We prove the correctness of the AKS algorithm [1] within the bounded arithmetic theory $T^{\text {count}}_2$ or, equivalently, the first-order consequences of the theory $\text {VTC}^0$ expanded by the smash function, which we denote by $\text {VTC}^0_2$. Our approach initially demonstrates the correctness within the theory $S^1_2 + \mathrm {iWPHP}$ augmented by two algebraic axioms and then shows that they are provable in $\text {VTC}^0_2$. The two axioms are: a generalized version of Fermat’s Little Theorem and an axiom adding a new function symbol which injectively maps roots of polynomials over a definable finite field to numbers bounded by the degree of the given polynomial. To obtain our main result, we also give new formalizations of parts of number theory and algebra:

• • In $\mathrm {PV}_1$: We formalize Legendre’s Formula on the prime factorization of $n!$, key properties of the Combinatorial Number System and the existence of cyclotomic polynomials over the finite fields $\mathbb {Z}/p$.

• • In $S^1_2$: We prove the inequality $\text {lcm}(1,\dots , 2n) \geq 2^n$.

• • In $\text {VTC}^0$: We verify the correctness of the Kung–Sieveking algorithm for polynomial division.

In 2014, the Islamic State of Iraq and Syria targeted the Yazidi ethno-religious minority in Sinjar, northern Iraq, abducting Yazidi boys aged 8 to 14 who endured violence, family separation and significant trauma exposure. Upon return, these children needed mental health care. This study investigates the availability of mental health services for male Yazidi former CAAFAGs (children associated with armed forces and armed groups) and discusses their rights under international legal frameworks.

The study used a convergent mixed-methods design involving male Yazidi former CAAFAGs and mental health providers in the Sinjar district and the Duhok governorate. Quantitative data were collected through a descriptive survey of thirty CAAFAGs and ten providers. Qualitative insights from semi-structured interviews with ten CAAFAGs and ten providers expanded on these findings, and the results were integrated into a joint display for interpretation.

Among the thirty CAAFAGs, 70% had not received any mental health care since their captivity. After captivity, 33% wanted (personal desire) mental health care; of those who wanted care, 80% received services through non-governmental organizations (NGOs). In contrast to this “personal desire” for care, 96.7% of male Yazidi former CAAFAGs acknowledged that they are in need of mental health care, yet only one is currently seeking it. Qualitative data revealed a gap in mental health and psychosocial support (MHPSS) services specifically for male CAAFAGs, as NGOs focused more on female survivors. It also identified financial, personnel and logistical challenges for NGOs, as well as discrepancies between CAAFAGs and providers regarding perceived willingness to receive mental health care.

CAAFAGs and providers recognize an urgent need for tailored, trauma-informed MHPSS and reintegration services for male Yazidi former CAAFAGs. While NGOs play an essential role in delivering mental health care, their focus is primarily on female survivors, leaving a gap in support for male CAAFAGs. International legal frameworks protecting child victims’ rights remain inadequately respected in practice. Addressing these gaps is crucial for CAAFAGs’ successful reintegration and rehabilitation.

Results of two archaeological surveys in southeastern Bolivia provide substantial information on migration patterns of precontact Guaraní groups into an understudied region of South America. Surveys were conducted within the rights-of-way of two pipelines across the Department of Santa Cruz, Bolivia. The pipeline corridors traversed 917 km of undeveloped areas of southeastern Bolivia, which are among the least understood in South American archaeology. In total, 71 archaeological sites were identified and tested resulting in more than 132,000 artifacts. Excavation results, radiocarbon dates, specialist analyses, and paleoenvironmental reconstruction fill a gap in our knowledge base for this crucial region of South America located at the interface between the Andes and Amazonia. Project results indicate early intrusions of small groups to the region by about 900 BC and increasingly more people by about AD 700. The Chiquitano Dry Forest was relatively densely occupied from about AD 1100 through AD 1600 compared to elsewhere in southeastern Bolivia. Our findings support and amplify other recent investigations of lowland South American precontact dispersal patterns.

We address the challenge of product configuration in the context of increasing customer demand for diverse and complex products. We propose a solution through a curated selection of product model benchmarks formulated in the Coom language, divided into three fragments of increasing complexity. Each fragment is accompanied by a corresponding example on bike configuration, and additional scalable product models are included in the CoomSuite, along with relevant resources. We outline an ASP-based workflow for solving Coom-based configuration problems, highlighting its adaptability to different paradigms and alternative ASP solutions. The CoomSuite aims to provide a comprehensive, accessible, and representative set of examples that can serve as a common ground for stakeholders in the field of product configuration.