Toward a Pathology of Value Circulation - A Typed Lifecycle Diagnostic

Posted on 2026-08-26 In Philosophy , Political Economy Views: Disqus: Word count in article: 9.2k Reading time ≈ 34 mins.

Abstract

One recurrent inferential risk in arguments about value circulation is movement
from an observed stock, flow, blockage, or return to a judgment about the
condition of a social system. This paper proposes a more restrained diagnostic
architecture. Within this architecture, a complete circulation report requires
double localization: first in a typed lifecycle of conditions,
generation, value, recognition, transmission, allocation, feedback, and later
conditions; then in an evaluative layer that
separates functional pathology, capability effect, harm, injustice,
exploitation, responsibility, and legal wrong. The proposal preserves a
researcher-origin seven-type taxonomy while identifying the lifecycle graph,
formalization, countermodels, and manuscript architecture as later
reconstructions. Formally, a fixed-environment deletion of a component weakly
contracts the supported path set and does so strictly whenever a supported path
uses that component. Material loss at the declared target additionally requires
the absence of an adequate substitute. A consequence for later conditions
requires an identified return coordinate and a
coordinate-specific monotone update relation. Two countermodels separate
throughput from regenerative reach: arbitrarily high activity can coexist with
absent return to later generative conditions, while zero current outward flow
can preserve an enforceable future-use route. Four further constructed
configurations involving adequate substitution, privacy- or ecology-preserving
restriction, constitutive recognition, and cross-carrier burden show how the
diagnostic can return negative, mixed, and unresolved results. The paper remains
an analytic and formal proposal. Empirical prevalence, a scalar measure of
circulation health, and a theory of injustice remain open research tasks. Its
contribution is an analytic instrument and a set of stopping rules whose
empirical usefulness, normative significance, and originality remain open to
testing.

Keywords: value circulation; generative justice; lifecycle

Discussion Paper Note

This paper is a preliminary discussion paper intended to share an evolving idea
and invite further dialogue, criticism, revision, and independent development.
Its definitions, distinctions, and formal constructions remain provisional.
Circulation across scholarly and practical communities is part of the purpose
of releasing the manuscript at this stage.

The author treats the viewpoints, concepts, and lines of reasoning presented
here as contributions to a shared field of inquiry. Similar or related ideas
may have appeared in other intellectual, cultural, and disciplinary traditions.
The manuscript therefore states its known antecedents, separates
researcher-origin material from later formal reconstruction, and leaves
historical priority open pending a systematic originality review.

The arguments should be understood as provisional and historically situated.
Readers are encouraged to question, test, revise, extend, reinterpret, or
independently develop the ideas presented here. Where appropriate,
acknowledgment of this paper as one point of encounter in the development of a
related idea is appreciated. Such acknowledgment records an intellectual route;
the ideas themselves remain available for criticism, revision, and independent
development.

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This page consolidates the manuscript’s publication status, licence,
development disclosure, research-programme relation, and suggested citation.

Status.
This working draft records an evolving stage of the author’s position and is
circulated for discussion. Definitions, section structure, formal statements,
and numbering remain subject to revision. Empirical prevalence, moral
evaluation, legal analysis, and policy design remain outside its present scope.

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Except where otherwise indicated, copyright 2026 Wanhong Huang. This work is
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International License (CC BY-NC 4.0). Subject to its terms, the licence permits
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Statement on the use of language models.
The exploratory discussions and preparation of this paper involved OpenAI’s
Codex. Codex supported exploratory dialogue, formal reconstruction, source
discovery followed by website verification, argumentative criticism, and
drafting in . The author selected the research questions, directed and
approved the theoretical commitments and epistemic status of the claims, and
bears sole responsibility for the manuscript, including its definitions,
formal constructions, taxonomy, arguments, conclusions, and errors. Authorship
credit remains with the human author. The access level and claim limit for every
cited source are recorded in the accompanying literature audit.

Related research programme.
This paper is project P015 and the first promoted paper in the research-stage
Generative Injustice programme. Earlier P005–P014 manuscripts provide
revisable companion analyses of generativity exploitation, propagation,
identification, cycles, commons, expansion, dependency, AI mediation, recovery,
and legal relations. They function as related, revisable project states; the
present argument states its own premises.

Suggested citation.
Huang, Wanhong. “Toward a Pathology of Value Circulation: A Typed Lifecycle
Diagnostic.” Working discussion paper, 2026.

1. Introduction

This section establishes the paper’s role, objective, and inferential boundary.
It first identifies the ambiguity in ordinary circulation language, then states
the double-localization proposal, its provenance, and its limited contribution,
and closes with the structure of the argument.

Circulation language compresses several questions that should remain separate.
A statement that “value circulates” may refer to production, exchange,
visibility, monetary payment, attribution, information, social recognition,
material support, or the renewal of conditions for later activity. The carrier
may be a person, group, organization, practice, ecosystem, or generation. The
value may be monetary, material, epistemic, expressive, recognitional,
ecological, or capability-related. The relevant horizon may cover one
transaction or several generations. These declarations distinguish the
incompatible readings that high and low circulation can otherwise support.

The paper addresses the following bounded question: how can a typed lifecycle
model distinguish candidate failures in generation, recognition, transmission,
allocation, feedback, and renewal while preserving alternative routes,
criterion-consistent retention, plural value, and the separation between functional and
normative judgment? The response is a double localization rule.

A proposed circulation diagnosis is doubly localized when it identifies
(i) the typed lifecycle component or configuration in which a declared
functional criterion is affected and (ii) the evaluative layer for which the
available evidence supplies an independent warrant.

Lifecycle localization distinguishes a condition, activity, value relation,
recognition mechanism, transmission or allocation relation, feedback path,
stock–flow configuration, and topology. Evaluative localization distinguishes
a functional anomaly from an effect on capability, harm, injustice,
exploitation, responsibility, and a legal wrong. Each evaluative localization
requires its own evidential warrant.

The genealogical basis is a seven-type taxonomy proposed by Wanhong Huang in a
research-note discussion dated 23 August 2026: missing conditions or
obstruction; recognition failure;
contamination of generativity; exploitation of generativity; appropriation of
produced value; interruption of a generative path; and absence of a circulation
route. The examples of unavailable organizational deployment and difficult
recognition of specialized research also belong to that researcher-origin
proposal. The English title, typed lifecycle, notation, expanded labels,
countermodels, audit method, and present architecture were developed through
AI-assisted reconstruction under the author’s direction. The author retains
responsibility for their use and revision. Bibliographic identities and the
bounded literature roles reported in Section 5 were checked
against linked journal, publisher, repository, or DOI pages on the same date.
This disclosure records provenance; evidential support and originality require
separate analyses.

The paper defends a deliberately limited position. A typed lifecycle can locate
candidate failures more precisely than an untyped flow metaphor. Under fixed
environmental assumptions, component deletion weakly contracts the supported
path set. Material target loss requires a separately declared adequacy rule and
the absence of an adequate substitute. Positive current throughput and positive
regenerative reach remain logically independent in both directions. These
results are elementary and conditional. Their contribution lies in inferential
discipline; their mathematics is elementary. Empirical frequency, moral
evaluation, legal rules, and policy recommendations remain outside the results.

Section 5 positions the proposal against verified
antecedents and states its attribution boundary. Section 6
defines the analytical vocabulary and preserves the seven-type genealogy.
Section 7 constructs the typed lifecycle in the order of
symbols, assumptions, transitions, stocks, recognition, paths, and observables.
Section 8 derives the conditional results.
Section 9 applies the diagnostic to six constructed
configurations. Section 10 specifies the evaluative layers and
stopping point. Section 11 records objections and defeat
conditions, and Section 12 states the remaining research
obligations and conservative conclusion.

2. Antecedent Positioning and Attribution Boundary

This section locates the proposal within a bounded set of verified literatures.
Its objective is to identify antecedent concepts, constrain attribution, and
clarify what each comparison can support. The discussion proceeds from the
named generative-justice corpus to circulation, valuation, reproduction,
commons, and model-transfer traditions.

Each bibliography entry includes a checked web location. Bibliographic identity
was verified for every item; position claims were limited to the metadata,
abstract, preview, repository text, or full text actually inspected. This
procedure verifies bibliographic identity at declared access levels;
interpretation and literature-wide originality require separate audits.

| @p0.19YY@

Literature cluster	Admissible role in this paper	Transfer limit
Generative justice	Bottom-up value circulation, unalienated plural value,
generator control, and nonlinear generative-justice modeling	The present
lifecycle taxonomy and formal diagnostic require separate attribution and an
originality audit
Capital circulation and reproduction	Distinctions among production,
circulation, realization, and reproduction	Transfer to a general conserved
measure of social value requires a separate argument
Valuation and commodity trajectories	Institutionally organized evaluation
and changing careers of valued objects	Regenerative return requires evidence
beyond movement and valuation
Social reproduction	Dependence of production on background reproductive
conditions	Reproduction and generativity remain distinguishable
analytical objects
Commons governance	Institutional diversity in common-pool resource
governance	Transfer beyond subtractable resources requires a new resource
ontology
Circular economy	Evidence of heterogeneous circulation vocabularies and
system boundaries	A social-value ontology and justice criterion require
separate arguments
Model-transfer methodology	Purpose-relative mapping, idealization, and
similarity discipline	Target-domain evidence requires explicit bridge
assumptions

Table. Verified antecedent roles and transfer limits

2.1 Generative-Justice Antecedent

This subsection establishes the nearest named antecedent and the associated
priority boundary. It summarizes only the roles supported by the verified
Eglash corpus and records the evidential status of an unlocated sentence from
the source discussion.

Eglash’s account of generative justice develops a bottom-up response to
alienation organized around the circulation of unalienated labor, ecological,
and expressive value (Eglash, 2016). The later mathematical toolkit
connects generative justice with value circulation, self-organization, and
nonlinear analysis (Eglash et al., 2017); work on basins of attraction places
attractor language within this program (Eglash & Garvey, 2014). Recent
work on computational reparations further emphasizes generator control and
circular value flow while describing its reported outcomes as primarily
micro- and meso-level (Eglash et al., 2024). These works supply
antecedents for the name
generative justice, plural circular value, generator control, and formal
or nonlinear modeling. Priority for these concepts belongs to the cited
antecedents.

The source discussion included a sentence attributed to Eglash concerning
diminished circulation in hydrological and sociological systems. Its exact
source and wording remain pending in the verified corpus, so the manuscript
reserves it for future source work. The cited works independently establish
circulation as a central feature of the generative-justice program. A close
precedent for the seven-type taxonomy, double localization, or their combination
remains an open literature question.

2.2 Circulation, Valuation, and Reproduction Traditions

This subsection supplies conceptual comparisons for the lifecycle stages. It
uses the sources as constraints on the proposal and keeps their distinct
objects and methods visible.

Marx’s analysis of the circulation process of capital and social reproduction
already prevents the identification of production with a completed circuit
(Marx, 2006). The present proposal addresses a distinct object:
heterogeneous social values across a typed lifecycle. Its borrowing is limited
to the discipline of distinguishing stages and conditions. Fraser’s account of production
as dependent on background conditions of social reproduction and care supplies
a further warning against treating visible production as a self-sufficient
process (Fraser, 2016). Generative renewal may include
maintenance and reproduction, while the terms remain analytically distinct
because generation can also diversify or transform what later activity makes
possible.

Appadurai’s account directs analysis toward commodity trajectories and the
politics through which value judgments attach to exchange and circulation
(Appadurai, 1986). Lamont’s comparative sociology of valuation and
evaluation emphasizes categorization, legitimation, heterarchies, and
institutional evaluative practices (Lamont, 2012). Together these
traditions constrain any simple picture in which independently given value
merely awaits accurate recognition. Section 7.5
therefore preserves detection, constitution, and hybrid semantics.

Ostrom’s comparative work documents diverse institutional arrangements for
governing common-pool resources (Ostrom, 1990). P015 takes this as a
prompt to examine how institutional arrangements shape routes and renewal. P015
formulates this transfer question as a separate development from Ostrom’s
result. The focal resource problems also warn against transferring subtractability to knowledge,
expression, or relational capability. Kirchherr, Reike, and Hekkert’s analysis of 114 circular-economy
definitions demonstrates substantial heterogeneity in the meaning and scope of
circularity and limited integration of social equity and future generations
(Kirchherr et al., 2017). Table 1 records these
admissible roles and limits. The table organizes the literature; originality
evaluation remains a separate audit.

2.3 Model-Transfer Discipline

This subsection fixes the status of the lifecycle model and its relation to
physical circulation. Its objective is to require explicit bridge assumptions
for conservation, substance identity, and evidential transfer.

Weisberg’s target-directed account of modeling makes the purpose of a model,
the features represented, the idealizations made, and the model–target
similarity relation explicit (Weisberg, 2013). That discipline is
especially important here. Water has physical conservation and transformation
properties under specified boundaries. Social value can be created, copied,
contested, constituted, consumed, degraded, or destroyed. The formal
construction below is therefore an open typed lifecycle. It contains sources,
sinks, use, loss, and conversion. Hydrological resemblance functions as a
purpose-relative analogy.
Material-flow analysis itself requires explicit system boundaries, levels, and
flow types (Fischer-Kowalski & ttler, 1998); that operational
discipline transfers here. Its physical ontology and conservation relations
remain confined to the source domain.

3. Analytical Vocabulary and Taxonomic Genealogy

This section defines the paper’s diagnostic objects and preserves their source
genealogy. It begins with the scope required for any application, then defines
generative circulation and candidate pathology, and finally maps the seven
source types to lifecycle loci and counterconditions.

A circulation inquiry has a scope specification

$$\Sigma=(\mathcal A,\mathcal K,\nu,\mathcal M,H;
a,\mathcal B;\chi,\vartheta;\mathcal I,\mathcal S;\mathcal U),$$

where $\mathcal A$ contains declared carriers, $\mathcal K$ value kinds,
$\nu$ an evaluative standpoint, $\mathcal M$ recognition mechanisms, $H$
an evaluation horizon, $a$ the focal arrangement, and $\mathcal B$ a
nonempty family of feasible comparison arrangements. The symbol $\chi$
denotes a functional criterion, $\vartheta$ records who selected it and under
which claimed authority, $\mathcal I$ declares admissible intervention
semantics, $\mathcal S$ fixes the searched substitute-route boundary, and
$\mathcal U$ supplies units or qualitative semantics for represented
variables.

The scope specification makes the selector of the functional criterion visible.
It also prevents a monetary flow, recognition count, ecological burden, and
capability change from entering a single quantity merely because each has been
called value.

Relative to $\Sigma$, generative circulation is the temporally extended
movement and transformation through which generated value, recognition,
material return, information, access, or another declared output helps sustain,
restore, diversify, or enlarge future realization conditions or effective
generative capabilities.

Production, movement, allocation, and renewal are distinct analytical roles.
A movement counts as generative circulation only through an identified relation
to later conditions under the declared horizon. This definition provides a
research target while leaving the necessity and desirability of return open.

A candidate circulation pathology is a supported degradation,
obstruction, capture, distortion, interruption, starvation, or closure affecting
a typed lifecycle component or configuration in focal arrangement $a$
relative to $(b,\chi,H)$, for some $b\in\mathcal B$, after substitutes in
$\mathcal S$, delays, criterion-consistent use or retention, and measurement
uncertainty have been considered.

The qualifier candidate records the normative loading of the word
pathology. A positive functional report means that a declared criterion
is materially impaired under a declared comparison. Moral authority and
wrongfulness require independent warrants.

For a component or configuration $z$ and $b\in\mathcal B$, let
$\mathsf{Stat}_{\chi}^{\Sigma}(z;b)\in{+,-,\pm,?}$. The value $+$ records
supported material impairment of $\chi$ in $a$ relative to $b$ under the
declared mechanism, intervention, and substitute boundary. The value $-$
records supported absence of that impairment under the same declarations. The
value $\pm$ preserves positive and negative component- or carrier-specific
statuses while an aggregation rule remains undeveloped. The value $?$ records
insufficient, incompatible, or unidentified premises. A profile is
baseline-sensitive when supported statuses differ across two members of
$\mathcal B$.

These statuses evaluate the declared candidate only. A negative status remains
local to the declared criterion, and a positive status reaches the functional
layer. Every further inference requires an independent bridge.

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Type	Source category	Lifecycle locus	Minimum diagnostic content	Central countercondition
I	Production blockage through missing conditions or obstruction	Conditions
and condition–activity transitions	Required resource, relation, permission,
or active blocking mechanism under a feasible comparison	Another viable
deployment route exists, or the condition is irrelevant
II	Recognition blockage	Value–recognition relation	Value
standpoint, recognition semantics, evidence channel, translation, and horizon	Alternative evaluative specification or constitutive difference
III	Generativity contamination	Activity, transition rule, incentive, or
feedback	Mechanism changing direction, objective, or process integrity	Change matches the declared process objective or focal specification
IV	Generativity exploitation	Capability across cycles	Capability effect
plus the separate standing, comparison, and benefit-through test	Depletion
alone; beneficiary-through or affected capability remains unsupported
V	Produced-value exploitation	Allocation, attribution, or appropriation	Contribution, entitlement, procedure, transfer, and beneficiary	Declared
gift, commons, contractual, or allocation rule matches the observed transfer;
its validity remains a later-layer question
VI	Generative-process interruption	Any essential temporal path	Removed
viable route, timing, substitutes, materiality, and target relevance	Delay or
rerouting preserves the relevant target
VII	Circulation-route absence	Transmission, feedback, renewal, or topology	Route, capacity, compatibility, access, and future-condition linkage	Retention, privacy, maintenance, incubation, or an ecological constraint preserves
viability

Table. Researcher-origin taxonomy and diagnostic translation

Table 2 preserves the source taxonomy through translation and
extension. Type I contains both condition deficiency and active obstruction
because the source proposal placed them together; applications should separate
them because their mechanisms and responses differ. Types IV and V retain the
researcher’s wording in the genealogy. In application, the functional stage should first report
capability depletion or output appropriation. The stronger term
exploitation is reserved for a separate diagnostic that includes
participant standing, an admissible comparison, affected capability, and a
benefit-through relation.

Those four exploitation conditions are imported from the author’s unpublished
companion project P005, an active and revisable theoretical draft whose
empirical validation remains pending. They delimit the exploitation coordinate;
P005 retains responsibility for their derivation and sufficiency.

The seven types overlap. An attribution rule can produce recognition failure,
appropriation, feedback starvation, and later capability contraction in one
case. Overlap is informative only when each label identifies an independently
specified mechanism. Exhaustiveness and mutual exclusion remain open
classification questions.

4. Typed Lifecycle Construction

This section constructs the formal instrument in a continuous order. It first
declares symbols and assumptions, then defines the temporal multigraph, an
optional typed stock–flow module, alternative recognition semantics, viable
paths, regenerative reach, and throughput. Each quantitative object is
conditional on operational semantics supplied by an application.

Table 3 groups the principal symbols by formal role. The final
column records the declaration that prevents a symbol from acquiring meaning
through notation alone.

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Symbol family	Formal role	Required declaration
$\Sigma$	Scope specification	Carriers, value kinds, standpoint, mechanisms, horizon, focal and comparison
arrangements, criterion and selector, interventions, substitutes, and semantics
$C,G,V,\widehat V$	Conditions, generative activity, value relation, and
assessment	Carrier association, temporal index, value ontology, and
observation status
$\mathcal L^\Sigma(x)$ and component maps	Typed temporal multigraph,
components, times, types, and carrier association	Node and edge semantics,
temporal order, and included system boundary
$s,f,q$	Typed stocks, flows, generation, use, loss, and conversion	Units,
source and sink boundary, and cross-kind conversion rule
$\mathcal O_{m,\nu},\Omega_{m,\nu}$	Detection and constitution mechanisms	Selected
recognition branch and the evidence or institutions on which it depends
$\mathcal R_H^\Sigma,w_\Sigma,\mathsf A_\chi^\Sigma$	Supported viable
paths, three-valued viability, and target adequacy	Compatibility, capacity,
timing, probability, feasibility, adequacy, and
unknown-status rule
$\mathcal R^{\Reg},\Thru_{J,k}^{\Sigma}$	Regenerative reach and typed
current throughput	Target condition, commensurable counted edges, interval,
and units
$\Pi_{z,b}^{\Sigma}$	Layered diagnostic profile	Independent warrant and
status vocabulary for every evaluative coordinate

Table. Principal symbols and application-level semantic obligations

4.1 Symbols and Carrier Association

This subsection distinguishes carriers from graph components and registers the
objects used by later results. The distinction prevents a person, institution,
event, lifecycle role, and value stock from becoming interchangeable graph
nodes.

Let $i,j\in\mathcal A$ denote typed carriers, $k,\ell\in\mathcal K$ value
kinds, $m\in\mathcal M$ a recognition mechanism, and $t\in[0,H]$ time.
Let $C_{i,t}$ be a possibly vector-valued realization condition, $G_{i,t}$
a typed generative activity, $V_{i,k,t}^{(\nu)}$ a value relation under
standpoint $\nu$, and $\widehat V_{i,k,t}^{(m,\nu)}$ an assessment under
mechanism $m$. Where units exist, $s_{i,k,t}$ denotes a stock and
$f_{ij,k,t}\geq0$ a directed flow. A graph node represents a typed state or
event; a carrier-association map identifies the carriers implicated in it.

4.2 Structural Assumptions

This subsection states the assumptions that make the construction interpretable
and the later derivations valid. The assumptions are application obligations;
target-case support remains an empirical obligation.

The carriers, value kinds, standpoint, recognition semantics, horizon, focal
arrangement, comparison family, criterion and selector, intervention semantics,
substitute boundary, and units in $\Sigma$ are declared before a diagnosis.
Quantitative variables share units only when an operational conversion has been
specified.

Lifecycle stages are analytical roles in a temporal multigraph. They may branch,
merge, recur, overlap, or remain absent. The displayed lifecycle treats a linear
sequence as one possible configuration.

A path’s compatibility, capacity, timing, probability, and feasibility rules are
declared independently of the desired diagnostic result. Unknown viability is
reported as unknown.

Every $b\in\mathcal B$ is feasible over the same carriers, value kinds, and
horizon as focal arrangement $a$. An intervention identifies a rule or
mechanism independently from the evaluated outcome.

Deletion, distortion, capture, capacity change, and adaptive rerouting are
distinct interventions. Materially available substitute routes within declared
boundary $\mathcal S$ are included in the graph; an incomplete substitute
search produces an unresolved report.

Any regenerative claim identifies a return or feedback coordinate, its target
condition coordinate, and the update relation connecting them. A
later-condition conclusion requires an explicit link to its target coordinate.

Functional pathology, capability effect, harm, injustice, exploitation,
responsibility, and legal wrong receive separate warrants. A positive value in
one coordinate reaches another coordinate only through an explicit bridge.

4.3 Temporal Lifecycle Graph

This subsection defines the structural object used for lifecycle localization.
It presents the familiar chain as a role register and assigns formal work to the
temporal multigraph. The chain remains a compact role register.

For every represented arrangement $x$, let

$$\mathcal L^\Sigma(x)=(N_x,E_x,\tau_x,\kappa_{N,x},\kappa_{E,x},\alpha_x)$$

be a directed temporal multigraph. The maps $\kappa_{N,x}$ and
$\kappa_{E,x}$ type nodes and edges, $\tau_x$ assigns times or intervals,
and $\alpha_x:N_x\cup E_x\to2^{\mathcal A}$ associates components with
carriers. Node
and edge roles can be drawn schematically as

$$\mathsf C_t\longrightarrow\mathsf G_t\longrightarrow\mathsf V_t
\longrightarrow\mathsf R_t\longrightarrow\mathsf T_t
\longrightarrow\mathsf D_t\longrightarrow\mathsf F_t
\longrightarrow\mathsf C_{t+1},$$

where the roles are conditions, generation, value, recognition, transmission,
distribution or return, feedback, and later conditions. Recognition may affect
generation before distribution is complete; several value kinds may branch from
one activity; and feedback may alter any later transition. Equation
(3) therefore names roles. Temporal linearity and cycle
completion remain additional hypotheses.

For a quantitative application, an edge may have a transition kernel
$K_{e,x}(y’\mid y,h_t,u_t)$ only after its state spaces and probability
semantics are supplied. The general construction uses a typed transition
relation $y\leadsto_{e,x}y’$, allowing deterministic, institutional, constitutive, and
qualitative edges. A stochastic kernel remains optional.

4.4 Typed Stock–Flow Module

This subsection provides an optional accounting module for value kinds with
meaningful units. Its objective is to represent creation, movement, use, loss,
and conversion while preserving cross-kind typing and an open-system boundary.

For such a value kind, define

$$s_{i,k,t+1}={}&s_{i,k,t}+q^{\mathrm{gen}}{i,k,t}
+\sum_j f{ji,k,t}-\sum_j f_{ij,k,t}
-q^{\mathrm{use}}{i,k,t}-q^{\mathrm{loss}}{i,k,t} \notag\
&+\sum_{\ell\neq k}q^{\ell\to k}{i,k,t}
-\sum{\ell\neq k}q^{k\to\ell}_{i,k,t}.$$

Every term in Equation (4) is expressed in the units of kind
$k$. The conversion output $q^{\ell\to k}_{i,k,t}$ and the corresponding
loss from kind $\ell$ require separate measurement. A conservation law across
carriers or kinds requires independent assumptions.

Later realization conditions follow a separate, potentially vector-valued
mapping

$$C_{i,t+1}=\Psi_i(C_{i,t},r_{i,t},\widehat V_{i,t},F_{i,t},\delta_{i,t},X_{i,t}),$$

where $r$ is a declared return, $F$ feedback, $\delta$ depletion or burden,
and $X$ external conditions. The update map determines the sign of every
coordinate of $C_{i,t+1}$. Crowding, dependency, contamination, and external
burden remain possible.

4.5 Recognition Semantics

This subsection preserves the unresolved relation between value and recognition.
It presents detection, constitution, and hybrid branches so that disagreement
between evaluators remains distinct from measurement error.

Under a detection interpretation,

$$\widehat V_{i,k,t}^{(m,\nu)}\in
\mathcal O_{m,\nu}!\left(V_{i,k,t}^{(\nu)},Z_{i,t},
R^{\mathrm{soc}}_t,I_t\right),$$

where $Z$ is available evidence, $R^{\mathrm{soc}}$ a recognition network,
and $I$ an institutional setting. The set-valued observation relation
$\mathcal O_{m,\nu}$ returns admissible assessments under the declared
evidence and mechanism; a probabilistic application must additionally supply
measurable state spaces and a probability kernel. This branch assumes that
$V^{(\nu)}$ is meaningful independently of $m$.

Under a constitution interpretation,

$$V_{i,k,t}^{(m,\nu)}=
\Omega_{m,\nu}(Z_{i,t},R^{\mathrm{soc}}_t,I_t),$$

so a difference between mechanisms can constitute different social or
institutional values. A hybrid model may allow an independently assessed
dimension to enter $\Omega_{m,\nu}$ while recognition changes another
dimension. The branch must be selected by value kind and defended; the notation
leaves the underlying value theory as a separate commitment.

4.6 Viable Paths, Regenerative Reach, and Throughput

This subsection defines the structural observables used in the results. It
separates practical reach from imaginable paths and separates current traffic
from a route to later realization conditions.

For temporally ordered nodes $s,v$ in arrangement $x$, let
$p=(n_0,e_1,n_1,\ldots,e_r,n_r)$ be a typed directed path in
$\mathcal L^\Sigma(x)$ with $n_0=s$, $n_r=v$, and times within $H$.
Let $w_\Sigma(p;x)\in\Vthree$ report supported viability, supported failure,
or unresolved viability. Define

$$\mathcal R_H^\Sigma(s,v;x)=
{p:p\text{ is typed and temporally admissible in }x,
\ w_\Sigma(p;x)=1}.$$

The uncertainty report retains unknown paths; the supported set in
Equation (8) contains paths with supported viability.

For carrier $i$ and a condition coordinate $c$, regenerative reach is the
supported set

$$\mathcal R_{i,c,H}^{\Reg}(x)=
\bigcup_{u\in N_x^{\mathrm{out}}}
\mathcal R_H^\Sigma(u,C^{x}_{i,c,t+H};x),$$

where $N_x^{\mathrm{out}}$ contains the declared output, return, or feedback
nodes. A path belongs to this set only when its target relation to the condition
coordinate has been specified.

Path-set loss and target-level material loss require separate objects. Define

$$P_\chi^\Sigma(s,v;x)=
\Phi_\chi^\Sigma!\left(\mathcal R_H^\Sigma(s,v;x)\right)
\in\mathcal D_\chi,$$

where $\mathcal D_\chi$ is an application-declared performance space. Let
$\mathcal Q_\chi\subseteq\mathcal D_\chi$ be the declared adequacy region.
Define

$$\mathsf A_\chi^\Sigma(s,v;x)
=\mathbf 1!\left[P_\chi^\Sigma(s,v;x)\in\mathcal Q_\chi\right].$$

A change from arrangement $x$ to $y$ produces material target loss
only when $\mathsf A_\chi^\Sigma(s,v;x)=1$ and
$\mathsf A_\chi^\Sigma(s,v;y)=0$. The functional $\Phi_\chi^\Sigma$ can
incorporate capacity, timing, destination, quality, and carrier coverage; the
application supplies all of those semantics.

For a declared set $J\subseteq E_x$ whose edges carry one commensurable value
kind $k$ in a common unit over interval $[t_0,t_1]$, define current
throughput as

$$\Thru_{J,k}^{\Sigma}(x;[t_0,t_1])
=\frac{1}{t_1-t_0}\sum_{e\in J}
\int_{t_0}^{t_1}f^x_{e,k}(t),dt.$$

The choice of $J$, $k$, units, arrangement, and interval is part of the
application record. Edges with unlike units receive a vector report or remain
separate. Typed throughput is one observable; system ordering requires an
additional rule.

5. Localization and Conditional Results

This section derives the formal consequences in dependency order. It begins with
a fixed-environment component intervention, adds a separate bridge to later
conditions, and then constructs high- and low-flow countermodels. Table
4 records the mathematical status and inferential limit of each
result.

| @p0.22p0.22YY@

Result	Mathematical status	Required dependence	Inferential boundary
Path-set contraction	Elementary conditional graph result	Fixed environment,
predeclared viability, coherent deletion	Target loss additionally requires a
declared adequacy failure
Weak condition non-increase	Conditional model consequence	Identified return,
fixed co-arguments, coordinate order, local weak monotonicity	Strict change,
non-monotone effects, burden, and conflict remain open
High-throughput configuration	Logical countermodel	Declared counted edges and
absent regenerative path	Prevalence remains an empirical question
Protected-reserve configuration	Temporal countermodel	Enforceable future-use
route and declared horizon	Retention evaluation remains case-specific
Layer separation	Reporting rule	Independent warrants for each coordinate	Normative inference requires an independent warrant

Table. Formal result status and inferential boundary

5.1 Fixed-Environment Component Intervention

This subsection isolates the fixed-environment setting analyzed here. It defines
the intervention, derives weak and strict path-set contraction, and records
adaptation as a different model.

For $e\in E_a$, let the pure deletion intervention form arrangement
$a^{-e}=I_e^{\mathrm{del}}(a)$, with
$ L^(a^-e)=(N_a,E_a\e,_a,
_N,a,_E,a,_a)$. The
intervention is fixed-environment: all remaining nodes, edges, timings,
capacities, and viability assignments stay fixed. Congestion relief, innovation,
institutional response, and strategic rerouting define another intervention and
must be analyzed by recomputing the graph.

Under Assumptions ?–? and a
fixed-environment deletion,

$$\mathcal R_H^{\Sigma}(s,v;a^{-e})
\subseteq \mathcal R_H^\Sigma(s,v;a).$$

The inclusion is strict exactly when at least one supported viable
$s$–$v$ path uses $e$.

Every path in $\mathcal L^\Sigma(a^{-e})$ uses edges in
$E_a\setminus{e}$, hence is also a path in $\mathcal L^\Sigma(a)$.
Fixed-environment viability gives it the same status in both graphs, which
proves Equation (13). If a
supported viable path uses $e$, that path is absent after deletion and the
inclusion is strict. Conversely, when every supported viable path avoids $e$,
every element of the original viable-path set remains, so the sets are equal.

Proposition ? is elementary. Its diagnostic value lies in
the assumptions it forces into view. A blocked edge is insufficient for
material target failure when an adequate substitute remains; an observed route outside the
horizon is insufficient when timing matters; and an unobserved alternative
leaves the result unresolved. Strict path loss and material importance remain
distinct when the lost routes are redundant in destination, capacity, or
quality. Formally, material target loss requires
$\mathsf A_\chi^\Sigma(s,v;a)=1$ and
$\mathsf A_\chi^\Sigma(s,v;a^{-e})=0$. Both adequacy equalities require the
application-level performance functional and adequacy region.

5.2 Later-Condition Bridge

This subsection states the additional premises required to move from path-set
contraction to a condition effect. It uses a coordinate-specific order and local
monotonicity; scalar ordering of whole systems remains outside the result.

Let $r_{i,c}^{a^{-e}}$ and $r_{i,c}^{a}$ be a declared return coordinate
under the deletion and focal arrangements. Let $\preceq_c$ order only
condition coordinate $c$.

Under Assumption ?, suppose
$r_{i,c}^{a^{-e}}<r_{i,c}^{a}$, every other argument of $\Psi_i$ is held
fixed across the two arrangements, and $\Psi_i$ is weakly increasing in that
return over the relevant range. Then

$$\Psi_i(C_i,r_{i,c}^{a^{-e}},\widehat V_i,F_i,\delta_i,X_i)
\preceq_c
\Psi_i(C_i,r_{i,c}^{a},\widehat V_i,F_i,\delta_i,X_i).$$

The first premise orders the identified return coordinate, and the second fixes
the remaining arguments of the update map. Local weak monotonicity in
$r_{i,c}$ then yields
Equation (14) by the definition of monotonicity.

The lower-return premise remains application-specific. An application connecting
Proposition ? to this result must separately identify how
the deleted paths change $r_{i,c}$. Threshold, crowding, contamination,
dependency, and burden effects that reverse the local order define
counterconditions. Every additional condition coordinate and carrier requires
separate analysis. These are substantive features, and
Configuration ? exhibits one.

5.3 Throughput and Regenerative Reach

This subsection separates current traffic from future-condition reach. It uses
two constructed systems to show that the observable in
Equation (12) is insufficient to identify the set in
Equation (9).

In focal arrangement $a$, let $J\subseteq E_a$ contain a closed loop of
edges that carry one commensurable value kind $k$, with constant flow
$M>0$ on every counted edge. Let every path from the loop’s output or
feedback nodes to $C^a_{i,c,t+H}$ be absent. Then

$$\Thru_{J,k}^{\Sigma}(a;[t_0,t_1])=|J|M,
\qquad
\mathcal R_{i,c,H}^{\Reg}(a)=\varnothing.$$

Taking $M$ arbitrarily large increases throughput while regenerative reach
remains empty.

At time $t$, let a retained stock have zero outward flow on the counted edge
set $J$ for declared kind $k$. Let a binding governance rule create a future-use edge at
$t+\Delta\leq t+H$ from the reserve to a required condition node, and let that
edge complete a viable route to $C^a_{i,c,t+H}$. Then

$$\Thru_{J,k}^{\Sigma}(a;[t,t+\epsilon])=0,
\qquad
\mathcal R_{i,c,H}^{\Reg}(a)\neq\varnothing.$$

Current low flow coexists with supported future regenerative reach.

Within the typed lifecycle construction,

$$\Thru_{J,k}^{\Sigma}(a;[t_0,t_1])>0
\nRightarrow \mathcal R_{i,c,H}^{\Reg}(a)\neq\varnothing,
\qquad
\mathcal R_{i,c,H}^{\Reg}(a)\neq\varnothing
\nRightarrow \Thru_{J,k}^{\Sigma}(a;[t_0,t_1])>0.$$

Configuration ? supplies arbitrarily high throughput
with empty regenerative reach. Configuration ? supplies zero
current throughput with nonempty future regenerative reach. The two
configurations defeat the implications in opposite directions.

The conclusion concerns logical implication within the construction. General
harm and benefit classifications require evidence about duration, control,
access, use, loss, substitutes, and affected carriers.

6. Diagnostic Configurations and Audit Method

This section tests structural implications and the reporting behavior of the
diagnostic. It first presents a reproducible audit sequence and then examines
the two formal countermodels and four additional constructed configurations.
The configurations fix only the fields needed for each logical point; they are
partial structural templates. Empirical cases and completed double-localized
audits require the remaining declarations.

| @p0.18p0.20p0.22Y@

Configuration | Lifecycle localization | Structural consequence | Required

Table. Constructed structural templates and remaining audit declarations

6.1 Lifecycle Audit Sequence

This subsection turns double localization into a reusable sequence. Its objective
is to expose the declarations and counterconditions that must precede a report.

The audit proceeds as follows:

declare $\Sigma$, including carrier, value kind, standpoint, recognition semantics, horizon, focal arrangement, comparison family, criterion and selector, intervention, substitute boundary, and units;
construct the typed temporal lifecycle and associate its components with carriers;
locate the proposed anomaly at a node, edge, path, loop, stock–flow configuration, or topology;
specify the intervention or mechanism and test substitutes, delays, buffers, criterion-consistent use, retention, maintenance, privacy, and measurement error;
report affected capability, continuity, autonomy, recognition, distribution, plurality, and ecological burden while preserving coordinate-specific outputs;
complete each evaluative coordinate separately and preserve negative, mixed, baseline-sensitive, or unresolved statuses.

Table 5 summarizes the partial outputs and the declarations
still required. A row records a structural template; occurrence in a particular
institution remains an empirical question.

6.2 Proxy and Substitute Configurations

This subsection applies the audit to throughput, retention, and route redundancy.
Its objective is to demonstrate that prominent indicators can support opposite
diagnoses after timing and alternatives are represented.

Configuration ? establishes empty regenerative reach
alongside positive typed throughput. It therefore blocks an inference from
current traffic to regeneration. Its full functional status remains unresolved
until a comparison, adequacy rule, and materiality threshold are supplied. Harm
and injustice remain unresolved because standing, protected-interest, and
wrongfulness premises remain undeclared.

Configuration ? defeats a low-flow proxy under the declared
horizon because the future-use edge preserves a target route. A full functional
report additionally depends on the rule’s enforceability, the reserve’s adequacy,
and present claims that may defeat the retention arrangement. The structural
template leaves the evaluation of saving or hoarding open.

Let two edge-disjoint viable paths $p_1,p_2$ in arrangement $a$ connect
source $s$ with target $v$, and let both satisfy the same timing, capacity,
compatibility, and target requirements. Delete an edge used only by $p_1$ to
form $a^{-e}$. The path set strictly contracts, yet $p_2$ preserves the
declared target at the required capacity, so
$ A_^(s,v;a)=
A_^(s,v;a^-e)=1$. The report is negative for material
target loss even though Proposition ? records strict
path-set contraction.

Configuration ? separates structural loss from material
functional loss. A real application would still examine switching cost,
congestion, distribution, and whether the substitute serves the same carriers.
Those questions show why path counting alone is an inadequate metric.

6.3 Protected-Condition and Recognition Configurations

This subsection tests two cases in which the apparent failure depends on the
criterion or ontology chosen. It preserves mixed and unresolved results and
maintains criterion and ontology plurality.

Let a rule remove a transmission edge that would increase an output coordinate
$o$, with $\chi=(\chi_o,\chi_c)$ a two-coordinate criterion whose aggregation
rule remains unspecified. The same edge would disclose protected information or reduce an
ecological condition $c$ below a declared viability threshold. Relative to
$\chi_o$, reach contracts; relative to $\chi_c$, the restriction preserves
the required condition. The coordinate-specific structural report is mixed, and
aggregation remains unspecified.

The normative status of privacy or ecological restriction remains a separate
question. The configuration shows that a criterion limited to outward movement
hides a protected dimension. Standing, proportionality, alternatives, and
burden distribution belong to the later evaluative audit.

Let mechanisms $m_1$ and $m_2$ organize different institutional forms of a
social value through Equation (7). A candidate artifact
receives a position under $m_2$ and none under $m_1$. Because the value kind
is partly constituted by each mechanism, the divergence between
$V^{(m_2,\nu)}$ and $V^{(m_1,\nu)}$ remains distinct from a measurement-error
term until an independently defended standard supplies the relevant relation. A recognition-
failure report remains unresolved until an independently defended standard
specifies what $m_1$ failed to recognize or wrongfully prevented.

Configuration ? blocks a common inference from
nonrecognition to detection failure. It also blocks the opposite inference that
existing recognition practices are self-validating. A hybrid account can
identify dimensions for which evidence supports detection and dimensions whose
social existence depends on institutional recognition.

6.4 Plural-Carrier Configuration

This subsection tests a return that satisfies the formal regeneration relation
for one carrier while burdening another. Its objective is to preserve
distribution and ecological or intergenerational conflict inside the report.

For some $b\in\mathcal B$, let focal arrangement $a$ contain a return
$r_A$ that increases carrier $A$’s condition coordinate under
Equation (5). Let production of that return impose an
external burden $\delta_B$ that lowers carrier $B$’s nonfungible condition
coordinate. Then

$$C_{A,c_A,t+1}^{a}\succ_{c_A} C_{A,c_A,t+1}^{b},
\qquad
C_{B,c_B,t+1}^{a}\prec_{c_B} C_{B,c_B,t+1}^{b}.$$

The circulation is regenerative for $A$ in coordinate $d$ and degenerative
for $B$ in coordinate $e$. Aggregate ranking requires a separate rule.

The configuration prevents “regenerative” from becoming a global honorific.
An evaluative conclusion requires an account of both carriers’ standing,
distribution, nonfungibility, ecological or intergenerational limits, procedure,
and available alternatives. The functional profile can preserve the conflict
while leaving its resolution to an independent evaluative argument.

7. Evaluative Layers and Inferential Stopping Point

This section completes double localization by specifying the evaluative report.
Its objective is to maintain separation between functional results and moral,
economic, responsibility, or legal conclusions.

| @p0.18YY@

Evaluative layer	Required warrant	Inferential boundary
Functional pathology	Typed mechanism, criterion, comparison, horizon,
substitutes, and uncertainty	Harm requires a further warrant beyond functional
loss
Capability effect	Carrier, affected repertoire or condition, materiality, and
comparison	Wrongfulness requires a further warrant beyond capability
contraction
Harm	Defended interest or well-being relation, causation or constitution, and
materiality	Injustice and exploitation require further warrants beyond harm
Injustice	Standing, procedure, distribution, domination, recognition, or
another defended principle	Beneficiary-through remains an independent
exploitation requirement
Exploitation	Participant standing, admissible comparison, affected capability,
and causal or constitutive benefit-through	Responsibility requires an
independent allocation principle
Responsibility	Agency or contribution, knowledge where relevant, capacity,
role, avoidability, and forward- or backward-looking principle	Legal duty
requires jurisdiction-specific authority
Legal wrong	Jurisdiction, authority, protected interest, duty, causation,
proof, defenses, and remedy	Legal status requires a jurisdiction-specific
legal analysis

Table. Evaluative layers and independent warrant requirements

For component or configuration $z$, define the report

$$\Pi_{z,b}^{\Sigma}=\langle
\mathsf{Stat}{\chi}^{\Sigma}(z;b),
\widehat{\mathsf{CapabilityEffect}},
\widehat{\Harm},
\widehat{\Injustice},
\widehat{\GEX},
\widehat{\Resp},
\widehat{\Law}
\rangle{z,b},$$

where $b\in\mathcal B$ and each coordinate takes the fixed-comparison statuses
positive, negative, mixed, or unresolved defined in
Definition ?. Baseline sensitivity is a property of
the family ${\Pi_{z,b}^{\Sigma}:b\in\mathcal B}$ when a coordinate’s
supported status changes with $b$. Table 6 states the minimum
kind of warrant required at each layer. The layers form an audit sequence;
scalar ordering remains outside the construction.

A lifecycle localization supports only the functional coordinate for which its
criterion and evidence were specified. Every additional evaluative coordinate
remains open until its independent warrant is supplied.

Claim ? functions as a reporting rule. Substantive relations
among harm, injustice, and exploitation require separate arguments. In a
developed case, the same evidence may support several layers. The rule requires
the inferential bridge to be stated. An effective circulation with an unjust
procedure illustrates injustice alongside functional adequacy. A route
contracted by a natural event or justified protective rule illustrates
functional pathology alongside justified conduct.

The exploitation coordinate receives special protection from terminological
drift. The source taxonomy uses exploitation for Types IV and V, while this
paper’s functional model can establish only depletion, contraction,
appropriation, or capture. A positive exploitation report additionally requires
participant standing, an independently admitted comparison, material effect on
generative capability, and a causal or constitutive benefit-through witness.
Intention, consent, domination, wrongfulness, responsibility, and remedy remain
further variables. Their full diagnostics remain future research tasks.

8. Objections and Defeat Conditions

This section subjects the proposal to ontological, formal, empirical, and
normative objections. Its objective is to identify the conditions under which a
component should be revised, narrowed, or abandoned. The responses emphasize
discrimination and disclosure.

8.1 Value Ontology and Taxonomic Discrimination

This subsection examines value reification, recognition, and the possibility
that the taxonomy merely collects familiar concepts. These objections remain
substantive research obligations.

The first objection is that a lifecycle graph turns contested value into a thing
that moves. The stock–flow module answers only part of the objection because it
is optional and typed. Material, monetary, and some informational quantities may
admit units; recognition, expressive importance, and capability may require
relations, orders, or qualitative states. Equations (6) and
(7) preserve the further possibility that recognition helps
constitute the value at issue. When an application lacks usable semantics, the
value coordinate should remain qualitative or the application should suspend
the model.

The second objection is taxonomic collage. Gatekeeping, nonrecognition,
appropriation, reproduction, accumulation, and commons governance have extensive
literatures. The paper treats them as established research domains. Its proposed
gain is local: a shared lifecycle can distinguish their loci, show where
mechanisms overlap, and enforce a common stopping rule. When the lifecycle
duplicates an antecedent framework’s discrimination in a target domain, the
antecedent framework should replace the redundant label.

The third objection concerns proliferation. Because tags are non-exclusive, any
unfavorable case could receive many labels. The audit answers by requiring
mechanism-specific evidence and counterconditions for every tag. A second label
is informative only when it identifies a distinct intervention, evidence
requirement, or consequence. Otherwise it is duplicate description.

8.2 Formal Scope and Empirical Identification

This subsection addresses linearization, elementary mathematics, adaptive
rerouting, and unobserved paths. Its objective is to separate what the formalism
proves from what an empirical application must identify.

Equation (3) invites a linear reading. The operative object
in Equation (2) is a temporal multigraph precisely because
recognition, generation, distribution, and feedback can be simultaneous,
recursive, delayed, or constitutive. A case requiring collective production,
joint transitions, or higher-order relations may require a hypergraph. This
paper confines its results to the multigraph construction; hyperpath semantics
remain an open extension.

The contraction result is mathematically elementary. Its content is the
fixed-environment intervention and the distinction among edge loss, strict path
loss, material target loss, and later-condition effect. Presenting set deletion
as a social theorem would be an overstatement. The result loses application
whenever the intervention changes other edges or viability assignments. Adaptive
rerouting, congestion relief, innovation, and strategic response require a new
graph and a comparative dynamic analysis.

Empirical identification supplies the strongest objection. Transition
mechanisms, alternative paths, feasible comparisons, recognition semantics, and
condition updates may remain unobserved. The paper’s response is three-valued
viability, explicit unknown status, and sensitivity across plausible
specifications. This provides a reporting discipline; an identification solution
remains open. A method that returns unresolved results frequently may be honest
and still prove too weak for practical use; comparative testing must decide that
issue.

8.3 Criterion Authority and Plural Carriers

This subsection examines the normative loading of pathology, conflicts among
carriers, and circulation’s physical imagery. Its objective is to preserve the
proposal as a functional instrument while disclosing the evaluative choices
inside that instrument.

Every functional criterion selects something to preserve or enable. Calling its
failure a pathology can give that selection an undeserved medical authority.
The scope specification therefore discloses the criterion, standpoint,
comparison, and carrier, while Claim ? blocks further
promotion. A stronger response would require a theory of which functional
criteria deserve public or moral authority; that theory remains an open task.

Carrier conflict prevents aggregate generativity from serving as a default
maximand. Configuration ? shows that one carrier’s
regeneration can accompany another’s nonfungible loss. A partial profile retains
that conflict. Any aggregation requires an independently defended account of
standing, distribution, ecological limits, and intergenerational choice.

Hydrological imagery creates a final risk. A physical cycle concerns specified
substances and conservation conditions; the present target contains sources,
sinks, copying, use, conversion, loss, and constitutive recognition. Following
the model-transfer discipline in Section 5.3, resemblance
is purpose-relative. The lifecycle model survives only if its typed mappings
increase target-domain discrimination. Evidence for the social mappings must
come from the target domain.

9. Research Obligations and Conservative Conclusion

This section records the work required before the framework can support
empirical, normative, or originality claims. It first states six research
obligations and then closes with the analytic contribution that survives while
those obligations remain open.

Complete a full-text, source-by-source comparison with the Eglash corpus. Record
terminology, formal structure, and differences before making an originality
claim. Admission of the unlocated circulation sentence requires verification of
its exact source, wording, and context.

Compare realist, constructivist, relational, pluralist, and institutional value
accounts, together with detection, constitution, and hybrid recognition models.
Specify which value kinds admit each branch and which failures each branch can
identify.

Develop at least two supported positive cases, two boundary cases, and two
negative cases. Each case must declare $\Sigma$, identify the mechanism and
alternatives, report uncertainty, and separate the evaluative layers. The six
constructed configurations in this paper function as test templates; an
empirical dossier remains required.

Provide observable meanings, units or qualitative semantics, horizons,
comparison families, intervention definitions, substitute-route searches, and
condition-update evidence. Include sensitivity and at least one case in which
the method withholds a diagnosis.

Develop independent accounts of standing, capability effect, harm, procedure,
distribution, recognition, domination, exploitation, responsibility, ecological
limits, and legal authority. Test functional pathology paired with justified
conduct, and test injustice paired with an absent exploitation relation, as
separate countercases.

Compare the lifecycle diagnostic with domain-specific alternatives. Remove a
category whose mechanism, evidence requirement, and consequence duplicate an
existing framework;
narrow the model when values lack usable semantics; and abandon the general
framework if unresolved classifications dominate discriminating ones.

The conservative conclusion is correspondingly modest. Value production,
current movement, and generative circulation are distinguishable because a
system can generate traffic while regenerative reach remains empty and can
preserve a later route during a period of current stillness. A typed lifecycle makes the
location of a proposed failure explicit. A fixed-environment deletion contracts
viable paths only in the elementary sense proved here, and a consequence for
later conditions requires additional empirical structure. The seven-type
taxonomy offers a revisable genealogy of candidate loci; its value depends on
whether applications can discriminate mechanisms and return negative, mixed,
and unresolved results.

Double localization is the paper’s stopping rule and its principal proposal. A
circulation diagnosis should state where in the lifecycle the candidate problem
occurs and which evaluative layer the evidence reaches. Everything beyond that
point remains a separate argument. This rule supplies the entry conditions for
a pathology-of-value-circulation research program with greater precision and
restraint.

Acknowledgments

This section records the dialogue that supplied a human intellectual stimulus
for the paper and assigns responsibility for the resulting manuscript.

The author thanks Ron Eglash for dialogue that stimulated reflection on the
consequences of diminished value circulation. That exchange motivated the
present effort to reconsider what a pathology of value circulation could mean
and to develop a preliminary formal diagnostic. The author bears sole
responsibility for the manuscript’s definitions, formal constructions,
taxonomy, arguments, conclusions, and errors.

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