Transactions in Generativity - Future Value, Attribution, and Institutional Form
Abstract
Some transactions concern a productive or creative capacity whose future
exercise can generate further capacities, outputs, relations, and options. A
present payment offers a compact exchange coordinate, while the transacted
position may also include control, licensing, attribution, participation,
reversion, governance, and exposure to uncertain downstream trajectories. This
paper proposes the term transaction in generativity for an arrangement
whose object includes a declared generativity or a material position governing
its future exercise. The proposed evaluation method preserves a typed profile
containing the trajectory law, reachable repertoire, position bundle, temporal
value coordinates, descendant rule, attribution registers, uncertainty, and
third-party standing. Three elementary results establish the framework’s formal
limits. First, an undiscounted infinite-horizon flow diverges when it remains
bounded below by a positive constant after some date. Second, normalized
descendant-allocation weights preserve an allocated total as a bookkeeping
identity. Third, equal current payments and equal expected output leave the
institutional position underidentified. Two countermodels further show that
equal expectations can preserve sharply different risk and option structures.
The paper compares sale, fixed-term licence, continuing return, equity,
stewardship, and shared governance as configurable ideal types. Each form
changes several positions and introduces its own monitoring, revision,
foreclosure, and third-party questions. The paper’s scope is conceptual and
formal. Empirical estimation, fair pricing, legal classification, universal
alienability, and general justice principles remain open research tasks. The
main proposal is a profile-preservation discipline for research on transactions
whose object extends beyond a present output.
Keywords: generativity; intertemporal value; descendant
Discussion Paper Note
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This working draft records an evolving stage of the author’s position and is
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evaluation, legal analysis, and institutional recommendation remain outside its
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Except where otherwise indicated, copyright 2026 Wanhong Huang. This work is
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Statement on the use of language models.
The exploratory discussions and preparation of this paper involved OpenAI’s
Codex. Codex supported exploratory dialogue, formal reconstruction, source
discovery followed by website verification, argumentative criticism, and
drafting in . The author selected the research questions, directed and
approved the theoretical commitments and epistemic status of the claims, and
bears sole responsibility for the manuscript, including its definitions,
formal constructions, taxonomy, arguments, conclusions, and errors. Authorship
credit remains with the human author. The access level and claim limit for every
cited source are recorded in the accompanying literature audit.
Related research programme.
This paper is project P016 and the second promoted paper in the research-stage
Generative Injustice programme. P015 develops a typed lifecycle
diagnostic for value circulation. Earlier P005–P014 manuscripts provide
revisable companion analyses of exploitation, propagation, identification,
cycles, commons, expansion, dependency, AI mediation, recovery, and legal
relations. These projects function as related research states; the present
argument states its own premises.
Suggested citation.
Huang, Wanhong. “Transactions in Generativity: Future Value, Attribution, and
Institutional Form.” Working discussion paper, 2026.
1. Introduction
This section establishes the paper’s object, motivation, central proposal, and
inferential boundary. It begins with the distinction between later effects and
a transacted future-generative position, then states the profile-preservation
principle, source provenance, formal status, and organization of the argument.
Many ordinary goods have later effects. A purchased tool may increase output;
a book may alter a reader’s work; a machine may generate a stream of services.
This temporal fact alone produces an expansive category with little analytic
discrimination. The narrower object considered here arises when an arrangement
directly changes a party’s exercise, access, control, alienation, licensing,
governance, attribution, return, or continuing participation concerning a
declared generativity. Examples may include an algorithmic capacity, a research
platform, a patent position, a productive infrastructure, a knowledge corpus,
or an organized practice. Each example remains provisional until its carrier,
domain, conditions, and relevant positions are declared.
The motivating question originated in a research discussion in which Wanhong
Huang rejected an earlier, overinclusive future-effects account. The correction
identified a transaction whose object is a generativity and proposed that its
value may extend over an indefinite future. Later dialogue introduced temporal
integrals, branching descendants, uncertainty, weighting functions,
attribution kernels, and continuing-return instruments. This manuscript retains
the original correction and reconstructs the later sequence under explicit
typing, integrability, allocation, and institutional assumptions.
A transaction in generativity is an arrangement whose object includes a
declared generativity or a material position concerning its future exercise,
access, control, alienation, licensing, governance, attribution, return, or
continuing participation.
Definition ? classifies the object of inquiry. Questions of
price, permission, validity, fairness, ownership, exploitation, responsibility,
and legal status require additional premises. This boundary supplies the
paper’s central methodological proposal.
Evaluation of a transaction in generativity should preserve a typed profile of
future trajectories, reachable possibilities, position changes, attribution
registers, uncertainty, and affected standing until an explicit argument
licenses compression, ordering, or institutional judgment.
The claim is a proposed research discipline. Its motivation comes from two
forms of underidentification. Equal expected output can accompany different
trajectory laws, and equal present payments can accompany different control,
participation, and reversion positions. Sections 7 and
9 give elementary countermodels for these statements.
The paper makes four bounded contributions. First, it integrates a transaction
ontology with temporal and stochastic valuation under declared assumptions.
Second, it distinguishes descendants, causal relations, contribution
allocations, and normative entitlements. Third, it represents institutional
forms as bundles of changing positions and continuing relations. Fourth, it
supplies a reporting method capable of returning comparative, mixed, and
unresolved results. The mathematical contributions are elementary conditional
results and bookkeeping identities. Empirical identification and normative
evaluation remain separate stages.
Section 5 positions the proposal against verified
antecedents. Section 6 defines the analytical registers.
Section 7 develops temporal and stochastic valuation.
Section 8 separates descendant and attribution relations.
Section 9 models institutional forms.
Section 10 tests the framework on constructed
configurations. Section 11 states defeat conditions, and
Section 12 records the research programme and conclusion.
2. Antecedent Architectures and Transfer Boundaries
This section establishes the paper’s intellectual location and controls the
transfer of concepts across fields. It organizes the literature into temporal
evaluation, cumulative generation and attribution, and institutional form. The
method is comparative: each source receives a licensed role and a transfer
limit. Table 1 summarizes the result.
| @p0.18p0.24YY@
| Family | Representative sources | Licensed role | Transfer boundary |
|---|---|---|---|
| Intertemporal evaluation | Ramsey; Koopmans; Weitzman; Chichilnisky | temporal streams, impatience, uncertain discounting, sustainable criteria | generativity, standing, and justice weights require separate definitions |
| Irreversible choice | Arrow and Fisher | option value under uncertainty and irreversibility | environmental assumptions require target-specific reconstruction |
| Cumulative innovation | Scotchmer; Green and Scotchmer; Furman and Stern | sequential creation, spillovers, profit division, institutional access | patent and research settings provide bounded domains |
| Causal and contribution formalisms | Shapley; Pearl; Halpern and Pearl | cooperative allocation, structural causation, actual-cause analysis | allocation, causation, desert, and entitlement retain distinct semantics |
| Control and governance | Grossman and Hart; Schlager and Ostrom; Ostrom | residual control, differentiated rights, institutional diversity, self-governance | local position vectors require domain and enforcement evidence |
| Alienability and generative justice | Radin; Eglash and colleagues | market-inalienability inquiry, generator control, circular value flow | the present definitions and results remain local proposals |
Table. Verified antecedent families and transfer boundaries
2.1 Temporal evaluation
This subsection identifies the mature intertemporal problems that constrain the
paper’s temporal notation. It moves from infinite-horizon saving and impatience
to uncertain discount rates, sustainable criteria, and irreversible choice.
Ramsey’s saving model and Koopmans’s axiomatic analysis of impatience establish
major antecedents for formal evaluation across time
(Ramsey, 1928; Koopmans, 1960). Weitzman’s gamma-discounting
model shows, within cost-benefit analysis, how uncertainty over constant rates
can generate a declining effective rate (Weitzman, 2001).
Chichilnisky develops axioms intended to preserve sensitivity to present and
distant-future welfare (Chichilnisky, 1996). These traditions
make the choice of a weighting function theoretically substantive. The
manuscript therefore indexes every temporal functional by its horizon, value
coordinate, evaluator, and weight.
Arrow and Fisher analyze environmental preservation under uncertainty and
irreversibility (Arrow & Fisher, 1974). Their source-domain
result motivates an option coordinate when present action closes future
possibilities. Application to knowledge, organizational capability, cultural
practice, or digital infrastructure requires an explicit target account of
irreversibility, learning, substitution, and standing.
2.2 Cumulative generation and attribution
This subsection locates descendant generation within prior work on cumulative
innovation, cooperative allocation, and structural causation. Its objective is
to preserve the differences among sequential production, causal ancestry,
cardinal contribution, and justified claims.
Scotchmer examines cumulative research and the allocation of incentives between
earlier and later innovators (Scotchmer, 1991). Green and Scotchmer
model profit division in sequential innovation (Green & Scotchmer, 1995).
Furman and Stern provide empirical evidence from biological resource centers
that institutional access can amplify cumulative research impact
(Furman & Stern, 2011). These works directly precede the paper’s
concern with downstream generation, while their patent, profit, and biological-
resource assumptions preserve domain boundaries.
Shapley’s cooperative-game value supplies a canonical allocation rule under a
specified characteristic function (Shapley, 1953). Pearl’s structural
causal framework and Halpern and Pearl’s analysis of actual causation supply
formal approaches to causal and counterfactual questions
(Pearl, 2009; Halpern & Pearl, 2005). The manuscript uses these
sources to impose a separation rule: a causal model, an allocation rule, a
contribution measure, and an entitlement principle are separately specified
objects.
2.3 Institutional form
This subsection establishes the antecedents for representing transactions as
bundles of positions. It connects residual control, differentiated rights,
institutional diversity, alienability, and generative-justice lineage.
Grossman and Hart analyze ownership through residual control rights under
incomplete contracts (Grossman & Hart, 1986). Schlager and Ostrom
distinguish access, withdrawal, management, exclusion, and alienation within
natural-resource regimes (Schlager & Ostrom, 1992). Ostrom’s study of
common-pool-resource governance establishes institutional diversity and
self-governance as serious alternatives within its domain
(Ostrom, 1990). The present position vector adapts this rights-bundle
lesson while adding attribution, continuing return, reversion, and governance
coordinates for a different analytic target.
Radin’s market-inalienability analysis establishes a major tradition in which
alienability itself becomes a substantive question (Radin, 1987).
Eglash and colleagues develop a generative-justice programme centered on
generator control and unalienated circular value flow
(Eglash et al., 2024). These sources are antecedents for the paper’s
questions. The transaction definition, formal profile, and institutional
comparison remain proposed constructions whose originality and value require
further audit.
3. Transaction Object and Analytical Registers
This section supplies the paper’s local vocabulary and complete specification
rule. It first types generativity and actor positions, then defines temporal,
descendant, attribution, and institutional registers, and closes with the
non-scalar transaction profile. Table 2 records the principal
symbols.
| @p0.18p0.24YY@
| Symbol | Object | Required declaration | Principal caution |
|---|---|---|---|
| $G\in\mathfrak G_d$ | domain-indexed generativity | carrier, domain, organization, conditions | latent organization and effective exercise remain distinct |
| $C,h,a$ | conditions, history, arrangement | scope, feasible actions, institutional setting | counterfactual variation requires an intervention semantics |
| $\Pos_i$ | actor position vector | effective rights, powers, obligations, enforcement | formal entitlement may diverge from practical access |
| $K_G$ | trajectory law | model class, conditioning data, identification status | probabilities may remain partially identified |
| $v_k$ | typed value flow | units, evaluator, carrier, sign convention | heterogeneous coordinates require explicit transformations |
| $\Desc_t$ | descendant set | causal graph, horizon, collision and interaction rule | ancestry can expand rapidly through shared causes |
| $\kappa^c,a,\kappa^n$ | causal, accounting, normative weights | semantics and normalization | one kernel serves one declared role |
| $\mathcal I$ | institutional form | position change, payments, duration, monitoring, revision, standing | labels such as licence or equity remain domain-dependent |
| $\Profile_{\mathcal T}$ | transaction profile | included coordinates and ordering rule | scalar compression requires a separate warrant |
Table. Principal symbols and analytical roles
A generativity $G\in\mathfrak G_d$ is a latent organization capable, under
declared realization conditions $C$, of producing or transforming a repertoire
of domain-$d$ outcomes, relations, capacities, or later generativities.
The term latent marks a capacity relative to conditions. Effective
exercise depends on access, feasible action, institutional support, and
constraints. An observed output provides evidence about one realization and
leaves the wider repertoire open.
For actor or collective $i$, let
$$\Pos_i=
(u_i,m_i,x_i,a_i,r_i,y_i,g_i,e_i)
\tag{1}$$
record effective positions concerning use or exercise $u$, management $m$,
exclusion $x$, alienation $a$, attribution $r$, continuing return $y$,
governance $g$, and exit or reversion $e$.
Each coordinate can be binary, graded, set-valued, or relational. A complete
application states its domain-specific semantics and enforcement conditions.
The vector serves as an analytic register with a narrower role than a universal
theory of property.
A complete specification for a candidate transaction is
$$\Theta_{\mathcal T}=
(d,G,C,h,A,\Pos^0,\Pos^1,H,K,\mathbf v,\Desc,
\bm\kappa,\mathcal I,S),
\tag{2}$$
where $A$ identifies affected actors and collectives, $H$ the horizon, $K$ the
trajectory representation, $\mathbf v$ the typed value coordinates, $\Desc$ the
descendant rule, $\bm\kappa$ the declared attribution registers, $\mathcal I$
the institutional form, and $S$ the standing of affected parties and publics.
The specification can contain unresolved entries. Such entries become reported
uncertainties. Completion records the research status of every entry; empirical
omniscience lies outside this requirement.
For a specified transaction $\mathcal T$, define
$$\Profile_{\mathcal T}
\left\langle
K_G,
\Paths^{H,\epsilon}(G,C),
\Delta\Pos,
\mathbf V^{m},
\mathbf V^{q},
\mathsf{Desc},
\mathsf{Attr},
\mathsf{Unc},
S
\right\rangle .
\tag{3}$$
Here $\Paths^{H,\epsilon}$ is a declared effective reachable repertoire;
$\mathbf V^{m}$ contains market or exchange summaries; $\mathbf V^{q}$ contains
separately defended evaluative coordinates; $\mathsf{Desc}$ and
$\mathsf{Attr}$ report descendant and attribution assumptions; and
$\mathsf{Unc}$ records identification and model uncertainty.
The profile preserves structural differences during analysis. A later decision
may select, order, aggregate, or discard coordinates through an explicit rule.
Table 3 previews the formal status of the results used in
the remaining sections.
| @p0.24p0.23YY@
| Result | Mathematical status | Required assumptions | Authorized conclusion |
|---|---|---|---|
| Sustained-flow divergence | elementary proposition | unit weight, infinite horizon, eventual positive lower bound | selected functional has extended value $+\infty$ |
| Exponential constant-flow value | elementary corollary | constant flow, positive rate | selected functional equals $c/r$ |
| Expectation-profile separation | countermodel | two declared laws with equal means | expectation leaves distributional structure open |
| Descendant allocation identity | bookkeeping proposition | finite or summable descendants, normalized weights | allocated totals equal the declared total |
| Present-coordinate underidentification | logical countermodel | equal payment, distinct position vectors | payment leaves institutional form open |
| Audit-vector separation | proposed reporting rule | coordinate-specific criteria and evidence | each status remains separately reviewable |
Table. Formal result ledger and inferential stopping points
4. Temporal and Stochastic Valuation
This section reconstructs the proposed future-value integral under explicit
mathematical conditions. It defines a trajectory-law functional, derives two
elementary special cases, and supplies a countermodel to scalar sufficiency. The
section treats each functional as an optional representation chosen for a
declared value coordinate.
Let $\Gamma_{t_0:H}$ be a measurable trajectory space and let
$K_G(d\gamma\mid h,C,a)$ be a probability law on it. For a value coordinate
$k$, let $v_k(t,\gamma)$ be jointly measurable and let
$w:[t_0,H]\rightarrow[0,\infty)$. The relevant iterated integral is licensed by
nonnegativity or absolute integrability.
Under Assumption ?, define
$$V_{k,w}(G;C,h,a,H)
\int_{\Gamma_{t_0:H}}
\int_{t_0}^{H}
w(t)v_k(t,\gamma),dt,
K_G(d\gamma\mid h,C,a).
\tag{4}$$
Definition ? includes deterministic trajectories
as degenerate laws. The evaluator, units, sign convention, horizon, and weight
remain part of the object. A market functional and a justice-relevant
functional can therefore use different inputs:
$$V^m_k=V_{k,w_m},
\qquad
V^q_k=V_{k,w_q}.
\tag{5}$$
Equation (5) states a register separation. Selection of $w_q$ requires an
independent normative argument.
Suppose $H=\infty$, $w(t)=1$, and there exist $T\ge t_0$ and $c>0$ such that
$v_k(t,\gamma)\ge c$ for all $t\ge T$ on a set of trajectories with probability
one. Then $V_{k,1}(G)=+\infty$.
Nonnegativity and monotonicity of integration give
$$V_{k,1}(G)
\ge
\int_{\Gamma}
\int_T^{\infty}c,dt,K_G(d\gamma)
=+\infty.$$
Proposition ? characterizes the selected functional. A
market price, alienability status, ownership relation, or continuing claim
requires further premises.
If $v_k(t,\gamma)=c\ge0$, $H=\infty$, and
$w(t)=e^{-r(t-t_0)}$ for $r>0$, then
$$V_{k,w}(G)=\int_{t_0}^{\infty}e^{-r(t-t_0)}c,dt=\frac{c}{r}.
\tag{6}$$
The contrast between Proposition ? and
Corollary ? makes the role of the weighting function
visible. The literature reviewed in Section 5 supplies
several theories of intertemporal evaluation. The present paper selects among
them only within a declared application.
Let transaction $\mathcal T_1$ produce terminal value $100$ with probability
one. Let $\mathcal T_2$ produce terminal value $10{,}000$ with probability
$0.01$ and value $0$ with probability $0.99$. Then
$$\mathbb E[V(\mathcal T_1)]
\mathbb E[V(\mathcal T_2)]
=100,
\qquad
K_1\neq K_2.
\tag{7}$$
The transactions can also differ in downside exposure, tail opportunity,
learning, reversibility, and feasible continuation.
Configuration ? establishes a logical separation.
Its numbers are constructed and carry a purely logical role. A decision rule may still rank
the transactions after declaring risk attitudes, standing, option treatment,
and relevant constraints. The profile-preservation principle keeps those
choices visible.
An infinite horizon creates further obligations. Tail behavior may determine
finiteness; value coordinates may change sign; the trajectory law may remain
partially identified; and future participants may differ from current parties.
A reachable-repertoire representation can therefore complement the integral:
$$\Paths^{H,\epsilon}(G,C)
{\gamma:\gamma\text{ remains feasible and viable under the declared rule}}.
\tag{8}$$
Set inclusion, distance, robustness, or a partial order can compare repertoires.
Each choice requires its own semantics.
5. Descendant Generation and Attribution
This section develops the branching part of the source discussion. It first
defines descendants within a causal model, then separates causal,
bookkeeping, contribution, and normative relations. A normalized allocation
identity supplies the sole arithmetic result; the substantive attribution
questions remain research obligations.
Relative to a declared causal model $M$, contrast $b$, horizon $H$, and domain
rule $d$, an event or generativity $z$ is a descendant of $G$ when the model
supports a relevant directed causal path from $G$ to $z$. Write the resulting
time-indexed set as $\Desc_t(G;M,b,H,d)$.
The definition requires a model and a contrast. Shared causes, mediation,
preemption, interaction, feedback, and copying can change the descendant set.
Structural causal models provide one formal route
(Pearl, 2009; Halpern & Pearl, 2005); historical and qualitative
process tracing may supply another route in suitable research designs.
For typed descendant values, define a causal bookkeeping functional
$$V^c_{k,w,\kappa^c}(G)
\int_{\Gamma}
\int_{t_0}^{H}
w(t)
\sum_{z\in\Desc_t(G)}
\kappa^c_G(z,t,\gamma)v_{k,z}(t,\gamma)
,dt,K_G(d\gamma).
\tag{9}$$
The causal weight $\kappa^c$ reports the semantics chosen by the causal model.
It can be binary, graded, interval-valued, or unresolved. Equation (9) leaves
interaction value and shared ancestry exposed.
For each descendant $z$, distinguish:
$$\mathsf{Cause}G(z),
\quad
a{G,z},
\quad
\mathsf{Contrib}_G(z),
\quad
\mathsf{Entitle}_G(z).
\tag{10}$$
These denote, respectively, a causal relation, an accounting allocation, a
contribution assessment, and a justified entitlement relation.
The accounting coordinate $a$ may be selected for auditability. The
contribution coordinate may use a cooperative-game rule in a fully specified
game, including a Shapley value (Shapley, 1953). The entitlement
coordinate may draw on consent, agreement, labor, need, expectation, public
interest, reciprocity, governance, or another defended ground. Equation (10)
preserves their independent semantics.
Let $\Desc_t$ be finite or absolutely summable. For each descendant $z$, let
$S(z)$ be the declared candidate source set and suppose
$$a_{G,z}\ge0,
\qquad
\sum_{G\in S(z)}a_{G,z}=1.
\tag{11}$$
Then the allocated total equals the declared descendant total:
$$\sum_G\sum_{z\in\Desc_t}a_{G,z}v_z
\sum_{z\in\Desc_t}v_z.
\tag{12}$$
Rearrange the finite or absolutely convergent sums and apply Equation (11):
$$\sum_G\sum_z a_{G,z}v_z
\sum_z\left(\sum_{G\in S(z)}a_{G,z}\right)v_z
\sum_zv_z.$$
Proposition ? is a bookkeeping identity. The weights can be
disputed, empirically unsupported, or normatively irrelevant while the identity
remains true.
A supported descendant relation licenses a causal report within its model. A
continuing return, ownership position, governance authority, or liability
requires a distinct institutional or normative ground.
Claim ? protects both sides of the problem. Immediate-output
accounting can miss cumulative dependence identified in innovation research
(Scotchmer, 1991; Green & Scotchmer, 1995). Unlimited origin
claims can suppress later contribution, access, and revision. The audit should
therefore report horizon, decay or persistence, shared ancestry, interaction,
later contributors, and contestability.
6. Institutional Forms and Position Changes
This section turns from future-value objects to institutional arrangements. It
defines an institutional form as a structured bundle, compares six ideal types,
and proves that current price underidentifies the bundle. The comparison is
analytic; domain-specific law, practice, and evidence determine actual forms.
For a transaction in generativity, an institutional form is
$$\mathcal I
(\Delta\Pos,P_0,\alpha,\tau,\rho,M,Q,S),
\tag{13}$$
where $\Delta\Pos$ records position changes, $P_0$ current transfers,
$\alpha$ contingent or continuing returns, $\tau$ duration and reversion,
$\rho$ revision and exit rules, $M$ monitoring and enforcement, $Q$ decision
and governance procedures, and $S$ affected standing.
Table 4 expands the position bundle. The coordinates adapt
rights-bundle and residual-control antecedents
(Grossman & Hart, 1986; Schlager & Ostrom, 1992) and add local
registers needed for the present research question.
| @p0.18p0.25YY@
| Coordinate | Analytical content | Effective evidence | Typical ambiguity |
|---|---|---|---|
| Exercise $u$ | ability to activate or use $G$ | access, capability, resources, permitted actions | nominal permission and practical access may diverge |
| Management $m$ | ability to shape operation and development | decision authority, budgets, technical control | managerial title may conceal external dependence |
| Exclusion $x$ | ability to determine access by others | enforceable rules and technical barriers | security, scarcity, rent, and stewardship can share a mechanism |
| Alienation $a$ | ability to transfer relevant positions | transfer rule, consent, legal authority | full, partial, conditional, and temporary forms differ |
| Attribution $r$ | claim to authorship, credit, or provenance | records, norms, verification, contest routes | attribution and economic return can separate |
| Return $y$ | claim to current or later benefit | payment rule, trigger, duration, accounting | return can preserve participation or sustain control |
| Governance $g$ | authority over rules and collective decisions | voting, representation, veto, delegation | voice, control, accountability, and deadlock differ |
| Exit or reversion $e$ | route to leave, restore, or recover positions | termination, portability, reversion, support | formal exit may preserve dependence |
Table. Position coordinates for transactions in generativity
Institutional labels compress these coordinates. Table 5
presents six ideal types as prompts for specification. A royalty can accompany a
sale or a licence; equity can carry income, voting, or liquidation positions;
stewardship can arise through several legal or informal forms; shared governance
can distribute voice through many decision rules.
| @p0.16p0.25YY@
| Ideal type | Stylized position change | Potential function | Primary audit exposure |
|---|---|---|---|
| Sale | broad transfer of exercise, control, exclusion, and alienation | finality, liquidity, concentrated decision authority | valuation, consent, residual dependence, future options |
| Fixed-term licence | scoped use with retained title and scheduled reversion | access, experimentation, bounded duration | scope creep, renewal leverage, monitoring, lock-in |
| Continuing return | present payment plus contingent share $\alpha$ | participation in later realization, risk sharing | duration, accounting control, surveillance, remote descendant claims |
| Equity | residual economic claim with class-dependent governance rights | pooled risk, participation in enterprise growth | dilution, control asymmetry, liquidity, entity-level spillover |
| Stewardship | management under declared purpose and beneficiary constraints | continuity, preservation, plural standing | authority, accountability, competence, purpose revision |
| Shared governance | distributed decision positions and procedures | voice, mutual adjustment, collective learning | transaction cost, capture, veto, deadlock, representation |
Table. Institutional ideal types and primary audit dimensions
There exist two coherent institutional forms $\mathcal I_1$ and
$\mathcal I_2$ such that
$$P_0(\mathcal I_1)=P_0(\mathcal I_2),
\qquad
\mathbb E[V(\mathcal I_1)]=\mathbb E[V(\mathcal I_2)],
\qquad
\Delta\Pos(\mathcal I_1)\neq\Delta\Pos(\mathcal I_2).
\tag{14}$$
Consequently, current payment and expected output underidentify institutional
form and the complete transaction profile.
Let $\mathcal I_1$ be a transfer of exercise and management for a fixed term
with reversion to the initial holder. Let $\mathcal I_2$ be a permanent transfer
of exercise, management, exclusion, and alienation. Assign the same current
payment and the same output trajectory law to both forms. Their position-change
vectors differ in duration, exclusion, alienation, and reversion. Hence the
first two equalities coexist with the third inequality.
The proof constructs a logical countermodel. Actual contracts may differ in
price and output precisely because positions differ. The proposition establishes
the information gap in a two-coordinate description.
A continuing-return schedule can be represented as
$$R_A
P_0
+
\int_{\Gamma}
\int_{t_0}^{H}
\sum_z\alpha_A(t,z,\gamma)v_z(t,\gamma)
,dt,K_G(d\gamma),
\tag{15}$$
when the integral exists. Its institutional meaning depends on descendant
scope, duration, audit authority, modification rules, later contributors,
transferability, and termination. The formula provides a payment description.
For evaluation, define a non-aggregated audit
$$\Audit_{\mathcal T}
\left\langle
J_{\mathrm{acquisition}},
J_{\mathrm{control}},
J_{\mathrm{trajectory}},
J_{\mathrm{attribution}},
J_{\mathrm{return}},
J_{\mathrm{options}},
J_{\mathrm{revisability}},
J_{\mathrm{third\ parties}}
\right\rangle,
\tag{16}$$
with each coordinate positive, adverse, mixed, baseline-sensitive, or
unresolved under a stated criterion. Aggregation requires a separate ordering
rule and conflict procedure.
7. Constructed Configurations and Comparative Method
This section tests the framework’s discrimination through six constructed
configurations. Their role is logical and methodological: each isolates a
combination of price, trajectory, position, and institutional form. Prevalence
estimation and named-institution classification require separate empirical work.
| @p0.17p0.25YY@
| Configuration | Fixed features | Profile difference | Required evidence |
|---|---|---|---|
| Equal-price sale and licence | same $P_0$, same modeled output | reversion, exclusion, alienation, exit | enforceability, dependence, alternatives, bargaining process |
| Equal-expectation trajectories | same expected value | downside, tail possibility, learning, resilience | model identification, risk-bearing, standing, option semantics |
| Participatory continuing return | bounded share and transparent accounting | sustained participation and risk sharing | duration, costs, consent, later contributors, realized effects |
| Foreclosing continuing return | remote descendants and originator veto | monitoring, control persistence, later-creator constraint | causal scope, governance, contestability, chilling effects |
| Purpose-bound stewardship | management under beneficiary and purpose rules | constrained alienation and plural standing | competence, accountability, purpose revision, beneficiary voice |
| Shared governance | distributed decision rights | voice and mutual adjustment with coordination cost | representation, capture, deadlock, speed, domain outcomes |
Table. Constructed configurations and unresolved evidence
Table 6 displays the principal contrast. Price equality
leaves position changes open. Expectation equality leaves trajectory structure
open. A continuing return changes participation and can also extend monitoring
or control. Stewardship changes purpose and standing. Shared governance changes
decision procedures and exposes coordination burdens.
7.1 Configuration analysis
This subsection applies the profile in a fixed sequence so that each constructed
case can be reproduced. The sequence begins with the object and ends at the
evaluative stopping point.
First, declare $G$, its carrier and domain, and the realization conditions.
Second, record $\Pos^0$ and $\Pos^1$ for every party with relevant standing.
Third, identify the current transfer, temporal horizon, trajectory law, and
reachable repertoire. Fourth, state descendant and attribution rules. Fifth,
specify duration, revision, reversion, monitoring, governance, and exit. Sixth,
report each audit coordinate with its evidence and uncertainty.
The equal-price sale and licence instantiate
Proposition ?. A licence may preserve reversion and
future participation while creating renewal leverage or monitoring burdens. A
sale may provide finality and liquidity while transferring wider future-control
positions. The comparison depends on the actors’ alternatives, bargaining
conditions, domain rules, and third-party effects.
The two continuing-return configurations share Equation (15) and differ in
institutional incidence. A bounded, auditable, revisable share can sustain a
relation between an originating contributor and later realization. A remote-
descendant share paired with veto or broad audit powers can burden later
contributors and preserve originator control. The payment form alone therefore
leaves the audit open.
Purpose-bound stewardship can preserve continuity, public benefit, ecological
limits, or collective memory. It can also centralize interpretive authority and
exclude affected groups. Shared governance can distribute voice and enable
learning; it can also generate capture, strategic veto, decision delay, or
unclear responsibility. Institutional comparison requires both intended
function and realized effect.
7.2 Empirical comparison design
This subsection converts the constructed contrasts into a later research
design. It defines the minimum evidence needed to move from a configuration to
a target-domain claim.
A comparative dossier should select one domain and identify matched or
process-comparable arrangements. It should document the initial position
bundle, bargaining and consent process, payment and risk allocation,
implementation, later position changes, outputs, descendant pathways,
revisions, exits, and third-party effects. Rival explanations should include
selection, underlying quality, capital access, management competence, network
position, regulatory change, and demand shocks.
Furman and Stern’s institutional study of cumulative research illustrates the
level of design needed to distinguish institutional effect from selection
(Furman & Stern, 2011). Its specific intervention and domain remain
separate from the six ideal types here. A later P016 empirical study could focus
on one setting such as research tools, platform creator relations, community
knowledge, or mission-bound infrastructure. Cross-domain generalization would
follow after domain-specific identification.
Before an ideal type acquires an empirical or evaluative ranking, the project
should supply at least two positive, two boundary, and two adverse cases within
a fixed domain, together with rival explanations and evidence concerning
effective positions over time.
8. Objections and Defeat Conditions
This section subjects the proposal to adversarial tests. It groups objections
by conceptual redundancy, formal choice, attribution, institutional idealization,
and normative scope. Each objection names a revision or defeat condition.
8.1 Conceptual redundancy
This subsection tests whether the proposed transaction category adds useful
discrimination beyond assets, contingent claims, intellectual property, and
incomplete-contract theory.
Many assets yield uncertain future services and revenues. Contingent claims can
represent state-dependent payment. Cumulative-innovation theory addresses
sequential value. Residual-control theory addresses incomplete contracts. The
paper earns a distinct role only when the combined profile of reachable
repertoires, plural positions, descendant attribution, revision, and third-party
standing changes the research question or comparison. If a target case reduces
adequately to an existing asset or contract model, the local generativity
vocabulary should be removed from that case.
8.2 Functional selection and scalar compression
This subsection tests whether the framework moves arbitrariness from one scalar
into a larger vector. The response is procedural and remains incomplete.
Horizon, weight, value coordinate, probability law, repertoire rule, and
ordering all require selection. The profile makes these choices inspectable and
postpones aggregation. A practical decision eventually requires a rule for
action. The next research stage should compare expected value, stochastic
dominance, robust decision, option-preserving, viability, and multi-criteria
approaches under one application. Profile preservation is useful only when it
clarifies that selection.
8.3 Attribution expansion
This subsection tests the tendency of descendant language to extend origin
claims through long causal chains.
A causal path can persist through many stages, while contribution becomes
interactive and later agents introduce independent work. The framework requires
a horizon, contrast, model, collision rule, later-contributor register, and
contest procedure. Causal status licenses a causal statement within the model.
Contribution and entitlement follow their own rules. A target application that
uses one numerical kernel for all four registers defeats the separation
principle.
8.4 Institutional idealization
This subsection tests the portability of the six institutional labels.
Sale, licence, royalty, equity, stewardship, and shared governance vary across
jurisdictions, industries, communities, and informal practices. The tables are
configuration prompts. An application must replace each row with operative
rights, effective powers, duration, enforcement, decision rules, and affected
standing. Legal conclusions require jurisdiction-specific primary authority.
Institutional recommendations require comparative evidence concerning benefits,
burdens, feasibility, and competence.
8.5 Normative scope and future standing
This subsection tests the relation between the analytic profile and justice.
Future value can belong to different actors, communities, publics, ecosystems,
or generations. Greater generativity can create harm, domination, ecological
burden, or exclusion. Current consent may coexist with constrained alternatives,
and future participants may lack representation. The audit therefore keeps
acquisition, control, trajectory, attribution, return, options, revisability,
and third-party standing separate. A justice conclusion requires an independent
account of standing, procedure, autonomy, distribution, non-domination,
ecological limit, and intergenerational obligation.
The project should narrow or abandon a component when it duplicates an existing
framework, lacks observable semantics, hides a contested evaluator, produces
equivalent descriptions across institutionally different forms, or converts
model structure into entitlement.
A systematic originality review may also show that the proposed synthesis has a
clear prior formulation. Such a result would shift the paper’s role toward
clarification, comparison, or application.
9. Research Obligations and Conclusion
This section consolidates the work required beyond the present position paper
and states its bounded conclusion. It orders the obligations from formal and
empirical identification through normative, legal, and originality analysis.
Specify estimands or bounds for trajectory laws, reachable repertoires, tail
behavior, substitution, and learning. Report model uncertainty and sensitivity
to horizon and weighting choices.
For each target domain, distinguish causal structure, accounting allocation,
contribution assessment, and normative entitlement. Supply rules for interaction,
shared ancestry, later contributors, decay or persistence, and contestability.
Replace ideal-type labels with effective position bundles, payment and risk
rules, duration, reversion, monitoring, governance, exit, enforcement, and
third-party standing. Compare intended function with realized effect.
Develop independent accounts of standing, intergenerational concern,
alienability, consent, control, distribution, public interest, and ecological
constraint. Use jurisdiction-specific primary authority for every legal
classification.
Extend the literature review across contingent claims, real options,
intellectual property, incomplete contracts, knowledge commons, benefit sharing,
intergenerational ethics, and theories of contribution. Identify equivalent
prior frameworks and test the incremental value of the proposed synthesis.
The paper began from a narrow correction: the object of inquiry is a
generativity or a material position concerning its future exercise. That
correction changes the analytical unit from one present output to a typed
transaction profile. Temporal functionals can summarize declared value streams;
their finiteness depends on horizon and weight. Trajectory laws and reachable
repertoires preserve risk and option structure. Descendant graphs preserve
propagation questions. Separate causal, accounting, contribution, and normative
registers preserve attribution discipline. Position vectors and institutional
forms preserve control, participation, reversion, monitoring, and governance.
The formal results are deliberately limited. A sustained positive flow makes
one undiscounted functional diverge. Normalized allocation weights preserve a
declared total. Equal expected values leave trajectory structure open. Equal
current payments leave institutional form open. These results support the
profile-preservation principle and leave substantive evaluation to declared
empirical and normative premises.
The proposed framework is therefore a research architecture for transactions
whose object extends through future generation. Its value will depend on
comparative discrimination, empirical identifiability, institutional realism,
normative clarity, and originality. Each remains revisable through the research
obligations above.
Acknowledgments
The author thanks Ron Eglash for dialogue that contributed to the wider research
setting in which questions of generativity and value circulation were developed.
The researcher-origin correction distinguishing a transaction in generativity
from an ordinary transaction with later effects supplied the starting point of
this paper. Formal reconstruction and manuscript preparation involved OpenAI’s
Codex as disclosed in the Notices. The author bears sole responsibility for the
manuscript’s definitions, formal constructions, institutional taxonomy,
arguments, conclusions, and errors.
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