Generativity Exploitation Propagation - A Conditional Network Model of Cascades and Buffers

Posted on 2026-08-26 In Philosophy , Political Economy Views: Disqus: Word count in article: 15k Reading time ≈ 54 mins.

Abstract

An actor whose effective generative capability is constrained may face altered
opportunities, pressures, and returns when choosing how to continue. One
possible response creates a second exploitative relation; cooperation, support,
exit, adaptation, and lost practical capacity can yield different outcomes.
This position paper develops generativity exploitation propagation as a
conditional causal relation between independently evaluated edges. The model
requires complete global arrangements, compatible edge-level baselines, a
coherent intervention on an upstream mechanism, a separately specified
downstream row-satisfaction target, and a material positive total-effect
screen. The source-aligned propagation label additionally requires a supported
material path through the intermediate actor’s capability, viability, or
response opportunities. The target remains distinct from its three-valued
research audit. Under a finite response-sufficiency restriction, the paper
derives a response-kernel identity for the total effect and a sign decomposition in which
vulnerability, non-appropriative alternatives, practical capacity, and return
can offset one another. A restricted open-cascade approximation yields an
expected-generation recursion and a finite subcritical resolvent. Entrywise
offspring-kernel reduction yields spectral attenuation under causally
comparable regimes, while leaving policy legitimacy and burden displacement
open. Countermodels separate propagation from succession, common shocks,
absorbed losses, downstream harm, incompatible baselines, and unresolved edge
audits. Around this construction the paper develops three further registers. A problem
analysis locates the transmitting quantity in subject-level continuation: an
actor sustains a trajectory across several generative domains jointly, so a
contraction confined to one domain can lower its capacity to continue at all and
compel a search for generative conditions elsewhere. The analysis further
establishes that edge diagnoses fail to compose, since succession, common
causation, and shared mechanisms remain consistent with two positive edge
findings, and that the existence of a capability contraction can be accessible
while its magnitude remains unidentified. A review locates the proposal among
threshold, cascade, systemic-risk, interference, and structural-exploitation
traditions, which divide into those modeling transmission without evaluating what
is transmitted and those evaluating relations without modeling transmission. A
normative argument then answers the question the model raises. Transmitted
pressure leaves the intermediate actor’s agency intact; the actor’s motivating
state is preservation of its own continuation rather than opportunism, which
makes the conduct both more susceptible to mitigation and more tractable to
institutional remedy through the availability of alternatives; and the upstream
actor acquires a distinct forward-looking burden, so that responsibility neither
migrates upstream nor disappears. A closed-cycle counterexample defeats the
inference from reciprocal role occupancy to cancellation and establishes that
distributive outcome and relational procedure are independent evaluative
registers, from which it follows that stability and subcriticality are dynamical
properties carrying no normative verdict. The propagation contrast is proposed as
a measure of structural contribution for social-connection accounts of
responsibility, which have lacked one. A political-economic register locates
coordinating power through value-chain governance types, states the mismatch
between the level at which the relations occur and the level at which mediating
capacity resides, and argues that existing instruments in this domain regulate
observable manifestations in place of couplings, so that an instrument can be
fully complied with while the transmission structure operates unchanged. Open
questions are collected by register. The construction establishes neither
prevalence nor inevitability, assigns no liability, recommends no institution,
and classifies no observed relation. It offers a revisable framework for
empirical and normative research on open exploitation cascades across AI and
non-AI domains.

Keywords: generativity exploitation; causal propagation;

Document Status, Preparation, and Reuse

This unnumbered section records the manuscript’s status, research genealogy,
preparation process, and reuse conditions. These statements govern the document
and carry no evidential weight for its substantive position.

Status and correspondence.
This paper is a revisable discussion document. Its definitions are proposals,
its mathematical results are conditional on declared assumptions, and its
empirical bridges remain open. Objections, counterexamples, corrections,
alternative formulations, and relevant literature are welcome at
mailto:huangwanhong@serendip.ngohuangwanhong@serendip.ngo.

Research genealogy.
The author-led exploratory discussion introduced secondary exploitation,
named Generativity Exploitation Propagation, generalized the problem
beyond AI, replaced an implication of necessity with a modal claim about
altered pressure and possibility, and supplied the closed-cycle robbery
counterexample that defeats the inference from reciprocal role occupancy to
cancellation. That counterexample is the source of
Thesis ?. The global-arrangement construction, causal
estimands, response kernel, offspring matrix, propositions, and the remaining
theses are later reconstructions and arguments. Their inclusion records
development of the proposal; it does not attribute these equations or arguments
to the initiating notes or to the cited literature.

Generative AI use.
Generative AI systems were used in the preparation of this work. Anthropic’s
Claude and OpenAI systems including ChatGPT and Codex supported exploratory
discussion, formal reconstruction, source discovery followed by verification,
and drafting in . The author determined the research questions,
theoretical commitments, and epistemic status of the claims and bears sole
responsibility for the manuscript, including its errors. None of these systems
is an author or holds authorship credit.

License.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0
International License (CC BY-NC 4.0). The license text is available at
https://creativecommons.org/licenses/by-nc/4.0/.

1. Introduction

An actor whose capacity to sustain its own work has been reduced must obtain
what it needs from somewhere. Where the accessible routes are cooperative,
restorative, or redistributive, the search ends there. Where they run through
another party’s generative capability, a second relation appears that resembles
the first. This paper examines whether the resemblance reflects a causal
connection, and what follows if it does.

The phenomenon was proposed as secondary exploitation and named
generativity exploitation propagation. Its initial statement was modal
and deliberately weak: an affected actor faces increased pressure, and a
downstream relation may follow. That weakness is a feature. A claim that
affected actors become exploiters is refuted by any actor who absorbs the loss,
exits, cooperates, or loses the practical capacity to appropriate from anyone,
and all of these occur. The claim worth defending concerns a shift in a
distribution of responses.

The difficulty is that two positive relations, however carefully diagnosed, do
not establish a connection between them. Four situations remain consistent with
every observation an edge-level diagnostic produces: the relations merely
succeed one another in time; a prior institutional change independently produced
both; a single mechanism reached both by separate routes while leaving the
intermediate actor’s position unchanged; or the first relation genuinely altered
that position and thereby raised the probability of the second. Only the last is
the phenomenon. The failure to distinguish them is structural rather than
evidential, since the edge diagnostic evaluates each relation against its own
comparison family without relating the two comparisons.

The paper’s response is a conditional causal construction with an explicit
second requirement. A propagation finding needs compatible global arrangements,
a coherent intervention on an upstream mechanism, a separately specified
downstream target, a material positive total effect, and a supported material
path through the intermediate actor’s capability, viability, or response
opportunities. The total effect alone is a necessary screen that the
shared-mechanism case passes, so the path requirement carries the distinction
that matters.

Four insights organize the argument. The first identifies what transmits.
A participant sustains a trajectory across several generative domains jointly,
so a contraction confined to one domain can lower its capacity to continue at
all and compel a search for conditions elsewhere. This portfolio structure
explains why an upstream relation in one domain can produce a downstream
relation in another, and why the transmitting quantity is subject-level
continuation rather than any single capability. The second concerns motivation.
What moves the intermediate actor is preservation of its own continuation, which
differs from opportunism in a way that matters: threshold-seeking terminates
when the threshold is met and is indifferent among routes that meet it. This
makes the conduct both more susceptible to mitigation and more tractable to
institutional remedy, since a participant satisfied by a cooperative route has
no stake in an appropriative one. The third concerns responsibility.
Transmitted pressure leaves the intermediate actor’s agency intact, mitigates
without extinguishing that actor’s burden, and generates a distinct
forward-looking burden on the upstream actor, so responsibility neither migrates
upstream nor disappears. A closed-cycle counterexample establishes that
reciprocal role occupancy cancels no constituent wrong, from which it follows
that distributive outcome and relational procedure are independent registers and
that stability and subcriticality carry no verdict. The fourth concerns
governance. Existing instruments in this domain regulate observable
manifestations rather than couplings between relations, so an instrument can be
fully complied with while the transmission structure operates unchanged.

The paper’s contribution is a framework in which a proposed cascade can be shown
to lack a coherent baseline, a causal intervention, a downstream diagnosis, a
path warrant, event-level descendant attribution, or a complete account of
affected actors. It proposes the propagation contrast as a measure of structural
contribution for accounts of responsibility that have lacked one. It establishes
no prevalence, no inevitability, and no liability, recommends no institution,
and classifies no observed relation.

The argument proceeds in eleven further sections. Section 4
analyzes the transmission problem. Section 5 reviews
transmission traditions. Section 6 argues the normative
theses. Section 7 describes the structures in which
transmitted pressure operates. Sections 8 through 11
construct the formal model. Section 12 states countermodels
and an empirical protocol. Section 13 collects open
questions by register, and Section 14 states limits and revision
conditions.

The philosophical and formal parts are formally independent, since every
proposition follows from declared model assumptions and no derivation cites a
thesis, and justificatorily dependent, since a conditional causal model
matters only if transmitted pressure changes how participants should be
assessed. Section 6.8 records what fails if each thesis is
rejected.

2. Analytical Scope and Propagation Position

This section defines the paper’s relational target, limited position, and
sequence of inquiry. It begins with three motivating configurations, states the
edge-to-edge possibility, distinguishes the resulting objects, and locates the
proposal without claiming empirical prevalence or literature-wide novelty.

2.1 Three Transmission Configurations

This subsection presents the situations that generate the research question.
Each is stated schematically, and none is classified by this paper.

Squeezed intermediary.
A lead organization sets terms that contract a supplier’s effective capacity to
operate on the previous basis. The supplier retains its practices and personnel.
What contracts is the set of viable ways to continue: margins, scheduling
latitude, and reinvestment capacity. The supplier then sets terms toward its own
workforce that it would previously have declined to set.

Displaced practitioner.
A practitioner’s professional capability is reorganized by an adopting
organization’s deployment of a mediating system. The practitioner retains the
skill and loses direction over its application. Continuing on the previous terms
becomes infeasible, and the practitioner takes a position in which another
participant’s capability is in turn constrained.

Foreclosed originator turned controller.
A participant whose generative trajectory was foreclosed by a controller
subsequently obtains control over conditions on which a third participant
depends, and exercises it as the original controller did. The first relation
altered which continuations were viable. The second relation is nonetheless the
participant’s own.

Each configuration raises the same two questions. Did the first relation
causally change the second, or did they merely occur in sequence? And if it did,
what follows for how each participant should be assessed? This paper answers the
first question formally and the second philosophically.

Suppose a relation benefits $X$ through a material contraction of $Y$’s
effective generative capability relative to an admitted comparison. That
contraction may alter $Y$’s capacity to continue, the responses available to
$Y$, and the returns attached to those responses. A later relation may then
benefit $Y$ through a contraction of $Z$’s capability. The motivating
sequence is therefore

$$X\leftarrow Y
\quad\leadsto\quad
Y\leftarrow Z,$$

where each arrow points from the affected participant toward the candidate
beneficiary. The notation records a role in one relation. An actor can occupy
different roles across edges, and no permanent actor type follows.

The sequence permits several continuations. Support, commons access,
redistribution, cooperation, exit, internal adaptation, or redundancy may
absorb the upstream change. The same change may also remove $Y$’s practical
capacity to appropriate from another participant. Propagation is consequently
a causal possibility under specified conditions, not a logical consequence of
the upstream relation.

Contemporary exploitation accounts disagree about the roles of vulnerability,
domination, unfair advantage, background structure, and anonymous social
organization (Vrousalis, 2013; Zwolinski, 2012; Wollner, 2019).
The present paper inherits an edge diagnostic from a companion capability
framework and asks a narrower dynamic question: when does a coherent change in
one diagnosed relation causally change the probability of another diagnosed
relation? It leaves the correct general theory of exploitation open.

Positive generativity-exploitation propagation is supported, relative to a
declared baseline pair and research specification, when a coherent intervention
on an upstream actor-linked mechanism produces a material positive total
contrast in a separately evaluated downstream generativity-exploitation target
under compatible global arrangements, and a separately supported material path
through the shared intermediate actor connects that intervention to the target.
An open cascade additionally requires event-level descendant attribution.

Claim ? separates six objects. An edge diagnosis
evaluates one relation. A propagation link connects two edge positions by
a positive total-effect screen and a supported path through the shared
intermediate actor. Succession records temporal order alone. An
open cascade joins supported links without feedback to an earlier edge.
A feedback cycle closes such a path and requires another model. A
candidate buffer modifies a declared propagation quantity; its normative
and institutional evaluation remains separate.

Where a source is used, the text states the specific constraint it supplies and
the inference it withholds. The verified corpus establishes antecedents,
methodological constraints, and rivals; it establishes neither the novelty nor
the empirical adequacy of the construction proposed here, and no source is cited
in support of a proposition or a countermodel.

3. The Transmission Problem

This section analyzes the problem the construction addresses. Its objective is
to show why edge-level diagnoses fail to compose, why the phenomenon must be
stated modally, and what a replacement account must therefore supply.

3.1 Secondary Exploitation as a Phenomenon

This subsection states the phenomenon in its original form and identifies what
in it requires reconstruction.

The initiating proposal was that an actor whose generativity has been exploited
may face increased pressure to exploit another. The proposal contains three
components worth separating. It asserts a directional relation between two
relations rather than between two states. It locates the connection in altered
viability and altered available responses. And it states the connection modally:
pressure increases, and the downstream relation may follow.

Each component resists a straightforward formalization. A relation between
relations requires the edge diagnostic to be applied twice under a single
coherent counterfactual structure, which the edge diagnostic alone does not
supply. Altered viability and altered responses are intermediate states that are
themselves consequences of the upstream relation, so conditioning on them
naively induces post-treatment bias. And a modal claim about pressure has no
natural binary rendering: it is a statement about a change in a distribution.

3.2 Subject-Level Continuation as the Transmitting Quantity

This subsection identifies what the original proposal locates between the two
relations, and states why that quantity gives the phenomenon its distinctive
character.

The proposal does not claim that an exploited participant acquires an appetite
for exploiting others. It claims something narrower and stranger. A participant
sustains a trajectory across several generative domains at once, and its
capacity to continue as a participant at all depends on that portfolio jointly.
Write this subject-level continuation capacity schematically as depending on the
participant’s effective capability across domains together with its available
conditions. A contraction confined to one domain can lower the participant’s
capacity to continue in general, because the domains are not independently
sustaining.

The participant then faces a constraint rather than a temptation: to continue at
all, it must obtain generative conditions, resources, or relations from
somewhere. That search is the transmitting quantity. Where the accessible routes
are cooperative, redistributive, or restorative, the search terminates without a
second exploitative relation. Where the accessible routes run through another
participant’s generative capability, the search produces one.

Two features of this structure matter for everything that follows. The
motivating state is self-continuation, so a model that represents the
intermediate actor as opportunistic misdescribes the mechanism. And the
transmission runs through a portfolio effect, so an upstream relation confined to
one domain can produce a downstream relation in an entirely different domain.
The framework accordingly indexes edges by domain and requires no
domain match between an upstream and a downstream relation.

Section 6 argues that the self-continuation structure has
normative consequences that neither an opportunism model nor a pure-victim model
captures.

3.3 Existence and Magnitude as Separate Problems

This subsection records an asymmetry that constrains the empirical program and
recurs in the open questions.

Generativity is latent, observed trajectories are samples, and the economically
relevant loss frequently lies in counterfactual trajectories that never occurred.
This makes the magnitude of a capability contraction difficult to establish even
where its existence is comparatively accessible: structural changes in
conditions, permissions, and opportunity sets can support an existence finding
while leaving valuation open.

The asymmetry propagates into the present model and worsens there. A propagation
contrast is a difference between downstream probabilities under two arms, so it
inherits the identification burden of both edge diagnoses plus the burden of the
intervention and path conditions. The framework therefore treats an unresolved
magnitude as an unresolved magnitude rather than converting it into a null
finding, and Section 13 records the resulting research
obligations.

3.4 Failure of Composition Across Edge Diagnoses

This subsection establishes that two positive edge diagnoses do not compose into
a transmission finding.

Suppose the upstream relation $X\leftarrow Y$ and the downstream relation
$Y\leftarrow Z$ each receive a positive edge diagnosis. Four distinct
situations remain consistent with those two findings.

Succession. The relations occur in temporal order with no causal dependence between them.
Common cause. A prior institutional change independently produces both, so intervening on the first leaves the second unchanged.
Shared mechanism without transmission. A single coherent exposure reaches both relations by separate branches, changing both probabilities while leaving the intermediate actor’s capability, viability, and response opportunities unchanged.
Genuine transmission. The first relation changes the intermediate actor’s position, and that change raises the probability of the second.

Only the fourth is the phenomenon. The first three are compatible with every
observation that the edge diagnostic produces, because the edge diagnostic
evaluates each relation against its own comparison family without relating the
two comparisons. Composition therefore fails, and the failure is structural
rather than evidential: no accumulation of edge-level evidence resolves it.

Two consequences follow for the construction. The comparison arrangements of the
two edges must be jointly realizable, since local comparisons chosen
independently may require the same indivisible resource in incompatible
positions. And the transmission claim requires an intervention on the upstream
mechanism together with a path condition through the intermediate actor, because
a total effect alone leaves case three standing.

This subsection states the gap that the paper’s formal and philosophical parts
each address.

The initiating proposal says that pressure increases, and it explicitly declines
to say that the downstream relation follows. The distinction is not a hedge. It
marks the difference between two claims with different truth conditions and
different normative consequences.

A necessitation claim would hold that an actor in the upstream-affected position
performs the downstream relation. It is refuted by a single actor who does not,
and the configurations of Section 3 all admit participants who absorb the
upstream change, exit, cooperate, or lose the practical capacity to appropriate
from anyone.

A pressure claim holds that the distribution over responses shifts. It is
compatible with wide individual divergence, and it is not refuted by any
particular actor’s conduct. This is what the formal model represents: the total
contrast of Definition ? is a difference of expectations, and the
response decomposition of Proposition ? makes it a difference
of response distributions.

The gap has a normative counterpart that the formal model does not address. If
pressure falls short of necessitation, the intermediate actor retains agency,
and the question of what the upstream relation does to the intermediate actor’s
responsibility remains open. Section 6 argues for a
specific answer.

3.6 Requirements on a Propagation Account

This subsection converts the analysis into the obligations discharged by the
formal construction.

The analysis yields five requirements. The account needs jointly realizable
comparison arrangements across both edges. It needs an intervention on an
interpretable upstream mechanism in place of an intervention on a diagnostic
label. It needs a downstream target whose meaning is stable across arms. It
needs a path condition through the intermediate actor, since a total effect
admits the shared-mechanism case. And it needs a reporting rule that preserves
negative and unresolved outcomes, since a modal claim about distributions will
frequently be unidentified.

Sections 8 through 11 discharge these in order.

4. Transmission Traditions and Rival Models

This section locates the proposal among established models of transmission
through networks. Its objective is bounded positioning: each tradition supplies
a formal or methodological constraint, none supplies an exploitation diagnosis,
and the combination remains a repository-specific construction.

4.1 Threshold, Cascade, and Complex Contagion

This subsection identifies the formal ancestors of the cascade vocabulary.

Granovetter’s threshold models show that aggregate outcomes of collective
behavior depend sensitively on the distribution of individual thresholds, so
that populations with similar average dispositions can produce entirely
different aggregate results (Granovetter, 1978). Watts extends the
analysis to random networks and identifies conditions under which global
cascades occur (Watts, 2002). Centola and Macy distinguish simple
from complex contagion and show that behaviors requiring social reinforcement
propagate differently from information (Centola & Macy, 2007), and Centola’s
online experiment establishes a topology effect in one health-behavior setting
(Centola, 5996).

These works supply the discipline that heterogeneous response rules and topology
jointly determine aggregate paths, and they justify the paper’s refusal to infer
a cascade from edge density. They supply no relational diagnosis: a threshold
model describes adoption of a behavior, and the present object requires each
adopted relation to be independently evaluated.

4.2 Systemic Risk and the Ambiguity of Connectivity

This subsection identifies the tradition that blocks a simple reading of
buffering.

Elliott, Golub, and Jackson analyze financial contagion through cross-holdings
and show that integration and diversification have non-monotone effects on
cascade extent (Elliott et al., 2014). Acemoglu, Ozdaglar, and Tahbaz-Salehi
show that the same network can be stabilizing for small shocks and destabilizing
for large ones (Acemoglu et al., 2015). Katz and Shapiro’s account of network
effects establishes separately that connection alters incentives and adoption
(Katz & Shapiro, 1994).

The constraint these impose is directly relevant to Section 11.
A structural change that lowers transmission under one shock regime may raise it
under another, so a buffer result must be stated relative to declared comparable
regimes. The paper accepts this constraint and states the attenuation result
entrywise and regime-relative.

4.3 Causal Inference Under Interference

This subsection identifies the methodological constraints on any transmission
estimand.

Hudgens and Halloran develop causal inference under interference and partial
interference structures (Hudgens & Halloran, 2008); Ogburn and VanderWeele
supply causal diagrams for interference (Ogburn & VanderWeele, 2014); and Aronow
and Samii estimate average causal effects under general interference through
declared exposure mappings (Aronow & Samii, 2017). Imai, Keele, and
Tingley separate the definition of a mediation effect from its identification,
estimation, and sensitivity analysis (Imai et al., 2010).

Two further results constrain observational work directly. Aral, Muchnik, and
Sundararajan distinguish influence-based contagion from homophily-driven
diffusion and find that naive estimates substantially overstate contagion
(Aral et al., 2009). Shalizi and Thomas prove that homophily and contagion
are generically confounded in observational network studies
(Shalizi & Thomas, 2011).

These supply the paper’s identification obligations and its insistence that a
positive association is not a propagation finding. They identify no estimand in
any dataset relevant to this paper.

4.4 Structural and Anonymous Exploitation

This subsection identifies the normative tradition closest to the paper’s
subject and the specific gap it leaves.

Vrousalis analyzes exploitation as self-enriching instrumentalization of
vulnerability within a domination relation (Vrousalis, 2013).
Zwolinski argues against strong inferences from background injustice to the
classification of a discrete transaction (Zwolinski, 2012).
Wollner analyzes anonymous exploitation that is non-individual, non-agential,
and structural (Wollner, 2019), which is the closest verified
treatment of exploitation obtaining without an identifiable exploiting agent.

The gap is specific. These accounts address whether a relation is exploitative
and whether structure suffices for that classification. None addresses the
dynamic question of whether one diagnosed relation causally changes the
probability of another, and none supplies a measure of that change. Wollner’s
anonymous structural relations and Young’s structural processes, discussed in
Section 6, describe the setting in which propagation
would operate without characterizing the propagation relation itself.

4.5 Comparative Summary of Traditions

This subsection consolidates the review. Table 1 records what
each tradition transmits, what it treats the transmitted item as, and the
constraint it imposes on the present construction.

| >p0.19

p0.20
X

Tradition	Transmitted object	Constraint imposed on the present construction
Threshold and cascade models (Granovetter, 1978; Watts, 2002)	Adoption of a behavior under heterogeneous thresholds	Aggregate paths depend on response-rule distribution and topology; density supports no cascade inference
Complex contagion (Centola & Macy, 2007; Centola, 5996)	Behavior requiring social reinforcement	Reinforcement and bridge structure change diffusion; a single transmission parameter is inadequate
Systemic risk (Elliott et al., 2014; Acemoglu et al., 2015)	Financial loss through cross-holdings	Connectivity effects are non-monotone in shock size; buffer results require declared comparable regimes
Network effects (Katz & Shapiro, 1994)	Value from adoption by others	Connection alters incentives without producing the capability relation at issue
Interference methodology (Hudgens & Halloran, 2008; Ogburn & VanderWeele, 2014; Aronow & Samii, 2017)	Treatment effects across units	Exposure mappings, interference scope, and estimand definition must be declared before estimation
Confounding results (Aral et al., 2009; Shalizi & Thomas, 2011)	Apparent influence in observational data	Homophily and contagion are generically confounded; association supports no transmission claim
Mediation methodology (Imai et al., 2010)	Effect through an intermediate variable	Definition, identification, estimation, and sensitivity remain separate obligations
Structural exploitation (Vrousalis, 2013; Zwolinski, 2012; Wollner, 2019)	Wrongful advantage within a structure	Structural location supports no automatic diagnosis; the dynamic relation between edges remains uncharacterized

Table. Transmission Traditions and the Constraints They Impose. Each tradition
supplies a formal, methodological, or normative constraint. None supplies a
relational diagnosis or an exploitation propagation result.

The traditions divide into those that model transmission without evaluating what
is transmitted, and those that evaluate relations without modeling transmission
between them. The present construction attempts to join the two, and the
attempt’s value depends on the arguments of Section 6.

5. Agency, Constraint, and Responsibility Under Transmission

This section argues for the five theses on which the framework’s significance
depends. Its objective is to answer the question the formal model raises and
cannot settle: if upstream exploitation raises the probability that an
intermediate actor enters a downstream exploitative relation, what follows for
how each participant should be assessed?

The question is unavoidable. A model that quantifies transmitted pressure
invites two opposite misreadings. On one, the intermediate actor becomes a mere
conduit whose conduct is fully explained by upstream constraint, so that
responsibility migrates upstream. On the other, the intermediate actor’s agency
renders the upstream relation irrelevant to the downstream one, so that
transmission carries no normative weight at all. Both are mistaken, and the
section argues for the position between them.

Each subsection states a thesis, argues for it, states the strongest objection
known to the author, and replies.

5.1 Pressure Without Necessitation

This subsection argues that the model’s central quantity leaves the intermediate
actor’s agency intact.

A positive propagation contrast is compatible with the full agency of the
intermediate actor. The quantity is a difference between response
distributions, and it entails nothing about any individual response.

The argument is available directly from the formal construction. By
Proposition ?, the total contrast satisfies
$\tau=\sum_r d(r)[\pi_1(r)-\pi_0(r)]$. This is a difference between two
distributions over a common response set. It is consistent with
$\tau>0$ that a majority of actors in the exposed arm select responses outside
$\mathcal R_Y^E$, and consistent that any particular actor selects the same
response in both arms. The model contains no individual-level determination and
supplies none.

The point generalizes beyond the formalism. Fischer and Ravizza analyze moral
responsibility through the reasons-responsiveness of the mechanism on which an
agent acts, in place of the availability of alternative possibilities
(Fischer & Ravizza, 1998). On such an account, altering the incentives an
agent faces leaves the agent responsible provided the mechanism remains
appropriately responsive to reasons. Upstream exploitation that changes
viability, alternatives, and returns changes the reasons in play. It does not,
in the ordinary range, replace a reasons-responsive mechanism with a
non-responsive one.

The strongest objection is that this holds only in the ordinary range, and that
sufficiently severe constraint does eliminate meaningful choice: when
$N_Y$ contains no accessible non-appropriative path, describing the resulting
conduct as the actor’s own is a fiction. The reply concedes the case and treats
it as a feature. The intermediate state of Definition ? contains
$N_Y$ and $C_Y^E$ as explicit coordinates precisely so that the limiting
case can be represented and identified. A framework in which the elimination of
alternatives was inexpressible would be worse. Thesis ? claims
compatibility with agency in the range where alternatives remain, and the
framework marks where that range ends.

5.2 Self-Continuation as the Motivating State

This subsection argues that the mechanism’s distinctive normative character
follows from what moves the intermediate actor.

Two familiar models of a participant who exploits after being exploited are both
available and both wrong for this mechanism. On an opportunism model, the
participant’s constraint supplies occasion and cover for conduct it was already
disposed toward. On a pure-victim model, the participant’s constraint is total,
and its conduct is the upstream actor’s conduct at one remove.

The intermediate actor’s motivating state is the preservation of its own
capacity to continue as a participant. This distinguishes the mechanism from
opportunism, and it makes the resulting conduct more rather than less
susceptible to institutional remedy.

The argument is that the mechanism’s structure fixes the motivating state.
Section 4 located transmission in a portfolio effect: a
contraction in one domain lowers the participant’s capacity to continue in
general, and the participant must obtain generative conditions from somewhere.
What the participant seeks is the restoration of a threshold, and this differs
from advantage-seeking in a respect that matters. Advantage-seeking is unbounded
and scales with opportunity. Threshold-seeking terminates when the threshold is
met, and it is indifferent among routes that meet it.

Two consequences follow. Normatively, threshold-seeking under constraint is the
paradigm case for mitigation, since the reasonable cost of refusal is exactly
what a justification would weigh, and here refusal may cost the participant its
continuation. Institutionally, indifference among routes is the mechanism’s
weak point: a participant that would be equally satisfied by a cooperative,
redistributive, or restorative route has no stake in the exploitative one. This
is the structural reason a buffer can work at all, and it explains why buffers
in this model act on the availability of alternatives rather than on the
participant’s dispositions.

The strongest objection is that the thesis is empirically optimistic and
politically convenient: real participants under constraint do sometimes acquire
dispositions, build capabilities around the exploitative route, and continue
past the point where the threshold is met, so that the threshold model describes
an initial episode rather than a settled pattern. The reply concedes this
entirely and marks the boundary. Thesis ? characterizes the
mechanism the model represents, which is a single transmission step under a
declared lag. Persistence, habituation, and the conversion of a constrained
response into a stable practice are feedback phenomena that the open-cascade
restriction of Section 11 explicitly excludes, and
Section 13 records them as unresolved. Where they obtain,
the mitigation available under Thesis ? correspondingly
weakens.

5.3 Constraint, Mitigation, and the Non-Transfer of Wrongfulness

This subsection argues for the paper’s central normative claim about
transmission.

Upstream exploitation does not transfer the downstream relation’s normative
character to the upstream actor. It can mitigate the intermediate actor’s
culpability without extinguishing it, and it generates a distinct upstream
responsibility for the structural effect produced.

The argument distinguishes two normative facts that a transmission finding
establishes together and that are frequently conflated.

The first concerns the intermediate actor. If the downstream relation satisfies
the edge diagnostic, then by the companion framework’s account a justificatory
burden falls on the party whose advantage runs through the affected position.
That party is the intermediate actor. Upstream constraint bears on how easily
the burden is discharged, since the availability of alternatives, the reasonable
cost of refusal, and the actor’s own position are exactly the considerations a
justification would cite. Constraint therefore mitigates, and the degree of
mitigation varies with $N_Y$ and $C_Y^E$.

The second concerns the upstream actor. A supported propagation link establishes
that intervening on the upstream mechanism changes the downstream target through
the intermediate actor’s position. The upstream actor thereby produced a
structural effect on relations to which it is not a party. That is a distinct
object of assessment, and it generates its own burden.

Neither fact cancels the other, and this is the substance of the thesis.
Transmission adds a burden upstream while reducing, without eliminating, the
burden downstream.

The strongest objection is that this double-counts: one downstream relation
generates two burdens, so the account inflates the total normative charge. The
reply is that the burdens have different objects and different bearers. The
intermediate actor’s burden concerns the relation it entered. The upstream
actor’s burden concerns a change it produced in the conditions under which
others act. An account that recognized only the first would leave upstream
actors free to reshape the conditions of others’ conduct without answering for
it; an account that recognized only the second would treat the intermediate
actor as an instrument. No quantity is counted twice, because no single quantity
is at issue.

5.4 The Circulation Argument and Its Defeat

This subsection defends the premise that the preceding thesis requires, using a
counterexample that arose in the source discussion.

Thesis ? denies that wrongfulness transfers. A natural
opposing view holds that when a participant is both affected and beneficiary
across a set of relations, the reciprocal occupancy of roles neutralizes the
constituent relations, so that a closed system of mutual appropriation is
normatively unobjectionable.

Reciprocal occupancy of affected and beneficiary positions across a set of
relations leaves the normative character of each constituent relation
unchanged. Closure and distributive neutrality cancel no constituent wrong.

The argument is a counterexample due to the source discussion rather than to
this reconstruction. Consider a closed set of participants in which each robs
and is robbed of equal value. The aggregate distribution is unchanged, every
participant occupies both roles, and no participant ends worse off in
holdings. Every constituent robbery remains wrongful. Cancellation therefore
fails, and it fails for a locatable reason: the wrongfulness of each relation
lies in how it was transacted, and a distributive fact about the aggregate does
not reach that property. Procedural and relational legitimacy form a register
that distributive outcomes do not settle.

The consequence for this paper is direct. Being upstream-affected is a fact
about a participant’s position in one relation. It does not enter the evaluation
of a different relation as a cancelling term. Section 6’s
mitigation claim survives because mitigation operates through the availability
of alternatives at the time of the second relation, which is a different route
from cancellation by role reciprocity.

The strongest objection is that robbery is a poor analogue, since it involves a
discrete wrongful act with a clear victim, whereas exploitation on the present
account is a structural relation that may be entered without intention. The
reply is that the counterexample is directed at a specific inference and needs
no closer analogy to defeat it. The inference under test moves from role
reciprocity and distributive neutrality to cancellation. Any case in which those
premises hold and cancellation fails refutes it. The full evaluation of closed
cycles, including stability, distribution, and procedural standing, requires the
companion cycle project and is not attempted here.

5.5 Separation of Outcome and Procedural Registers

This subsection states the general distinction that the circulation
counterexample establishes, and applies it to the dynamic results.

The robbery case refutes cancellation because it separates two registers that a
purely distributive evaluation collapses. One register asks whether participants’
generative capability ultimately remained stable or increased. The other asks
how each participant’s capability was used, constrained, or appropriated along
the way. The robbery cycle scores neutrally on the first and badly on the
second, which is possible only if the registers are independent.

Distributive outcome and relational procedure are independent evaluative
registers for a transmission structure. Neither determines the other, and a
complete assessment reports both.

The argument for independence in one direction is the robbery cycle. The
argument in the other direction is equally available: an arrangement can be
procedurally impeccable, with full consent, disclosure, and recourse at every
step, while producing a distribution in which one participant’s generative
capability is progressively exhausted. Neither register is redundant.

This thesis has direct consequences for the dynamic results, and stating it
prevents a systematic misreading of them. Stability is a dynamical property and
belongs to neither register: a structure that reproduces itself period after
period may be stable because participants are satisfied or stable because they
have no exit. Slave systems, monopolies, and predator–prey systems are all
stable. Nothing follows from stability alone about either outcome or procedure.

The same holds for the spectral quantities of Section 11. A
subcritical offspring kernel reports that expected cascade totals are finite. It
reports nothing about how the residual is distributed and nothing about how each
constituent relation was transacted. Thesis ? draws the
consequence for buffer evaluation; Thesis ? states the general
principle from which it follows.

5.6 Forward-Looking Upstream Responsibility

This subsection identifies the kind of responsibility the upstream burden is,
and states the paper’s contribution to an existing account.

The upstream burden established by a propagation finding is forward-looking
responsibility for structural processes rather than backward-looking liability
for a specific downstream act. The propagation contrast supplies a measure of
structural contribution that such accounts have lacked.

Young distinguishes a liability model of responsibility, which isolates a
perpetrator and traces a causal line to a discrete wrong, from a social
connection model, on which all who contribute through their actions to
structural processes producing injustice bear responsibility to work to remedy
it (Young, 2006; Young, 2011). The social connection
model is forward-looking, shared, and discharged through collective action in
place of blame.

The upstream burden fits this description precisely. The upstream actor did not
perform the downstream relation and may have neither foreseen nor intended it.
What the actor did was alter conditions under which others act, in a way that
raised the probability of relations satisfying the diagnostic. That is
participation in a structural process, and the appropriate response is alteration
of the mechanism in place of compensation for a particular downstream event.

The paper’s contribution runs in the other direction. A recurring difficulty for
social-connection accounts is that participation in structural processes admits
of no natural measure, so the resulting responsibility resists differentiation
among participants. The propagation contrast supplies a candidate measure: the
change in the downstream target attributable to a coherent intervention on a
specific actor’s mechanism, through a specified path. Where it is identified or
bounded, it distinguishes participants by structural contribution in place of
treating all connection as equivalent. This is a proposal about what such a
measure could be, and it inherits every identification limit stated in
Section 12.

The strongest objection is that Young’s model deliberately avoids assigning
differentiated blame, and that supplying a measure reintroduces the liability
model she rejects. The reply distinguishes the measure’s use. Differentiating
forward-looking obligation by structural contribution is not the same as
assigning backward-looking blame for a discrete wrong: the former asks who is
positioned to alter the process and how much their alteration would matter, and
the propagation contrast answers exactly that question. Nothing in the measure
supports a claim that the upstream actor performed the downstream relation.

5.7 Attenuation Without Justice

This subsection argues that the paper’s dynamic buffer result carries no
normative endorsement, and converts a disclaimer into an argued position.

A regime that reduces expected cascade totals may be less just than the regime
it replaces. Dynamic attenuation and normative improvement are independent
properties.

The argument proceeds from what Proposition ? establishes and
what it omits. The proposition states that entrywise domination of offspring
kernels implies spectral domination, so a buffered regime has a weakly smaller
expected cascade. The premise $K_B\leq K_0$ constrains expected counts of
attributed child edges by type. It says nothing about three further matters.

It says nothing about incidence: the residual cascade may fall entirely on
participants who bore little of it before, so a lower total can accompany a more
concentrated burden. It says nothing about omitted edge types: a buffer that
prevents transmission along modeled types while creating an unmodeled type
reduces the measured kernel and not the phenomenon. And it says nothing about
the buffer’s own relational character: a buffer supplied by an actor who thereby
acquires control over the recipient’s realization conditions may itself satisfy
the edge diagnostic, so that attenuation is purchased with a new exploitative
relation.

The third case deserves emphasis, since it is the one the framework is uniquely
positioned to detect. Support, lending, stewardship, and infrastructure
provision all reduce downstream pressure and all create dependence. The edge
diagnostic applies to the buffering relation exactly as it applies to any other,
and a complete evaluation must run it.

The strongest objection is that this makes the buffer result useless for policy,
since any candidate intervention can be met with the observation that it might
be unjust. The reply is that the thesis specifies what a complete buffer
evaluation contains: the attenuation contrast, an incidence report, an
omitted-type audit, and an edge diagnosis of the buffering relation itself.
That is a demanding standard and a satisfiable one, and it is more useful than a
spectral comparison presented as an endorsement.

5.8 Dependence of the Framework on the Theses

This subsection records what fails if each thesis is rejected, so that a reader
can locate a disagreement precisely.

Rejecting Thesis ? converts the model into a claim about
individual determination that its own mathematics does not support, and the
honest response would be to restate the paper as a study of aggregate rates with
no implication for any actor. Rejecting Thesis ? returns the
mechanism to an opportunism model, which removes the basis for mitigation and
removes the reason buffers act on alternatives in place of dispositions.
Rejecting Thesis ? collapses
the two burdens into one: either responsibility migrates entirely upstream, in
which case the intermediate actor’s downstream relation requires no
justification, or it remains entirely downstream, in which case a propagation
finding has no normative consequence and the paper’s motivation fails. Rejecting
Thesis ? reopens the cancellation inference and, with it, the
view that upstream victimization neutralizes downstream conduct. Rejecting
Thesis ? permits distributive outcome to settle the assessment,
which the circulation counterexample contradicts, and licenses reading stability
and subcriticality as normative results. Rejecting
Thesis ? leaves the upstream burden uncharacterized, and the
paper would retain its formal results while losing its account of what they are
for. Rejecting Thesis ? permits the spectral result to be
read as a policy endorsement, which the paper’s own countermodels contradict.
Rejecting Thesis ? would establish that existing instruments already
reach the couplings the model describes, which would narrow the paper’s
political-economic contribution to a restatement.

Theses ? and ? are load-bearing and are the
most vulnerable. The first carries the paper’s normative content, and the second
carries its claim to contribute something to an existing account of structural
responsibility. Thesis ? is the most empirically exposed,
since it characterizes a motivating state that observation may not bear out.
Direct challenge to any of the three is welcome.

Every proposition in Sections 8 through 12
survives the rejection of all seven theses. What fails is the reason to have
constructed the model.

6. Political Economy of Transmitted Pressure

This section describes the structures in which transmitted pressure operates.
Its objective is to identify the arrangements that make the formal construction
worth applying, and to state why buffer placement is a distributive decision in
place of a technical one.

6.1 Squeeze Structures in Production Chains

This subsection identifies the paradigm empirical structure of transmitted
pressure and the verified evidence for it.

Anner analyzes the purchasing practices of lead firms in garment supply chains
and finds that price pressure and compressed lead times imposed on suppliers are
associated with deteriorating conditions and rights for workers in supplier
factories (Anner, 2020). The structure is the paper’s squeezed-
intermediary configuration in an observed setting: a lead firm alters the terms
on which a supplier can viably operate, and the supplier alters the terms on
which its workforce operates.

The case is instructive for what it supplies and what it leaves open. It
supplies evidence that pressure imposed at one point in a chain is associated
with degraded relations at the next, which is the empirical pattern the model
represents. It leaves open every question the model requires: whether the
association survives a coherent intervention on lead-firm practice, whether the
supplier’s conduct satisfies an independently constructed edge diagnostic,
whether the comparison arrangements at the two points are jointly realizable,
and whether the path runs through the supplier’s altered viability or through a
direct route. The paper cites the work for the structure and claims no
propagation finding in that setting.

6.2 The Provider, Adopter, and Practitioner Configuration

This subsection applies the actor separation to the configuration that motivated
the research program.

A mediating system is supplied by a provider that controls its access terms,
deployed by an adopting organization that reorganizes work around it, and
encountered by practitioners whose capability is reconfigured. Transmission in
this configuration can run along several distinct routes, and conflating them
produces the shared-mechanism error of Section 4.

The provider may alter the adopter’s viable operating basis, and the adopter may
then alter the practitioner’s position: this is transmission through the
intermediate actor. Alternatively, the provider’s single decision may reach both
the adopter’s terms and the practitioner’s position by separate routes: this is
a shared mechanism, and it passes the total-effect screen while failing the path
condition. The two are empirically similar and normatively different. Under
transmission, the adopter bears a mitigated but real burden for its own
relation, and the provider bears a structural burden. Under a shared mechanism,
the adopter’s burden is unmitigated by any upstream effect on its position,
since its position did not change.

The distinction is the practical payoff of requiring
$\mathsf E_\iota$ in addition to $\mathsf E_\tau$.

6.3 Chain Governance and the Location of Coordinating Power

This subsection identifies where the capacity to alter a transmission structure
resides, using a verified account of how production chains are coordinated.

Gereffi, Humphrey, and Sturgeon distinguish governance forms in global value
chains along the complexity of transactions, the codifiability of information,
and supplier capability, yielding market, modular, relational, captive, and
hierarchical types (Gereffi et al., 2005). The typology matters here for a
reason independent of its original purpose. Each governance type distributes
coordinating power differently, and coordinating power is what an upstream
mechanism intervention requires.

In captive and hierarchical configurations, a lead actor sets terms that
propagate downward, and a coherent intervention on the upstream mechanism is
well defined because there is an identifiable party whose practice constitutes
it. In market configurations, terms emerge from many uncoordinated exchanges, and
an intervention on a single actor’s mechanism may be neither available nor
consequential. The propagation model’s central estimand therefore presupposes a
governance form in which the upstream mechanism is a locus of decision, and
Section 13 records the diffuse case as unresolved.

6.4 The Five-Position System and the Intervention Question

This subsection states the question the political-economic register is organized
around and identifies the actors among whom it must be answered.

The research program that generated this paper identified five economic
positions in a mediated configuration: the system itself, users and historical
contributors, workers and professional practices, organizations adopting the
system, and providers controlling it. Capital and mediating institutions were
subsequently distinguished as further positions. The intervention question is
whether the coupling between one position’s gain and another’s capability
contraction can be broken without destroying the generativity at issue.

That last qualification does the work. Foreclosing the mechanism by foreclosing
the practice would satisfy the propagation model trivially and defeat the
purpose. An adequate intervention must reduce the transmission quantity while
preserving, or expanding, the generative capability of the participants
involved. The formal result of Section 11 supplies only the
first half of that criterion, which is the substance of
Thesis ?.

6.5 Level Mismatch Between Relations and Mediation Capacity

This subsection states the paper’s political-economic insight and supports it
with a verified regulatory example.

The relations the model describes occur among firms, workers, users, providers,
and adopting organizations. The capacity to alter the background conditions
under which all of them interact is concentrated at the state and supranational
level, because those institutions can change permissions, obligations, and
liabilities across an entire configuration at once. There is accordingly a
mismatch between the level at which the relations occur and the level at which
coordinating capacity resides.

Ostrom’s analysis of polycentric governance is the relevant structural response.
She argues that complex economic systems are frequently governed by multiple
overlapping centers of decision at different scales, and that neither pure market
nor pure central-state models capture how such systems are actually organized
(Ostrom, 2010). On that view the mismatch is not an anomaly to be
resolved by relocating all authority upward; it is the normal condition, and the
question becomes which decision center is positioned to alter which coupling.

A verified example indicates both the availability and the current limits of
supranational mediation. The European Union’s AI regulation entered into force on
1 August 2024 and became applicable on 2 August 2026, with prohibited-practice
rules applying from 2 February 2025, governance and general-purpose model
obligations from 2 August 2025, and obligations for systems used in employment
and other listed high-risk areas from 2 December 2027
(Commission, 2026). The instrument distinguishes providers from deployers, which
is the actor separation this paper requires, and it operates at the level where
coordinating capacity resides.

Its targets, however, are observable manifestations: prohibited practices, risk
management, transparency, oversight, and the classification of listed high-risk
uses. Capability contraction as such is not among them, and neither is the
transmission of pressure from one relation to another. This yields the paper’s
political-economic observation.

Existing governance instruments in this domain regulate observable
manifestations of a configuration in place of the couplings between relations.
An instrument can therefore be fully complied with while the transmission
structure the model describes operates unchanged.

The argument is that manifestation targeting and coupling targeting have
different extensions. A transparency obligation is satisfied by disclosure and
leaves terms unaltered. A risk-classification regime attaches duties to a
system’s use in a listed area and is silent about what a compliant deployment
does to a supplier’s viability three relations away. Compliance is assessed
relation by relation, and the transmission quantity is a property of a pair of
relations under a counterfactual, which no relation-local audit evaluates.

The strongest objection is that this demands the impossible: couplings are
counterfactual quantities, frequently unidentified, and no workable regulatory
instrument can be built on an estimand the paper itself concedes is often
unresolved. The reply concedes the difficulty and denies that it settles the
matter. Thesis ? is a diagnosis rather than a proposal, and it is
compatible with the conclusion that coupling targeting is infeasible. What it
excludes is the inference from compliance to absence of transmission. Reporting
obligations that record terms imposed on counterparties, and their effects on
counterparty viability, would be a weaker instrument sensitive to the structure
without requiring identification of a causal contrast, and
Section 13 lists the design question as open.

6.6 Buffer Placement as a Distributive Decision

This subsection states why the location of a candidate buffer is a political
question.

Thesis ? establishes that attenuation does not entail
improvement. The political-economic form of that result concerns placement. A
buffer can be placed at the upstream mechanism, at the intermediate actor’s
viability, at the intermediate actor’s alternatives, or at the downstream
participant’s protection. These placements produce different incidence, different
dependence relations, and different beneficiaries, and they may produce similar
spectral attenuation.

A buffer placed at the intermediate actor’s viability relieves pressure while
leaving the upstream mechanism intact, and it positions the buffer’s supplier as
a controller of the intermediate actor’s realization conditions. A buffer placed
at the upstream mechanism alters the conditions that generated the pressure and
concentrates the cost on the upstream actor. A buffer placed at the downstream
participant protects that participant without addressing either prior relation.
A buffer placed at the intermediate actor’s alternatives acts on the quantity
Thesis ? identifies as decisive, since a participant seeking
a threshold is indifferent among routes that meet it.

These are distributive choices, and the formal result ranks none of them. The
paper therefore treats buffer evaluation as requiring the four-part standard of
Thesis ?, and it makes no institutional recommendation.

7. Diagnostic Edge States and Global Arrangements

This section establishes the paper’s edge-level dependency and global
comparison domain. Its objective is to preserve baseline sensitivity,
three-valued uncertainty, and joint feasibility before any causal link or
network path is constructed.

| >p0.20

p0.24
X
p0.20

Object	Primitive record	Additional warrant
Edge row	Complete arrangement, admitted baseline, standing, mechanism,
capability comparison, benefit-through witness	P005-compatible diagnostic
construction	$1,0,?$
Total downstream screen	Upstream row, downstream target, baseline pair	Coherent mechanism intervention, global compatibility, material total causal
contrast	supported, rejected, unresolved
Propagation link	Positive total-effect screen and typed intermediate state	Coherent stochastic mediator intervention, time order, material path
identification or bounds	supported, rejected, unresolved
Realized open cascade	Time-ordered edge and link records	Independent
validation of every constituent and declared descendant attribution	supported, defeated, indeterminate
Expected cascade	Finite type system and offspring kernel	First-moment
model, open horizon, controlled interference, kernel estimation	Conditional
mathematical consequence
Candidate buffer	Comparable buffered and reference regimes	Causal modifier
contrast, complete edge vocabulary, displacement audit	Attenuating, null,
amplifying, unresolved

Table. Analytical Objects and Evidence Requirements. Each row identifies a
distinct inferential object; movement downward requires the preceding objects
and the additional evidence shown. The table organizes claims and supplies no
evidence.

Table 2 prevents a common compression: an observed
network, an audited edge, a causal link, and an expected cascade are different
research objects. Threshold and cascade models demonstrate that aggregate
paths can depend sensitively on heterogeneous response rules and topology
(Granovetter, 1978; Watts, 2002). Models of complex contagion
further show that reinforcement and bridge structure can change diffusion
(Centola & Macy, 2007); an online experiment establishes a topology effect
for one health-behavior setting (Centola, 5996). These works discipline
the cascade vocabulary. They provide no exploitation diagnosis for the present
model.

An oriented edge position

$$u=(X\leftarrow Y,d_u,t,\omega_u)$$

specifies a candidate beneficiary $X$, an affected participant $Y$, a
generative domain $d_u$, time $t$, and a complete edge-diagnostic
specification $\omega_u$. A downstream position
$v=(Y\leftarrow Z,d_v,t+2,\omega_v)$ shares $Y$ in a different role.
Temporal placement alone does not make $v$ a causal descendant of $u$.

The inherited edge diagnostic evaluates a focal complete arrangement relative
to independently admitted comparison arrangements. For one resolved row, its
binary substantive targets are baseline admissibility $\Lambda^*$,
participant standing $\mathsf S^*$, an actor-linked mechanism
$\mathsf M^*$, material capability disadvantage $\mathsf D^*$, and a
typed benefit-through witness $\mathsf W^*$. The superscript distinguishes
these model-relative targets from the three-valued research statuses used to
assess them. The current paper uses the components without reopening their
normative sufficiency.

Fix a pre-intervention history $H_{t^-}=h$, a finite horizon $0{:}T$, and a
family $\boldsymbol\Omega_{0:T}(h)$ of complete dynamic arrangements. Each
arrangement specifies actors, institutions, resources, transition laws,
interference, constitutive rules, and benefit maps. For every edge $e$ and
stage $s$, let

$$\pi_{e,s}:\boldsymbol\Omega_{0:T}(h)\longrightarrow\mathfrak R_{e,s}$$

be a restriction to its edge-local arrangement. An admitted baseline pair
$(b_u,b_v)$ has the binary model-relative compatibility target

$$\Comp^*_{u,v,t}(b_u,b_v)=1
\quad\Longleftrightarrow\quad
\exists\boldsymbol\omega\in\boldsymbol\Omega_{0:T}(h):
\ \pi_{u,t}(\boldsymbol\omega)=b_u,
\ \pi_{v,t+2}(\boldsymbol\omega)=b_v.$$

Its distinct research audit is

$$\widehat{\Comp}_{u,v,t}(b_u,b_v)\in\Vthree.$$

The audit equals $1$ when an adequate construction supports or exhibits a
joint witness, $0$ when an adequate argument establishes joint
infeasibility, and $?$ when the existential target remains unresolved.

Separate technical feasibility of $b_u$ and $b_v$ therefore leaves joint
compatibility open. The same indivisible resource, institutional power, or
actor position cannot silently occupy inconsistent locations in a path-level
comparison.

For a fully specified downstream arrangement $r_v$ and admitted row $b_v$,
define the model-relative substantive target

$$D^*_{v,b_v}(r_v)

\mathbf 1!\left{
\Lambda^*_{v,b_v}
=\mathsf S^*_{v,b_v}
=\mathsf M^*_{v,b_v}
=\mathsf D^*_{v,b_v}
=\mathsf W^*_{v,b_v}
=1
\right}
\in{0,1}.$$

Its research audit is

$$\widehat g_{v,b_v}(r_v)\in\Vthree:={1,0,?},$$

where $?$ records unresolved standing, mechanism, capability comparison,
witness, admission, measurement, or identification. An unresolved audit does
not assign $D^*=0$.

The distinction in Definition ? separates ontic variation
within the declared model from evidence about that variation. A family of
targets may be required when evaluative disagreement is constitutively plural.
The binary target is then one specification-relative member rather than a
privileged hidden truth.

8. Staged Causal Structure and Intermediate States

This section constructs the causal object that connects two edge positions.
It defines the intervention, temporal stages, intermediate state, necessary
total-effect screen, and required intermediate-actor path, with audit and
causal dependencies kept distinct.

Figure 1. Time-Unfolded Propagation and Audit Structure. Solid arrows display the proposed causal sequence; the upper row lists research conditions rather than physical causes. $B$ denotes a candidate regime modifier. The diagram is an agent-added analytical construction and contains no empirical result.

Figure 1 makes the intervention target explicit.
The exposure is an actor-linked mechanism, rule, policy, access condition, or
complete arrangement arm. It is never an intervention on the audit label or on
the evaluative conjunction itself.

Let $A_{u,t}\in{1,0}$ select the focal upstream mechanism and a predeclared
feasible replacement within two complete global arrangements. The focal arm
has a supported upstream row. Define the potential intermediate state

$$L_{Y,t+1}(a)

\left(
\mathsf K_Y(a),\Sigma_Y(a),
\mathcal R_Y^{\mathrm{feas}}(a),N_Y(a),C_Y^E(a),Q_Y(a)
\right),$$

where $\mathsf K_Y$ is enriched effective generative capability,
$\Sigma_Y$ is an optional declared viability coordinate,
$\mathcal R_Y^{\mathrm{feas}}$ is a feasible-response correspondence,
$N_Y$ records accessible cooperative, supportive, adaptive, or exit paths,
$C_Y^E$ records capacity and opportunity for candidate appropriative
responses, and $Q_Y$ records their attainable typed return. A response
$R_{Y,t+1}(a)$ is selected through a declared kernel conditional on
$L_{Y,t+1}(a)$ and pre-treatment history $h$.

The scalar $\Sigma_Y$ describes a restricted survival-mediated subtype only
after its domain, order, and threshold are defended. Capability, bargaining
position, alternatives, opportunity, and return can change without crossing a
single viability threshold.

The two exposure arms are coherent complete arrangements; the baseline pair is
compatible; pre-treatment history excludes descendants of $A_{u,t}$; the
downstream domain, carrier, horizon, admissibility rule, capability order,
materiality schedule, and benefit types are fixed or connected by a defended
transport map; and the exposure mapping, affected neighborhood, anticipation,
spillovers, and descendant-attribution rule are declared. Identification uses
consistency, positivity and exchangeability, a justified alternative, or
explicit bounds.

These requirements follow causal-inference work on interference, contagion
paths, and exposure mappings (Hudgens & Halloran, 2008; Ogburn & VanderWeele, 2014; Aronow & Samii, 2017).
They also respond to the generic confounding of influence, homophily, and
covariate effects in observational networks
(Aral et al., 2009; Shalizi & Thomas, 2011). The references discipline the
research design; they do not identify the present estimand in any dataset.

For a compatible admitted pair $(b_u,b_v)$, define

$$\tau_{u\leadsto v}^{b_u,b_v}(h)

\mathbb E!\left[
D^*_{v,b_v,t+2}(1)-D^*_{v,b_v,t+2}(0)
\mid H_{t^-}=h
\right].$$

Given a predeclared materiality threshold $\eta_P\geq0$, let
$\Evid_\tau\in\Vthree$ equal $1$ when adequate evidence or a valid bound
supports $\tau_{u\leadsto v}^{b_u,b_v}(h)>\eta_P$, equal $0$ when it
supports the complementary inequality, and equal $?$ when intervention,
target, common support, identification, or materiality remains unresolved.
Let $\mathsf{Val}_{g_v}\in\Vthree$ record whether the downstream P005
construction and measurement connect evidence in both arms to one stable
substantive target. This validity field does not require the downstream target
to equal $1$ in both arms.

Let the strong conjunction $\wedge_3$ on $\Vthree$ return $1$ when all
inputs are $1$, $0$ when at least one prerequisite is adequately rejected,
and $?$ otherwise. The baseline-pair total-effect screen is

$$\widehat t_{u\leadsto v}^{b_u,b_v}

\widehat g_{u,b_u}
\wedge_3\widehat{\Comp}{u,v}
\wedge_3\App{A_u}
\wedge_3\App_{D_v^*}
\wedge_3\mathsf{Val}{g_v}
\wedge_3\Evid{\tau}.$$

Writing
$ g_v=( g_v,b_v(1),
g_v,b_v(0))$, retain the full total-effect profile

$$\Pi^T_{u\leadsto v}(h)

\left\langle
b_u,b_v,\widehat{\Comp},\widehat g_u,
\App_{A_u},\App_{D_v^*},\mathsf{Val}_{g_v},
\widehat{\mathbf g}v,\Evid_\tau,\widehat t,
\mathcal E,\mathcal U
\right\rangle{(b_u,b_v)},$$

where $\mathcal E$ and $\mathcal U$ record evidence and uncertainty. A
positive total-effect screen remains insufficient for the propagation label.

Let $D^*_{v,b_v}(a,l)$ denote the downstream target under exposure $a$ and a
coherent intervention setting the intermediate state to $l$. Draw
$\widetilde L_Y(a)$ from the declared conditional distribution of
$L_{Y,t+1}(a)$ given $h$. The proposed path contrast is

$$\iota_{u\leadsto v}^{L;b_u,b_v}(h)

\mathbb E!\left[
D^*_{v,b_v}!\left(1,\widetilde L_Y(1)\right)
-D^*_{v,b_v}!\left(1,\widetilde L_Y(0)\right)
\mid H_{t^-}=h
\right].$$

Causal-mediation methodology separates the definition of an effect from its
identification, estimation, and sensitivity analysis
(Imai et al., 2010). That general discipline is the relevant antecedent
here. Definition ? is an agent-added stochastic
interventional proposal and is not a formula attributed to that source.

A positive total contrast in Definition ? does not identify
Definition ?. The path contrast requires coherent intervention
semantics for the relevant component, temporal priority, mediator–outcome
confounding control or bounds, and an adequate interference model.

Fix a predeclared path-materiality threshold $\eta_L\geq0$. Let
$\Evid_\iota\in\Vthree$ equal $1$ when adequate evidence or a valid bound
supports $\iota_{u\leadsto v}^{L;b_u,b_v}(h)>\eta_L$, equal $0$ when it
supports the complementary inequality, and equal $?$ when the mediator
intervention, path identification, or materiality remains unresolved. The
final baseline-pair propagation audit and profile are

$$\widehat p_{u\leadsto v}^{b_u,b_v}(h)
&=
\widehat t_{u\leadsto v}^{b_u,b_v}(h)
\wedge_3\Evid_\iota,
\
\Pi^P_{u\leadsto v}(h)
&=
\left\langle
\Pi^T_{u\leadsto v}(h),\Evid_\iota,\widehat p
\right\rangle_{(b_u,b_v)}.$$

Every admitted baseline pair remains in the report; an unreported aggregation
rule cannot create an unqualified verdict.

The total-effect screen and the intermediate-actor path perform different
work. A common mechanism can directly cause both edge rows, producing
$\tau>\eta_P$, while leaving $L_Y(1)=L_Y(0)$ and hence
$\iota=0$. Such a case passes the total-effect screen and fails the proposed
propagation audit. A survival-mediated subtype additionally requires
a predeclared material contrast such as

$$\Sigma_Y(1)<\underline\Sigma_Y\leq\Sigma_Y(0).$$

That inequality neither defines general propagation nor establishes a positive
downstream effect.

9. Response-Kernel Decomposition and Sign Conditions

This section derives a finite special case that locates the total-effect sign in
changes to response probabilities. The derivation proceeds from a common
response support and invariant downstream map to an illustrative selection
model, with every restriction stated before interpretation.

The response set
$\mathcal R_Y={r_1,\ldots,r_q}$ is finite and has common support under both
exposure arms. For each arm $a$ and response $r$, define the potential-outcome
conditional kernel

$$d_{a;v,b_v}(r)

\Pr!\left(
D^*_{v,b_v,t+2}(a)=1
\mid R_{Y,t+1}(a)=r,H_{t^-}=h
\right)$$

and assume response sufficiency:
$d_{a;v,b_v}(r)=d_{v,b_v}(r)$ for both arms. Thus every
downstream-relevant direct exposure path is absorbed into the response type;
any remaining direct path invalidates the identity below or requires an
arm-indexed kernel. An interventional reading

$$d_{v,b_v}(r)

\Pr!\left(
D^*_{v,b_v,t+2}=1
\mid \operatorname{do}(R_{Y,t+1}=r),H_{t^-}=h
\right)$$

requires further composition and identification assumptions for the mediator.
Let $\pi_a(r)=\Pr(R_{Y,t+1}(a)=r\mid h)$.

Under Assumption ?, the arm-specific downstream probability
and total downstream contrast satisfy

$$p_a
&=
\Pr(D^*_{v,b_v,t+2}(a)=1\mid h)

\sum_{r\in\mathcal R_Y}d_{v,b_v}(r)\pi_a(r),
\
\tau_{u\leadsto v}^{b_u,b_v}(h)
&=
\sum_{r\in\mathcal R_Y}
d_{v,b_v}(r)\bigl[\pi_1(r)-\pi_0(r)\bigr].$$

Partition the downstream probability under each arm by the finite response
set. The law of total probability gives
$p_a=\sum_r d_{a;v,b_v}(r)\pi_a(r)$; response sufficiency replaces the
arm-indexed kernel with $d_{v,b_v}(r)$, yielding
Equation (2). Subtract the $a=0$ expression from the
$a=1$ expression to obtain Equation (3). The proof is
algebraic. Interpreting $d$ as an intervention on response requires the
additional assumptions stated in Assumption ?.

Suppose
$\mathcal R_Y=\mathcal R_Y^E\mathbin{\dot\cup}\mathcal R_Y^{\bar E}$, with
$d(r)=1$ on $\mathcal R_Y^E$ and $d(r)=0$ on
$\mathcal R_Y^{\bar E}$. Then

$$\tau_{u\leadsto v}^{b_u,b_v}(h)

\pi_1(\mathcal R_Y^E)-\pi_0(\mathcal R_Y^E).$$

Membership in $\mathcal R_Y^E$ still requires an independently resolved
downstream row. Responses outside that set may be harmful, dominating, or
otherwise objectionable while failing the declared generativity-exploitation
target. Proposition ? and Corollary ?
decompose the necessary total-effect screen only; neither result supplies the
path evidence required by Definition ?.

Consider the illustrative two-class selection model

$$p_a

\ell!\left(
\alpha+\beta v_Y(a)-\eta n_Y(a)
+\kappa c_Y^E(a)+\zeta q_Y(a)
\right),$$

where $\ell:\R\to(0,1)$ is strictly increasing; $v_Y$ is a declared vulnerability or
viability deficit; $n_Y$ is accessible non-appropriative response
availability; $c_Y^E$ is practical capacity and opportunity for candidate
appropriative responses; $q_Y$ is attainable typed return; and
$\beta,\eta,\kappa,\zeta>0$. With
$\Delta x=x(1)-x(0)$,

$$\operatorname{sgn}(p_1-p_0)

\operatorname{sgn}!\left(
\beta\Delta v_Y-\eta\Delta n_Y
+\kappa\Delta c_Y^E+\zeta\Delta q_Y
\right).$$

Subtract the two linear indices. Strict monotonicity of $\ell$ preserves their
order, which yields the stated sign equality.

Proposition ? formalizes a limited implication of the initiating
idea. Greater vulnerability and fewer alternatives can increase the modeled
downstream probability. Changes in capacity, opportunity, and return can
offset or reverse that pressure. For example, with
$\beta=1$, $\kappa=3$, $\Delta v_Y=1$,
$\Delta c_Y^E=-1$, and the remaining changes equal to zero, the index change
is (-2). An upstream loss can increase need while removing the practical
means of producing the downstream target.

The coefficient signs, variables, and link are empirical hypotheses within a
restricted model. Network effects can alter incentives and adoption without
producing the capability relation at issue (Katz & Shapiro, 1994).
Financial-network models also show that connectivity can be stabilizing or
destabilizing depending on integration and shock magnitude
(Elliott et al., 2014; Acemoglu et al., 2015). These comparison models
reinforce the conditional sign; they supply no parameter values for
Proposition ?.

10. Open Cascades and Candidate Buffers

This section lifts one supported link into a restricted open-cascade
approximation. It defines realized and expected objects separately, derives the
first-moment recursion and subcritical resolvent, and states a limited
comparison between candidate buffer regimes.

A realized open cascade is a finite time-ordered path or branching family in
which every edge event occurs, every adjacent propagation audit is independently
supported under compatible global arrangements, and every downstream event has
event-level causal-descendant attribution under a predeclared scheme.
Observed events combined only with positive average link effects form an
evidentially supported probabilistic cascade; they do not establish that
the realized downstream events were caused by their proposed parents. One
resolved zero defeats the claimed path; one unresolved required constituent
makes it indeterminate. Causal feedback to an earlier edge changes the object
to a feedback cycle and lies outside this definition.

Definition ? is stricter than observing many edges in a dense
network. Threshold and contagion models offer useful formal ancestors for
heterogeneous transition and reinforcement
(Granovetter, 1978; Watts, 2002; Centola & Macy, 2007); the
present cascade also requires independent relational diagnoses and causal
links. The event-level attribution condition is an additional, explicitly
scheme-relative burden beyond a positive population-average contrast.

Let $\mathcal U={1,\ldots,p}$ be a fixed finite set of resolved edge types
and let $\mathbf Z_n$ be a row vector counting causally attributed edges by
type in generation $n$. The horizon precedes material feedback closure;
baselines are jointly compatible; collisions, multiple-parent causation, and
interference have a declared attribution rule; conditional first moments are
finite; and a fixed nonnegative kernel $K$ satisfies

$$\mathbb E[\mathbf Z_{n+1}\mid\mathbf Z_n]

\mathbf Z_nK.$$

An entry $K_{uv}$ is an expected number of type-$v$ child edges causally
attributed to one type-$u$ parent within this approximation. It is neither an
adjacency weight nor an observed transition frequency.

Under Assumption ?, for deterministic $\mathbf Z_0$,

$$\mathbb E[\mathbf Z_n]=\mathbf Z_0K^n.$$

Iterated expectation gives
$\mathbb E[\mathbf Z_{n+1}]=\mathbb E[\mathbf Z_n]K$. Induction from
$\mathbf Z_0$ yields the result.

Under Assumption ?, if the spectral radius satisfies
$\rho(K)<1$, then $K^n\to0$ and

$$\mathbb E!\left[\sum_{n=0}^{\infty}\mathbf Z_n\right]

\mathbf Z_0\sum_{n=0}^{\infty}K^n

\mathbf Z_0(I-K)^{-1}.$$

For a finite matrix with $\rho(K)<1$, the Neumann series converges to
$(I-K)^{-1}$ and $K^n\to0$. Substitute
Proposition ? and exchange expectation with the nonnegative
partial sums; monotone convergence yields the identity.

The matrix lineage is standard nonnegative-matrix theory
(Seneta, 2006). Multitype branching theory supplies a broader
stochastic ancestor (Athreya & Ney, 1972). Proposition ?
concerns expected counts within the declared first-moment model. Almost-sure
extinction, survival probability, tail risk, and realized cascade size require
a fully specified offspring process and additional assumptions. When
$\rho(K)>1$, expected growth is possible only from types reaching a Perron
class with growth above one; this condition supplies no empirical prevalence
claim.

At the link level, a candidate buffer $B\in{1,0}$ has separate total and
intermediate-path attenuation contrasts

$$\Delta^{\mathrm{buf}}{\tau,u\leadsto v}
&=
\tau{u\leadsto v}(B=0)-\tau_{u\leadsto v}(B=1),\
\Delta^{\mathrm{buf}}{\iota,u\leadsto v}
&=
\iota{u\leadsto v}^{L}(B=0)-\iota_{u\leadsto v}^{L}(B=1).$$

A positive first value supports total-effect attenuation; a positive second
value supports attenuation of the declared intermediate path. Termination of
the paper’s propagation status requires adequate support that the buffered
total contrast is at or below $\eta_P$, the buffered path contrast is at or
below $\eta_L$, or another required audit field is resolved as zero.

Let $K_B$ and $K_0$ describe causally comparable buffered and reference
regimes with identical edge types, target definitions, baseline maps, horizon,
and descendant attribution. If

$$0\leq K_B\leq K_0
\quad\text{entrywise},$$

then $\rho(K_B)\leq\rho(K_0)$. If additionally $\rho(K_B)<1$, the buffered
regime has a finite expected cascade total under
Proposition ?.

Spectral-radius monotonicity for finite nonnegative matrices gives the first
inequality. The second statement follows from
Proposition ? applied to $K_B$.

The condition $K_B\leq K_0$ is a causal assumption or empirical result rather
than a definition of support, public provision, commons access, redistribution,
portability, or exit. A local reduction can shift burdens to omitted actors,
create a new edge type, or reduce the affected participant’s capability. The
proposition therefore supplies a conditional dynamic comparison and no policy
endorsement.

11. Countermodels and Empirical Identification

This section subjects the construction to negative and indeterminate cases and
then translates its dependencies into a bounded empirical protocol. The
countermodels expose which apparent cascades fail the causal, diagnostic,
compatibility, or scope requirements.

| >p0.18

p0.25
p0.29
X

Structure	Apparent pattern	Missing or contrary condition	Admissible result
Complete absorption	Positive upstream row followed by an unchanged
downstream relation	Redundancy, reserves, or support gives
$L_Y(1)=L_Y(0)$ on relevant coordinates, with no retained direct exposure
path	$\tau=0$; positive propagation rejected for the row pair
Common shock	Upstream and downstream rows occur in sequence	A prior
institutional shock causes both; intervention on the upstream mechanism leaves
the target unchanged	Observational association with $\tau=0$
Shared mechanism without transmission	The coherent exposure changes both
edge-row probabilities	Direct branches reach the two rows while
$L_Y(1)=L_Y(0)$, so $\tau>\eta_P$ and $\iota=0$	Positive total-effect
screen; propagation rejected
Expanded alternatives	Upstream loss and timely cooperative support occur	$N_Y$ expands enough to reduce the downstream target probability	Null or
negative contrast
Lost response capacity	Vulnerability rises while practical capacity for the
candidate response falls	The capacity term offsets the vulnerability term	Negative contrast is possible
Harm without benefit-through	$Y$’s response harms $Z$	$Y$’s specified
benefit is independent of $Z$’s affected capability state	Causal harm
transmission;
downstream GEX target $D^*=0$
Incompatible baselines	Both local comparisons appear favorable	The same
indivisible resource is required in incompatible positions	$\Comp^*=0$, $\widehat{\Comp}=0$; no coherent path comparison
Unresolved downstream row	A plausible downstream mechanism is observed	Standing, materiality, or benefit-through remains unresolved	Propagation
audit $?$
Dense simultaneous network	Many related edges appear together	Temporal
order and descendant attribution are absent	Network occurrence without an
open cascade

Table. Propagation Countermodels and Diagnostic Outcomes. The cases are
formal or hypothetical structures, not empirical classifications. A downstream
harm counts as generativity exploitation only after an independent edge
diagnosis.

Table 3 shows why two positive-looking relations cannot
by themselves establish propagation. The common-shock case is especially
important because homophily, selection, and shared causes can mimic influence
in network data (Aral et al., 2009; Shalizi & Thomas, 2011). The capacity
case also protects agency: similarly constrained actors can choose different
paths, and an average contrast supplies no deterministic prediction of an
individual response.

An empirical study should proceed in dependency order:

select a restricted domain with observable actor roles, mechanisms, timing, response opportunities, and downstream relations;
construct upstream and downstream baseline-relative edge profiles before examining the desired propagation result;
embed local comparisons in compatible global arrangements and defend any diagnostic-transport map;
define the upstream mechanism intervention, treatment versions, and a network exposure mapping;
measure or bound capability, optional viability, alternative availability, response capacity, and attainable return at the declared lag;
specify the downstream substantive target and its research audit separately, and validate that both arms remain connected to that target;
address anticipation, selection, time-varying confounding, missingness, interference, and changing topology;
estimate or bound the necessary total-effect screen, then identify or bound the required intermediate-actor path under its stronger assumptions;
evaluate absorbed, common-shock, shared-mechanism, harmful, and incompatible-baseline negative cases; and
report every admitted baseline pair, uncertainty reason, and displaced third-party edge.

Randomized exposure mappings can support causal estimands under declared
interference structures (Aronow & Samii, 2017); partial-interference
and contagion-path frameworks provide additional designs
(Hudgens & Halloran, 2008; Ogburn & VanderWeele, 2014). Evolving roles and
institutional relations may defeat these designs. Historical comparison,
partial identification, simulation, or explicit indeterminacy can then be more
honest than a point estimate.

12. Open Questions Across Registers

This section collects the questions the paper leaves unresolved, organized by
the register in which each would be answered. Its objective is to separate
questions that further formal work could settle from questions requiring
empirical evidence, normative argument, or institutional design, and to mark
which of them the paper’s own theses have made pressing.

The four formal open problems stated in Section 14 concern
compatible global comparison families, interference-aware path identification,
branching exit conditions, and buffer completeness. The questions below are of a
different kind and are not reducible to them.

12.1 Conceptual and Formal Questions

This subsection lists questions about the construction’s objects.

Section 4 locates transmission in a portfolio effect, whereby a
contraction confined to one generative domain lowers a participant’s capacity to
continue in general. Which aggregation structures over domains produce this
behavior, which permit substitution between domains, and what evidence would
distinguish them for a given participant?

Thesis ? characterizes the intermediate actor as seeking a
continuation threshold. Under what conditions does a constrained response
persist beyond the point at which the threshold is met, converting a
transmission step into a stable practice? A persistence result would bound the
mitigation available under Thesis ?.

Section 4 records that the existence of a capability contraction
may be accessible while its magnitude remains unidentified. Which propagation
conclusions survive on existence evidence alone, and can a useful ordinal
propagation statement be defined without a cardinal contrast?

12.2 Normative Questions

This subsection lists questions the paper’s theses raise and do not settle.

Thesis ? establishes that constraint mitigates without
extinguishing the intermediate actor’s burden, and leaves the function
unspecified. What relation should hold between the availability of
non-appropriative alternatives and the degree of mitigation, and does complete
elimination of alternatives extinguish the burden or merely minimize it?

Thesis ? proposes the propagation contrast as a measure of
structural contribution. When several upstream actors contribute to the same
downstream relation, how should their contrasts be combined, and does the
resulting apportionment behave acceptably under overdetermination, where each
contribution would suffice alone?

The downstream participant is affected by a structure it did not enter and
cannot alter. Does a propagation finding generate any claim held by that
participant against the upstream actor, given that the two stand in no direct
relation, and does the answer depend on the mediating actor’s culpability?

Thesis ? establishes that distributive outcome and relational
procedure are independent and that a complete assessment reports both. It
supplies no rule for cases in which they conflict, and whether a general rule
exists remains open.

12.3 Political-Economic and Institutional Questions

This subsection lists questions about intervention and governance.

Thesis ? holds that existing instruments target manifestations in
place of couplings, while conceding that couplings are counterfactual and
frequently unidentified. Can a reporting or liability instrument be designed
that is sensitive to transmission structure without requiring identification of
a causal contrast, and what would it require parties to record?

Under polycentric governance, which decision center is positioned to alter which
coupling, and what determines whether an intervention at one level displaces
pressure to a level outside its jurisdiction?

The propagation estimand presupposes a governance form in which the upstream
mechanism is a locus of decision. What replaces it where terms emerge from many
uncoordinated exchanges and no single actor’s practice constitutes the
mechanism?

The intervention question asks whether the coupling between one position’s gain
and another’s capability contraction can be broken while preserving the
generativity at issue. No candidate intervention in this paper has been shown
to satisfy both halves of that criterion.

12.4 Empirical Questions

This subsection lists what evidence would be needed and what currently exists.

No empirical case validates the proposed path, the sign of any response
parameter, the offspring kernel, or any candidate buffer. The verified evidence
in Section 7 establishes an association between
lead-firm practices and supplier-level conditions in one sector; it leaves the
intervention, the edge diagnoses, the compatibility of arrangements, and the path
condition entirely open.

The priority questions are whether a restricted domain exists in which upstream
mechanisms admit credible variation; whether intermediate capability, viability,
alternatives, and response capacity can be measured at a declared lag; whether
the sign decomposition’s offsetting terms can be separately estimated, since the
model permits an upstream contraction to reduce downstream probability by
removing practical capacity; and whether negative cases can be found, since a
framework that never returns a negative finding in practice would be
unfalsifiable regardless of its formal capacity to do so.

13. Limits and Revisable Research Program

This section consolidates the paper’s contribution, limitations, open
obligations, and defeat conditions. It closes at the level of a conditional
causal framework and reserves feedback, responsibility, and institutional
evaluation for separate research.

The construction has four limited contributions. First, it distinguishes an
edge audit, a total-effect screen, an intermediate-actor propagation link, and
an open cascade. Second, it carries complete arrangements, admitted baselines,
diagnostic transport, and three-valued uncertainty into the network model.
Third, it derives a finite response-kernel identity whose total-effect sign
depends on pressure, alternatives, capacity, and return. Fourth, it derives
first-moment open-cascade and spectral attenuation results under explicit
finite-matrix assumptions.

The model retains substantial limitations. P005 edge rows remain contestable
and baseline-sensitive. Global compatibility can be difficult to establish.
The binary target may inadequately represent plural evaluative specifications.
Social structures may permit bounds or historical comparisons while resisting
a manipulable exposure. Intermediate states can be post-treatment,
multidimensional, and partially observed. Network interference and adaptive
topology can invalidate the finite response and branching restrictions. A
scalar viability projection can erase autonomy, direction, exit, and
nonfungible losses. The current corpus contains no empirical case validating
the proposed path, sign model, offspring kernel, or buffer.

Develop a constraint-sensitive method for constructing or bounding jointly
feasible global arrangements from baseline-relative edge comparisons without
assigning scarce resources or institutional positions inconsistently.

Identify or bound the total and stochastic-interventional path contrasts when
actor roles, network exposure, mediator–outcome confounding, and topology
change over time.

Specify observable conditions marking the failure of the open-cascade
approximation through path collision, repeated actors, feedback closure,
strategic adaptation, saturation, or incompatible descendant attribution.

Evaluate candidate buffers in a complete edge vocabulary that records newly
created dependency, displaced burdens, capability effects, beneficiary change,
and unequal access to the buffer.

Several questions remain deliberately separate. Feedback closure, cycle
stability, distribution across a closed set of participants, and systemic traps
require a cycle model; Section 6 defeats one inference
about reciprocal role occupancy without supplying that model. Recovery and
institutional intervention evaluation require lifecycle criteria. Legal
liability, remedy, and the doctrinal treatment of duress require jurisdictional
arguments that Section 6 does not attempt: its claims
concern moral assessment and forward-looking obligation. AI can intensify or
reveal the proposed mechanism, while the definition itself contains no AI
requirement.

The paper’s normative content is confined to the five theses and their stated
dependencies. It assigns no liability, recommends no institution, and classifies
no observed relation.

The framework should be narrowed or abandoned if edge rows cannot be specified
without circularity, upstream mechanisms admit no coherent contrast, local
baselines cannot be embedded in compatible global arrangements, target meaning
cannot be transported across arms, or intermediary descriptions add no
discriminating content beyond a post hoc narrative. It also loses novelty if
verified antecedents already perform the same integration without the new
vocabulary. Current sources establish relevant traditions and constraints,
not a literature-wide originality result.

The resulting position is conservative. Generativity-exploitation propagation
is a coherent candidate causal relation when independently evaluated edges are
connected by compatible global counterfactuals and a material positive
total downstream contrast together with a supported material path through the
shared intermediate actor. The same formalism preserves null, negative, and
unresolved outcomes. Its practical value may lie in showing precisely where a
proposed cascade lacks a coherent baseline, causal intervention, downstream
diagnosis, path warrant, event-level descendant attribution, or complete
account of affected actors.

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Abstract

Document Status, Preparation, and Reuse

1. Introduction

2. Analytical Scope and Propagation Position

2.1 Three Transmission Configurations

3. The Transmission Problem

3.1 Secondary Exploitation as a Phenomenon

3.2 Subject-Level Continuation as the Transmitting Quantity

3.3 Existence and Magnitude as Separate Problems

3.4 Failure of Composition Across Edge Diagnoses

3.5 The Modal Gap Between Pressure and Necessitation

3.6 Requirements on a Propagation Account

4. Transmission Traditions and Rival Models

4.1 Threshold, Cascade, and Complex Contagion

4.2 Systemic Risk and the Ambiguity of Connectivity

4.3 Causal Inference Under Interference

4.4 Structural and Anonymous Exploitation

4.5 Comparative Summary of Traditions

5. Agency, Constraint, and Responsibility Under Transmission

5.1 Pressure Without Necessitation

5.2 Self-Continuation as the Motivating State

5.3 Constraint, Mitigation, and the Non-Transfer of Wrongfulness

5.4 The Circulation Argument and Its Defeat

5.5 Separation of Outcome and Procedural Registers

5.6 Forward-Looking Upstream Responsibility

5.7 Attenuation Without Justice

5.8 Dependence of the Framework on the Theses

6. Political Economy of Transmitted Pressure

6.1 Squeeze Structures in Production Chains

6.2 The Provider, Adopter, and Practitioner Configuration

6.3 Chain Governance and the Location of Coordinating Power

6.4 The Five-Position System and the Intervention Question

6.5 Level Mismatch Between Relations and Mediation Capacity

6.6 Buffer Placement as a Distributive Decision

7. Diagnostic Edge States and Global Arrangements

$$D^*_{v,b_v}(r_v)

8. Staged Causal Structure and Intermediate States

$$L_{Y,t+1}(a)

$$\tau_{u\leadsto v}^{b_u,b_v}(h)

$$\widehat t_{u\leadsto v}^{b_u,b_v}

$$\Pi^T_{u\leadsto v}(h)

$$\iota_{u\leadsto v}^{L;b_u,b_v}(h)

9. Response-Kernel Decomposition and Sign Conditions

$$d_{a;v,b_v}(r)

$$d_{v,b_v}(r)

$$p_a&=\Pr(D^*_{v,b_v,t+2}(a)=1\mid h)

$$\tau_{u\leadsto v}^{b_u,b_v}(h)

$$p_a

$$\operatorname{sgn}(p_1-p_0)

10. Open Cascades and Candidate Buffers

$$\mathbb E[\mathbf Z_{n+1}\mid\mathbf Z_n]

$$\mathbb E!\left[\sum_{n=0}^{\infty}\mathbf Z_n\right]

\mathbf Z_0\sum_{n=0}^{\infty}K^n

11. Countermodels and Empirical Identification

12. Open Questions Across Registers

12.1 Conceptual and Formal Questions

12.2 Normative Questions

12.3 Political-Economic and Institutional Questions

12.4 Empirical Questions

13. Limits and Revisable Research Program

References

$$p_a
&=
\Pr(D^*_{v,b_v,t+2}(a)=1\mid h)