Introducing Repository Stability

Abstract

Drawing from engineering systems and control theory, we introduce a framework to understand repository stability, which is a repository activity capacity to return to equilibrium following disturbances - such as a sudden influx of bug reports, key contributor departures, or a spike in feature requests. The framework quantifies stability through four indicators: commit patterns, issue resolution, pull request processing, and community engagement, measuring development consistency, problem-solving efficiency, integration effectiveness, and sustainable participation, respectively. These indicators are synthesized into a Composite Stability Index (CSI) that provides a normalized measure of repository health proxied by its stability. Finally, the framework introduces several important theoretical properties that validate its usefulness as a measure of repository health and stability. At a conceptual phase and open to debate, our work establishes mathematical criteria for evaluating repository stability and proposes new ways to understand sustainable development practices. The framework bridges control theory concepts with modern collaborative software development, providing a foundation for future empirical validation.

Full text

arXiv:2504.00542v1 [cs.SE] 1 Apr 2025
Introducing Repository Stability
Giuseppe Destefanis1, Silvia Bartolucci2, Daniel Graziotin3, Rumyana Neykova1, Marco Ortu4
1Brunel University London, UK
2University College London, UK
3University of Hohenheim, Germany
4University of Cagliari, Italy
{giuseppe.destefanis,rumyana.neykova}@brunel.ac.uk
s.bartolucci@ucl.ac.uk
graziotin@uni-hohenheim.de
marco.ortu@unica.it
ABSTRACT
Drawing from engineering systems and control theory, we intro-
duce a framework to understand repository stability, which is a
repository activity capacity to return to equilibrium following dis-
turbances - such as a sudden influx of bug reports, key contributor
departures, or a spike in feature requests. The framework quanti-
fies stability through four indicators: commit patterns, issue reso-
lution, pull request processing, and community engagement, mea-
suring development consistency, problem-solving efficiency, inte-
gration effectiveness, and sustainable participation, respectively.
These indicators are synthesized into a Composite Stability Index
(CSI) that provides a normalized measure of repository health prox-
ied by its stability. Finally, the framework introduces several im-
portant theoretical properties that validate its usefulness as a mea-
sure of repository health and stability. At a conceptual phase and
open to debate, our work establishes mathematical criteria for eval-
uating repository stability and proposes new ways to understand
sustainable development practices. The framework bridges control
theory concepts with modern collaborative software development,
providing a foundation for future empirical validation.
KEYWORDS
Stability, repository, development
1 INTRODUCTION
Understanding when a software project is in a healthy state re-
mains a critical yet unsolved challenge in software development.
While repositories provide extensive data about project activities,
from code changes to community interactions, current approaches
struggle to convert this wealth of information into actionable in-
sights about project health [1, 2]. This gap affects both practition-
ers managing projects and researchers studying software develop-
ment.
In this paper, we propose a new perspective: viewing project
health through the lens of stability [3, 4]. We envision reposito-
ries as dynamic systems whose health manifests in their capacity
to handle disturbances while maintaining consistent development
practices.
Drawing from control theory [5], we introduce a framework
that reimagines repository analysis. Just as engineering systems
naturally seek equilibrium after physical perturbations, we pro-
pose that healthy software projects demonstrate stability when fac-
ing disruptions - from sudden increases in bug reports to key con-
tributor departures to spikes in feature requests. This perspective
opens new possibilities for understanding and maintaining project
health and sustainability [6]. Our framework improves repository
analysis through four measurable indicators: commit frequency, is-
sue resolution rate, pull request merge rate, and community ac-
tivity, synthesized into a Composite Stability Index (CSI). This
mathematical foundation provides a new perspective in how we
evaluate and predict project health, moving beyond traditional sta-
tistical approaches to capture the dynamic nature of software de-
velopment.
The potential impact of our stability-based vision is threefold:
(1) it enables systematic, quantitative evaluation of reposito ry health,
(2) it paves the way for data-driven project management through
clear stability metrics, and (3) it opens new research directions in
empirical software engineering. By bridging control theory and
repository analysis, we offer a rigorous yet practical approach to a
fundamental challenge.
We address the research question: How can we systematically
define and measure repository stability to reflect and predict project
sustainability?
Our goal is to spark a paradigm shift in how we analyze and
maintain software projects, establishing stability as a fundamental
lens for understanding project health.
2 RELATED WORK
The concept of stability has evolved across multiple domains, from
control theory to software engineering [5], yet a unified approach
to repository stability remains elusive. While Lyapunov’s work
[7] and Leigh’s contributions [8] established rigorous mathemat-
ical foundations for analyzing dynamic systems, their frameworks
have not been adapted to the specific challenges of software repos-
itories, which serve as the technical infrastructure where code and
related artifacts of software projects are stored and managed.
The distributed systems community, through works like Tabuada
et al. [9] and Stankovic [10], advanced our understanding of stabil-
ity through bounded disturbances and performance metrics. How-
ever, these approaches, focused on technical states, have not cap-
tured the rich socio-technical dynamics that characterize modern
repository evolution as part of broader project ecosystems.

FSE2025 - IVR, June 2025, Trondheim, Norway Destefanis, et al.
Software engineering has explored stability from various per-
spectives. Jazayeri et al. [11] pioneered architectural stability mea-
sures for evolution, while Yau et al. [12] developed foundational
metrics for code stability. Yet these valuable approaches address
only isolated aspects of repository dynamics without considering
repositories as complete dynamic systems.
In parallel, significant research has addressed project health, which
relates to but differs from repository stability. A project involves
the full software development effort—people, processes, goals, and
resources—while a repository is the technical artifact storing code
and development history. The CHAOSS project represents a ma-
jor initiative for standardizing health metrics for open source com-
munities1. As Goggins et al. [13] note, open source project health
fundamentally concerns "a project’s ability to continue to produce
quality software," but current approaches struggle to convert repos-
itory trace data into actio nable insights abo ut overall project health.
Project health has been conceptualized through various lenses:
activity-based measures [14], community growth and diversity [15],
and operational sustainability [16]. Crowston et al. [14] defined
success through metrics related to project output, process quality,
and team outcomes, while Daniel et al. [15] emphasized the impor-
tance of social diversity in distributed communities.
Jansen [17] expanded the scope beyond individual projects to
ecosystem-level health through measures of productivity, robust-
ness, and niche creation. The evaluation of project health often
distinguishes between sustainability (the long-term ability to main-
tain development momentum) and survivability (resilience when
facing disruptions). Raja and Tretter [18] introduced a viability in-
dex measuring vigor, resilience, and organization to assess a project’s
capacity to overcome challenges. Despite these advances, as Gog-
gins et al. [13] argue, effective health assessment requires consid-
ering comparison, transparency, trajectory, and visualization prin-
ciples when analyzing repository data.
Traditional repository mining, as demonstrated by Kagdi et al.
[19] and Hammad et al. [20], has revealed valuable historical pat-
terns [21]. However, these approaches often treat repositories as
static artifacts, missing the opportunity to understand their dy-
namic, evolving nature as systems that exhibit stability properties
analogous to those in control theory.
Salama et al. [4] surveyed stability across software artifacts; their
work revealed an important gap: the absence of a unified theoret-
ical foundation for repository stability. Our work aims at filling
this gap by integrating control theory principles with repository
dynamics, enabling systematic analysis of both structural and be-
havioral stability through well-defined metrics and thresholds.
While existing frameworks emphasize narratives and contex-
tual understanding across multiple dimensions of project health,
our stability-based approach offers a complementary mathemati-
cal perspective by applying control theory principles to quantify a
repository’s ability to maintain equilibrium after experiencing dis-
turbances. This foundation enables systematic evaluation of stabil-
ity as a key dimension of overall repository health, bridging theo-
retical rigor with practical utility.
1https://chaoss.community/
3 THEORETICAL FOUNDATION FROM
CONTROL THEORY
In control theory, stability is fundamentally concerned with a sys-
tem’s behavior over time and its response to perturbations. A sys-
tem is considered stable if, when disturbed from equilibrium, it
tends to return to its equilibrium state. More formally, for a dy-
namical system described by
¤𝑥=𝑓(𝑥, 𝑡 ),(1)
where 𝑥represents the state vector and 𝑡represents time, stability
is often characterized using Lyapunov stability theory. A system
is considered stable if for any 𝜖>0, there exists a 𝛿>0 such that:
k𝑥(𝑡0)k <𝛿=⇒ k𝑥(𝑡)k <𝜖, ∀𝑡≥𝑡0.(2)
3.1 Repository as a Dynamical System
The conceptualization of a repository as a dynamical system emerges
from key observations about software development patterns. Soft-
ware repositories exhibit continuous evolution through time, with
state changes driven by developer interactions, mirroring classical
dynamical systems in physics or engineering. These repositories
feature complex feedback mechanisms where code changes trigger
reviews and subsequent modifications, creating interconnected ac-
tivity cycles. They encompass both deterministic elements, such
as automated workflows, and stochastic components such as vary-
ing developer activity patterns, resembling mixed deterministic-
stochastic systems. Repositories demonstrate equilibrium-seeking
behavior, alternating between periods of intense development and
stabilization, analogous to classical dynamical systems. The mea-
surable metrics –commits, issues, pull requests, and branch activ-
ities – serve as state variables that evolve according to rules gov-
erned by technical and social factors. This conceptualization en-
ables the application of dynamical systems analysis techniques to
quantify and understand repository stability.
Let 𝑅(𝑡)represent the state of a repository at time 𝑡, defined as
a vector:
𝑅(𝑡)=[𝑐(𝑡), 𝑖 (𝑡), 𝑝 (𝑡), 𝑎 (𝑡)]𝑇,(3)
where:
•𝑐(𝑡): Commit frequency function;
•𝑖(𝑡): Issue resolution rate function;
•𝑝(𝑡): Pull request merge rate function;
•𝑎(𝑡): Activity engagement function.
These four components have been specifically chosen based on
available repository metrics that represent fundamental dimensions
of repository activity and health. The commit frequency function
𝑐(𝑡)captures the development momentum and intensity of code
changes, providing insights into the project’s active development
patterns through commit timestamps and frequencies. The issue
resolution rate function 𝑖(𝑡)reflects the project’s ability to handle
and resolve problems, calculated through the analysis of issue cre-
ation and closure timestamps. The pull request merge rate function
𝑝(𝑡)measures the effectiveness of the code review and integration
processes, derived from pull request lifecycle data. Finally, the ac-
tivity engagement function 𝑎(𝑡)provides insight into the overall

Introducing Repository Stability FSE2025 - IVR, June 2025, Trondheim, Norway
repository engagement through comment activity and interaction
patterns, replacing the branch lifetime metric with a more readily
available measure of repository vitality. Each component is defined
as follows:
Commit Frequency Function.
𝑐(𝑡)=
𝑁𝑐(𝑡, 𝑡 +Δ𝑡)
Δ𝑡,(4)
where 𝑁𝑐(𝑡, 𝑡 +Δ𝑡)represents the number of commits in the time
interval [𝑡, 𝑡 +Δ𝑡], directly measurable from our commit history
data.
Issue Resolution Rate.
𝑖(𝑡)=
𝑁𝑐𝑙𝑜𝑠 𝑒𝑑
𝑖(𝑡, 𝑡 +Δ𝑡)
𝑁𝑡𝑜𝑡 𝑎𝑙
𝑖(𝑡)·1
1+𝑇𝑟𝑒 𝑠𝑜𝑙𝑢𝑡 𝑖𝑜𝑛 (𝑡),(5)
where 𝑁𝑐𝑙𝑜𝑠𝑒𝑑
𝑖represents closed issues, 𝑁𝑡𝑜 𝑡𝑎𝑙
𝑖represents total is-
sues, and 𝑇𝑟 𝑒𝑠𝑜 𝑙𝑢𝑡 𝑖𝑜𝑛 (𝑡)is the average resolution time for issues
closed in the interval [𝑡 , 𝑡 +Δ𝑡].
Pull Request Merge Rate.
𝑝(𝑡)=
𝑁𝑚𝑒𝑟𝑔𝑒𝑑
𝑝(𝑡, 𝑡 +Δ𝑡)
𝑁𝑡𝑜𝑡 𝑎𝑙
𝑝(𝑡)·1
1+𝑇𝑟𝑒 𝑣𝑖 𝑒𝑤 (𝑡),(6)
where 𝑁𝑚𝑒𝑟𝑔𝑒𝑑
𝑝represents merged pull requests, 𝑁𝑡𝑜𝑡𝑎𝑙
𝑝represents
total pull requests, and 𝑇𝑟 𝑒 𝑣𝑖𝑒 𝑤 (𝑡)is the average review time for
pull requests in the interval [𝑡 , 𝑡 +Δ𝑡].
Activity Engagement Function.
𝑎(𝑡)=
𝑁𝑐𝑜𝑚𝑚𝑒𝑛𝑡𝑠 (𝑡 , 𝑡 +Δ𝑡)
𝑁𝑖𝑠𝑠𝑢 𝑒𝑠 (𝑡) + 𝑁𝑝𝑟 𝑠 (𝑡)·𝑁𝑎𝑐𝑡𝑖 𝑣𝑒 _𝑢𝑠𝑒𝑟 𝑠 (𝑡, 𝑡 +Δ𝑡)
𝑁𝑡𝑜𝑡 𝑎𝑙_𝑢𝑠𝑒𝑟 𝑠 (𝑡)(7)
where 𝑁𝑐𝑜𝑚𝑚𝑒𝑛𝑡𝑠 (𝑡 , 𝑡 +Δ𝑡)represents the number of comments
in the interval [𝑡 , 𝑡 +Δ𝑡],𝑁𝑖𝑠𝑠𝑢𝑒𝑠 (𝑡)=𝑁𝑡 𝑜𝑡𝑎𝑙
𝑖(𝑡) − 𝑁𝑐𝑙 𝑜𝑠𝑒 𝑑
𝑖(𝑡)and
𝑁𝑝𝑟 𝑠 (𝑡)=𝑁𝑡𝑜𝑡𝑎𝑙
𝑝(𝑡) − 𝑁𝑚𝑒𝑟𝑔𝑒𝑑
𝑝(𝑡)represent the number of open is-
sues and pu ll requests at time 𝑡respectively, and 𝑁𝑎𝑐𝑡𝑖 𝑣𝑒 _𝑢𝑠𝑒𝑟 𝑠 (𝑡, 𝑡 +
Δ𝑡)represents users who have engaged with the repository through
comments, commits, or pull requests in the interval [𝑡 , 𝑡 +Δ𝑡].
4 REPOSITORY-STABILITY DEFINITION
We define the stability of a repository through a framework that
considers both the individual metrics and their interrelationships.
A repository’s stability is characterized by consistent development
patterns, efficient issue resolution, effective pull request manage-
ment, and sustained community engagement.
Definition 4.1 (Stability). A repository 𝑅(𝑡)is considered stable
if it satisfies all of the following criteria over an observation period
[𝑡0, 𝑡0+𝑇].
1. Commit Pattern Stability:

𝑑𝑐 (𝑡)
𝑑𝑡 
≤𝛼𝑐,∀𝑡∈ [𝑡0,𝑡 0+𝑇],(8)
where 𝛼𝑐represents the maximum allowable rate of change in com-
mit frequency (the highest acceptable value that the rate of change
in commit frequency can have for a repositor y to still be considered
stable). This criterion ensures that development activity maintains
a consistent rhythm without extreme fluctuations that could indi-
cate project’s instability. The threshold is defined as
𝛼𝑐=
𝜎daily commits
𝜇daily commits
≤0.5.(9)
The coefficient of variation threshold 𝛼𝑐provides a measure of
commit frequency stability. We propose 𝛼𝑐=0.5 as an initial value
because this would indicate that the standard deviation remains
less than half the mean, thus allowing for natural variations, while
potentially identifying problematic patterns such as long periods
of inactivity followed by a burst of commits. This relative mea-
sure accommodates projects of different sizes and activity levels,
although empirical validation is neede d to confirm its effectiveness.
2. Issue Management Stability:
𝑖(𝑡) ≥ 𝛽𝑖and 𝑇𝑟 𝑒𝑠𝑜𝑙𝑢𝑡 𝑖𝑜𝑛 (𝑡) ≤ 𝜏𝑖,∀𝑡∈ [𝑡0,𝑡 0+𝑇],(10)
where
•𝛽𝑖is the minimum acceptable issue resolution rate (prop osed
value: 0.3);
•𝜏𝑖is the maximum acceptable average resolution time (pro-
posed value: 14 days);
•𝑇𝑟𝑒 𝑠𝑜𝑙𝑢𝑡 𝑖𝑜𝑛 (𝑡)is t he moving average of issue resolution time.
The thresholds for issue management stability reflect considera-
tions in modern software development practices. We propose 𝛽𝑖=
0.3 for the minimum resolution rate, acknowledging that not all is-
sues require immediate resolution – some may be feature requests,
duplicates, or issues that soon become obsolete. For the maximum
resolution time, here we consider 14 days, aligning with sprint cy-
cles of two weeks in agile development. These are initial proposed
values, but empirical validation is required to determine their effec-
tiveness across different project sizes and development intensities.
3. Pull Request Processing Stability:
𝑝(𝑡) ≥ 𝛽𝑝and 𝑇𝑟𝑒 𝑣𝑖𝑒 𝑤 (𝑡) ≤ 𝜏𝑝,∀𝑡∈ [𝑡0, 𝑡0+𝑇],(11)
where
•𝛽𝑝is the minimum acceptable pul l request merge rate (thresh-
old: 0.4);
•𝜏𝑝is the maximum acceptable average review time (thresh-
old: 5 days);
•𝑇𝑟𝑒 𝑣𝑖𝑒 𝑤 (𝑡)is the moving average of pull request review time.
The proposed 𝛽𝑝=0.4 pull request merge rate acknowledges
that, while some requests warrant rejection due to experimental
nature or needed revisions, maintaining an overly low rate may un-
necessarily impede contributions. The five-day maximum review
period strikes a balance between enabling thorough code evalua-
tion and maintaining development momentum. These initial thresh-
olds aim to optimize between quality control and velocity, though
their effectiveness will need to be validated through implementa-
tion data.
4. Community Engagement Stability:
𝑎(𝑡) ≥ 𝛾𝑎and 𝑁𝑎𝑐𝑡𝑖 𝑣𝑒_𝑢𝑠𝑒𝑟 𝑠 (𝑡)
𝑁𝑡𝑜𝑡 𝑎𝑙_𝑢𝑠𝑒𝑟 𝑠 (𝑡)≥𝛿𝑎,∀𝑡∈ [𝑡0,𝑡 0+𝑇],(12)
where

FSE2025 - IVR, June 2025, Trondheim, Norway Destefanis, et al.
•𝛾𝑎is the minimum acceptable activity ratio (threshold: pro-
posed value 0.25);
•𝛿𝑎is the minimum acceptable active user ratio (threshold:
proposed value 0.15).
The activity function 𝑎(𝑡)here is the same as defined in Sec-
tion 3.1 (see Eq. 7), measuring both the intensity of interactions
through comment ratios and the breadth of community participa-
tion through user activity ratios. The thresholds ensure that the
repository maintains both sufficient discussion density, relative to
open items, and broad community involvement.
4.1 Stability Thresholds
We represent the proposed threshold values for each metric as a
threshold matrix:
T. Matrix Θ=𝛼𝑐𝛽𝑖𝜏𝑖𝛽𝑝𝜏𝑝𝛾𝑎𝛿𝑎
0.5 0.3 14 0.4 5 0.25 0.15.(13)
These initial threshold values represent educat ed estimations based
on the authors’ experience with repository analysis and software
development processes. The commit pattern threshold (𝛼𝑐=0.5)
allows for natural variations while still identifying erratic behav-
ior. Issue and pull request thresholds balance timely response with
thorough processing. Community engagement thresholds aim to
ensure broad participation. We acknowledge these are initial pro-
posals that must be empirically validated in future studies.
4.2 Composite Stability Index
To provide a single quantitative measure of stability, we define the
Composite Stability Index (CSI) as a weighted sum of normalized
stability metrics:
𝐶𝑆 𝐼 (𝑡)=𝑤𝑐𝜙𝑐(𝑐(𝑡))+𝑤𝑖𝜙𝑖(𝑖(𝑡))+𝑤𝑝𝜙𝑝(𝑝(𝑡))+𝑤𝑎𝜙𝑎(𝑎(𝑡)) .(14)
The weights reflect the relative importance of each stability com-
ponent, and their sum must equal 1, with commit pattern stability
given slightly higher priority due to its direct reflection of devel-
opment activity. The weight vector is defined as
𝑊=[𝑤𝑐,𝑤𝑖, 𝑤𝑝, 𝑤𝑎]=[0.3,0.25,0.25,0.2].(15)
Each component is normalized through a function 𝜙𝑘that maps
the raw metrics to a [0,1]scale, ensuring comparable contribut ions
to the final index:
𝜙𝑘(𝑥)=(1−|𝑥−𝜇𝑘|
𝜎𝑘if |𝑥−𝜇𝑘| ≤ 𝜎𝑘,
0 otherwise .(16)
The target values 𝜇𝑘and acceptable deviations 𝜎𝑘are defined
for each component based on their respective thresholds:
•For commit pattern stability (𝜙𝑐):
–𝜇𝑐=0.25 (target coefficient of variation);
–𝜎𝑐=0.25 (allowing variation up to the 0.5 threshold).
•For issue management stability (𝜙𝑖):
–𝜇𝑖=0.4 (target resolution rate);
–𝜎𝑖=0.1 (allowing variation down to the 0.3 threshold).
•For pull request stability (𝜙𝑝):
–𝜇𝑝=0.5 (target merge rate);
–𝜎𝑝=0.1 (allowing variation down to the 0.4 threshold).
•For community engagement stability (𝜙𝑎):
–𝜇𝑎=0.35 (target activity ratio);
–𝜎𝑎=0.1 (allowing variation down to the 0.25 threshold).
Target values (𝜇𝑘) and deviations (𝜎𝑘) are set to encourage im-
provement beyond minimum thresholds, while ensuring that meet-
ing these minimums contributes positively to the CSI. We propose
a CSI threshold of 0.7 for overall stability, requiring components
to perform consistently above their minimum thresholds, while
accommodating temporary fluctuations. This weighted and nor-
malized scoring system enables both monitoring overall repositor y
health and diagnosing specific areas requiring attention when the
CSI falls below the threshold.
5 MATHEMATICAL PROPERTIES
The proposed Repository-Stability framework exhibits important
theoretical properties that validate its usefulness as a measure of
repository health and stability:
1. Boundedness The Composite Stability Index (CSI) is bounded
by design:
0≤𝐶𝑆 𝐼 (𝑡) ≤ 1,∀𝑡∈ [𝑡0, 𝑡0+𝑇].(17)
This boundedness property ensures that stability measures are nor-
malized and comparable across different repositories and time pe-
riods.
2. Piecewise Continuity The stability measure should be piece-
wise continuous with respect to all its component metrics. Within
each piece defined by |𝑥−𝜇𝑘| ≤ 𝜎𝑘, for any metrics 𝑚1, 𝑚2:
|𝑚1−𝑚2|<𝛿=⇒ |𝐶 𝑆𝐼 (𝑚1) − 𝐶 𝑆𝐼 (𝑚2)| <𝜖 . (18)
This property ensures that small changes in repository metrics re-
sult in proportional changes in the stability measure within each
regime.
3. Long-Term Stability If a repository’s metrics stabilize over
time (i.e., the system approaches an equilibrium), the Composite
Stability Index (CSI) should converge to a constant value:
lim
𝑡→∞ 𝐶𝑆 𝐼 (𝑡)=constant .(19)
This property reflects the long-term stability of a repository. In
engineering, stable systems often approach equilibrium states as
disturbances diminish over time. For a repository, this could cor-
respond to regular commit patterns, balanced issue resolution and
pull request processing, and consistent community engagement.
If each metric 𝜙𝑘(𝑥𝑘(𝑡)) stabilizes over time, such that:
lim
𝑡→∞ 𝜙𝑘(𝑥𝑘(𝑡)) =𝜙∞
𝑘,(20)
then the Composite Stability Index (CSI) converges to:
lim
𝑡→∞ 𝐶𝑆 𝐼 (𝑡)=Õ
𝑘
𝑤𝑘𝜙∞
𝑘,(21)
where𝑤𝑘are the weights assigned to each metric. This result shows
that the CSI becomes a weighted sum of the asymptotic values of
the individual metrics, providing a clear mathematical representa-
tion of the long-term behavior of the repository.
Conditions for Convergence: Metrics such as commit frequency,
issue resolution rate, and pull request merge rate must exhibit b ounded

Introducing Repository Stability FSE2025 - IVR, June 2025, Trondheim, Norway
fluctuations or a decaying trend toward equilibrium. For instance,
commit frequency 𝑐(𝑡)stabilizes if:
𝑑𝑐 (𝑡)
𝑑𝑡 →0 as 𝑡→ ∞ .(22)
While theoretical at this stage, this property could be empiri-
cally tested by analyzing historical data from reposito ries over long
periods. Stable repositories should display convergence trends in
their CSI values, whereas repositories with irregular or unsustain-
able practices may show divergence or high variability.
Practical Implications: Repositories with erratic behavior (e.g.,
bursts of activity followed by dormancy) may not exhibit conver-
gence, signaling instability, while stable repositories demonstrate
convergence, reflecting healthy long-term development practices.
This property provides a diagnostic tool for identifying reposito-
ries requiring intervention to achieve sustained stability. When sta-
bility metrics consistently fall below their thresholds, automated
monitoring systems can identify specific areas requiring attention.
For commit pattern instability, the system would highlight devel-
opment cycle issues; for degrading pull request processing, it would
indicate review process inefficiencies. Developers can then imple-
ment targeted interventions, which may include restructu ring sprint
planning to stabilize commit patterns, or redistributing review re-
sponsibilities to improve pull request processing. T hese metric-specific
corrections allow teams to address stability issues b efore they com-
promise overall project health, transforming theoretical stability
measures into practical maintenance tools within existing devel-
opment workflows.
6 CONCLUSION AND OPEN CHALLENGES
We introduced a theoretical framework for analyzing repository
stability through the lens of control theory. The framework’s four
core components — commit patterns, issue resolution, pull request
processing, and community engagement — provide a compl ete view
of repository stability, while remaining computationally tractable.
Through the newly introduced Composite Stability Index, we offer
a tool to measure and monitor repository health through its sta-
bility characteristics. Our framework makes several fundamental
assumptions: that repositories exhibit equilibrium-seeking behav-
ior similar to physical systems, that stability can be meaningfully
quantified through our chosen metrics, and that these measures
capture the essential dynamics of software development. These
assumptions, while grounded in software engineering practices,
open critical questions for the research community:
1) To what extent can universal stability thresholds be established,
or do they inherently depend on repository context? This question
builds on prior work by Jansen [17], who observed that metrics
may have different meanings for different projects. While our frame-
work proposes initial thresholds (e.g., 𝛼𝑐=0.5 for commit pattern
stability), empirical research across diverse repositories is needed
to determine whether universal thresholds exist or if contextual
adaptation is necessary. A promising hypothesis is that reposito-
ries within similar domains (e.g., system libraries vs. web applica-
tions) share similar optimal stability thresholds.
2) Under what conditions does the control theory analogy hold for
software repositories, and which differences could b e brought by open-
source and proprietary software development? This question extends
Salama et al.’s [4] work on stability concepts in software engineer-
ing, exploring whether open-source repositories follow different
equilibrium patterns than proprietary ones. Factors such as gov-
ernance structures [18] and corporate engagement [15] likely in-
fluence stability dynamics. We hypothesize that repositories with
corporate backing exhibit different recovery patterns following dis-
turbances than community-driven projects.
3) What mathematical models could better represent the complex in-
teractions between stability components while maintaining practical
applicability? Building on Filieri et al.’s [5] application of control
theory to software engineering, future work could explore non-
linear models that capture emergent interactions between stability
components. For instance, the relationship between issue resolu-
tion and community engagement might be b etter modeled through
coupled differential equations that capture feedback mechanisms.
4) How do different socio-technical factors — from team structure
to development methodologies to community norms — affect our no-
tion of stability? This question connects with Goggins et al.’s [13]
emphasis on social context in health assessment. We hypothesize
that repositories with explicit governance mechanisms (e.g., de-
fined contribution processes) exhibit higher stability in the face
of similar disturbances compared to those with ad-hoc structures.
Future research could categorize repositories based on these socio-
technical factors and analyze their CSI patterns.
5) How can this theoretical framework inform practical tools for project
maintenance while accounting for the social nature of software devel-
opment? This bridges theory with practice. Stability metrics could
be integrated into project dashboards that provide early warnings
of declining stability, with visualizations that will help interpret
complex stability data in context. These questions point to rich op-
portunities in both theoretical and empirical directions — from val-
idating the framework through large-scale repository analysis, to
empirically defining threshold values, to investigating non-linear
stability metrics — potentially transforming how we understand
and evaluate software projects’ health.
Future work should directly compare our stability framework
with traditional repository health metrics to validate whether our
approach captures dynamic aspects of development that static met-
rics miss. User studies with development teams could reveal how
our framework translates from a theoretical mo del to practical mon-
itoring tools.
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