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arxiv: 2606.24095 · v1 · pith:HIWVPKSKnew · submitted 2026-06-23 · ⚛️ physics.soc-ph

Regimes of Influence in Trust-Uncertainty Gated Networks

Razieh Masoumi , Ahana Biswas , Yu-Ru Lin This is my paper

Pith reviewed 2026-06-25 22:32 UTC · model grok-4.3

classification ⚛️ physics.soc-ph
keywords trust and distrustopinion dynamicssocial networksinfluence regimeshub-periphery reversalambivalencebelief updatesthreshold gating
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The pith

Trust and uncertainty thresholds create regimes where either high-degree hubs or peripheral agents dominate collective beliefs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models simultaneous trust and distrust in directed relationships to compute net trust and uncertainty, which together decide whether an agent updates its beliefs from that source. Varying the two thresholds produces four regimes that differ in how readily they admit influence. Across these regimes the authors identify a consistent reversal: selective thresholds let high-degree agents control long-run states while concordant thresholds remove many high-degree channels through uncertainty filtering, allowing lower-degree agents greater leverage. The reversal is observed in both synthetic and empirical networks. The central point is that belief dynamics are shaped by how ambivalence gates influence, not by network structure alone.

Core claim

Gated Network Credence encodes separate trust and distrust values on each directed edge. These values yield net trust (willingness to rely on the source) and uncertainty (conflict within the relationship). Agents update beliefs only when net trust exceeds one threshold and uncertainty falls below another, producing an effective influence graph. Sweeping the thresholds reveals four regimes—Pluralistic, Selective, Concordant, and Fortified—and a hub-periphery reversal: high-degree agents dominate in the Selective regime while stringent uncertainty filtering in the Concordant regime disproportionately removes their active channels, enabling peripheral agents to exert greater leverage over colle

What carries the argument

Gated Network Credence, which computes net trust and uncertainty from separate trust and distrust assessments on each directed edge to gate belief updates and define the effective influence graph.

If this is right

  • The topology of the effective influence graph determines long-run belief states once the thresholds are fixed.
  • The four regimes differ systematically in openness to trust and conflict.
  • The hub-periphery reversal is independent of whether the underlying network is synthetic or empirical.
  • Collective equilibria therefore depend jointly on network structure and on how relational ambivalence gates updates.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Platform designs that adjust uncertainty visibility could shift influence toward or away from high-degree accounts.
  • The same gating logic might be tested in laboratory experiments where participants report both trust and distrust toward information sources.
  • Extending the thresholds to time-varying values could link regime switches to observed changes in polarization or consensus speed.

Load-bearing premise

Belief updates occur only when net trust exceeds a threshold and uncertainty falls below another threshold, after which the resulting graph topology alone drives long-run states.

What would settle it

Measuring trust and distrust separately in an empirical social network, sweeping the two thresholds, and finding no consistent switch from hub-dominated to periphery-dominated influence would falsify the reversal.

Figures

Figures reproduced from arXiv: 2606.24095 by Ahana Biswas, Razieh Masoumi, Yu-Ru Lin.

Figure 1
Figure 1. Figure 1: (a)⃝1 Two-dimensional credence space for a directed relationship with separate trust τ and distrust δ assessments. The coordinate (T, U), indicating net trust and uncertainty, is obtained from (τ, δ) via T = τ − δ and U = τ + δ − 1. The horizontal line U = 0 corresponds to the conventional one-dimensional case in which trust and distrust are treated as perfectly coupled opposites. ⃝2 Phase diagram of long-… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Long-run consensus belief state b ∗ versus prestige bias ps on an Erdős–Rényi network (N = 5000, p = 0.01). Top: Selective regime (F); bottom: Concordant regime (G). Left column fixes ρ = −0.4 and varies promoter prevalence x. Right column fixes x = 0.25 and varies trust–distrust coupling strength ρ. Shaded bands indicate variability across 100 independent realizations. (b) Conditional distribution of … view at source ↗
Figure 3
Figure 3. Figure 3: Spectral characterization of long-run influence after filtering. The normalized left zero [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Bitcoin-OTC reputation network; node color indicates community membership (larger red, smaller blue). (b) Network-averaged long-run belief ⟨b ∗ ⟩ versus prestige bias ps for the Selective regime (F) in the top row and the Concordant regime (G) in the bottom row. Left panels fix trust–distrust coupling ρ = −0.4; lines correspond to different positive promoter fractions x. Right panels fix x = 0.2; line … view at source ↗
Figure 5
Figure 5. Figure 5: (a) Directed follow network of U.S. state legislators on X: node color encodes legislators’ party affiliation (blue for Democrats, red for Republicans). (b-c) Network-averaged long-run be￾lief ⟨b ∗ ⟩ versus prestige bias ps under the Selective (F) and Concordant (G) regimes. Lines are color coded by positive promoter fraction x ∈ {0.05, 0.10, 0.20, 0.30, 0.40}. (d) Binned summaries of the long-run influenc… view at source ↗
read the original abstract

In many social communities, individuals can simultaneously trust and distrust the same source, a feature standard opinion-dynamics models often ignore. We formalize this ambivalence with Gated Network Credence, in which each directed relationship encodes distinct trust and distrust assessments. These jointly determine "net trust" - the willingness to rely on a source - and "uncertainty" - the conflict between trust and distrust within the same relationship. Agents update beliefs only when net trust exceeds a threshold and uncertainty falls below another, yielding an effective influence graph whose topology drives long-run belief states. Sweeping both thresholds uncovers four regimes - Pluralistic, Selective, Concordant, and Fortified - that differ in openness to trust and conflict. We find a consistent hub-periphery reversal: in the Selective regime, high-degree agents dominate influence, whereas in the Concordant regime, stringent uncertainty filtering disproportionately removes active influence channels associated with high-degree agents, enabling peripheral lower-degree agents to exert greater leverage over the collective equilibrium. This reversal holds across synthetic and empirical networks. Our results show that belief dynamics depend not only on network structure but also on how relational ambivalence between trust and distrust gates interpersonal influence.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The paper introduces Gated Network Credence to formalize ambivalence in directed social relationships by encoding separate trust and distrust values. These determine net trust (willingness to rely on a source) and uncertainty (internal conflict within the relationship). Belief updates occur only when net trust exceeds one threshold and uncertainty falls below another, producing an effective influence graph whose topology governs long-run states. Threshold sweeps identify four regimes (Pluralistic, Selective, Concordant, Fortified) differing in openness to trust and conflict. The central result is a hub-periphery reversal: high-degree agents dominate influence in the Selective regime, while stringent uncertainty filtering in the Concordant regime removes high-degree channels and elevates peripheral agents. The reversal is reported to hold on both synthetic and empirical networks.

Significance. If the simulation results are robust, the work is significant because it demonstrates that relational ambivalence can produce regime-dependent reversals in influence structure that are not predicted by network topology alone. Extending the finding to empirical networks strengthens its potential relevance for modeling collective belief dynamics in real social systems.

minor comments (1)
  1. Abstract: the four regimes are named but not briefly characterized by their threshold ranges or openness properties, which would help readers map the parameter space to the reported behaviors.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the thorough summary and positive assessment of the manuscript's significance. The recommendation of minor revision is noted. No specific major comments were provided in the report, so we have no points to address point-by-point at this stage. We will incorporate any minor suggestions during revision.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's core construction defines net trust and uncertainty from trust/distrust pairs, then gates updates on explicit thresholds to produce an effective influence graph; regimes are obtained by sweeping those thresholds and the reported hub-periphery reversal is an observed simulation outcome on both synthetic and empirical networks. No step reduces a claimed prediction or first-principles result to its own inputs by construction, no load-bearing self-citation is invoked, and no parameter is fitted then relabeled as a prediction. The derivation chain is therefore self-contained model exploration rather than tautological.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

Based on abstract only; the model introduces new parameters (thresholds) and a new formal construct whose grounding is not derivable from prior literature.

free parameters (2)
  • net trust threshold
    Value above which agents update beliefs; swept to define regimes.
  • uncertainty threshold
    Value below which uncertainty must fall for update; swept to define regimes.
axioms (1)
  • domain assumption Each directed relationship encodes distinct trust and distrust assessments that jointly determine net trust and uncertainty
    Core modeling choice stated in the abstract.
invented entities (1)
  • Gated Network Credence no independent evidence
    purpose: Formalize simultaneous trust and distrust in a single relationship
    New modeling object introduced by the paper.

pith-pipeline@v0.9.1-grok · 5739 in / 1284 out tokens · 41339 ms · 2026-06-25T22:32:21.390334+00:00 · methodology

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Reference graph

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