Self-Reproducing Generative Power - Dependency, Counter-Power, and Closure

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Abstract

Power can persist through law, habit, coordination, external scarcity, or
organizational inertia. A narrower mechanism appears when present exercise
changes a condition of future power and that change returns as greater later
power. This paper proposes the term self-reproducing generative power for
that mediated return. The proposal is actor-, target-, domain-, action-,
comparison-, and horizon-specific. Three candidate paths receive separate
treatment. A material path runs through practical exit and dependence. A
counter-power path runs through contraction of viable contestation. An
institutional-legitimation path runs through justificatory assertion, audience
uptake, institutional conversion, and later power. Under a local differentiable
model, each path contributes a chain-rule product to the one-step power
multiplier. The direct persistence term remains algebraically separate. The
result measures local mediated return; multidimensional stability depends on
the full Jacobian and nonlinear regime. A set-valued construction defines
counter-power through efficacious actions that preserve a declared viability
condition. A finite-trace countermodel then establishes that an observed
trajectory of power and dependence underdetermines an endogenous return loop
across unrestricted model classes. The paper therefore requires edge-specific
causal evidence, plausible rivals, longitudinal-confounding analysis, and
strategic-response analysis. Self-reproduction, restricted closure, domination,
injustice, generativity exploitation, responsibility, and legal wrong remain
separate registers. The current contribution is a revisable mechanism grammar,
a conditional local derivation, an identification warning, and a comparative
research programme. Empirical prevalence, historical application, normative
evaluation, and legal classification remain open.

Keywords: power; dependence; counter-power; closure;

Discussion Paper Note

This paper is a preliminary discussion paper intended to share an evolving idea
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Its definitions, distinctions, and formal constructions remain provisional.
Circulation across scholarly and practical communities is part of the purpose
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The author treats the viewpoints, concepts, and lines of reasoning presented
here as contributions to a shared field of inquiry. Similar or related ideas
may have appeared in other intellectual, cultural, and disciplinary traditions.
The manuscript therefore states its known antecedents, separates the
researcher-origin proposal from later formal reconstruction, and leaves
historical priority open pending a systematic originality review.

The arguments should be understood as provisional and historically situated.
Readers are encouraged to question, test, revise, extend, reinterpret, or
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acknowledgment of this paper as one point of encounter in the development of a
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This working draft records an evolving stage of the author’s position and is
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application, normative evaluation, legal analysis, and policy design remain
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Except where otherwise indicated, copyright 2026 Wanhong Huang. This work is
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Statement on the use of language models.
The exploratory discussions and preparation of this paper involved OpenAI’s
Codex. Codex supported exploratory dialogue, formal reconstruction, source
discovery followed by website verification, argumentative criticism, and
drafting in . The author selected the research questions, directed and
approved the theoretical commitments and epistemic status of the claims, and
bears sole responsibility for the manuscript, including its definitions,
formal constructions, taxonomy, arguments, conclusions, and errors. Authorship
credit remains with the human author. The access level and claim limit for every
cited source are recorded in the accompanying literature audit.

Related research programme.
This paper is project P018 and the fourth promoted paper in the research-stage
Generative Injustice programme. P010 studies control and accumulation of
realization conditions. P011 studies an open-then-enclose dependency mechanism.
P015 develops a typed lifecycle diagnostic for value circulation, P016 develops
transaction ontology and future-generative positions, and P017 supplies a
source-target transfer firewall for ocean-inspired relational models. The
present paper adds a mediated future-power return, counter-power, institutional
legitimation, and closure architecture. Later projects retain responsibility
for criticality, viable escape, dynamic consent, and portability.

Suggested citation.
Huang, Wanhong. “Self-Reproducing Generative Power: Dependency, Counter-Power,
and Closure.” Working discussion paper, 2026.

1. Introduction

This section establishes the motivating configuration, the paper’s mechanism
question, its limited position, and the sequence of argument. It begins with
the researcher-origin example, distinguishes mediated self-reproduction from
several forms of persistence, and states the contributions developed in the
later sections.

Consider a relation in which actor $A$ currently controls resources,
permissions, or conditions relevant to actor $B$’s independence. Exercise of
that control prevents $B$ from acquiring work, funds, relations, or other
means required to leave the relation. Dependence then grows. The resulting
dependence supports the continuation or enlargement of $A$’s power. A further
step can occur when $A$ presents the produced dependence as evidence that
continued control is helpful, prudent, or necessary, and an institution
converts that justification into renewed authority or resources.

Wanhong Huang proposed this configuration during a wider inquiry into
generative justice and value circulation. The proposal first described
control that blocks resources for independence and thereby maintains itself.
It then identified a justificatory reversal in which the controller invokes
control-produced dependence as proof of help. A later refinement shifted the
object from rights in general to powers capable of acting on the conditions of
future power. This paper reconstructs that insight as a causal mechanism and
keeps the later correction central.

Several familiar processes can produce the same visible sequence of continuing
power. A legal office can renew through constitutional procedure. An
organization can persist through coordination and sunk cost. A party can remain
dependent because of an external shock. Two groups can reproduce a shared
institution through mutual support. A power relation can continue through
direct inertia. These processes motivate a narrower definition.

Fix a source actor, affected actor, domain, action class, comparison regime, and
horizon. A focal power is self-reproducing over a path when present
exercise changes at least one condition of future focal power and the mediated
change makes a positive material contribution to later focal power.

The adjective generative names the mechanism’s action on conditions that
produce, preserve, expand, contest, or replace power. It carries neither a
positive moral valence nor a claim about generativity as a universal substance.
The definition directs attention to a return path:

$$\text{present exercise}
\longrightarrow
\text{condition of future power}
\longrightarrow
\text{future focal power}.$$

Self-reproducing generative power is best studied as a family of typed,
path-specific causal mechanisms. Material dependence, viable counter-power,
and institutional legitimation form three candidate return paths. A restricted
closure classification additionally requires contraction of practical exit,
counter-power, or revisability. Normative and legal classifications require
their own premises and evidence.

Four contributions support Claim ?. First, the paper defines a
typed power coordinate and separates power capacity from present exercise.
Second, it decomposes the three return paths and derives their local chain-rule
contributions. Third, it defines viable counter-power as a set of efficacious
actions satisfying a transition-safety condition. Fourth, it constructs a
finite-trace rival showing that observed persistence and dependence leave the
endogenous loop underdetermined across unrestricted model classes.

Section 5 positions the proposal within power, dependence,
non-domination, exit, organizational, and institutional traditions.
Section 6 defines the state and causal estimand.
Section 7 develops the paths and local derivation.
Section 8 separates counter-power, closure, and normative
registers. Section 9 establishes finite-trace
underdetermination and identifies causal obligations.
Section 10 presents a comparative empirical programme.
Section 11 records open obligations and the current position.

2. Antecedent Theories and Contribution Boundary

This section locates the proposed mechanism within established traditions and
defines the paper’s contribution boundary. It moves from relational power and
dependence through agenda control, disciplinary formation, non-domination,
exit, resource dependence, path dependence, institutional reproduction, and
generative justice. Table 1 records the licensed relation
and the remaining transfer obligation.

| @P0.22YY@

Tradition Licensed antecedent role P018 contribution boundary
Relational power and dependence Power concerns specified relations and targets; dependence structures
relational power. Adds a mediated return from present exercise through changed conditions to
later focal power.
Agenda and multidimensional power Procedures, agendas, consent, and latent conflict widen the observable field. Adds time-indexed condition change and edge-specific future-power estimands.
Discipline and subject formation Power can organize conduct, institutions, capacities, and subjects. Represents one bounded causal grammar and leaves historical interpretation
to domain research.
Non-domination Dependence, arbitrariness, uncontrolled capacity, and contestability carry
distinct normative importance. Keeps self-reproduction, closure, and domination in separate registers.
Exit and resource dependence Exit, voice, substitution, and environmental reliance shape organizational
relations. Specifies focal production of dependence and its return as later power.
Institutional reproduction Increasing returns, sequence, self-reinforcement, and de facto investment can
sustain institutions and outcomes. Separates focal mediated return from path dependence, coordination, and
external replay.
Generative justice Unalienated circulation returns value to the communities and entities that
generate it. Studies a candidate pathology in which present power redirects conditions
into its own future reproduction.

Table. Antecedent traditions and contribution boundaries

Dahl’s relational definition makes actors and targets explicit
(Dahl, 1957). Emerson connects power and dependence within exchange
relations (Emerson, 1962). Bachrach and Baratz broaden power analysis
toward agenda control and nondecision (Bachrach & Baratz, 1962), while Lukes
places decision, agenda, preference, consent, and domination within a wider
debate (Lukes, 2026). These lineages support careful typing. They leave
open the present paper’s particular temporal mechanism.

Foucault’s study of discipline provides a major ancestor for analyses of power
that organize conduct, institutions, and subjects (Foucault, 1995).
The present construction adopts a limited lesson: power can act through the
conditions under which conduct and capacity become possible. Its causal
estimands and path equations are proposals of this manuscript.

Republican theory directs attention to freedom as non-domination and to
institutions of contestation (Pettit, 1999). Lovett develops an
account linking domination with dependency and arbitrary power
(Lovett, 2010). These works motivate the counter-power and
arbitrariness coordinates. Their normative criteria retain authority within
their own theories. P018 supplies a causal mechanism and a closure profile.

Hirschman’s exit, voice, and loyalty framework distinguishes responses to
organizational decline (Hirschman, 1970). Pfeffer and Salancik analyze
organizational dependence on environmental resources and the control such
dependence permits (Pfeffer & Salancik, 1978). These traditions support
attention to substitution, portability, and external support. P018 asks
whether focal exercise helped produce the dependence and whether that
dependence materially increased later focal power.

Path-dependence research emphasizes increasing returns, sequence, costly
reversal, and critical junctures (Pierson, 2000; Mahoney, 2000).
Greif and Laitin model endogenous institutional change through
self-reinforcement (Greif & Laitin, 2004). Acemoglu and Robinson show how
investment in de facto political power can preserve outcomes across formal
institutional change (Acemoglu & Robinson, 2008). Tilly develops relational
and organizational mechanisms of durable inequality
(Tilly, 1999). These are close ancestors. The present paper asks for
a focal intervention, declared mediators, and a return to the same typed power
coordinate.

Eglash and collaborators describe generative justice through unalienated value
flows that return benefits to value-generating human and nonhuman communities
(Eglash et al., 2024). That programme motivates the wider inquiry. The
paper studies a possible reverse circulation in which power changes generative
conditions and captures the return as future power. The literature connection
is programmatic; the definitions and formal construction presented here remain
the author’s responsibility.

2.1 Adjacent Project Boundary

This subsection distinguishes P018 from two adjacent manuscripts in the same
research programme. Its role is to preserve cumulative development while
preventing the present mechanism from absorbing earlier questions.

P010 studies control, distribution, and accumulation of realization
conditions. Its focal structure can exist without a dyadic relation between the
advantaged and constrained parties. P011 studies an open-then-enclose sequence
in which invited reliance creates a dependency option for the opening party.
P018 asks a further causal question: did present exercise change dependence,
counter-power, or institutional authorization in a way that increased later
focal power? The future-power return and closure profile are the new objects.

3. Typed Power and Recursive Conditions

This section specifies the model’s objects, domains, and causal target. It first
defines a context-indexed power coordinate, then distinguishes power capacity
from exercise, introduces the mediator state, and gives a path-specific
self-reproduction estimand. Table 2 summarizes the symbols used
throughout the formal argument.

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Symbol Type Interpretation requirement
$P_t^{A\to B,d,\chi}$ Context-specific power coordinate Capacity of $A$ to affect $B$’s declared action or condition class
$\chi$ in domain $d$.
$A_t^P$ Exercise intervention Specified use of focal power at time $t$, with a coherent disabling
comparison.
$E_t$ Practical exit coordinate Effective access to a declared alternative under costs, information,
timing, and safety constraints.
$D_t$ Dependence coordinate Reliance on the focal actor or relation for declared realization
conditions.
$\Counter_t$ Set-valued counter-power Viable actions capable of review, refusal, substitution, revocation,
coalition, appeal, or replacement.
$J_t^a,J_t^u,J_t^i$ Legitimation stages Assertion, relevant-audience uptake, and institutional conversion.
$\Rev_t$ Revisability coordinate Practical capacity to alter the focal relation, its terms, or its holder.
$Z_t,U_t$ Background and exogenous state Observed or latent conditions and exogenous inputs with declared causal
roles.

Table. Typed symbols for the recursive-power model

A power coordinate $P_t^{A\to B,d,\chi}$ measures or orders $A$’s capacity
at time $t$ to affect $B$’s declared action or condition class $\chi$ in
domain $d$, relative to a stated comparison and horizon. Comparisons across
coordinates require an independently defended aggregation or partial order.

Definition ? follows the relational discipline of
power theory while adding temporal and intervention detail. An employment
permission, control of a resource, agenda authority, a review veto, and
interpersonal influence belong to different coordinates until a theory relates
them. Vector-valued and partially ordered profiles are available when a scalar
would erase those differences.

The state used in this paper is

$$S_t

\bigl(P_t,E_t,D_t,\Counter_t,J_t^a,J_t^u,J_t^i,\Rev_t,Z_t\bigr),$$

with transition

$$S_{t+1}

\Psi_t(S_t,A_t^P,A_t^B,U_{t+1}).$$

The superscripts on $P_t$ are suppressed after the context is fixed.
$A_t^B$ records actions by $B$ or aligned actors, including resistance,
coalition, substitution, and learning.

An exercise comparison consists of an enabling intervention $a^1$ and a
disabling intervention $a^0$ that refer to the same focal power, time,
target, domain, action class, horizon, and relevant background arrangement.
Differences introduced to make either intervention feasible are recorded as
part of the comparison.

Coherence matters because disabling a control action can require replacement
support, altered authority, or a changed institutional environment. A
comparison that removes both the controller and the resource controlled would
mix exercise with resource absence. A comparison that supplies independent
support may estimate the effect of a safeguard. The two questions deserve
separate designs.

For a declared causal path $\pi$ from present exercise to later focal power,
define the edge-intervention contrast

$$\SR_{\pi}(t,h)

\mathbb E!\left[
P_{t+h}(a^1;\pi)-P_{t+h}(a^0;\pi)
\right].$$

The notation $(a;\pi)$ means that the intervention is transmitted along the
declared edges while assignments on other pathways follow the stated causal
model.

A focal power satisfies the self-reproduction screen over
$(t,h,\pi)$ when $\SR_{\pi}(t,h)>\epsilon_P$ and $\pi$ contains at
least one condition of future power changed by present exercise.

The material threshold $\epsilon_P$ prevents arbitrarily small modeled
effects from carrying the classification. Its value is domain-specific. A
direct coefficient from $P_t$ to $P_{t+h}$ records persistence. The
mediator requirement identifies the generative return.

Every use of Equation 3 declares the causal graph, intervention
semantics, consistency conditions, interference scope, positivity conditions,
mediator ordering, and assumptions supporting identification or bounds.

Assumption ? turns the definition into a research obligation.
Equation 3 remains a proposed estimand until a design supports it.
Observed dependence, power, and time order can motivate the path; they provide
limited causal resolution by themselves.

4. Causal Return Paths and Local Loop Gain

This section develops the mechanism’s internal structure and formal
consequences. It presents three path families, derives their local chain-rule
terms, assembles the one-step multiplier, and states the boundary between
mediated return and full-system stability. Table 3 summarizes the
paths before the derivation.

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Path family Causal sequence Decisive breakpoint examples
Material dependence Exercise lowers practical exit; reduced exit increases dependence;
dependence increases later focal power. Redundant provision preserves exit; dependence follows an external shock;
dependence receives limited institutional conversion.
Counter-power Exercise contracts viable contestation; reduced contestation increases later
focal power. Review remains effective; resistance expands coalition capacity; contestation
has limited effect on the focal coordinate.
Institutional legitimation Exercise contributes to dependence; dependence supports an assertion;
audiences take it up; institutions convert it; converted authority or resources
increase later focal power. Assertion lacks uptake; uptake lacks institutional conversion; converted
rules remain dormant; independent reasons explain renewal.

Table. Candidate return paths and decisive breakpoints

4.1 Material and Counter-Power Returns

This subsection defines the two shorter return paths. Its objective is to expose
the sign and evidence target of every edge while preserving alternative
mechanisms at each transition.

The material path is

$$\pi_M:\quad
A_t^P
\longrightarrow E_{t+1}\downarrow
\longrightarrow D_{t+1}\uparrow
\longrightarrow P_{t+h}\uparrow.$$

The first edge concerns practical exit. Formal permission to leave can coexist
with unavailable transport, funds, records, information, care, employment, or
safe alternatives. The second edge concerns dependence on the focal relation
for a declared condition. The third edge requires a conversion mechanism from
dependence to future power, such as renewed authority, controlled access,
compliance leverage, or resource allocation.

The counter-power path is

$$\pi_Q:\quad
A_t^P
\longrightarrow \Counter_{t+1}\downarrow
\longrightarrow P_{t+h}\uparrow.$$

The set contraction can involve appeal, refusal, coalition, review,
substitution, oversight, revocation, or replacement. An application must state
which actions belong to the domain and how their efficacy and transition safety
are evaluated.

4.2 Institutional Legitimation Return

This subsection decomposes the justificatory reversal into institutional
stages. Its objective is to give discourse, interpretation, decision, and
future-power effects their own evidence targets.

$$\begin{aligned}
\pi_J:\quad
A_t^P
&\longrightarrow E_{t+1}\downarrow
\longrightarrow D_{t+1}\uparrow
\longrightarrow J_{t+1}^{a} \
&\longrightarrow J_{t+2}^{u}
\longrightarrow J_{t+3}^{i}
\longrightarrow P_{t+h}\uparrow.
\end{aligned}$$

Here $J^a$ is an assertion that dependence supports continuation. $J^u$ is
uptake by a relevant audience, such as a decision maker, constituency,
profession, organization, or administrative body. $J^i$ is conversion into a
rule, mandate, budget, credential, permission, enforcement resource, or
replacement barrier. The final edge measures whether that converted object
changes later focal power.

This decomposition protects two distinctions. Text frequency can establish
the presence of a phrase while leaving uptake open. Audience acceptance can
shape interpretation while leaving formal or material authority unchanged.
Institutional analysis begins where the relevant decision pathway is specified.

4.3 Local Derivative Decomposition

This subsection derives the local contribution of each return path. Its role is
mathematical and limited: the derivation states a first-order result under a
differentiable, path-declared model and then identifies the additional
conditions required for a stability claim.

Around a reference state $s^*$, the scalarized transition components are
differentiable. The declared paths, a direct persistence term, and a remainder
exhaust the first-order derivative of $P_{t+1}$ with respect to $P_t$.

Use subscripts to denote partial derivatives evaluated at $s^*$. Along the
material composition $P’=f_D(D)$, $D=f_E(E)$, and $E=f_P(P)$, the chain
rule gives

$$L_M

\frac{\partial P’}{\partial D}
\frac{\partial D}{\partial E}
\frac{\partial E}{\partial P}

P’_D D_E E_P.$$

A common positive-return sign pattern is $E_P<0$, $D_E<0$, and
$P’_D>0$. Each sign is an empirical target. Independent provision can make
$E_P=0$; institutional refusal to convert dependence into authority can make
$P’_D=0$; organized resistance can make $P’_D<0$.

For the counter-power composition,

$$L_Q

\frac{\partial P’}{\partial Q}
\frac{\partial Q}{\partial P}

P’_Q Q_P.$$

A positive return can arise when current power contracts effective
counter-power and effective counter-power constrains later focal power, giving
two negative derivatives. Protected review can yield $Q_P=0$, while
mobilizing backlash can yield $Q_P>0$.

For the legitimation composition,

$$L_J

P’{J^i}
J^i{J^u}
J^u_{J^a}
J^a_D
D_E
E_P.$$

One zero factor interrupts the first-order path. A controller’s assertion with
limited uptake gives $J^u_{J^a}=0$. Audience uptake with an effective
institutional veto gives $J^i_{J^u}=0$.

Under Assumption ?, the three declared first-order
mediated contributions are the products in
Equations 7–9. If $\rho$ denotes the direct persistence
derivative and $L_R$ the remainder, then

$$\frac{\partial P_{t+1}}{\partial P_t}

\rho+L_M+L_Q+L_J+L_R.$$

Apply the chain rule to each differentiable composition. Add the direct
derivative, the three path derivatives, and the declared remainder under the
first-order exhaustiveness part of Assumption ?.

For an isolated one-dimensional map whose derivative equals the right side of
Equation 10, the reference point is locally attracting when
the absolute multiplier is below one and locally repelling when it exceeds one.

Corollary ? has a narrow domain. Multidimensional stability
depends on the full Jacobian. Delays, switching, nonlinear interactions, noise,
thresholds, and strategic adaptation can change the conclusion. A positive
mediated return can coexist with a stable system. A persistent system can have
$\rho>0$ and $L_M=L_Q=L_J=0$. The distinction between self-reproduction and
stability is therefore structural.

5. Counter-Power, Closure, and Normative Registers

This section defines viable counter-power, constructs open and closed recursive
configurations, and preserves the normative firewall. Its objective is to show
how self-reproduction can occur within contrasting institutional profiles and
which additional coordinates make closure a stronger classification.

5.1 Viable Counter-Power

This subsection turns counter-power from a label into a set-valued target. It
requires each candidate action to combine practical availability, efficacy, and
transition safety under a declared horizon.

Let $K$ be a viability set, $\bar P$ a focal-power threshold, and
$\alpha$ a tolerated transition risk.

$$\Counter_B(s_t;h,K,\alpha)

\left{
q\in\mathcal U_B(s_t):
\Pr!\left(
P_{t+h}\le\bar P,,
S_{t:t+h}\in K
\mid \operatorname{do}(q)
\right)
\ge 1-\alpha
\right}.$$

The viability set can encode physical safety, subsistence, legal standing,
continuity of care, informational integrity, or other domain-specific minima.
The power threshold can represent revocation, review, replacement, bounded
scope, or another declared efficacy condition. Set inclusion provides one
comparison:

$$\Counter_B^m(s_t)\subsetneq\Counter_B^b(s_t).$$

A preorder or several incomparable dimensions may be preferable when actions
serve different values. A scalar $Q_t=\mu(\Counter_B)$ requires a defended
measure $\mu$.

5.2 Recursive Maintenance and Restricted Closure

This subsection separates self-reproducing maintenance from restricted closure.
It develops the distinction through constructed configurations and a
multi-register profile.

A self-reproducing power relation is a restricted generative power
closure candidate when its operation materially contracts practical exit,
viable counter-power, or revisability relative to a coherent comparison.

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Configuration Mediated return Exit, counter-power, and revisability Current classification
Constitutional renewal Public institutions reproduce administrative and electoral conditions. Elections, review, revocation, opposition, and replacement remain effective. Open recursive maintenance candidate.
Mutual coordination Participants invest in shared rules that preserve the institution. Revision remains symmetrical and practical alternatives remain accessible. Mutually sustained institution candidate.
External-shock dependence Focal exercise has limited causal contribution. Exit contracts because of an outside event. Dependence with an exogenous rival.
Assertion without uptake Controller invokes dependence. Relevant audiences reject or ignore the assertion. Justificatory event with an interrupted legitimation path.
Redundant provision Focal exercise attempts to restrict one route. Independent resources preserve practical exit and counter-power. Blocked material return path.
Recursive closure One or more mediated paths increase later focal power. Practical exit, viable contestation, or revisability materially contracts. Restricted closure candidate.

Table. Constructed recursive configurations and classification boundaries

Table 4 contains two cases with positive recursive
maintenance and open institutional profiles. It also contains several
mechanism-breaking cases. These configurations support a formal independence
result.

The mediated self-reproduction screen in
Definition ? is insufficient by itself for the restricted
closure classification in Definition ?.

Construct a constitutional renewal configuration in which current institutional
power invests in future elections, public administration, review, and
contestability. Suppose the investment makes a positive mediated contribution
to later institutional capacity, so Definition ? is satisfied.
Let practical exit, viable counter-power, and revisability remain equal to or
greater than their comparison values. Definition ? then remains
unsatisfied. The two classifications are logically independent in this
direction.

The proposition leaves the empirical plausibility and normative quality of the
constructed arrangement open. Its role is logical. Protective institutions can
reproduce enabling conditions while preserving plural contestation.

This subsection records the independent questions required for stronger
classifications. Table 5 keeps causal, institutional, moral,
responsibility, and legal registers distinct.

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Register Additional target Required inquiry
Self-reproduction Positive mediated return to later focal power. Path-specific causal evidence and material threshold.
Restricted closure Contraction of practical exit, viable counter-power, or revisability. Set, threshold, institutional, and comparison analysis.
Domination Dependence, arbitrariness, uncontrolled capacity, status, or another
theory-specific condition. Explicit domination theory and case evidence.
Injustice Standing, baseline, procedure, distribution, recognition, and justification. Normative bridge argument and plural-value analysis.
Generativity exploitation Capability contraction and candidate benefit produced or sustained through
that contraction. Baseline-relative capability and benefit-through analysis.
Responsibility Contribution, knowledge, capacity, role, duty, excuse, and remedy. Actor-specific causal and normative analysis.
Legal wrong Legal relation, jurisdiction, proof, defense, and remedy. Verified primary authority and case-specific facts.

Table. Registers beyond the recursive-power mechanism

The profile can be written

$$\Gamma_{A\to B}

\left\langle
\SR_{\pi_M},\SR_{\pi_Q},\SR_{\pi_J},
\Delta E,\Delta\Counter,\Delta\Rev,
\Auth,\Arb,\Prop,\Benefit,\mathsf{Legal}
\right\rangle.$$

Equation 13 provides an inspectable profile while leaving
aggregation and sufficient moral conditions to the relevant normative theory.
A case can change classification when one coordinate or its underlying
evidence changes.

6. Identification and Finite-Trace Underdetermination

This section establishes an identification limit and turns each return path
into an empirical obligation. It first constructs a finite-trace rival, then
links mediation and longitudinal-confounding methods to the proposed estimands,
and finally records plausible substantive alternatives.

6.1 Finite-Trace Countermodel

This subsection proves a limited underdetermination result. Its role is to
block inference from an observed persistent sequence to an endogenous return
loop across unrestricted model classes.

For every finite deterministic observed trajectory $y_{0:T}$ generated by a
candidate endogenous recursive-power model $\mathcal M_E$, an exogenous replay
model $\mathcal M_X$ exists that generates the same trajectory and differs
under an intervention on current focal power.

For each $t<T$, define an exogenous input $U_{t+1}=y_{t+1}$. Let the replay
model have transition

$$Y_{t+1}=U_{t+1}.$$

Both models generate $Y_{0:T}=y_{0:T}$ for the realized trace. In
$\mathcal M_X$, later observations are fixed by the exogenous inputs, so an
intervention on the current focal-power coordinate leaves the replayed future
fixed. By construction, $\mathcal M_E$ can assign a mediated effect to that
intervention. The models agree observationally on the finite trace and differ
interventionally.

The replay model is deliberately permissive. Proposition ?
establishes a logical limit and offers a benchmark for stronger comparisons.
Empirical work should compare the recursive mechanism with direct inertia,
external scarcity, common shocks, mutual coordination, authorized delegation,
organizational sunk cost, and preexisting incapacity.

6.2 Edge-Specific Causal Obligations

This subsection translates the three paths into separable evidence targets. Its
objective is to make revision possible at the level of one edge while retaining
independent results elsewhere. Table 6 gives a compact design
matrix.

| @P0.21YY@

Edge Candidate evidence Principal rivals and absorbers
$A^P\to E$ Resource, rule, portability, information, or access change under a coherent
exercise comparison. External scarcity, prior exit cost, redundant provision, anticipatory exit.
$E\to D$ Substitution failure, switching burden, continuation loss, reachable-set
contraction. Chosen specialization, temporary need, independent alternatives.
$D\to P’$ Renewal, delegated authority, resource transfer, compliance leverage. Independent authorization, fiduciary duty, resistance, declining
controllability.
$A^P\to\Counter$ Changed efficacy of review, appeal, refusal, coalition, oversight, or
replacement. Protected institutions, substitute channels, mobilizing backlash.
$\Counter\to P’$ Reversal, revocation, replacement, or credible constraint. Symbolic process, weak implementation, external persistence.
$D\to J^a\to J^u$ Decision records, framing, endorsement, voting, professional or
administrative uptake. Generic rhetoric, contrary interpretation, independent reason.
$J^u\to J^i\to P’$ Rule, mandate, budget, discretion, enforcement, scope, or duration change. Veto, dormant rule, implementation failure, countervailing authority.

Table. Edge-specific evidence and rival mechanisms

Causal mediation research emphasizes definitions, identification assumptions,
estimation, and sensitivity analysis across model forms
(Imai et al., 2010). The present paths require that discipline. Their
sequential mediators create further complications because current exercise can
change later confounders of mediator and outcome.

Marginal structural models were developed for settings in which time-varying
confounders are themselves affected by earlier treatment
(Robins et al., 2000). This lineage identifies a relevant method family.
An application still needs its own estimand, treatment strategy, positivity
assessment, censoring model, interference scope, and sensitivity analysis.
Partial identification or qualitative process tracing may be more defensible
when those requirements exceed the available evidence.

6.3 Interference and Strategic Response

This subsection records two features that can change the meaning of every path.
Its role is to prevent a static individual-level design from absorbing network
effects and strategic adaptation.

Power relations can involve interference. One actor’s exit can alter another’s
outside option; one coalition can create counter-power for several parties; an
institutional decision can apply to a population; public measurement can
change discourse. The unit of analysis and interference neighborhood therefore
belong in the case signature.

Actors can also anticipate intervention. A power holder can move restrictions
to an unmeasured channel, supply symbolic exit, or accelerate institutional
conversion. Affected actors can conceal preparation, build coalitions, or
convert a restriction into mobilization. These responses can reverse local
derivative signs and create delayed effects. A strategic model becomes
appropriate after the application specifies actors, information, action sets,
timing, and objectives.

7. Comparative Empirical Programme

This section converts the mechanism grammar into a staged research programme.
It defines the case signature, comparison strategy, configuration sample, and
promotion criteria. The method treats positive, boundary, and negative cases as
necessary parts of mechanism development.

7.1 Case Signature and Longitudinal Phases

This subsection specifies the minimum description required before measurement.
Its objective is to align the causal graph with the institutional history of a
case.

A case signature records

$$\mathcal C

\langle
A,B,d,\chi,t,h,
P,A^P,E,D,\Counter,J^a,J^u,J^i,\Rev,
Z,K,\mathcal B
\rangle,$$

where $\mathcal B$ is the comparison regime. The accompanying narrative
separates acquisition, authorization, exercise, condition change, dependence,
counter-power change, justification, institutional conversion, later power,
review, release, and restoration.

The sequence should preserve evolving roles. A recipient can become a
co-governor; a controller can lose formal authority while retaining resource
control; an outside provider can create a second dependence; a protected
review body can become captured. Each transition updates the typed state in
place of inheriting a fixed role label.

7.2 Comparative Configuration Sample

This subsection proposes a minimum comparative sample. Its role is to expose
the theory to configurations that share surface features and differ in causal
structure.

| @P0.18P0.24YY@

Case role Shared visible pattern Mechanism target Selection value
Positive material case Power, reduced exit, dependence, later power Every edge of $\pi_M$ Tests the shortest researcher-origin path.
Positive legitimation case Dependence and public justification Assertion, uptake, institutional conversion, later power Tests the strongest multi-stage claim.
Open recursive case Institution reproduces enabling conditions Positive return with preserved contestability Tests closure independence.
External-shock boundary Exit contraction and dependence Zero focal contribution to initial contraction Tests causal-source discrimination.
Rhetorical boundary Controller asserts necessity Limited uptake or conversion Tests discourse-to-institution separation.
Redundant-support negative Attempted restriction Practical exit and counter-power remain effective Tests absorption and safeguard mechanisms.
Inertial negative Long-lived focal power Direct persistence with limited mediated return Tests persistence separation.

Table. Minimum comparative configuration sample

Table 7 is a design requirement and leaves case availability
open. Historical and colonial research would require primary sources, area
scholarship, temporal process evidence, rival mechanisms, and collaboration
adequate to the domain. Household, care, and developmental relations would
require capacity, vulnerability, fiduciary, and safeguarding theories.
Organizational and platform research would require institutional, technical,
labor, and market evidence.

7.3 Evidence Profile and Promotion Rule

This subsection defines graduated evidence states. Its role is to replace a
single binary verdict with an inspectable record of which edges and rivals
receive support.

Let

$$\begin{aligned}
\mathcal E_{\mathrm{loop}}
=\bigl\langle{}
&E_{P\to E},E_{E\to D},E_{D\to P’},E_{P\to Q},E_{Q\to P’},\
&E_{D\to J^a},E_{J^a\to J^u},E_{J^u\to J^i},E_{J^i\to P’},
E_{\mathrm{rivals}},E_{\mathrm{robust}}
\bigr\rangle .
\end{aligned}$$

Each coordinate records the design, estimand, data, assumptions, result,
uncertainty, and principal sensitivity analysis. The research report can then
use five graduated statuses:

$$\begin{gathered}
\text{path proposed}
\prec\text{edge supported}
\prec\text{path supported under assumptions}\
{}\prec\text{comparative mechanism supported}
\prec\text{replicated mechanism}.
\end{gathered}$$

Before analysis, each application states the edge results, rival-model results,
measurement failures, sensitivity thresholds, and strategic responses that
would narrow or retire each proposed path.

Prospective defeat conditions protect revision at the right level. If
redundant provision preserves exit, the material path narrows. If assertion
receives uptake while institutional conversion remains limited, a discourse
result survives and the future-power return narrows. If a focal loop exists
with small magnitude, the causal mechanism survives and system-level
explanatory priority narrows.

8. Research Obligations and Conclusion

This section consolidates the paper’s open tasks and bounded conclusion. It
groups the remaining work into conceptual, causal, comparative, dynamical, and
normative obligations and then restates the position at its present evidential
level.

Develop domain-specific measures or partial orders for focal power, practical
exit, dependence, viable counter-power, revisability, and institutional
conversion. Report disagreements among reasonable specifications.

Specify coherent exercise interventions, longitudinal confounding structure,
mediator ordering, interference scope, strategic response, positivity, and
sensitivity analysis for every claimed path.

Test positive, open-recursive, boundary, and negative configurations within a
bounded domain before proposing cross-domain invariants.

For any stability, attractor, metastability, or transition claim, specify the
full dynamical system and derive the relevant Jacobian, nonlinear, stochastic,
delay, switching, or strategic result.

State the theory and evidence connecting a supported causal path to closure,
domination, injustice, generativity exploitation, responsibility, remedy, or
legal classification.

Complete a systematic full-text review of power reproduction, elite
reproduction, dependency, legitimation, organizational lock-in,
counter-power, and institutional self-reinforcement before asserting
historical priority or comparative novelty.

The paper’s current result is modest and usable. A power relation is
self-reproducing in the proposed sense when present exercise changes a
condition of future focal power and that condition returns as a positive
material contribution to later power. Material dependence, counter-power
impairment, and institutional legitimation provide three path families. Their
local derivatives can be separated from direct persistence under a declared
differentiable model. A finite observed trajectory leaves the endogenous loop
underdetermined across unrestricted rivals. Closure and normative verdicts
require additional coordinates.

This architecture supports a disciplined research programme. It asks which
edge operates, which rival absorbs the effect, which intervention remains
coherent, which counter-power is practically viable, and which conclusion the
current evidence can bear. It also allows protective or democratic institutions
to reproduce enabling conditions while preserving contestability. The
mechanism becomes more informative as applications supply sharper types,
comparisons, causal designs, and defeat conditions.

Acknowledgments

I thank Ron Eglash for dialogue that helped motivate the wider inquiry into
generative justice and value circulation. This paper develops a preliminary
formal diagnostic for powers that redirect conditions into their own future
reproduction. Its definitions, formal constructions, taxonomy, arguments, and
conclusions are the author’s responsibility.

The exploratory discussion, source discovery followed by website verification,
formal reconstruction, criticism, and drafting were conducted with
support from OpenAI’s Codex under the author’s direction. The author selected
and approved the manuscript’s theoretical commitments and bears sole
responsibility for its content and errors. I also acknowledge the antecedent
traditions cited throughout the paper and invite correction where the proposed
construction overlooks relevant prior work.

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