It is known that for a uniform morphic sequence $\boldsymbol u = \langle u_n\rangle _{n=0}^\infty $ and an algebraic number $\beta $ such that $|\beta |>1$, the number $[\![ \boldsymbol {u} ]\!] _\beta :=\sum _{n=0}^\infty ({u_n}/{\beta ^n})$ either lies in $\mathbb Q(\beta )$ or is transcendental. In this paper, we show a similar rational–transcendental dichotomy for sequences defined by irreducible Pisot morphisms on binary alphabets. Subject to the Pisot conjecture (an irreducible Pisot morphism has pure discrete spectrum), we generalise the latter result to arbitrary finite alphabets. In certain cases, we are able to show transcendence of $[\![ \boldsymbol {u}]\!] _{\beta }$ outright. In particular, for $k\geq 2$, if $\boldsymbol u$ is the k-Bonacci word, then $[\![ \boldsymbol {u}]\!] _{\beta }$ is transcendental.

Reviving Gould and Lewontin’s critique of adaptationism, Singh’s subjective selection favors truth over useful simplification. Nonetheless, while psychologically plausible, its explanatory power remains limited. Moreover, by treating evolved psychology as fixed, it neglects gene-culture coevolution. The result is a vision of cultural evolution whose expansiveness risks outpacing its scientific utility.

Singh’s framework of subjective selection compellingly links individual cognition to cultural convergence. My commentary emphasizes that subjective selection is hierarchically mediated: not all individuals have equal capacity to shape or transmit their evaluations. Hierarchies of influence, authority, and interdependence determine whose perceptions are amplified into cultural traditions. Accounting for inequality and social power clarifies how the cultural manifold reflects both shared psychology and the unequal distribution of influence within human societies.

This commentary welcomes Singh’s shift from dual inheritance to individual psychology but argues that his model remains incomplete without evolutionary foundations. Cultural variants are not adopted merely because they appear useful – they appeal to evolved motivational systems shaped by natural selection. Integrating adaptive goals, producer–consumer dynamics, and ecological variation transforms subjective selection into a genuinely evolutionary-ecological framework.

Singh compellingly describes some psychological factors that shape selection of cultural variants, but his approach gives insufficient attention to how culture shapes psychology. We argue the subjective selection account needs to pay greater attention to the psychological nuances of goal pursuit, cultural shaping of both perceived and “actual” effectiveness, and importance of social consensus cues.

Citizens do not directly observe democratic backsliding and, as a result, may hesitate to respond to subversion. We develop a model of third-party oversight bodies, such as the media or courts, that detect and assess actions that may be subversive to democracy and inform citizens. Oversight deters subversion, disciplines incumbents, and enables corrective actions by providing credible information about ambiguous incumbent behavior to citizens. However, when the oversight body is contested, citizens may doubt the intent behind its criticisms. When the oversight body is cautious in its criticisms, it elicits negative inferences about its intentions, what we term a fake news effect. The consequences are severe, undermining oversight and enabling backsliding. Democratic accountability depends on reliable sources of information and elected officials’ commitment to upholding norms of conduct.

Building on Beilinson’s work, ‘constructible sheaves are holonomic’, we introduce the notion of holonomicity for étale sheaves, without assuming a priori constructibility. We establish the converse of Beilinson’s result, showing that holonomic sheaves are indeed constructible. This can be seen as an étale analogue of Kashiwara’s theorem on holonomic ${\mathcal D}_X$-modules.

We study the identification of individual-level associations when only aggregate data are available. We characterize the biases of, and relationships among, canonical ecological inference (EI) estimators. We use these results to develop a partial identification approach: monotone EI. The approach exploits information about one or both of the following conditional associations: (1) outcome differences between groups within the same neighborhood and (2) outcome differences within the same group between neighborhoods with different group compositions. We show how assumptions about the sign of these conditional associations, whether individually or in relation to one another, can yield informative sharp bounds. We illustrate our results using county-level data to study differences in COVID-19 vaccination rates among Republicans and Democrats in the United States.

In this work, the life cycle of Gnathostoma turgidum was studied both in natural temporary water bodies and under experimental conditions, with materials collected from the municipality of San Francisco Ixhuatán, Oaxaca. Adult nematodes inhabit the interstitial layers of the stomach in the definitive host (Didelphis virginiana) and release their eggs into the environment via faeces, typically in a dry environment. Under these conditions, the eggs remain quiescent until the onset of the rainy season. Development of early third-stage larvae occurs in cyclopoid copepods. Fry acts as transport and/or intermediate hosts, while frogs (Lithobates forreri) serve as obligatory intermediate hosts for advanced third-stage larvae, ultimately transmitting the parasites to the definitive host. Notably, the precocity phenomenon, typical of larval development in intermediate hosts, occurs in this species within the definitive host. Precocity is likely a response to host behaviour or other ecological factors that restrict transmission to narrow spatial and temporal windows. Adults die at the end of the rainy season. The marked seasonality of this species is mainly attributed to the combination of two factors: (i) the seasonal predation of frogs by the definitive host, and (ii) expulsion of adult stages as immune-mediated ‘self-cure’. This study represents the first documentation of birds acting as paratenic hosts for this nematode.

Singh’s model accounts for cultural convergence but not moral progress. Historical expansions in moral status and the decline of cruel punishment constitute principled departures from parochial utility optimization. Empathy, reflective override, and institutional scaffolding support such breakthroughs. Moral progress therefore functions as a counter-attractor dynamic that enables systematic divergence from utility-based equilibria and requires explanatory resources beyond subjective selection alone.

Language exemplifies Singh’s super-attractor concept while testing the explanatory limits of subjective selection, which is just one of the processes of cultural evolution. Subjective selection explains many linguistic features through speakers’ instrumental goals. However, other types of processes also shape language evolution: some, related to learning and perception, for instance, will not involve intentions or conscious selection. Others involve intentionally creating and transforming linguistic constructions rather than merely selecting them from random mutations.

We praise many aspects of this paper that bring forward previously underemphasized content. We would caution against presenting it as an alternative group-level selection. Indeed, subjective selection may serve to generate a mechanistic understanding of the underlying system upon which group selection operates. Such an approach would address the circularity in the supposition that subjective selection explains cultural patterns.

A massive amount of research examines the representation of public opinion by policymakers, increasingly on actual policy actions. The work often provides evidence of a positive association between expressed public preferences and policy, but only some of the time and only to some degree, and there is even less evidence of responsiveness. This essay delves into the conditions for responsiveness, focusing on public demand for policy and policy supply, building on what research on the subjects reveals. The examination makes clear that policy responsiveness requires a great deal of both the represented and the representatives (and scholars too) and that these conditions are not easily met, though sometimes are. The emergent structure seemingly is much as empirical democratic theory would predict, and helps account for patterns of policy “responsiveness” we observe. The concluding section contemplates future research.