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Content Exploration Beyond the Feed: Creator Supply and the Shared Corpus
\raggedbottom
\title{Content Exploration Beyond the Feed: Creator Supply and the Shared Corpus}
\author{Yuanyuan Shen}
\affiliation{\institution{Snap Inc.}\city{New York}\state{NY}\country{USA}}
\email{[email removed]}
\author{Yiren Yan}
\affiliation{\institution{Snap Inc.}\city{Palo Alto}\state{CA}\country{USA}}
\email{[email removed]}
\author{Wenjie Li}
\authornote{Work done while at Snap Inc.}
\affiliation{\institution{Snap Inc.}\city{Palo Alto}\state{CA}\country{USA}}
\email{[email removed]}
\author{Chunhui Zhu}
\affiliation{\institution{Snap Inc.}\city{Palo Alto}\state{CA}\country{USA}}
\email{[email removed]}
\begin{abstract}
Industrial recommenders give new content initial views through budgeted exploration, then use early performance to decide further delivery. On many short-video platforms, exploration is the primary route by which new videos reach viewers. Viewer-side tests measure consumption, while the published budget objectives we review omit creator response. We analyze four experiments on a major short-video platform. An eight-month creator ablation finds that production exploration raises videos posted per creator by 8.55\% and creators posting at least once by 7.10\% relative to a minimal floor. A budget-matched reallocation raises creator participation with no detectable short-run viewer-side change. A year-long viewer ablation separately finds 1.74\% more video views but 2.13\% less view time.
A delivered view creates immediate feed value, can trigger organic take-up, and can induce creator supply. Take-up and supply replenish a shared corpus, creating two measurement limits. Viewer-side A/B tests cancel the corpus effect when both arms consume the same corpus. Giving each arm its own corpus avoids cancellation, but turnover still controls the horizon. If the corpus turns over at rate $\omega$ per posting cycle, a $t$-cycle experiment expresses at most $\omega t$ of the eventual corpus effect. More users reduce noise without making the corpus turn faster. Before the corpus path visibly bends, data cannot distinguish a modest fast effect from an arbitrarily large slow one, so a valid confidence interval may lack a finite upper endpoint.
As predicted, the three-week co-diverted experiment cannot determine whether the eventual corpus effect is positive or negative. Within the window, it identifies the direct feed effect, and an exploratory cohort analysis detects organic lift after exploration ends. Together, the experiments establish a positive creator response, measure the gross corpus flow visible within three weeks, and show the design and duration needed to identify total value.
\end{abstract}
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\keywords{content cold-start, content distribution, creator economy, two-sided platforms, bandits, short-video}
\maketitle
\section{Introduction}
\label{sec:intro}
Short-video platforms receive enormous volumes of new uploads, most of which
initially reach few viewers. Ranking models favor content with an observed
response, so new videos lack the history needed to compete. \emph{Exploration}
gives them initial views. On many short-video platforms, exploration is the
primary distribution channel for most new videos.
\begingroup
\setlength{\emergencystretch}{2em}
Platforms commonly give each new video an \emph{exposure budget} and use early
performance to decide whether to release more views~\citep{shen2025aliboost,gudmundsson2026pinequalizer,wang2025item,jeon2025epinet,chen2025kuaishou}.
We study systems that allocate exposure in stages before each video's
exploration period ends. A video
that clears an early bar receives more exposure. A video that misses it leaves
the exploration pool (\S\ref{sec:related}).
\par
\endgroup
This design creates an evaluation problem. Viewer-side A/B tests can show
mixed or negative consumption effects even though exploration supplies most
new-video distribution. Related systems report the same short-window
pattern~\citep{su2024exploration,chen2021values}. Longer one-sided tests share
the same corpus across arms, so its contribution cancels at every horizon.
On the major short-video platform we study, an eight-month creator ablation
shows that production exploration raises videos posted per creator by 8.55\%
and creators posting at least once by 7.10\% relative to a minimal floor.
A separate budget-matched reallocation raises creator participation with no
detectable short-run viewer-side change. A year-long viewer ablation finds
1.74\% more video views and 2.13\% less view time relative to disablement. The
viewer path shows no sustained buildup over twelve months. These results
establish a positive creator response and isolate the immediate viewer trade-off.
Prior isolated-submarket experiments establish two corpus links:
exploration expands the discoverable corpus, and random thinning shows that
reducing the corpus lowers satisfied-user counts~\citep{su2024exploration}.
We ask how a deployed budgeted mechanism can measure the resulting value. The
creator ablation measures the posting response that replenishes the corpus,
and the viewer ablation measures the immediate feed trade-off. Co-diversion
jointly randomizes matched creator and viewer submarkets, so each arm develops
its own corpus. Our three-week probe lands at the estimation floor predicted by
the theory. At that horizon, a cohort analysis measures gross corpus flow,
while the aggregate asymptote remains unsigned.
\Cref{fig:causal-map} maps the three channels to the designs that identify
them.
\ifextendedbuild\else\newpage\fi
\ifextendedbuild
\begin{figure*}[t]
\centering
\resizebox{0.68\textwidth}{!}{
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>={Latex[length=2.4mm,width=2.1mm]},
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fastbox/.style={box, fill=orange!16, draw=orange!55!black},
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\node[fill=blue!4, draw=blue!20, rounded corners=4pt,
inner xsep=7pt, inner ysep=6pt, fit=(creator)(corpus)(future)]
(slowband) {};
\end{scope}
\node[font=\scriptsize\itshape, text=blue!35!black, anchor=south]
at ([xshift=0.7cm]slowband.north) {slow channels};
\draw[flow] (explore) -- node[elab, above] {immediate} (feed);
\draw[flow] (explore) -- node[elab, left] {response} (creator);
\draw[flow] (explore) -- node[elab, above, sloped, pos=0.45] {take-up} (corpus);
\draw[flow] (creator) -- node[elab, above] {new posts} (corpus);
\draw[flow] (corpus) -- node[elab, above] {serves} (future);
\node[abtag] (vtag) at (5.2,0.82) {viewer-side A/B};
\node[abtag] (ctag) at (0,-1.05) {creator-side A/B};
\node[abtag] (dtag) at (5.2,-1.05) {co-diverted A/B};
\draw[measure] (vtag) -- (feed);
\draw[measure] (ctag) -- (creator);
\draw[measure] (dtag) -- (future);
\end{tikzpicture}
}
\caption{Value channels and identifying designs. Exploration has an immediate feed effect,
can change creator supply, and feeds a shared corpus through both take-up and
new posts. The shaded channels express slowly. Each dashed design reaches a
different channel. A one-sided design shares the corpus across arms, so that
channel cancels. A separate budget-matched co-diverted variant perturbs allocation at
fixed nominal budget and measures the creator response (\S\ref{sec:reallocation}).}
\label{fig:causal-map}
\end{figure*}
\else
\begin{figure}[t]
\centering
\resizebox{\columnwidth}{!}{
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(slowband) {};
\end{scope}
\node[font=\scriptsize\itshape, text=blue!35!black, anchor=south]
at ([xshift=0.7cm]slowband.north) {slow channels};
\draw[flow] (explore) -- node[elab, above] {immediate} (feed);
\draw[flow] (explore) -- node[elab, left] {response} (creator);
\draw[flow] (explore) -- node[elab, above, sloped, pos=0.45] {take-up} (corpus);
\draw[flow] (creator) -- node[elab, above] {new posts} (corpus);
\draw[flow] (corpus) -- node[elab, above] {serves} (future);
\node[abtag] (vtag) at (5.2,0.82) {viewer-side A/B};
\node[abtag] (ctag) at (0,-1.05) {creator-side A/B};
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\draw[measure] (vtag) -- (feed);
\draw[measure] (ctag) -- (creator);
\draw[measure] (dtag) -- (future);
\end{tikzpicture}
}
\caption{Value channels and identifying designs. Exploration has an immediate feed effect,
can change creator supply, and feeds a shared corpus through both take-up and
new posts. The shaded channels express slowly. Each dashed design reaches a
different channel. A one-sided design shares the corpus across arms, so that
channel cancels. A separate budget-matched co-diverted variant perturbs allocation at
fixed nominal budget and measures the creator response (\S\ref{sec:reallocation}).}
\label{fig:causal-map}
\end{figure}
\fi
Published cold-start systems score and budget videos with viewer and corpus
quantities such as predicted discoverability and click-through. None of the
systems we review includes the creator's later posting response in its
\emph{budget} objective. Production feed ranking outside this class has modeled
creator incentives for years~\citep{tu2019feedback}
(\S\ref{sec:related}).
\begingroup
\setlength{\emergencystretch}{2em}
Cold-start systems must decide within the delivery window whether a video
receives more exposure or leaves the pool. At that point, the system observes
only fast viewer signals. The delayed posting response and corpus turnover
therefore require offline estimates. Historical creator experiments and
corpus-age data supply those estimates, and budget objectives can use them as
priors. A horizon-matched creator
experiment identifies the supply response. Co-diversion retains the
shared-corpus channel (\S\ref{sec:creator-ablation} and \S\ref{sec:probe}).
\par
\endgroup
We model the ecosystem that exploration feeds and test its channels with four
experiments on a major short-video platform (\S\ref{sec:budget-problem}). The
linear model supports the value accounting. The timing results require only
corpus turnover and survive without linearity (\S\ref{sec:measurement}).
The two long-running ablations compare the mechanism with disablement or a
minimal floor, so their estimands are invariant to allocator details. The
budget-matched experiment separately changes allocation at a fixed nominal
budget. We contribute a valuation and measurement framework for these rules.
Algorithm design lies outside our scope. We make three contributions:
\begin{enumerate}[leftmargin=*, nosep]
\item \textbf{Signed creator response.} An eight-month ablation of production
exploration raises videos posted per creator by 8.55\% and creators posting
at least once by 7.10\% above a minimal floor. The published cold-start budget
objectives we review omit this response.
A budget-matched reallocation raises creator participation with no detectable
short-run viewer cost (\S\ref{sec:experiments}).
\item \textbf{Value and identification.} We separate a delivered view's value
into the immediate view, organic take-up, and induced creator supply, then map
each channel to its identifying randomization. A posting loop with gain
$\mathcal{R}$ amplifies posting by $1/(1-\mathcal{R})$. One-sided designs identify the
direct and supply channels but
exclude the shared corpus by construction. These are distinct estimands, and
the designs determine which net signs are identified
(\S\ref{sec:dynamics}, \S\ref{sec:value}, \S\ref{sec:experiments}).
\item \textbf{Corpus horizon.} Only isolated cells retain the corpus
contribution in their contrast, and they must wait for the corpus itself to
turn over. Under a monotone stock transition with turnover $\omega$, a
$t$-cycle experiment expresses at most $\omega t$ of
the asymptote. Additional users reduce noise but cannot advance that
transition. The three-week probe lands at the predicted estimation floor. An
exploratory cohort analysis measures gross corpus flow at the feasible
horizon, while the aggregate asymptote and net value after displacement
remain unresolved. This result separates what three weeks can identify from
what requires a longer isolated trajectory
(\Cref{thm:horizon,prop:detection}; \S\ref{sec:probe}).
\end{enumerate}
The long-running ablations estimate a viewer-feed effect after substitution
and an aggregate posting response. These effects use
different units, so we report them separately. A total-value estimate requires
a common scale. Unlike
one-off traffic grants, the ablations measure a standing mechanism on both market
sides over months. The shared-corpus value requires co-diversion at the
prescribed horizon~\citep{su2024exploration}. Below a curvature threshold, that
design can lower-bound an expressed increment while the asymptote still lacks a
finite upper bound (\S\ref{sec:probe}).
\section{Related Work}
\label{sec:related}
\par\vspace{1pt}\noindent\textbf{Content Cold-Start in Recommender Systems.}\hspace{0.5em plus 0.1em minus 0.05em}
Cold-start is among collaborative filtering's oldest
problems~\citep{schein2002methods,lops2011content,lee2019melu}, met on video
platforms with a dedicated exploration phase before full
recommendation~\citep{covington2016deep}. We treat that phase as a first-class
distribution channel carrying creator as well as viewer value.
\par\vspace{1pt}\noindent\textbf{Long-Term and Slow-Expressing Effects.}\hspace{0.5em plus 0.1em minus 0.05em}
\begingroup
\setlength{\emergencystretch}{2em}
Short experiments are known to mismeasure long-run impact, with slow
expression treated as a \emph{user-side} phenomenon to be estimated around.
Existing methods include cohort and stepped-wedge designs for user
learning~\citep{hohnhold2015longterm}, surrogate
indices~\citep{athey2019surrogate}, and temporal designs for
carryover~\citep{basse2023longterm}. Here the slowness is structural, a
two-sided supply loop with a corpus stock, and the question is when the
long-run effect is observable at all. Together, \Cref{thm:horizon,cor:duality},
the $N^{-1/3}$ detection law of \Cref{prop:detection}, and the $N^{-1/5}$
estimation law of \Cref{thm:curvature} bound what a finite-length experiment can see of the equilibrium effect. The gain--relaxation
relation is classical in Markov mixing and critical slowing down. The
phenomenon of unbounded confidence sets behind \Cref{thm:curvature} is classical
in weakly identified models~\citep{gleser1987nonexistence,dufour1997impossibility}.
We specialize these results to the exponential-approach family, derive an
operational curvature constant and horizon laws, and tie them to exploration's
equilibrium value.
\par
\endgroup
\par\vspace{1pt}\noindent\textbf{Industrial Cold-Start Allocation.}\hspace{0.5em plus 0.1em minus 0.05em}
Published cold-start systems share two features. New items receive a
per-item exposure allocation, and continued exposure is gated on early
performance. \citet{wang2025item} allocate per-item traffic under a global
budget with a floor and ceiling by inverting a learned discoverability
probability. \citet{wang2025itemcentric} screen candidates using a Beta
posterior that balances satisfaction against item quality.
\citet{jeon2025epinet} reserve quota below an impression threshold, and
\citet{chen2025kuaishou} pair an exposure floor with flow steered toward
quality content. The full mechanism analyzed here adds a bounded delivery
window with escalation and withdrawal, as in the tiered system of
\citet{shen2025aliboost}. The platform we study runs this mechanism class,
although published accounts differ in how much of its structure they report.
\par\vspace{1pt}\noindent\textbf{Objectives and Their Timing.}\hspace{0.5em plus 0.1em minus 0.05em}
The systems differ in what determines the budget.
\citet{wang2025item} maximize the number of items becoming ``discoverable
post exploration.'' The tiered system above budgets on predicted
click-through and gates escalation on realized CTR. None of the systems
reviewed above includes a term for
the creator's subsequent supply behavior \emph{in its budget objective}, a
statement about the published record that the structural argument of
\S\ref{sec:intro} predicts. That system motivates its design partly by
producer incentives, yet no producer variable enters its budget rule.
The gap is specific to this class. \citet{tu2019feedback} reshape a production
feed's feedback distribution to nurture creators, raising creation at no
measured consumer cost. \citet{wang2025dynamic} derive allocation policies
that price creators' future growth. The settings differ in cadence. Feed
ranking can adapt against long-run outcomes, whereas a cold-start budget must
be set, escalated, and withdrawn within a bounded window whose exit gate
returns to viewer-side evidence. Removing that gate reportedly degrades
viewer-side metrics~\citep{shen2025aliboost}, yet its creator-side cost is
unmeasured.
Two prior results sit closest to ours.
With two separate interventions, \citet{su2024exploration} establish that
exploration grows the discoverable corpus through joint user and corpus
co-diversion. They then show that random corpus thinning costs satisfied
users, with the benefit accruing over months. \citet{shen2026isolation}
characterize the cost imposed by co-diversion itself. We
identify the creator-supply response to a standing budgeted mechanism,
separate structural cancellation from horizon attenuation, and derive the
design and information limits that govern direct measurement of the
corpus-mediated consequence.
\par\vspace{1pt}\noindent\textbf{Adjacent Lines.}\hspace{0.5em plus 0.1em minus 0.05em}
Prior systems in this family used bandit exploration~\citep{li2010contextual,chen2021values}.
It valued a view for information about an arm. Budgeted allocation instead
prices the view as a distribution quantity (\Cref{prop:gradient}). Ad delivery under
budgets~\citep{mehta2007adwords,balseiro2019learning} contributes the
mechanics but prices impressions in a common currency and omits the creator's
behavioral response. Field experiments on two-sided platforms
establish that exposure causally shapes creator supply.
Randomized traffic raises production by $5.87\%$~\citep{hu2024traffic}.
Additional impressions produce higher-quality and more diverse output~\citep{xia2025supporting},
as do peer awards~\citep{burtch2022peer}. Theory connects demand allocation to
participation~\citep{rochet2003platform,caillaud2003chicken,bhargava2022creator,qian2024digital}.
Closest to our reading, \citet{yao2024unveiling} formalize the trade-off in
theory and simulation. Our ablations price a standing production mechanism
on both market sides over months. Prior experiments study one-off traffic
grants over weeks. Fairness work on provider-side
exposure~\citep{abdollahpouri2019managing,burke2017multisided} studies
minimum-exposure guarantees as commitments, while this class grants floors
for operational reasons.
\section{The Mechanism and Its Ecosystem}
\label{sec:problem}
\subsection{Budgeted Exploration as Practiced}
\label{sec:budget-problem}
Creators submit content items into an \emph{exploration pool} $\mathcal{P}_t$.
Each item $s$ remains eligible in the pool for at most $T_{\max}$, its
time-to-live (TTL). The pool competes for an aggregate exploration capacity
of $V_t$ views. A
\emph{view budget} $B(s) \in \mathbb{Z}_{\geq 0}$ is the target
number of exploration views to deliver to $s$ within its TTL, subject to
capacity and continued eligibility.
\begin{definition}[Budgeted Exploration Problem]
Given pool $\mathcal{P}_t$, capacity $V_t$, and a value function
$U(s, B)$ for delivering $B$ views to content item $s$, choose
budgets to
\begin{equation}
\begin{aligned}
\max_{\{B(s)\}_{s \in \mathcal{P}_t}} \;\; & \sum_{s \in \mathcal{P}_t} U(s, B(s)) \\[-1pt]
\text{s.t.} \;\; & \sum_{s \in \mathcal{P}_t} B(s) \leq V_t,
\quad B_{\min} \leq B(s) \leq B_{\max} \;\; \forall s,
\end{aligned}
\label{eq:budgeted}
\end{equation}
where $B_{\min}$ is a minimum budget guarantee (cold-start views) for every
content item and $B_{\max}$ a per-item ceiling.
\end{definition}
Industrial practice resolves this generically
(\S\ref{sec:related}). Every eligible item receives the
guarantee $B_{\min}$ before any viewer response exists. Views above it,
\emph{escalation}, are conditioned on early response inside the window.
Delivery of the remainder stops, \emph{withdrawal}, when the budget is
exhausted, expires, or repeatedly misses viewer-response criteria.
Both decisions must rely on the fastest-expressing
quantities available, and \Cref{thm:horizon} will show that decisions made
on those quantities are exactly the ones blind to the creator-supply and
corpus-stock channels of \Cref{prop:gradient}. The platform we measure runs
a standard member of this class. How budgets are set is platform-specific.
The theory conditions on the resulting budgets, while the ablations compare
the mechanism with its absence or a minimal floor. Both analyses apply without
specifying the platform's particular budget-setting rule.
Budget assignment is decoupled from delivery. The contract requires only that
each content item receive its target views from relevant viewers within its TTL,
and a dedicated funnel, ranking boosts, quotas, or guaranteed-delivery
pacing honor it equally, so the valuation and evaluation transfer to any of
them.
\subsection{An Ecosystem Model}
\label{sec:dynamics}
Whether budgeted exploration pays for itself is put to viewer-side A/B tests,
whose consumption results can be mixed or negative
(\S\ref{sec:viewer-ablation}). The viewer-side contrast identifies only the
immediate feed trade-off.
Feedback value compounds over periods and grows with persistence. No short
window can observe a slow effect, whether it is an A/B test's measurement
window or the mechanism's own gate.
\par\vspace{1pt}\noindent\textbf{States.}\hspace{0.5em plus 0.1em minus 0.05em}
We work in discrete time. One \emph{period} is a submission-feedback cycle
that includes submission, exploration views within TTL, and the creator's next
posting decisions. Its calendar length is a platform property external to the model.
Two state variables describe the ecosystem at period $t$. The first is $\Lambda_t$, the new
submission rate or \emph{supply}. The second is $K_t$, the \emph{organic corpus} of
content items remaining in organic distribution after their exploration window.
\par\vspace{1pt}\noindent\textbf{Model ingredients.}\hspace{0.5em plus 0.1em minus 0.05em}
Six ingredients parameterize the model. The baseline submission rate is
$\Lambda_0$. The \emph{creator response} $g(\cdot)$ gives expected
next-period submissions as a function of views received. We assume it is
increasing and \emph{concave}, consistent with the saturating responses
reported in field experiments~\citep{hu2024traffic,xia2025supporting}.
Expected total views are $\bar{V}(B) = B + q(B)\,V_{\mathrm{org}}$.
This expression includes $B$ delivered exploration views plus, with \emph{organic take-up}
probability $q(B)$, a further $V_{\mathrm{org}}$ organic views. We assume $q$ is
nondecreasing and all view-value weights are nonnegative. The corpus turns
over at per-period rate $\omega \in (0,1)$. Viewer value is $\eta$ per
corpus unit and period, so aggregate consumption (total view time, say) is
locally affine in the stock, $E_t = \eta\,K_t + \text{const}$, the
constant carrying consumption outside the corpus.
Writing $\eta_{\mathrm{o}}$ for gross value per organic view, our
normalization sets $\eta/\omega=\eta_{\mathrm{o}}V_{\mathrm{org}}$: both sides are
the lifetime organic value of one taken-up item.
\par\vspace{1pt}\noindent\textbf{Dynamics.}\hspace{0.5em plus 0.1em minus 0.05em}
These ingredients give a pair of linear recursions.
\begin{equation}
\Lambda_{t+1} = \Lambda_0 + \mathcal{R}\,\Lambda_t,
\qquad
K_{t+1} = (1-\omega)\,K_t + q(B)\,\Lambda_t .
\label{eq:dynamics}
\end{equation}
The first says next period's supply is the baseline plus a fed-back share of
this period's supply. The second says the corpus retains a fraction
$1-\omega$ and gains the taken-up share of new submissions.
\ifextendedbuild
Where the recursions settle, and what one more delivered view is worth once
the loop has run its course, follow directly.
\begin{proposition}[Exploration multiplier]
\label{prop:multiplier}
For $\mathcal{R} < 1$, the dynamics~\eqref{eq:dynamics} converge to
\[
\Lambda^* = \frac{\Lambda_0}{1-\mathcal{R}},
\qquad
K^* = \frac{q(B)}{\omega}\,\Lambda^*,
\]
and one additional delivered view yields $\delta/(1-\mathcal{R})$
cumulative additional submissions over the ecosystem's response. Every induced
submission attracts views that induce further submissions, producing the multiplier.
\end{proposition}
\begin{proof}
The affine recursion for $\Lambda_t$ contracts to its unique fixed point
$\Lambda_0/(1-\mathcal{R})$. Substituting into the $K$ recursion gives
$K^*$. A marginal view induces $\delta$ submissions, which
induce $\delta\mathcal{R}$, then $\delta\mathcal{R}^2$, summing to
$\delta/(1-\mathcal{R})$.
\end{proof}
\fi
\par\vspace{1pt}\noindent\textbf{Gain and sensitivity.}\hspace{0.5em plus 0.1em minus 0.05em}
The creator
response enters through two distinct quantities. The \emph{loop gain} is
$\mathcal{R} \triangleq g\bigl(\bar V(B)\bigr)$, the expected
number of \emph{further} submissions one submission induces and the
eigenvalue of the supply recursion. The \emph{sensitivity} is
$\delta \triangleq g'(\bar V(B))$. It is the marginal
posting response to one additional delivered view, and the quantity that
values a view. The recursions are mean-field approximations. Both $\delta$ and $q$ are population
averages, and the subscripted $\delta_c$, $q'_s$ of
\Cref{prop:gradient} are their individual-level counterparts. A healthy
platform is \emph{subcritical}, with $\mathcal{R} < 1$. Each submission then induces less
than one additional submission, so the supply loop remains stable. The budget $B$ is the
lever through which the platform sets $\mathcal{R}$.
\par\vspace{1pt}\noindent\textbf{Supply loop and corpus stock.}\hspace{0.5em plus 0.1em minus 0.05em}
Stacked as $x_t = (\Lambda_t, K_t)$, the recursions read
$x_{t+1} = M x_t + u$ with eigenvalues $\mathcal{R}$ (the \emph{supply loop}) and
$1-\omega$ (the \emph{corpus stock}). The two play different roles. The
supply loop governs how much a view is worth. The corpus stock governs how
long an experiment must run before that value is visible. No result below
requires the corpus to be slower than the supply loop: because
$1-\omega$ is mechanical turnover and involves $g$ nowhere,
the horizon bound holds for any creator response and any ordering of the
two eigenvalues (\Cref{thm:horizon}).
\begin{remark}[Fixed capacity]
\label{rem:capacity}
Fixing the per-item budget is compatible with finite capacity. Under
\eqref{eq:budgeted}, a larger pool lowers views per item through
$V/\Lambda$, adding negative feedback. Ignoring that congestion can
overstate the supply multiplier. The timing statements remain unchanged because
they depend on $\omega$ alone. The local elasticity derivation
is in Appendix~\ref{app:dynamics}. Concavity is needed only near current budgets,
where the field evidence above is most direct.
\end{remark}
\par\vspace{1pt}\noindent\textbf{The value of a view and its multiplier.}\hspace{0.5em plus 0.1em minus 0.05em}
The dynamics converge to $\Lambda^* = \Lambda_0/(1-\mathcal{R})$ and
$K^* = q(B)\,\Lambda^*/\omega$. One marginal delivered view
induces $\delta$ submissions, whose descendants form the geometric sum
$\delta\sum_{k\geq0}\mathcal{R}^k=\delta/(1-\mathcal{R})$
(Proposition~\ref{prop:multiplier}). Valuing a view by its direct
response alone therefore understates its worth by the factor
$1/(1-\mathcal{R})$, which grows without bound as the platform approaches
criticality, $\mathcal{R} \to 1$.
\begin{remark}[Scope of the linear model]
\label{rem:scope}
\eqref{eq:dynamics} is the tangent description of a subcritical ecosystem
at steady state, including $V_{\mathrm{org}}$. The \emph{multiplier} applies locally at
that steady state. \Cref{thm:horizon}'s bound carries no such restriction. The
$\eta$'s are gross values. An on/off
contrast measures the gap \emph{net} of displaced impressions, the
decision-relevant quantity. Additional nonnegative feedbacks would raise the
spectral radius of $M$. Opposite-sign feedbacks such as crowd-out or quality
dilution can lower it and lie outside this model
(Appendix~\ref{app:dynamics}).
\end{remark}
\section{Value and Measurability}
\label{sec:theory}
\subsection{What a Delivered View Is Worth}
\label{sec:value}
The multiplier of \S\ref{sec:dynamics} values the supply loop as a whole. An
allocator needs something finer, the value of one more view to one particular
content item. Under the same model, that value separates into three channels. They are
the posting that the view induces, the view itself, and organic take-up.
\begin{proposition}[Marginal value of a view]
\label{prop:gradient}
Under~\eqref{eq:dynamics}, the cumulative consumption value of one
additional view delivered to content item $s$ from creator $c$ with
budget $B(s)$ is
\[
\mathrm{MV}(s)
= \underbrace{\delta_c\, v^*}_{\text{direct creator channel}}
+ \underbrace{\eta_{\mathrm{e}}}_{\text{the view itself}}
+ \underbrace{q'_s(B)\,V_{\mathrm{org}}\bigl(\eta_{\mathrm{o}}
+ \delta_c v^*\bigr)}_{\text{take-up channel}},
\]
where $\eta_{\mathrm{o}}, \eta_{\mathrm{e}}$ are gross per-view consumption
values of organic and exploration delivery,
$v^* = (\eta_{\mathrm{o}}\bar qV_{\mathrm{org}} + \eta_{\mathrm{e}}\barB)/(1-\mathcal{R})$
is the total consumption value of one submission, and $\bar q, \barB$
are pool averages.
\end{proposition}
\noindent\emph{Proof sketch.} A marginal view raises total views by
$1 + q'_sV_{\mathrm{org}}$ and induces $\delta_c(1 + q'_sV_{\mathrm{org}})$
submissions, each worth $v^*$, which already sums the descendant chain
(Appendix~\ref{app:dynamics}).
The take-up term multiplies a small probability change by a large reward. One
extra view barely changes the probability of organic take-up, but conditional
on take-up, the item receives $V_{\mathrm{org}}$ additional organic views in expectation.
Two readings of \Cref{prop:gradient} matter later:\par\smallskip
\textbf{(1) Budget scale and ranking.} At the resolution identified here, a
pool-level creator sensitivity re-prices the budget's shadow value but supplies
no new within-pool ranking signal. Creator-term re-ranking requires variation
in $\delta_c$ across content items, which none of our designs identifies.
The proposition shows where that heterogeneity would enter. The view-itself term
has no item subscript and drops from the allocator's comparison. The varying
terms are proportional to $q'_s$ and $\delta_c$. Organic
reach $V_{\mathrm{org}}$ weights take-up and enters $v^*$, which values induced supply. A
view is worth more near the take-up margin, where $q'_s$ is
largest, and when conditional organic reach is larger. The latter can
represent demand per unit supply, coverage, diversity, or freshness. When
organic delivery already reaches nearly every item, $q'_s$ approaches
zero and an extra view buys little beyond itself.
\textbf{(2) Sign.} A randomized contrast measures \emph{net} of the displaced
impression, so a negative measured direct effect is consistent with
$\eta_{\mathrm{e}} > 0$ (\Cref{rem:scope}). Subtracting the same opportunity
cost from every candidate leaves their ordering unchanged, but varying that
cost across candidates can change the ranking.
\subsection{What a Measurement Can See}
\label{sec:measurement}
\Cref{prop:gradient}'s take-up and creator channels are deferred, and this
subsection explains why they are hard to observe. The creator channel arrives a posting cycle late and
compounds over the supply loop. The take-up channel pays off only through
organic distribution that the corpus has yet to deliver. We
analyze the extreme member of the intervention family, switching exploration
off entirely, because it perturbs the corpus stock with the largest possible
asymptotic gap. Any milder test, such as a budget change or parameter tweak,
moves the same stock at the same turnover toward a smaller gap. The switch-off
case is a best-case benchmark for what a fixed horizon can express.
Consumption quantities such as $E_t$ enter below only as observables of the
corpus stock $K_t$, which is not directly observed.
\par\vspace{1pt}\noindent\textbf{Multiplier and horizon.}\hspace{0.5em plus 0.1em minus 0.05em}
For a feedback loop with eigenvalue $\lambda\in(0,1)$, define its equilibrium
multiplier $A(\lambda) \triangleq 1/(1-\lambda)$, the steady-state response to
one unit of input added each period. Its
\emph{relaxation time} is
$\tau(\lambda) \triangleq 1/\ln(1/\lambda)$, so a switch decays as $\lambda^t$.
Both grow without bound as $\lambda$ approaches $1$: stronger feedback also
means slower forgetting. The timing results concern the transient after a
switch, so production need not remain at equilibrium.
The dynamics~\eqref{eq:dynamics} contain two such modes. The supply mode
has eigenvalue $\mathcal{R}$, the number of posts induced per post, and carries the
comparatively fast posting multiplier. The corpus mode has eigenvalue
$1-\omega$, its per-period retention, and sets the experiment's clock.
Beyond the immediate slot value, viewer-side effects are corpus-mediated. The
model locates them in time. A short window
reveals only a fraction of a slow corpus effect even without noise.
\begin{theorem}[Horizon blindness]
\label{thm:horizon}
Disable exploration at $t=0$ from equilibrium and write $E^*$ for pre-switch
equilibrium consumption. With consumption affine in the corpus as above, the
gap decomposes as
$E^*-E_t = \Delta_{\mathrm{direct}} + \Delta_{\mathrm{corpus}}\,F(t)$, the direct
term present from the first period. If the corpus retains a fraction
$1-\omega$ per period and its post-switch inflow stays at or above its
eventual level, then
\[
F(t) \;\le\; 1-(1-\omega)^t \;\le\; \omega t \qquad \text{for every integer } t \ge 1.
\]
\end{theorem}
\noindent\emph{Proof sketch.} Among inflow paths satisfying this condition, an
immediate jump to the eventual post-switch inflow maximizes the corpus gap at every date. Iterating the
stock recursion then gives the normalized gap
$1-(1-\omega)^t$. Bernoulli's inequality gives the second bound.
The bound is the operational result. At horizon $t$, at most a
$\omega t$ fraction of the eventual corpus gap has materialized, even
without noise. The linear model
locates the delay. If take-up changes immediately, the first
period expresses a fraction $\omega$. If corpus inflow changes only after
posting responds, onset is quadratic. When the supply response settles
before the corpus has appreciably turned over, the gap thereafter follows
an approximately linear ramp whose
extrapolated delay lies between zero and one post-switch supply-loop multiplier
$A(\mathcal{R}_{\mathrm{off}})=1/(1-\mathcal{R}_{\mathrm{off}})$, where $\mathcal{R}_{\mathrm{off}}$ is the post-switch loop gain.
The delayed endpoint attains that upper limit.
The closed-form path, including mixtures of the two cases, is in
Appendix~\ref{app:dynamics}. This timing reconciles mixed or negative short
viewer-side readings with a valuable mechanism: the corpus-mediated demand
value arrives on the slow eigenvalue, after the window closes.
Equilibrium gain and relaxation time coincide to within one period. A
coverage target multiplies that time only by its logarithm.
\begin{corollary}[Value and measurability duality]
\label{cor:duality}
Consider a stable nonnegative ecosystem $x_{t+1} = M x_t + u$ and a
feedback loop with real eigenvalue $\lambda \in (0,1)$.
\begin{enumerate}[nosep,leftmargin=1.6em,label=(\roman*)]
\item the equilibrium multiplier $A(\lambda)$ and relaxation time
$\tau(\lambda)$ coincide to within one period, so
$\tau(\lambda) \le A(\lambda) \le \tau(\lambda)+1$. Observing a
$(1-\varepsilon)$ fraction of a switch requires the horizon
$t_\varepsilon = \ln(1/\varepsilon)\,\tau(\lambda)$.
\item consequently an experiment of length $t$ reads the partial sum
$\sum_{k<t}\lambda^{k} \le t$, whatever the true multiplier
$A(\lambda)$.
\end{enumerate}
Within the linear model, no parameter regime of such a loop combines large equilibrium value with a short measurement horizon.
\end{corollary}
\noindent Part (ii) is the operational form (full proof in Appendix~\ref{app:dynamics}).
What a test can read is bounded by its own duration, so a gap settling at
$\Delta_\infty$ reads early as $\Delta_\infty\omega t$. The multiplier is
achieved \emph{by} the slowness. The corpus stock instantiates the corollary
at eigenvalue $1-\omega$. Its gain is $1/\omega$, and its relaxation
time lies within one period of that value. The more evergreen the corpus, the
more stock a unit of inflow buys and the longer any test must run to see a
fixed fraction of it.
Adding users does not change that clock. It only sharpens the reading of
wherever the clock stands. Appendix~\ref{app:illustrations} works these results
at illustrative magnitudes.
\begin{proposition}[Sample size cannot buy horizon]
\label{prop:detection}
Consider an on/off experiment with $N$ users per arm on a corpus-stock
metric with asymptotic gap $\Delta_\infty$, read at horizon $t$ in the early
regime $\omega t \ll 1$.
(i) The expressed fraction
$\Delta(t)/\Delta_\infty \approx \omega t$ is independent of $N$.
Larger samples estimate the same attenuated number more precisely.
(ii) Even mere detection of the attenuated gap is horizon-bound. With
per-user noise scale $\sigma$ and detection level $z$, a snapshot analysis
first detects at
$t_{\det} = \frac{z\sigma\sqrt{2/N}}{\Delta_\infty \omega}
\propto N^{-1/2}$,
and a cumulative analysis with independent per-period noise at
$t_{\det} = \bigl(\tfrac{2\sqrt{2}\,z\sigma}
{\Delta_\infty \omega \sqrt{N}}\bigr)^{2/3} \propto N^{-1/3}$.
\end{proposition}
\begin{proof}[Proof sketch]
(i) follows from \Cref{thm:horizon}, whose statement contains no $N$. For (ii), equate the
gap $\Delta_\infty\omega t$ (snapshot) or its running mean (cumulative,
standard error $\sigma\sqrt{2/(Nt)}$) to $z$ times its standard error and
solve for $t$.
\end{proof}
Detecting a nonzero finite-horizon effect is easier than estimating its
asymptote.
\begin{theorem}[Estimation floor]
\label{thm:curvature}
Let $y_t$ be the observed between-arm contrast in a corpus-stock metric at
horizon $t$. For $t=1,\ldots,T$, suppose
\[
y_t \;=\; c+\Delta_\infty\bigl(1-e^{-\omega t}\bigr)+\varepsilon_t,
\qquad \varepsilon_t \stackrel{\mathrm{iid}}{\sim} N(0,\,s^2),
\]
with level $c$ and rate $\omega$ unknown and
$s^2 = 2\sigma_{\mathrm{eff}}^2/N$ for $N$ users per arm, where
$\sigma_{\mathrm{eff}}$ is the effective per-user transient-noise scale. Define the
\emph{curvature signal-to-noise ratio}
\[
\mathcal{C} \;=\; \frac{\Delta_\infty\,\omega^{2}\sqrt{S_4}}{2s},
\qquad S_4 = \textstyle\sum_{t \le T} t^{4}.
\]
Whenever $\mathcal{C} \le 1$, every confidence procedure for
$\Delta_\infty$ with uniform coverage $1-\alpha$ over positive amplitudes
and rates returns an infinite upper endpoint with probability at least
$\tfrac12-\alpha$. Raising $N$ moves the crossing $\mathcal{C}=1$ only as
$T \propto N^{-1/5}$, improving to $N^{-1/3}$ once $\omega$ is estimated
from auxiliary data.
\end{theorem}
\noindent The proof, a two-point total-variation indistinguishability
argument over a matched-product family, appears in Appendix~\ref{app:floors},
with the panel reduction at Lemma~\ref{lem:panel} and the formal
statement at Theorem~\ref{thm:floor}. The construction holds the early slope
$\Delta_\infty\omega$ fixed while sending $\omega\to0$ and
$\Delta_\infty\to\infty$. Below the threshold these paths are
statistically indistinguishable. Until the trajectory visibly bends,
monotonicity can still supply an increment lower bound. The slow component
is the corpus stock. The regimes in which exploration is most valuable
are those in which feasible-horizon inference may admit only an increment
lower bound, and \S\ref{sec:probe} uses a horizon-matched endpoint accordingly.
Figure~\ref{fig:floor-demo} and
Figure~\ref{fig:supp-two-ends} visualize the estimation floor and delay
family.
\ifextendedbuild
The theorem treats the contrast series as independent draws with a single
noise scale. Panel data earns that form: persistent per-user differences drop
out once the level is profiled, serial correlation is absorbed into
$\sigma_{\mathrm{eff}}$, and only a unit root would change the exponents.
\begin{lemma}[Panel reduction]
\label{lem:panel}
Let per-user outcomes carry persistent user effects of arbitrary variance
$\sigma_\alpha^2$ and stationary transient noise, so that
$\mathrm{Cov}(\eta_s, \eta_t) = \tfrac{2}{N}\bigl[\sigma_\alpha^2 +
\gamma(s-t)\bigr]$. Then:
(i) because $\mathbf{1}$ is an eigenvector of the persistent component,
profiling any nuisance set containing the intercept
$\Delta_{\mathrm{direct}}$ renders every information quantity below
\emph{independent of $\sigma_\alpha^2$}, and persistent effects can only
enlarge the impossibility region of \Cref{thm:floor};
(ii) for AR(1) transient noise with parameter $\rho$ and marginal variance
$\sigma^2$, all statements hold with
$\sigma_{\mathrm{eff}}^2 = \sigma^2(1+\rho)/(1-\rho)$, up to a factor
$1 + O\bigl(\rho/((1-\rho)T)\bigr)$, by the exact tridiagonal form of the
AR(1) inverse;
(iii) stationarity is necessary: under random-walk user drift the $T^5$
information accumulation below degrades to $T^3$, because a unit root
mimics the ramp. Stationarity is diagnosable in logs: the variance of
user-mean-centered outcomes must not grow with the window.
\end{lemma}
\noindent The proof is in Appendix~\ref{app:floors}. Part (iii) is why
\S\ref{sec:experiments} reports a stationarity check rather than assuming it.
\fi
\par\vspace{1pt}\noindent\textbf{Drift.}\hspace{0.5em plus 0.1em minus 0.05em} A changing environment moves the steady state without changing
timing or identification. \Cref{thm:horizon} uses only the corpus stock's
retention and holds pathwise under time-varying turnover, the gain--relaxation
relation survives because both are monotone in the same $\lambda$, and the
exponents in \Cref{prop:detection} follow from that algebra alone
(Appendix~\ref{app:dynamics}). Unmodelled drift only widens the region with no
finite upper bound. The multiplier and \Cref{prop:gradient}'s level are
local statements. The probe in \S\ref{sec:probe} imports drift from the
concurrent ablation. Each design contrasts arms at a common date, so
shared changes in viewer taste or the corpus drop out.
\subsection{What Each Design Identifies}
\label{sec:designs}
Each randomization holds a different part of the ecosystem in common between
its arms. What is common cancels.
\begin{proposition}[What each randomization design identifies]
\label{prop:identification}
In the model~\eqref{eq:dynamics}, suppose an experiment holds a fraction $p$
of one side of the market at the perturbed condition (the floored arm).
Treat immediate within-feed substitution as part of the direct channel, and
suppose any remaining change in organic consumption is mediated by the shared
corpus state.
The following statements hold.
\begin{enumerate}[nosep,leftmargin=1.6em,label=(\roman*)]
\item \textbf{Viewer-side.} Disabling exploration delivery in enrolled
users' feeds identifies the direct channel exactly at every horizon and
arm size. Corpus-mediated consumption is common to both arms and cancels.
\item \textbf{Creator-side.} Holding enrolled creators' content at the
floor identifies the equilibrium supply response
$\Lambda_0\bigl[(1-\mathcal{R})^{-1} - (1-\mathcal{R}_{\mathrm{f}})^{-1}\bigr]$
\emph{at the perturbed aggregate}, up to a capacity-release term
$\epsilon(p)$. Here $\mathcal{R}_{\mathrm{f}}$ is the floored arm's loop gain.
The term $\epsilon(p)$ is nonnegative because flooring can only raise delivery in
the non-floored arm relative to full rollout. It scales with the floored
market share and is absent from the co-diverted design, where an isolated
submarket exchanges no capacity with the platform. Whatever consumption the
induced corpus generates is common to both arms and therefore cancels from the contrast.
\item \textbf{Co-diverted.} Isolating matched creator and viewer
submarkets retains the corpus-mediated component in the contrast,
attenuated by the general $F(t)$ of \Cref{thm:horizon}. This differs from
the one-sided cancellation of (i)--(ii). Flooring the submarket's own creators lowers
its own supply, so the cell sits toward the theorem's delayed end.
\end{enumerate}
In particular, the corpus channel enters no one-sided contrast at any
horizon or sample size. It enters only under co-diversion and expresses a
fixed fraction at horizons of order $1/\omega$.
\end{proposition}
\noindent For (i)--(ii), subtracting arm means cancels the common $K_t$.
Under co-diversion each cell evolves its own $K_t$, so subtraction
retains their stock gap. The capacity-release sign in (ii) follows because
flooring enrolled traffic frees nonnegative capacity for the remaining pool.
Appendix~\ref{app:dynamics} gives the full algebra.
These designs identify population aggregates. Per-item $q'_s$ and
$\delta_c$ remain unidentified. An external turnover estimate improves corpus
estimation from $N^{-1/5}$ to $N^{-1/3}$.
\begin{table}[t]
\centering
\caption{Identification map for the four randomized designs. The final
column gives the sample-size law. For the fast channels it sharpens the
estimate at a fixed horizon. For the corpus rows it sets the required
horizon.}
\label{tab:design-map}
\footnotesize
\setlength{\tabcolsep}{3.5pt}
\begin{tabular}{@{}llll@{}}
\toprule
Target & Design & Required horizon & Rate in $N$ \\
\midrule
Direct effect & Viewer ablation & Immediate & $N^{-1/2}$ \\
Supply response & Creator ablation & Supply loop $\tau(\mathcal{R})$ & $N^{-1/2}$ \\
Allocation response & Budget reallocation & Supply loop $\tau(\mathcal{R})$ & $N^{-1/2}$ \\
Corpus ramp & Co-diversion & Early ramp & $N^{-1/3}$ \\
Corpus asymptote & Co-diversion & Curvature threshold & $N^{-1/5}$ \\
\bottomrule
\end{tabular}
\end{table}
\section{Testing the Identification Map}
\label{sec:experiments}
The four experiments identify complementary channels. Each tests the channel
and time path assigned to it by
\Cref{tab:design-map}. Two long-running
one-sided ablations identify the direct link and the supply response in sign,
although shared capacity can overstate the latter under full rollout. Two
co-diverted experiments test budget reallocation
(\S\ref{sec:reallocation}) and the delayed corpus response
(\S\ref{sec:probe}), which one-sided designs exclude by construction.
In both ablations, randomization and analysis units coincide, so effects are
differences of window-aggregated means at the randomized-unit level, with
unit-level standard errors and no clustering. Enrollment is fixed at randomization. Where used,
variance reduction regresses outcomes on their pre-experiment
values~\citep{deng2013cuped}. The creator first stage is mechanical. Exploration
views per video rise by the budget-to-floor gap (levels withheld). Arm shares
agree within hundredths of a percentage point, with no sample-ratio mismatch. We
report effect sizes with $95\%$ intervals. Tabulated rows are a subset of each analysis's full outcome
family. The probe reports the endpoints specified in its experiment design.
Each co-diverted experiment realizes one pair of matched submarkets, so its
intervals condition on that pair.
\subsection{Qualitative Predictions}
\label{sec:simulation}
The theory implies three signatures independent of effect size. They are a direct step, a
supply response that can build after onset, and a corpus ramp as isolated
stocks diverge. Cumulative and non-overlapping period estimates reveal whether
a gap ramps or stays level. One-sided ablations reach the first two responses.
Only co-diversion can express the corpus ramp. \Cref{fig:observed-evidence}
shows the two observed time paths and the turnover sensitivity below.
\subsection{Viewer Ablation of the Direct Channel}
\label{sec:viewer-ablation}
The viewer ablation ran for over a year, enrolling eight percent of users
randomized between production exploration and full disablement.
Creators are common to both arms, so each arm draws from the same corpus
supplied by the surrounding creator population. The contrast isolates the
\emph{direct channel}, which is the effect of exploration delivery in enrolled
viewers' feeds after within-feed substitution. It excludes corpus effects. Its
length separates persistent response from launch novelty and spans a full
seasonal cycle.
\begin{table}[t]
\centering
\caption{Randomized effects at the tested operating points. Relative arm
differences have 95\% CIs. Positive values favor production in Panels A--B
and reallocation in Panel C. The panels isolate a mixed direct trade-off, a
signed supply response, and a budget-matched participation gain.}
\label{tab:ablations}
\normalsize
\setlength{\tabcolsep}{4pt}
\begin{tabular*}{0.96\columnwidth}{@{\extracolsep{\fill}}lrr@{}}
\toprule
Metric & Rel.\ change (\%) & 95\% CI \\
\midrule
\multicolumn{3}{@{}l}{\textbf{Panel A: Viewer ablation} (\S\ref{sec:viewer-ablation})} \\
Video views & $+1.74$ & $[+1.57, +1.90]$ \\
View time & $-2.13$ & $[-2.28, -1.98]$ \\
Views under $1.5\,s$ & $+7.49$ & $[+7.28, +7.70]$ \\
Video favorites & $-2.32$ & $[-2.72, -1.92]$ \\
\midrule
\multicolumn{3}{@{}l}{\textbf{Panel B: Creator ablation} (\S\ref{sec:creator-ablation})} \\
Videos posted per creator & $+8.55$ & $[+7.14, +9.96]$ \\
Creators posting at least once & $+7.10$ & $[+6.60, +7.59]$ \\
\midrule
\multicolumn{3}{@{}l}{\textbf{Panel C: Budget-matched reallocation} (\S\ref{sec:reallocation})} \\
Creators posting at least once & $+0.77$ & $[+0.35, +1.19]$ \\
Videos posted per creator & $+0.92$ & $[+0.05, +1.79]$ \\
View time & $+0.01$ & $[-0.14, +0.16]$ \\
Video views & $-0.06$ & $[-0.21, +0.09]$ \\
Video favorites & $+0.15$ & $[-0.44, +0.74]$ \\
\bottomrule
\end{tabular*}
\end{table}
\begin{figure*}[t]
\centering
\includegraphics[width=0.87\textwidth]{figures/observed_evidence_three_panel.pdf}
\caption{Observed time paths and turnover sensitivity. \textbf{(a)} The year-long viewer contrast
appears within weeks and stays level until a common operating-point shift,
matching the direct-step prediction. Intervals are approximate.
\textbf{(b)} The eight-month posting response, indexed to its first measured
period, is descriptive and follows onset with a plateau.
\textbf{(c)} The corpus-asymptote conclusion depends on the assumed turnover. The
36-day case rules out offsetting either direct view-time cost (the ablation's
$-2.13\%$, drawn dashed, and the probe's own $-1.02\%$ step), whereas the
360-day case admits either sign. Panels (a)--(b) use finer analysis periods
than the appendix's series. Their shapes agree (Appendix~\ref{app:timepath}).}
\label{fig:observed-evidence}
\end{figure*}
Table~\ref{tab:ablations} (Panel A) reports a mixed direct effect. Video views
rise 1.74\% while view time falls 2.13\%. Views under $1.5\,s$ rise $7.5\%$,
shifting the view mix toward brief views. Favorites move with view time
($-2.3\%$). Exploration increases viewing starts while reducing viewing duration at
this operating point. This is the direct-feed component of the allocation problem.
\Cref{prop:gradient} also requires the creator response.
The cumulative and non-overlapping period series in Appendix~\ref{app:timepath}
confirm the reading. The gap is close to full size within weeks. Thereafter
the period contrast stays level across most of the window and then attenuates,
tracking a decline in exploration's share of the feed. Cumulative video views
move from $+2.02\%$ early in the window to $+2.32\%$ at the peak and
$+1.74\%$ at the end. Immediacy without a sustained ramp is the direct
channel's signature under the reading rule of \S\ref{sec:simulation}. The
shared corpus contributes zero to this contrast.
The concurrent creator ablation randomizes a different population, yet its
consumption changes sign at the same calendar boundary ($+1.11\%$ on video
views just before it), as shown in Appendix~\ref{app:timepath}. Because the experiments began
months apart, the same calendar-date break indicates a common operating-point
shift. Since both designs exclude the corpus term
(\Cref{prop:identification}(i)--(ii)), this concurrent movement also supplies the
drift estimate imported by \S\ref{sec:probe}.
\subsection{Creator Ablation of Content Supply}
\label{sec:creator-ablation}
The creator ablation ran for eight months, enrolling eight percent of the
platform's creators, with about four percent in each arm.
This share also sizes the interference term, with $p/(1-p) \approx 0.04$.
Creators in the \emph{floored} arm receive a minimal exploration budget per
video, and their videos remain eligible for organic retrieval. Creators in the
\emph{production} arm receive production exploration budgets (absolute levels withheld for
confidentiality). This two-dose comparison
falls short of a strict on/off but measures the supply response directly.
Only the budget above the floor differs between arms.
Across eight months, exploration raises videos posted per creator by 8.55\%
(Table~\ref{tab:ablations}, Panel B). It also raises the number of creators
posting at least once by 7.10\%. The two outcomes identify aggregate and
extensive-margin supply responses.
Unlike randomized traffic grants lasting a few weeks, this contrast compares
the standing production mechanism with a minimal floor over eight months.
The effect on videos posted per creator is $+5.9\%\pm3.4$ ($95\%$) in the first
measured period, below the $+8.55\%$ whole-window average. Together with the
later plateau in \Cref{fig:observed-evidence}b, this pattern is consistent with
an onset period. The increase in creators posting at least once locates part of
the response on the extensive margin.
Because the two creator arms compete in a shared marketplace,
\Cref{prop:identification}(ii) implies capacity-release inflation at order
$p/(1-p)$, so the contrast upper-bounds the full-rollout effect at this operating point
(Appendix~\ref{app:dynamics}). The co-diverted probe later provides a descriptive
comparison without that shared-capacity term. Recovering the guarantee's total value would
require a zero-exploration creator arm.
\subsection{Budget-Matched Reallocation of Exposure}
\label{sec:reallocation}
The ablations identify the effects of exploration presence. \Cref{prop:gradient}
also characterizes fixed-budget allocation. A two-week co-diverted experiment holds nominal budget fixed while
spreading exposure across more videos in matched cells. Its design fixes the
arm contrast, horizon, and endpoints. By concavity, the
marginal posting response is larger at lower exposure. Promotion thresholds implement the
shift. A penultimate-day spend diagnostic puts realized per-creator budgets
within about $3\%$ across arms, with the reallocated arm slightly lower, so
any residual dose imbalance biases its posting response downward.
The experiment identifies the randomized reallocation contrast and leaves
pure breadth elasticity open. The horizon
targets fast supply. Creators posting at least once increase by $0.77\%$, and
videos posted per creator increase by $0.92\%$. Every viewer-side interval includes zero
(Table~\ref{tab:ablations}, Panel C). This is the predicted signature of higher
creator participation without a detectable short-run viewer cost
(Appendix~\ref{app:matched-budget}).
\subsection{Co-Diverted Probe of the Corpus Response}
\label{sec:probe}
The probe co-diverts viewers and creators into isolated production and floored
submarkets~\citep{masoero2021multiple,brennan2023symbiosis}. Consumption uses
viewer-level means. Posting uses creator-level means. With one partition per
arm, intervals condition on these submarkets. Matched isolation cancels the
common consumption cost while letting cells approach different steady
states~\citep{shen2026isolation}.
We test video views and view time for a step followed by a delayed ramp. Video
favorites per delivered view provide a quality endpoint sensitive to composition.
The experiment runs for three weeks from switch-on. The corpus estimator omits
the first seven days because videos already in their exploration windows are only
partially exposed to the intervention.
The model predicts an immediate step plus a delayed corpus ramp at rate
$\omega$, while the concurrent one-sided ablation stays flat
(\Cref{thm:horizon}). Because early data identify only the slope
$\Delta_{\mathrm{corpus}}\,\allowbreak\omega$, we report asymptote intervals
conditional on turnover and a shape-robust increment.
The 36-day timescale is the measured kernel's single-rate equivalent. The 360-day
timescale is the eligibility horizon. They are fixed-turnover sensitivity cases.
Kernel calibration and estimator details are in Appendix~\ref{app:estimator}.
Platform policy caps matched-submarket isolation at three weeks because its
ecosystem cost grows with duration~\citep{shen2026isolation}. At this horizon,
\Cref{thm:curvature} predicts an identified direct step but a potentially
unsigned corpus asymptote (Figure~\ref{fig:floor-demo}).
\begin{table}[t]
\centering
\caption{Co-diverted three-week readout at the calibrated estimation floor.
Entries are relative changes with 95\% CIs. Panel B gives intervals for the
set-identified corpus asymptote under two turnover timescales. Panel C gives feasible-horizon
gross flow; its implied whole-cell contribution is a derived range. Posting is quoted as estimate $\pm$ margin. Panels C--D retain
the inferential qualifications stated in text.}
\label{tab:probe}
\small
\setlength{\tabcolsep}{3pt}
\begin{tabular*}{0.96\columnwidth}{@{\extracolsep{\fill}}lr@{}}
\toprule
Quantity & Estimate \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Panel A: Direct step}} \\
Video views & $+0.43\ [+0.30, +0.57]$ \\
View time & $-1.02\ [-1.14, -0.89]$ \\
Video favorites / delivered view & $-0.87\ [-1.21, -0.53]$ \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Panel B: Corpus asymptote by turnover timescale}} \\
Video views, 36-day timescale & $[-0.28, +0.70]$ \\
View time, 36-day timescale & $[-0.93, +0.30]$ \\
Video views, 360-day timescale & $[-2.77, +7.04]$ \\
View time, 360-day timescale & $[-9.30, +2.95]$ \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Panel C: Feasible-horizon corpus flow}} \\
\shortstack[l]{Organic view time in cohort slice\\Implied whole-cell contribution} &
\shortstack[r]{$+37.9\ [+37.1, +38.7]$\\$+0.1$--$+0.2$ pp} \\
\midrule
\multicolumn{2}{@{}l}{\textbf{Panel D: Videos posted per creator at a matched 21-day horizon}} \\
In-cell design & $+0.63 \pm 0.44$ \\
One-sided design & $+2.79 \pm 0.89$ \\
\bottomrule
\end{tabular*}
\end{table}
\Cref{tab:probe} collects the readout. The direct step repeats the viewer
ablation's signs and is smaller, consistent with the probe's later operating
point. Video favorites per delivered view confound reception with composition.
The estimates use an equal-length pre-period difference because video views and
favorites were imbalanced before the switch.
\begingroup
\setlength{\emergencystretch}{2em}
The corpus readout lands at the predicted estimation floor. Without fixing a
turnover timescale, neither the ramp fit nor the shape-robust increment yields
a finite two-sided upper bound on the corpus asymptote
(Appendix~\ref{app:estimator}). Under the 36-day turnover timescale,
the auxiliary analysis rules out a corpus benefit large enough to offset the
direct view-time cost. Under the 360-day timescale, either sign remains possible
(\Cref{tab:probe}, Panel B).
The aggregate corpus asymptote remains unsigned at three weeks.
\par
\endgroup
\par\vspace{1pt}\noindent\textbf{Feasible-horizon corpus flow.}\hspace{0.5em plus 0.1em minus 0.05em}
Before the aggregate trajectory bends, the theory targets the effect expressed
at horizon $t$. An extrapolated asymptote is premature. A cohort decomposition
measures feasible-horizon gross flow among videos posted during the experiment
and later served organically after their exploration windows. By construction,
exploration can no longer deliver these videos (Appendix~\ref{app:cohortledger}). In matched
cells, organic view time is $37.9\%$ higher in a slice representing
$0.3$--$0.5\%$ of cell consumption, equivalent to $0.1$--$0.2$ percentage
points of the whole-cell contrast (\Cref{tab:probe}). Videos posted before the
experiment show no detectable difference after the first seven days. The pattern first appeared in a $1\%$
discovery sample. Because the full-population calculation reuses those users,
we retain its exploratory status. It measures gross corpus flow by the
feasible horizon. The net asymptote after displacement remains unresolved
(Appendix~\ref{app:cohortledger}).
\par\vspace{1pt}\noindent\textbf{In-cell supply.}\hspace{0.5em plus 0.1em minus 0.05em}
With a comparable exploration first stage and the same horizon and
instrument, in-cell posting is roughly a quarter of the one-sided response
(\Cref{tab:probe}, Panel D). The ratio is descriptive because the
populations, seasons, reach, and exposure composition differ. It leaves
$\epsilon(p)$ and the rollout asymptote unidentified.
\subsection{What the Four Experiments Establish}
\label{sec:virtuous-cycle}
The experiments form an identification sequence across distinct estimands.
The measured timescales match the model's assignment of roles: the posting
response plateaus within a few measured periods
(\Cref{fig:observed-evidence}b), while the two candidate corpus timescales range
from comparable to roughly an order of magnitude longer than the posting
response (\S\ref{sec:probe}).
\Cref{tab:claims} records the findings and nearest limits.
\begin{table}[b]
\centering
\caption{What the four experiments establish. Signs apply at the realized
horizon. Co-diverted rows condition on the realized submarkets.}
\label{tab:claims}
\small
\setlength{\tabcolsep}{3pt}
\begin{tabular}{@{}>{\raggedright\arraybackslash}p{0.18\columnwidth}
>{\raggedright\arraybackslash}p{0.39\columnwidth}
>{\raggedright\arraybackslash}p{0.35\columnwidth}@{}}
\toprule
Experiment & Identified finding & Leaves open \\
\midrule
Viewer ablation & Direct feed trade-off: video views $+$, time $-$ & Shared-corpus effect \\
\addlinespace[2.5pt]
Creator ablation & Supply response: posting $+$ & Full-rollout magnitude and corpus value \\
\addlinespace[2.5pt]
Budget reallocation & Reallocation contrast: participation $+$; viewer CIs span 0 & Breadth elasticity and long-run corpus value \\
\addlinespace[2.5pt]
Co-diverted & Direct step mixed; exploratory gross cohort flow $+$ & Net corpus asymptote at three weeks \\
\bottomrule
\end{tabular}
\end{table}
\section{Discussion}
\label{sec:discussion}
The creator-side response is consistent with creators on the margin of
continued participation, where modest distribution separates occasional
from regular posting~\citep{bhargava2022creator,qian2024digital}. Organic
delivery accrues mostly to videos that have demonstrated strong early performance, which is
why exploration is the primary channel for most new videos
(\S\ref{sec:intro}) and the platform's direct lever over the long tail. \Cref{prop:gradient} shows where the creator
response enters value accounting. Our designs identify only its gross
aggregate. Per-item sensitivity and the common net-value scale required to
prescribe an objective remain unidentified.
\par\vspace{1pt}\noindent\textbf{Implications for Practice.}\hspace{0.5em plus 0.1em minus 0.05em}
Each result yields a design implication.
\begin{enumerate}[nosep,leftmargin=1.6em]
\item \textbf{A mixed viewer A/B identifies only the direct trade-off.} A viewer-side
contrast excludes creator response by construction. On the platform we study,
production exploration raises videos posted per creator by 8.55\% and creators
posting at least once by 7.10\%.
\item \textbf{A neutral result leaves shared-corpus value unresolved.}
The shared-corpus term cancels from a one-sided viewer contrast. A short
co-diverted contrast identifies only the finite-horizon increment
(\Cref{thm:horizon}). The asymptote remains unresolved. Neither result alone
identifies total value.
\item \textbf{Estimate the slow factors offline and import them.} Traffic
cannot rescue the gate's short window (\Cref{prop:detection}). Budget
policies follow a planning cadence that can incorporate offline estimates
from past randomized cohorts or quasi-experimental variation. Historical
data on yield by video age can estimate corpus turnover.
\item \textbf{Match the design to the channel.} Viewer-side randomization
measures the direct channel, and creator-side randomization measures the
aggregate supply response at the tested operating point. Only co-diversion
retains the corpus channel required to estimate its asymptote
(\Cref{tab:design-map}). The exploratory
cohort analysis measures gross corpus flow at a feasible horizon using videos
posted during the experiment and served organically after their exploration windows
(\Cref{tab:probe}; \S\ref{sec:probe}).
\item \textbf{Plan in calendar time.} A tenfold increase in users reduces the required
horizon by at most a factor of $3.2$. Below the curvature threshold (\Cref{thm:curvature}),
use the finite-horizon increment and any model-restricted lower bound as the
reported endpoints.
Plan horizons from turnover, effect-size, and noise inputs.
\item \textbf{Treat allocation as a separate experimental margin.} At a
fixed nominal budget, reallocation raises creator participation with no
detectable viewer-side change (\S\ref{sec:reallocation}).
\end{enumerate}
\par\vspace{1pt}\noindent\textbf{Limitations.}\hspace{0.5em plus 0.1em minus 0.05em}
The ablations estimate the budget's effects at the tested operating point.
The reallocation experiment tests one direction of allocation there, leaving
the allocation rule unidentified (\S\ref{sec:reallocation}).
Open questions include posting-response persistence, generalizability
beyond one platform, and whether a learned allocation rule improves on the
production rule~\citep{swaminathan2015self,jeon2025epinet}. Nothing
measured here depends on that rule (\S\ref{sec:budget-problem}).
\section{Conclusion}
\label{sec:conclusion}
Content exploration reaches beyond the feed by changing creator participation
and replenishing the shared corpus. Standard one-sided viewer tests identify
only the direct feed channel. Our decomposition separates a delivered view into immediate value,
organic take-up, and induced creator supply. The latter two pay off through the
shared corpus. Horizon blindness bounds what any experiment or the mechanism's
own gate can observe of that deferred value.
Relative to a minimal floor, production exploration raises videos posted per
creator by 8.55\% and creators posting at least once by 7.10\%. At a matched
nominal budget, reallocation raises creator participation with no detectable
short-run viewer-side change. The viewer ablation raises video views while
lowering view time, a mixed direct trade-off. These outcomes use different
units, and total viewer value remains unidentified because one-sided designs
cancel the corpus term. The co-diverted probe reaches that term, but its sign remains
unresolved under both reported turnover scenarios. Evaluating exploration as an
ecosystem intervention requires matching the randomization to the target channel
and planning the horizon from corpus turnover.
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