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Fast Response or Silence: Conversation Persistence in an Artificial Intelligence Agent Social Network
Recent advances in large language models (LLMs) have enabled a new class of autonomous artificial intelligence (AI) agents capable of sustained interaction with digital environments. One manifestation of this capability is Moltbook, a social network launched in January 2026 that restricts posting privileges to AI agents while permitting human observation willison2026moltbook. In this paper, an AI agent account denotes an account whose posting and commenting actions are generated by an LLM-driven agent process rather than direct human operation. In the first archived week, the platform accumulated over 25{,}000 such agent accounts and 119{,}677 posts simulamet2026observatoryarchive, creating a large, accessible dataset of agent-to-agent interaction.
This emergence of agent-populated social platforms raises fundamental questions about collective AI behavior. Can autonomous agents sustain the extended, multi-turn dialogues necessary for meaningful collaboration? How might architectural constraints---particularly context-window limitations and periodic activation schedules---shape the temporal dynamics of agent discourse? And what distinguishes agent-driven conversations from human-driven ones in structural and temporal terms?
Early public commentary proposed that Moltbook agents may be better at initiating projects than sustaining them and may follow roughly 4-hour check-in routines alexander2026afterweekend,willison2026moltbook. We use these statements as qualitative hypothesis motivation only, not as factual evidence; empirical claims in this paper are derived from the archived Observatory data. Because per-account heartbeat events are unobserved, we test only aggregate periodic signatures, allowing for weak detectability under dephasing/jitter. This framing is paired with finite context windows, which motivate tests of rapid within-thread staleness.
Conversation persistence can be interpreted through canonical constructs in service systems and stochastic-process modeling. Aggregate availability and heartbeat schedules correspond to time-varying service capacity and cyclic service regimes whitt2004efficiency,jouini2010online. Staleness decay corresponds to abandonment and impatience mechanisms in waiting systems whitt2004efficiency,reed2012hazard,jouini2010online. Reply incidence corresponds to completion/throughput outcomes under constrained capacity, and thread depth corresponds to branching stability versus subcriticality harris1963theory. This mapping motivates the measurement-target design used in this study.
From an operations research and management science (OR/MS) decision-support perspective, the platform is a distributed service system in which pending parent comments are competing jobs for limited agent attention. The operational design problem is to allocate limited intervention budget across incidence-lift levers (for example resurfacing or visibility reminders) versus timing-lift levers (for example memory/context support) to maximize downstream coordination throughput, such as conversation depth and repeat participation (re-entry). In this framing, our contribution is not only descriptive: the incidence margin diagnoses participation bottlenecks, while the conditional timing margin diagnoses latency bottlenecks, and the two margins define a policy-priority control panel.
Our objective is to formalize and empirically validate a two-part control panel for conversational persistence in Moltbook's first week: (i) direct-reply incidence and (ii) conditional reply latency. We map these two margins to depth and related thread-structure outcomes (branching, reciprocity, and re-entry). We include heterogeneity analyses only when they clarify which margin constrains coordination.
We do not attempt dedicated thread-duration inference, nor do we treat cross-platform baseline comparison mechanics or detailed periodicity machinery as primary claims. Thread duration is reported only as an ancillary descriptive metric, and Reddit baseline context and periodicity are treated as secondary contextual checks.
\paragraph{Identification scope} This paper reports observational measurement targets from archived first-week data and does not identify causal intervention effects. Periodicity and cross-platform baseline comparisons are contextual checks rather than primary identification strategies. For heartbeat periodicity, we distinguish statistical rejection of exact uniformity from practical signal strength: at large \(N\), Rayleigh tests can reject uniformity even when concentration is too small to imply meaningful global synchronization. Accordingly, patterns described as consistent with architectural constraints are also compatible with alternative platform-side explanations such as ranking/visibility effects, moderation throttling, or batched/scheduled agent execution.
Guided by the horizon-limited cascade framework in (ref) and prior qualitative commentary used for hypothesis motivation willison2026moltbook, alexander2026afterweekend, we test four hypotheses. H1a posits short exponential-equivalent kernel half-life (diagnostic) values consistent with architectural staleness constraints. H1b posits that heartbeat scheduling can generate aggregate periodic structure near the hypothesized cadence ($\tau \approx 4$ hours) when check-ins are sufficiently synchronized; under dephasing or jitter, aggregate detectability may be weak in finite samples. H2 posits shallower, more root-concentrated Moltbook trees than human-platform baselines, with lower reciprocity and conditioning-sensitive re-entry profiles; the re-entry contrast is treated as conditioning-sensitive and may change direction across baseline conditioning sets. H3 posits topic-level moderation of persistence, including systematic differences in kernel half-life diagnostic values and depth across submolts. H4 posits that agent-level claim-status covariates are associated with variation in reply incidence and conversational persistence.
We operationalize these hypotheses via the measurement targets defined in (ref) and the estimators in (ref), and evaluate them in (ref). For compact orientation, H1a/H1b correspond to (ref), H2 to (ref), H3 to (ref), and H4 to (ref).
In this first-week snapshot, Moltbook conversations are predominantly star-shaped, with minute-scale kernel half-life diagnostic values, low direct-reply incidence, and minimal reciprocity. Periodicity effect size is weak (\(r=0.0308\)); Rayleigh testing rejects exact uniformity at large \(N\), but spectral diagnostics do not show a strong 4-hour line. A run-scoped Reddit baseline shows materially longer persistence and deeper threads. Taken together, these patterns are compatible with a “low-incidence/fast-conditional-response” regime and indicate that incidence, not conditional latency, is the dominant operational bottleneck at minute-to-hour horizons in this snapshot.
Aligned to this objective, the paper delivers three contributions. First, we formalize an OR diagnostic for horizon throughput \(q_h\): a decomposition into incidence and conditional timing on a common risk set, with a derived cost-adjusted priority rule for deciding whether to invest in participation uplift or latency reduction as formalized in (ref). This turns a standard survival decomposition into a decision-support control panel. Second, using the Moltbook Observatory Archive simulamet2026observatoryarchive, we provide an analytic decision-support evaluation of that control panel using observed margins: we quantify how incidence versus conditional timing changes propagate to depth and re-entry-relevant coordination pressure under budgeted interventions. Third, we differentiate this contribution from conversation-cascade studies that typically emphasize unconditional delay or geometry summaries crane2008robust,rizoiu2017expecting,gomez2013structure,aragon2017thread,meital2024branch: by separating incidence from conditional speed under right-censoring and then mapping both to OR targets, we identify which margin is operationally binding rather than treating persistence as a single aggregate statistic.
The remainder of this paper is organized as follows. (ref) reviews stochastic-process foundations for interaction persistence, then network structure and agent-platform context. (ref) presents the minimal model and primary measurement targets. (ref) describes data construction and preprocessing. (ref) details estimation and empirical procedures. (ref) reports empirical findings and model-consistency checks. (ref) interprets implications, including short downstream design considerations. (ref) addresses limitations and ethical considerations. (ref) concludes with key takeaways and future work.
This section positions the paper against prior work that is directly operationalized in our empirical design. We organize the review around three pillars that map one-to-one to the measurement targets in (ref): event-time reinforcement, censored time-to-reply analysis, and branching/cascade structure. We then place agent-populated social platforms as the application context.
Self-exciting point-process models provide a canonical way to represent temporal reinforcement: each event raises short-run intensity for subsequent events, with decay over time hawkes1971spectra. This class has been used both in operations-facing settings and in online interaction systems. Within service operations, recent work applies Hawkes-style formulations to co-production interaction streams daw2025coproduction. In computational social systems, related models have been used to describe popularity bursts, response cascades, and diffusion timing on digital platforms crane2008robust,zhao2015seismic,rizoiu2017expecting. Across these domains, the common mechanism is that recent activity makes near-term follow-up activity more likely.
Our use of this pillar is intentionally measurement-first rather than model-first. We do not claim that a fully specified Hawkes process is identified as the data-generating process for Moltbook. Instead, Hawkes intuition motivates how we interpret the availability--staleness mechanism and why a recency-sensitive timescale is relevant. This is why the exponential-equivalent half-life is treated as a secondary diagnostic summary, while the primary estimands remain direct-reply incidence and conditional reply timing.
Survival and hazard frameworks are the standard statistical foundation for time-to-event outcomes under censoring cox1972regression. In service systems, these tools connect naturally to abandonment and impatience: even when potential service opportunities exist, many cases do not complete within the observation horizon whitt2004efficiency,reed2012hazard,jouini2010online. That logic maps directly to reply dynamics in threaded conversations, where many parent--child opportunities remain unrealized during finite windows.
This paper therefore adopts a two-part persistence decomposition that is consistent with hazard-based reasoning: an incidence margin (whether a direct reply occurs) and a conditional timing margin (how fast it occurs when it does). The decomposition is designed to separate distinct operational bottlenecks. Low incidence indicates scarce engagement capacity on candidate parent comments, whereas slower conditional timing indicates latency conditional on engagement. This separation is central to our OR diagnosis and to the estimands reported in the main results.
Branching-process theory links local reproduction behavior to global cascade geometry harris1963theory. In subcritical regimes, trees remain shallow and mass concentrates near roots; in higher-reproduction regimes, deeper tails become more prevalent. This provides the structural bridge from reply-level persistence mechanisms to thread-level coordination outcomes.
Empirical discussion-network studies provide concrete structural benchmarks. gomez2013structure document strong root bias in online discussion cascades, aragon2017thread relate threaded interfaces to reciprocity, and meital2024branch show that temporal and structural signals jointly shape where replies attach in Reddit trees. We use this strand as context for our structural readouts, specifically depth profiles, branching-by-depth, reciprocity, and re-entry. In our framework, these are consequences of the persistence regime rather than separate primary mechanisms.
The rise of LLM-based agent systems makes these measurement questions operationally salient in a new domain. Early simulation evidence shows that small groups of language-model agents can form relationships and coordinate in controlled environments park2023generative. Moltbook extends that setting to a public, large-scale platform with archived interaction traces simulamet2026observatoryarchive, enabling direct observation of agent-to-agent discussion dynamics.
Relative to prior literature, our contribution is not to introduce a new stochastic-process class. Instead, we provide a mechanism-to-measurement mapping for an agent-populated service setting: event-time reinforcement intuition motivates timing diagnostics, survival logic motivates the two-part incidence/timing decomposition under censoring, and branching logic links those estimands to depth and coordination limits in observed thread structure.
This section defines the measurement targets (estimands) used to quantify conversation persistence and thread structure in agent social networks. We introduce a two-part decomposition of persistence into direct-reply incidence and conditional reply timing, define structural outcomes (depth, branching, reciprocity, and re-entry), and derive an operational diagnostic that links these margins to horizon throughput.
We interpret persistence through two mechanisms. First, platform-level availability captures when agents are active and likely to observe threads. Second, within-thread staleness captures how reply propensity falls as a parent comment ages.
We represent exposure/resurfacing effects through an effective participation amplitude,
where \(\bar{\alpha}_i\) is baseline reply propensity and \(\xi_i\) is an exposure multiplier that absorbs visibility/ranking and resurfacing effects in observational data. Staleness is captured by a decay-rate parameter \(\beta_i\). The joint interpretation is mechanistic rather than causal: higher availability/exposure and slower staleness decay are associated with greater observed persistence.
Let \(\mathcal{J}\) denote threads (root posts). For thread \(j\in\mathcal{J}\), events are indexed by \(n\in\{0,1,\ldots,N_j\}\), with \(n=0\) the root and \(n\ge 1\) comments. Event \(n\) is \((t_{jn},a_{jn},p_{jn})\), where \(t_{jn}\) is timestamp, \(a_{jn}\) author, and \(p_{jn}\in\{0,\ldots,n-1\}\) its parent index.
Depth is defined recursively:
Maximum thread depth is \(D_j:=\max_{0\le n\le N_j} d_{jn}\).
For node \((j,n)\), let \(c_{jn}:=\#\{r>n: p_{jr}=n\}\) be its direct-child count. The branching-factor profile by depth is
which distinguishes root-heavy star patterns from deeper cascading activity.
For thread \(j\), define directed reply edges
Let
be the unordered dyads with at least one directional reply. Thread-level reciprocity is
Thread-level re-entry is
As in the empirical implementation, this definition conditions on non-root comments; root author \(a_{j0}\) enters only if it appears later in comments.
For each candidate parent comment \(m\), let \(T_m\) denote first direct-reply time (if any), \(C_m\) right-censoring time from parent timestamp to observation end, and \[ s_m:=\min(T_m,C_m), \qquad \delta_m:=\mathbf{1}\{T_m\le C_m\}. \] All incidence and timing estimands in this paper are defined for non-root comments as candidate parents (comment-to-comment replies), not for root posts.
The empirical persistence model is two-part:
and
This is a hurdle / cure-style decomposition of persistence into a participation margin (whether any direct reply occurs) and a conditional timing margin (how quickly replies arrive once participation occurs).
Primary estimands are:
For decision support at horizon \(h\), define the risk set \[ R_h:=\{C_m\ge h\ \text{or}\ T_m\le h\}, \] and horizon throughput \[ q_h:=\mathbb{P}(T_m\le h\mid R_h). \] Define two margins on the same risk set: \[ \pi_h:=\mathbb{P}(\delta_m=1\mid R_h),\qquad \phi_h:=\mathbb{P}(T_m\le h\mid \delta_m=1,R_h). \] By the law of total probability,
Hence, for local intervention-induced changes,
Using the branching-style depth proxy \(\mathbb{P}(D_j\ge K)\approx q_h^{K-1}\), first-order gains in depth-\(K\) throughput are proportional to the same weighted sum in (ref). Therefore, with intervention costs \((c_\pi,c_\phi)\), a one-step operational priority rule is \[ I_\pi:=\frac{\phi_h\,\Delta\pi_h}{c_\pi},\qquad I_\phi:=\frac{\pi_h\,\Delta\phi_h}{c_\phi}, \] prioritizing the larger index. This is a decision-support diagnostic under observed margins, not a causal policy-effect estimator.
We analyze the Moltbook Observatory Archive as the primary source for agent-driven conversations and use a run-scoped curated Reddit corpus as secondary contextual baseline data.
Our primary dataset is the Moltbook Observatory Archive simulamet2026observatoryarchive, a publicly available snapshot covering January 28 to February 4, 2026, the first week after Moltbook's public launch.
Because the archive is updated through incremental exports and possible backfills, we treat dump_date (when available) as a snapshot identifier and construct a canonical latest-state view by deduplicating on primary keys and retaining the most recent record. The archive contains six relational tables (agents, posts, comments, submolts, snapshots, \texttt{word_frequency}).
The comments table is central to our analysis. Each row includes a unique comment identifier, a post identifier, an author identifier, a parent-comment identifier (null for direct replies to the root post), a Coordinated Universal Time (UTC) timestamp, and an observed score snapshot. The parent linkage enables full thread-tree reconstruction for depth, branching, and reply-chain analyses.
Preprocessing combines schema harmonization, deterministic tree reconstruction, and integrity checks before feature construction. In this snapshot, canonical comments contain 223,317 unique comment identifiers from 226,173 raw comment rows. Referential checks pass: every comments.post_id maps to a valid post, every non-null comments.parent_id maps to a valid comment, and no negative parent or post lags are observed. Timestamps are normalized to UTC and each thread is shifted so that its root post is at \(t=0\). We classify submolts into six deterministic labels (Builder/Technical, Philosophy/Meta, Social/Casual, Creative, Spam/Low-Signal, Other) using a fixed keyword mapping to avoid post hoc relabeling. Because deterministic keyword mapping is coarse, we assess sensitivity to alternative keyword trigger lists and exclusion rules to verify that the Social/Casual versus Philosophy/Meta heterogeneity direction used for H3 interpretation is robust.
Author identifiers are nearly complete but not perfect. In this snapshot, 906 of 223,317 comments (0.41%) have missing author identifiers, concentrated in 254 threads where all comment authors are missing (0.73% of threads). We retain these rows in canonical thread reconstruction, count resolved commenter identifiers only for participant metrics, and treat author-based interaction metrics as undefined when no commenter identifiers are observed.
Event-time analyses use UTC timestamps. The canonical timeline contains a 41.7-hour gap (2026-01-31 10:37:53Z to 2026-02-02 04:20:50Z), so periodicity analyses are run on contiguous segments rather than under a continuous-coverage assumption. Raw-archive diagnostics indicate this break is comment-stream-specific rather than a full platform halt: within the same interval the archive still records 38,166 posts, 39 snapshot rows, and 5,039 word-frequency rows, while comment records are absent. This pattern is consistent with archive-side comment coverage interruption, but without independent platform uptime logs we cannot fully distinguish archive incompleteness from true near-zero comment generation during the interval.
Among threads with at least one comment (\(N=34{,}730\)), mean comments per post is 6.43 and mean maximum depth is 1.38.
To contextualize Moltbook dynamics, we analyze a curated Reddit corpus drawn from six subreddits: r/MachineLearning, r/Python, r/artificial, r/datascience, r/learnprogramming, and r/programming. The corpus includes 1,772 submissions and 9,878 comments, with 1,104 threads containing at least one comment; timestamps span 2026-01-31T00:03:20Z to 2026-02-04T23:59:34Z.
Validation checks on curated tables pass, with two upstream caveats that bound interpretation: 1,570 comments were dropped during curation because submission identifiers were missing, and collection logs record 2 non-200/error responses.
This Reddit corpus is used as descriptive baseline context: we estimate Reddit-side geometry, survival, and periodicity metrics using the same estimators as for Moltbook in (ref). Ethical and terms-of-use considerations are discussed in (ref).
Estimands are defined in (ref). This section focuses on estimation algorithms and empirical procedures. Low-level operational settings (binning, detrending, and bootstrap mechanics) are summarized where they are used.
For each thread \(j\), we compute node depths from (ref), record the maximum depth \(D_j\), and summarize the empirical depth distribution with mean maximum depth, median maximum depth, and tail probabilities \(\mathbb{P}(D_j \ge k)\) for \(k=1,\ldots,10\). We estimate an effective depth-tail slope \(\hat{s}_{\mathrm{depth}}\) by zero-intercept least squares on \(\log \mathbb{P}(D_j \ge k)\). Because the analysis conditions on threads with at least one comment, \(\mathbb{P}(D_j \ge 1)=1\) by construction; the fit is therefore identified by \(k\ge2\). This log-tail summary is reported descriptively rather than as an exact reproduction-mean estimator; branching interpretations are heuristic.
We additionally compute branching-factor profiles by depth, \(\bar c_k = \mathbb{E}[\text{children at depth }k]\), including the root branching factor, to distinguish root-heavy star patterns from deeper cascades.
Reciprocity is measured from directed dyads within threads as the fraction of dyads with bidirectional replies, and reciprocal-chain length is defined as the maximal alternating exchange between two agents. Re-entry is measured by \(\mathrm{RE}_j\) in (ref). Missing-author-identifier handling rules are deterministic.
For each at-risk comment (candidate parent) \(m\) in thread \(j\), we define first-direct-reply survival time
If no direct reply is observed, the unit is right-censored at the observation boundary. Because the canonical timeline contains a 41.7-hour coverage gap, we do not impute unobserved replies across that interval. To assess whether this gap can artifactually inflate fast conditional-response signals, we run four robustness checks: gap-disambiguation diagnostics across raw archive tables, contiguous-window recomputation (pre-gap and post-gap), gap-overlap exclusions (\(X\in\{6,24\}\) hours before gap start), and horizon-standardized \(\mathbb{P}(\delta=1,T\le t)\) at \(t\in\{30\mathrm{s},5\mathrm{min},1\mathrm{h}\}\) using explicit risk sets. We report these robustness checks in the Results section.
\paragraph{Part 1: incidence model} Primary incidence readouts are horizon-standardized probabilities at fixed follow-up windows \(h\in\{5\mathrm{min},1\mathrm{h}\}\) using the risk-set estimator defined in (ref). We report the in-window ever-reply share \(\hat p_{\mathrm{obs}}\) only as a secondary descriptive metric. Claimed-status and submolt comparisons use the same horizon-specific risk-set construction within each stratum.
For each parent unit, event indicator \(\delta_m\) is modeled with a complementary log-log (cloglog) generalized linear model:
which aligns with a discrete-time hazard interpretation and the asymmetric tail behavior of rare-event incidence. Here this is appropriate because most candidate parents receive no direct reply in-window. Covariates \(x_m\) include categorical indicators for submolt category and claimed-status group. Inference uses two-way clustered covariance by thread and author to address within-thread dependence and repeated-author dependence.
\paragraph{Part 2: conditional timing model} Among replied parents \((\delta_m=1)\), we report empirical conditional-time estimands directly: \(\tilde s_{0.5}\), \(\tilde s_{0.9}\), \(\tilde s_{0.95}\), \(\mathbb{P}(T_m\le 30\mathrm{s}\mid \delta_m=1)\), and \(\mathbb{P}(T_m\le 5\mathrm{min}\mid \delta_m=1)\). We also report their unconditional counterparts \(\mathbb{P}(\delta_m=1,T_m\le t)\) for \(t\in\{30\mathrm{s},5\mathrm{min}\}\). For parametric shape diagnostics, we fit Weibull and lognormal-style alternatives to \(T_m\mid \delta_m=1\).
For kernel diagnostics, we fit an exponential-kernel hazard with \(b(t)=1\) as a timescale-separation approximation for identifying \(\beta\), while periodic modulation is tested separately at the aggregate level in the periodicity analysis below.
We estimate \((\alpha,\beta)\) by maximum likelihood under an exponential-kernel hazard model with constant \(b(t)=1\):
We also fit a Weibull alternative,
to assess departures from exponential decay.
Given high censoring, we report incidence and conditional-speed estimands as primary readouts; \(p_\infty=1-\exp(-\hat\alpha/\hat\beta)\) and the kernel half-life diagnostic are reported only as secondary diagnostics. We report stratified pooled estimates by submolt category and claim status, plus one-parent-per-thread sensitivity readouts to bound within-thread clustering effects.
Uncertainty is quantified with thread-cluster bootstrap confidence intervals using fixed deterministic resampling settings.
Because the canonical timeline contains a 41.7-hour gap, heartbeat-scale periodicity is evaluated on the longest contiguous segment only. The main-text periodicity readout is event-time modulo-4-hour concentration \(r\), Rayleigh \(Z\), Monte Carlo \(p\)-value, and a coarse-grid detectability reference \(\kappa^\star\) (the first tested \(\kappa\) on the coarse grid \(0.0, 0.2, \ldots\) that reaches 80% simulated power at observed sample size, not a sharp threshold). Power spectral density (PSD) and first-order autoregressive (AR(1)) calibration checks, plus bin-width sensitivity, are used as additional diagnostics.
To contextualize Moltbook against a human-platform baseline, we compute the same geometry and two-part reply estimands on a run-scoped Reddit corpus.
All analyses are run in Python with fixed seeds and deterministic preprocessing for reproducability.
We report Moltbook results from the curated Observatory Archive snapshot and Reddit full-scale baseline results from the run-scoped curated Reddit corpus. We organize Results by hypothesis-native blocks: H1a (persistence decomposition into incidence versus conditional timing), H2 (structural signatures including reciprocity/re-entry), H3 (topic moderation), and H4 (agent covariates). We also report H1b periodicity diagnostics and a contemporaneous Reddit baseline for context. Metric terminology follows the canonical glossary in (ref).
Using one survival unit per at-risk non-root comment (candidate parent), the primary two-part sample includes 223,316 parents. All incidence and timing estimands in this section are defined for non-root comments as candidate parents (comment-to-comment replies), not for root posts. Primary incidence is horizon-standardized: \(p_{5\mathrm{m}}=9.42\%\) and \(p_{1\mathrm{h}}=9.82\%\). The in-window ever-reply share is 9.60% (95% bootstrap confidence interval (CI): [9.45%, 9.76%]) and is treated as a secondary coverage-conditional descriptive metric. The conditional median reply time is 4.55 seconds (95% bootstrap CI: [4.53, 4.58] seconds), with \(t_{90}=50.05\) seconds. Claimed-status heterogeneity remains large after follow-up standardization: claimed \(p_{5\mathrm{m}}=18.95\%\), \(p_{1\mathrm{h}}=19.56\%\), versus unclaimed \(p_{5\mathrm{m}}=8.48\%\), \(p_{1\mathrm{h}}=8.86\%\) (\(\approx 2.2\times\)). Conditional medians are similar (4.42 [4.38, 4.45] seconds for claimed vs.\ 4.59 [4.57, 4.62] seconds for unclaimed), but the conditional upper tail is much faster for claimed accounts (\(t_{90}=6.29\) seconds, 95% bootstrap CI: [6.06, 6.83], vs.\ 63.40 seconds, 95% bootstrap CI: [52.95, 77.31]; \(\approx 10.1\times\)). Claimed/unclaimed rows exclude parents with missing author identifier (\(n=906\)), so these strata sum to \(N=222{,}410\) rather than the overall \(N=223{,}316\). Because parent units share threads and repeated authors, inference on claimed-status contrasts is dependence-limited in this snapshot; we treat these contrasts as exploratory descriptive evidence. Conditional on a reply occurring, 88.30% arrive within 30 seconds and 98.06% within 5 minutes. This is the core low-incidence / very-fast-conditional-speed pattern.
(ref) visualizes the same two-regime pattern: Moltbook mass is concentrated at the seconds-to-minute scale, while Reddit is substantially shifted to longer delays.
The incidence model ((ref)) is used here as a calibration/sensitivity diagnostic for part-1 incidence rather than as a standalone inferential test for claim status. It is calibrated to the secondary ever-reply incidence margin: observed \(p_{\mathrm{obs}}=0.096304\) and mean fitted incidence 0.096319 (absolute error \(1.52\times 10^{-5}\), \(N=222{,}410\), where claim-status rows exclude missing-author parents (\(n=906\))). Relative to Social/Casual (reference), non-reference submolts have negative cloglog coefficients (from \(-1.62\) to \(-2.56\)). The claimed-group coefficient is positive (\(+0.844\)) but has wide two-way-clustered uncertainty (95% CI: [\(-0.39\), 2.08]). Accordingly, claim-status interpretation relies on the follow-up-standardized descriptive contrasts in (ref).
Parametric conditional-time models are used here as misspecification diagnostics rather than as successful structural fits. Observed-versus-fitted diagnostics show modest calibration for in-window event probability (Moltbook: 9.60% observed vs.\ 9.91% fitted; Reddit: 36.20% observed vs.\ 38.70% fitted) but large early-quantile errors. For Moltbook, fitted \(p_{50}\) is 39.94 seconds versus 4.55 seconds observed, and fitted \(p_{90}\) is 134.98 seconds versus 50.05 seconds observed. Analogous quantile overstatement appears for Reddit. We therefore do not treat parametric timing fits as primary evidence for reply-speed shape. Main-text timing inference relies on nonparametric conditional quantiles and early-window probabilities, and the kernel half-life remains a secondary diagnostic only.
Coverage-gap diagnostics indicate a comment-stream interruption in the archive rather than complete platform inactivity. The post-gap contiguous window (220,460 parents) reproduces the headline decomposition closely: incidence 9.71%, \(t_{50}=4.55\) seconds, and \(t_{90}=48.66\) seconds versus 9.60%, 4.55 seconds, and 50.05 seconds in the full window. Excluding parents whose reply opportunity overlaps the gap (\(X=6\) or 24 hours before gap start) produces numerically identical values in this snapshot. The pre-gap contiguous window is only 2.86 hours (2,856 parents; 30 observed replies), so those estimates are reported as low-power sensitivity only. Horizon-standardized risk-set probabilities remain close at short horizons (30 seconds and 5 minutes) and rise modestly at 1 hour, consistent with short-follow-up censoring near the observation boundary.
Moltbook conversation trees are shallow ((ref)): mean maximum depth is 1.38 (95% bootstrap confidence interval (CI): [1.37, 1.38]), median maximum depth is 1, the proportion reaching depth 5+ is 0.006% (95% bootstrap CI: [0.000%, 0.014%]), and the proportion reaching depth 10+ is 0.000%.
Fitting a geometric log-tail slope to empirical \(\mathbb{P}(D_j \geq k)\) for \(k\ge2\), motivated by the bound \(\mathbb{P}(D_j \geq k) \leq \mu^k\), gives an effective depth-tail slope estimate \(\hat{s}_{\mathrm{depth}}=0.154\). We report \(\hat{s}_{\mathrm{depth}}\) as a descriptive depth-tail metric (not a directly identified branching ratio); under a heuristic branching interpretation, this indicates rapid depth-tail decay compatible with a strongly subcritical regime.
(ref) shows strong root concentration. The root receives 5.57 direct replies on average, while depth-1 and depth-2 nodes receive 0.153 and 0.008 direct replies, respectively. This is the expected star-shaped pattern under rapid branching decay. We evaluate the corresponding thread-size consistency implication in the next subsection.
Dyadic reciprocity is low: 1,621 of 162,430 dyads are bidirectional (0.998%). Reciprocal chains are short (median chain length 2; mean 2.09). Thread-level re-entry is also limited, with mean 0.195 and median 0.167. Missing-author-identifier sensitivity is small: restricting to threads with complete commenter identifiers (34,476 of 34,730 threads; 99.3%) leaves re-entry and pooled dyadic reciprocity unchanged at reported precision (mean re-entry 0.20; pooled reciprocity 1,621/162,430 \(=1.0\%\)). The only visible shift is mean unique participants per thread, from 4.57 to 4.60.
As a back-of-the-envelope coherence calculation, we combine two summaries from this snapshot: the root offspring mean \(\mu_0 \approx 5.57\) and an effective depth-tail slope estimate \(\hat{s}_{\mathrm{depth}} \approx 0.154\). Applying the root-special branching heuristic \(\mathbb{E}[N_j]\approx \mu_0/(1-\mu)\) with the heuristic mapping \(\mu \approx \hat{s}_{\mathrm{depth}}\) gives \(\mathbb{E}[N_j] \approx \mu_0/(1-\hat{s}_{\mathrm{depth}}) \approx 6.6\) comments per thread, close to the observed mean of 6.43 comments per thread.
Model-to-observable coherence checks map fitted \((\alpha,\beta)\)-style primitives to observables reported in the paper; this is an in-sample calibration diagnostic rather than an independent out-of-sample test. Incidence calibration is tight overall (9.91% predicted vs.\ 9.60% observed) and remains close across claimed/unclaimed and submolt strata. The same coarse fit systematically underpredicts non-root branching (for example, overall 0.104 predicted vs.\ 0.134 observed) while overpredicting deeper tails \((\Pr(D\ge3),\Pr(D\ge5))\). This sign pattern is consistent with the strong depth dependence visible in (ref): branching is highly concentrated at the root and then drops sharply at depths 1 and 2. A coarse homogeneous non-root fit therefore misallocates branching mass across depths and is interpreted as a descriptive consistency check rather than an exact structural equality.
One-parent-per-thread sensitivity lowers pooled incidence from 9.60% to 7.21%, indicating that within-thread clustering contributes to level differences in the incidence margin. Conditional timing changes are materially smaller: \(t_{50}\) shifts from 4.55 to 4.51 seconds and \(t_{90}\) from 50.05 to 41.08 seconds. The kernel half-life diagnostic correspondingly decreases from 0.685 to 0.436 minutes. These checks preserve the main interpretation that persistence limits in this snapshot are dominated by whether replies occur rather than by slow conditional reply speed.
The primary stratified pattern is incidence/speed heterogeneity. Social/Casual has the highest incidence (10.95%) and very fast conditional timing (\(t_{90}=24.83\) seconds), whereas Builder/Technical and Philosophy/Meta have low incidence with materially slower conditional tails (\(t_{90}=434.87\) seconds [7.25 minutes] and \(2868.78\) seconds [47.81 minutes], respectively). Category-cluster bootstrap intervals preserve this ranking: Social/Casual remains high-incidence/fast-tail, while Philosophy/Meta remains low-incidence/slow-tail with low median re-entry. Follow-up-standardized incidence at fixed horizons yields the same ordering; for example, Social/Casual has \(p_{5\mathrm{m}}=10.80\%\) and \(p_{1\mathrm{h}}=11.21\%\), while Philosophy/Meta has \(p_{5\mathrm{m}}=1.32\%\) and \(p_{1\mathrm{h}}=1.70\%\). Because submolt categories are assigned by deterministic keyword triggers on submolt names, we assess keyword-mapping sensitivity under alternative trigger lists and exclusion rules; the Social/Casual versus Philosophy/Meta incidence/tail ordering is unchanged across these variants.
Claim-status heterogeneity is reported directly in (ref): claimed accounts have higher incidence and materially faster upper-tail conditional timing than unclaimed accounts.
On the longest contiguous segment (63.5 hours; \(N=220{,}461\) events), modulo-4-hour concentration is small (\(r=0.0308\)) even though Rayleigh testing rejects exact uniformity (\(Z=209.57\), Monte Carlo \(p=5\times10^{-6}\)). At this sample size, the detectability simulation reports \(\kappa^\star=0.2\) as the first tested grid point with at least 80% power on the coarse grid \(0.0,0.2,\ldots\), so it should not be read as a sharp threshold. The corresponding mean resultant length at \(\kappa=0.2\) is \(\rho\approx0.0995\), still well above observed \(r=0.0308\). We therefore interpret the result as statistical non-uniformity with extremely weak concentration, not a practically strong global four-hour synchronization signal. PSD/AR(1) and bin-width diagnostics similarly show no dominant four-hour line.
To contextualize Moltbook against a human-platform baseline, we compute the same estimators on a contemporaneous run-scoped Reddit corpus. Under shared estimators, Reddit exhibits substantially deeper threads and longer reply persistence than Moltbook. Matched-overlap support is sparse (813 pairs; 2.34% of Moltbook threads), and matched-subset survival on Moltbook has only 22 events, so matched cross-platform designs are underpowered in this snapshot.
The headline pattern is stable: low horizon-standardized incidence (\(p_{5\mathrm{m}}=9.42\%\), \(p_{1\mathrm{h}}=9.82\%\)) with very fast conditional timing, plus shallow, root-concentrated thread geometry and limited reciprocity/re-entry. Coverage-gap sensitivities preserve this post-gap decomposition readout, and one-parent-per-thread sensitivity lowers secondary ever-reply incidence levels without changing the qualitative speed-vs-incidence interpretation. H1a is supported; H2--H4 are partially supported and interpreted descriptively under the stated dependence and identification limits. Topic and claim heterogeneity remain substantial, while periodicity and Reddit comparisons are retained as secondary contextual checks rather than primary identification pillars.
We interpret the empirical patterns in (ref) through the model framework in (ref), focusing on collective behavior, platform design, and identification scope. The evidence combines shallow geometry, incidence-versus-conditional-timing decomposition, and model-to-data checks; cross-platform baseline analyses provide secondary context.
The primary persistence readout is two-part: low horizon-standardized incidence (\(p_{5\mathrm{m}}=9.42\%\), \(p_{1\mathrm{h}}=9.82\%\)) and very fast conditional reply speed (\(t_{50}=4.55\) seconds, \(t_{90}=50.05\) seconds, \(t_{95}=132.23\) seconds). Secondary ever-reply incidence is 9.60% in-window. Together, these values imply that most parents receive no observed direct reply even at a one-hour horizon.
This pattern is compatible with finite context retention, rapid task switching, and weak return-to-thread memory support, but it is not uniquely diagnostic. Similar incidence/latency signatures could also arise from ranking/visibility effects, moderation throttling, or batched/scheduled execution. The kernel half-life diagnostic remains useful as a secondary timescale diagnostic, but the incidence/conditional-speed split is the operationally informative summary for coordination limits.
Shallow, root-heavy trees are consistent with a low effective depth-tail slope (\(\hat{s}_{\mathrm{depth}}=0.154\)) and rapidly decaying depth tails. Under a heuristic branching interpretation in (ref), this pattern is compatible with low effective non-root reproduction. Low reciprocity and modest re-entry in the overall sample further support a broadcast-dominant interaction pattern, while cross-platform re-entry direction remains conditioning-sensitive.
The in-sample model-to-observable coherence check is consistent with this interpretation: predicted and observed incidence align closely overall and by key strata, but the model underpredicts non-root branching while overpredicting depth tails. This indicates that the fitted timing/incidence dynamics are directionally consistent for incidence but miss strong depth dependence in cascade geometry. As shown in (ref), branching is root-heavy and then decays sharply with depth, so a coarse homogeneous non-root approximation can misallocate mass across depths and distort tail probabilities.
These dynamics matter for multi-step coordination tasks. If engagement decays on seconds-to-few-minutes conditional timescales and repeated participation is limited, projects requiring extended deliberation or multi-day follow-through are difficult to sustain without explicit coordination scaffolds. Updated heterogeneity analyses suggest meaningful differences by account status in horizon-standardized incidence, but mechanism-level attribution requires richer exposure controls.
The incidence/timing decomposition yields a concrete budgeted control problem. For any operational horizon \(h\), (ref) defines \(q_h=\pi_h\phi_h\), where \(\pi_h\) is participation incidence and \(\phi_h\) is conditional speed. For depth-throughput targets \(\Pr(D_j\ge K)\approx q_h^{K-1}\), local gains are proportional to \(\phi_h\Delta\pi_h+\pi_h\Delta\phi_h\). The one-step policy rule is therefore: invest the next budget unit in incidence levers when \(\phi_h\Delta\pi_h/c_\pi > \pi_h\Delta\phi_h/c_\phi\), and in timing levers otherwise.
Using observed Moltbook margins at \(h=5\) minutes, \(q_{5\mathrm{m}}=0.0942\) and \(\phi_{5\mathrm{m}}=\mathbb{P}(T\le5\mathrm{m}\mid\delta=1)=0.9806\), which implies \(\pi_{5\mathrm{m}}=q_{5\mathrm{m}}/\phi_{5\mathrm{m}}\approx0.0961\). Under bounded improvements \(\Delta\pi_{5\mathrm{m}}\le1-\pi_{5\mathrm{m}}\) and \(\Delta\phi_{5\mathrm{m}}\le1-\phi_{5\mathrm{m}}\), the maximal lift in \(q_{5\mathrm{m}}\) from incidence is \(\phi_{5\mathrm{m}}(1-\pi_{5\mathrm{m}})=0.8864\), versus \(\pi_{5\mathrm{m}}(1-\phi_{5\mathrm{m}})=0.00186\) from timing (about \(476\times\) smaller). For equal absolute one-percentage-point improvements, the same dominance appears: \(\Delta q_{5\mathrm{m}}=0.9806\) pp from incidence versus 0.0961 pp from timing.
Operationally, this first-week regime is incidence-constrained at minute-to-hour horizons: resurfacing and attention-allocation policies dominate memory-speed optimizations for moving depth and re-entry outcomes. This is a decision-support implication under observed margins, not a causal policy-effect estimate.
Reply incidence and conditional reply speed are portable metrics for comparing collective persistence across agent communities and model generations; the kernel half-life diagnostic is secondary for timescale interpretation. This separation also matters methodologically: unconditional delay summaries can conflate non-response with slow response under censoring, while the two-part margins retain that distinction. The current cross-platform results provide descriptive baseline context under shared estimators and are not a primary identification strategy, especially given limited matched-overlap support (2.34% of Moltbook threads; 22 Moltbook events in matched survival).
Periodicity remains secondary: Rayleigh testing rejects exact modulo-4-hour uniformity at large \(N\), but concentration is extremely small and PSD diagnostics show no dominant 4-hour line, so we do not treat this as a practically meaningful global synchronization signal.
Sharper mechanism attribution still requires richer exposure controls and more granular semantic alignment. Because Moltbook is rapidly evolving, longitudinal tracking is necessary to determine whether the persistence gap narrows as agents, moderation, and interface design mature.
We discuss the principal limitations of this study and the main ethical considerations in analyzing AI-agent social-network activity.
This analysis is based on a first-week snapshot of Moltbook (January 28--February 4, 2026) rather than a longitudinal panel. The observation window also contains a 41.7-hour coverage gap, which limits periodicity resolution and can leave reply opportunities unobserved around the gap interval. Estimates of reply incidence, reply timing, and thread duration should therefore be interpreted as conditional on observed coverage in this early period. We therefore report contiguous-window, gap-overlap-exclusion, and horizon-standardized sensitivity checks; these preserve the post-gap headline pattern but cannot recover unobserved replies that may have occurred during the gap itself.
Cross-platform evidence remains observational and descriptive. Residual confounding from exposure, ranking, moderation, and finer semantic differences limits direct platform-to-platform comparability, and Reddit curation introduces known caveats (including records dropped for missing submission identifiers and a small number of collection request errors). Accordingly, cross-platform contrasts are used as secondary contextual evidence rather than as the study's core causal pillar.
Behavioral attribution and model specification are necessarily simplified. We cannot fully separate autonomous agent behavior from human-guided operation, and the baseline exponential-kernel formulation is an intentionally coarse representation of timing dynamics. Richer hierarchical, re-entry, and visibility-weighted formulations are appropriate for future estimation under longer windows and richer exposure data.
The study uses publicly available Moltbook data and archive-based Reddit data without attempting to identify human operators behind accounts. Analysis is focused on aggregate interaction patterns, and Reddit usernames are anonymized in curated outputs.
Findings about persistence dynamics could be misused to engineer artificial engagement or conceal weak coordination. To mitigate this risk, the manuscript emphasizes descriptive and mechanistic interpretation over optimization guidance and reports uncertainty and identification limits explicitly.
The work has dual-use implications. Better understanding of multi-agent persistence can support beneficial system design (for example, improved memory and coordination scaffolds) while also informing more capable autonomous interaction systems. Given that the underlying behaviors are publicly observable, we treat transparent, well-qualified analysis as the most responsible scientific approach.
This paper measured conversational persistence on Moltbook during its first week of public operation using a two-part definition: direct-reply incidence and conditional reply speed. In this snapshot, the core pattern is low-incidence/very-fast-conditional response: horizon-standardized incidence is \(p_{5\mathrm{m}}=9.42\%\) and \(p_{1\mathrm{h}}=9.82\%\), while conditional reply times are concentrated in seconds (\(t_{50}=4.55\) seconds, \(t_{90}=50.05\) seconds, \(t_{95}=132.23\) seconds). The in-window ever-reply share (9.60%) is a secondary descriptive metric. Most comments receive no direct reply, reciprocal interaction is uncommon, and thread geometry is shallow and root-heavy.
Model-to-observable validation shows tight calibration for reply incidence overall and across key strata, while the same model underpredicts non-root branching and overpredicts deep-tail depth probabilities, consistent with unmodeled depth dependence in branching-by-depth profiles. A one-parent-per-thread robustness check lowers pooled incidence but leaves conditional median speed nearly unchanged, indicating that the central limitation is whether replies occur, not how fast they arrive once they do. The kernel half-life diagnostic is informative as a secondary exponential-equivalent timescale readout but is not the primary persistence metric.
For context, a contemporaneous Reddit corpus analyzed with the same estimators shows substantially deeper threads, higher direct-reply incidence, and hour-scale persistence diagnostics. This baseline contrast remains observational, non-causal, and secondary; matched-overlap support is limited (2.34% of Moltbook threads; 22 Moltbook events in matched survival). The main next step is longitudinal measurement with richer exposure controls (visibility, ranking, notifications) and richer agent-level models, enabling sharper tests of lever-based intervention hypotheses such as memory aids, thread summarization, and explicit re-entry prompts, including trade-offs across incidence, conditional speed, and thread depth. In this first-week snapshot, the evidence is consistent with the hypothesis that early agent social platforms are more effective at initiating interactions than sustaining multi-turn conversations without additional coordination scaffolds. These design implications should be interpreted as model-consistent decision-support hypotheses, not as experimentally validated causal intervention effects.
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This supplementary material provides additional mathematical details and proofs, robustness and diagnostic analyses, cross-platform matching mechanics, and reproducibility information that complement the main manuscript.
Table (ref) provides a compact map from each hypothesis to its measurement targets, the main-manuscript section(s) where each readout is reported, and the headline empirical finding. It is included here to make the empirical results and supplementary diagnostics easier to navigate.