in the age of algorithms. T2 remains binding in the most concealed scenarios: the object of registration is the bent action-space, not the wielder's face.
Four. The bystander's neutral stance does not exist at the network level. Silence outputs no counter-vector and is, in network topology, a zero-resistance conducting node, objectively amplifying the power gradient. The apparatus is the crystallization of the organized C-network (M3).
Five. Decay cannot be evaded by any stable power structure. Decay is driven jointly by T3 remainder, T5 seam-thinning, and dominant-layer migration pressure (M4). When decay arrives is determined by many factors; whether decay arrives is determined by structure.
Morphology presupposes no severing-mode or cultivating-mode direction. All positions on the three criteria axes are neutral. Whether a form becomes severing-mode power depends on whether T6's locking action is triggered, not on morphological position. The full dynamics of severing-mode power are left to P6; the full dynamics of cultivating-mode power are left to P5; resistance and dissolution are left to P7.
The work of P2 is complete. P3 (the chapter on recognition) takes up the dynamics of recognition next.
Acknowledgments
This series stands in duality with the SAE Moral Law series, which the author developed jointly with Zesi Chen (陈则思). This paper benefited from the outline-audit observations provided by the four-AI collaborative research methodology (Zilu, Zigong, Zixia, Gongxihua); outline v1.1 integrated their fourteen revision recommendations in full, and the present body benefited from a further round of audit producing eight additional integrated refinements before final signature.
(The Chinese version of this paper was authored by Han Qin on 2026-05-25; the English version is an independent rewrite, not a translation. 2026-05-30.)