Abstract: Triple-negative breast cancer (TNBC) remains a major therapeutic challenge, largely due to the persistence of drug-tolerant breast cancer stem cell (BCSC) populations that can with-stand cytotoxic stress and drive disease relapse. Although interleukin-1 recep-tor-associated kinase 2 (IRAK2) has been implicated in inflammatory signaling and en-do-plasmic reticulum stress responses, its functional role in the development of acquired chemotherapy resistance in BCSCs has not been fully elucidated. In this study, we inves-tigated whether IRAK2 contributes to the maintenance of a drug-tolerant phenotype in BCSC1, MDA-MB-231, and MDA-MB-468 cells. Exposure to chemotherapeutic agents in-duced IRAK2 mRNA expression in most drug-cell line combinations, while BCSC1 cells exhibited a functionally resistant phenotype following 5-fluorouracil (5-FU) treatment. Stable or doxycycline-inducible IRAK2 knockdown significantly impaired cell prolifera-tion, prevented post-treatment recovery after 5-FU exposure, reduced sphere-forming ca-pacity, and attenuated the 5-FU-induced expression of the drug transporters ABCC3 and ABCC4. Collectively, these findings identify IRAK2 as a key mediator of stress-adaptive signaling that promotes chemotherapy tolerance and stemness-associated survival mech-anisms in TNBC-derived BCSCs. IRAK2 therefore represents both a potential biomarker of emerging chemoresistance and a promising therapeutic target for combination strategies aimed at eradicating drug-tolerant cancer stem cell populations.

Abstract: Background: Appendiceal epithelial lesions are rare and heterogeneous. Evidence regarding vascular endothelial growth factor A (VEGF-A) expression in localized appendiceal lesions is limited. We compared VEGF-A immunoreactivity across diagnostic subtypes and explored associations with histological features. Methods: This retrospective exploratory study included 73 histologically confirmed appendiceal lesions. Formalin-fixed, paraffin-embedded tissue was assessed for predominant VEGF-A staining intensity and percentage of positive neoplastic epithelial cells. Their product was reported as a modified immunoreactivity score (0-300). Permutation-based nonparametric tests, multiplicity correction, and diagnosis-adjusted sensitivity analyses were used. Results: VEGF-A staining was present in 71/73 cases. Median immunoreactivity scores were 205 for adenocarcinoma, 170 for hyperplastic polyp, 180 for low-grade appendiceal mucinous neoplasm, and 100 for sessile serrated lesion; the overall difference was not significant (p = 0.075). No histological-feature association remained significant after false-discovery-rate correction. Surface nuclear stratification was not significant in the global analysis (p = 0.051; q = 0.169), pairwise analysis, within-subtype analyses, or diagnosis-adjusted sensitivity analysis (p = 0.278). VEGF-A measures did not differ between acute and incidental presentations; patients with acute presentations were younger (p = 0.007). Conclusions: VEGF-A immunoreactivity was common, but no robust subtype-specific or histology-specific pattern was identified. These exploratory findings do not establish clinical utility and require confirmation in larger controlled cohorts.

Abstract: Noble metal-supported catalysts exhibit superior catalytic activity, versatility, and accessibility, making them highly promising for the catalytic oxidation of HCHO under ambient conditions. In the process of defining catalytic performance, metal-support interactions (MSIs), which are characterized by the alteration of active site availability, electronic structure tuning, and increased dispersion of metal nanoparticles, play a vital role. These interactions are among the many influencing aspects that play a role. This review comprehensively analyzes recent advancements in the mechanisms underlying MSIs, particularly focusing on strong metal-support interactions (SMSI) and electronic metal-support interactions (EMSI). It is to establish a comprehensive theoretical framework for atomic-level catalyst design optimization by clarifying how SMSI and EMSI accurately control charge transfer and catalytic active site creation. Furthermore, the review highlights current challenges and future perspectives in utilizing MSIs for efficient formaldehyde (HCHO) oxidation, facilitating the development of advanced catalysts toward practical industrial applications.

Abstract: Background: Coronary artery calcification (CAC) is a critical marker of subclinical atherosclerosis, yet its primary diagnostic tool, coronary computed tomography (CT), is limited by cost and radiation. We aimed to develop and validate a robust machine learning framework to identify significant CAC (Agatston score ≥100) using features extracted from routine 12-lead electrocardiograms (ECGs), including legacy archives stored as PDFs. Methods: This retrospective study utilized 382 consecutive patient records. A novel signal-processing pipeline was developed to convert PDF-based ECGs into standardized 500-Hz digital waveforms (WFDB format). From these signals, 360 morphological and temporal features were extracted using the NeuroKit2 library. To ensure clinical reliability and prevent optimistic bias, a Balanced Random Forest (BRF) classifier was integrated into a repeated “inner-outer” nested cross-validation framework combined with Minimum Redundancy Maximum Relevance (mRMR) feature selection. Results: The mRMR-BRF model demonstrated high diagnostic accuracy with a grand mean AUC of 0.8211 (95% CI: 0.8018–0.8404), outperforming standard algorithms. Explainability analysis via SHAP identified age, ST-segment level in lead V4, T/QRS ratio in lead III, and QRS duration dispersion as the most significant predictors. These features suggest that latent electrical signatures of subclinical myocardial remodeling and impaired perfusion are detectable via AI-enhanced ECG analysis. Conclusion: Our framework establishes digitized 12-lead ECGs as a scalable and non-invasive digital biomarker for significant CAC. By enabling the quantitative analysis of legacy PDF archives and providing high predictive stability through nested validation, this approach offers a cost-effective pre-screening tool to prioritize high-risk patients for definitive imaging and early preventive intervention.

Abstract: In addition to the electrogenic microorganisms, e.g. bacteria, that can be found in communities that are wired together in circuits carrying electrons in and out of biological cells, strong evidence exists that there are wireless connections between micro-organisms that pass information to one another at a distance in virtue of electromagnetic signals. One needs electromagnetic antennae to send or receive signals as they pass information back and forth between living microorganisms. We here discuss the properties of DNA and RNA long polymer molecules regarding their utility as antennae. As well as emitting or absorbing radiation photons these antennae also emit and absorb phonons, i.e. acoustic signals. The coupling between sound waves and electromagnetic waves is very appreciable due to and described by biological piezoelectricity. Biological phases of condensed matter also exhibit chiral symmetry breaking, i.e. “handedness” symmetry breaking, between right and left-handed electronic states. Describing two spin components (say up and down) times two chirality components (say left and right) ultimately requires four component electron wave functions as discovered by Dirac even if the electrons are moving at velocities much less than light speed. Coupled with the quasi-one dimensional nature of long polymer molecules this yields bound Bose condensed bound particle-hole pairs constituting a Tomonaga-Luttinger liquid similar in some ways to the Bardeen-Cooper-Schriefer Bose condensed bound electron pairs found in superconductors. One similarity is that transport weak links in the Bose condensate fluid flow yield Josephson effects described by a quantum pendulum, e.g. a sine Gordon field theory. The coherent phase in the Tomonaga-Luttinger liquid is the difference between the right- and left-handed electronic phases as first demonstrated by Coleman via the conversion of the massive Thirring model into a Josephson type pendulum model. The complete theory of wireless communication between biological organisms is only beginning to be developed. The basic DNA and RNA microbe antennae must be wired in nature as a coherent phased antenna array for appreciable communication bit rates radiated through large distances. Finally, acoustic and/or radio frequency electromagnetic radiation carrying sufficient communication information should be of use medically as a possible alternative to chemical medicines and/or vaccines in the treatment of illness; for a most recent example in the COVID-19 virus with its RNA internal antenna.

Abstract: Decades of thermoelectric-materials research are recorded in tens of thousands of papers, but the quantitative results — Seebeck coefficients, conductivities, figures of merit, doping strategies, synthesis conditions — remain locked in unstructured prose, inaccessible to systematic analysis or machine learning. We present a literature knowledge graph that extracts and structures this information at scale. Using large-language-model information extraction over the parsed full text of 10,158 thermoelectric papers, the graph captures 166,178 records across 13 entity types: 22,317 material mentions, 24,121 property measurements, 7,443 dopant/modification records, 32,306 scientific claims, 14,304 experimental conditions, and derived research-coverage, novelty, and failure signals, each attributed to its source paper by DOI and aligned to an OWL ontology. An independent audit on a stratified 300-paper sample gives an extraction precision of 0.97 and a recall of ~0.85 on content-bearing papers. The graph is released in five interoperable formats (CSV, JSON, JSON-LD, RDF/Turtle with 1.11 million triples, and GraphML with 166,178 nodes and 156,020 edges), enabling literature-scale trend analysis, research-gap discovery, and the fusion of literature evidence with computational materials features.

Abstract: A completed recognition should remain distinguishable from its reversal. We formulate this demand using a ledger of binary state changes. For a closed run, the primitive debit and credit increments balance; reversal therefore leaves the same state-account record. A phase account can retain the missing sign. When its domain is the complement of a recognized trajectory, nonzero winding is equivalent to the homological requirement that selects three dimensions in the companion paper. The account-domain restriction is an explicit premise; an ordered posting history can retain reversal information outside this restriction. We also compare cubical processes whose recognized and registering trajectories are spheres of the same dimension k. Under the stated ambient homology hypotheses their substrate dimension is 2k+1. With additive tally costs and a sequential ledger, a loop costs exactly eight units to traverse, or nine including a unit phase account. An explicit closed schedule attains the surface minimum of ninety primitive units; every higher process costs more than the loop. Least cost therefore selects loops within this admissible class. The higher-dimensional alternatives are constructed.

Abstract: Background/Objectives: Frozen triage narratives may contain prognostic information not captured by urgency categories or vital signs. We evaluated their incremental value for hospital admission and subsequent critical outcomes among adults assigned Emergency Severity Index (ESI) levels 3-5. Methods: This single-center retrospective study used routine electronic records from 1 April 2025 to 30 June 2026. Models were developed using 51,735 visits (4852 admissions) in April-December 2025 and evaluated without refitting in 40,433 visits in January-June 2026. Hospital admission included accepted interhospital inpatient transfers. Separate models predicted index-hospital ICU transfer or death among completed, observable episodes, including 285 development events. ESI-only, structured, text-only and combined logistic models were compared using discrimination, calibration and patient-cluster bootstrap intervals. Grouped cross-validation and fixed model variants assessed overfitting and source-quality sensitivity. Results: Temporal evaluation included 3517 admissions (8.70%). Adding text increased admission AUROC from 0.763 to 0.835 (95% CI 0.828-0.841) and average precision from 0.246 to 0.340. The combined model had a calibration slope of 1.083 and observed-to-expected ratio of 0.982. Among 39,697 secondary-analysis visits, 177 had ICU transfer or death (0.446%); combined AUROC was 0.924 (95% CI 0.908-0.940) and average precision 0.076. Text gains persisted without the seven measured fields or their missingness indicators. Conclusions: Frozen triage text added predictive information in a later calendar period. Admission prediction estimates recorded disposition rather than medical necessity. Low critical-outcome precision, incomplete follow-up exclusions and single-center design preclude clinical deployment without further validation. No specific research funding or registration identifier was reported.

Abstract: Background: Sickle cell disease (SCD) is a condition of persistent inflammation and coagulation that includes both haemolysis, vaso-occlusion and organ damage result from this interplay. However, does not by itself, account for the variation in disease severity among individuals. Objectives: To examine whether trained immunity can be a potential mechanistic framework connecting chronic haemolysis to the long-term vaso-inflammatory activity in SCD, and therapeutic implications as well as knowledge gaps. Methods: Narrative review of recent literature synthesis on trained immunity. Results: Recent findings suggest that labile heme, cell-free Haemoglobin S, oxidative stress, and damage signals can activate the innate immune system, and contribute to the promotion of metabolic, transcriptional, and epigenetic changes. These changes could exacerbate the activation of the endothelium, neutrophil extracellular traps, and platelet-leukocyte interactions, complement activation, immunothrombosis, and further vaso-occlusion. Possible interventions include heme scavenging, manipulation of IL-1β and TLR4/MD-2 signaling, and the use of BTK inhibitors as well as changing metabolic or epigenetic programs. Yet, direct evidence of bona fide trained immunity in human sickle cell disease remains limited. Conclusion: The mechanism of trained immunity could provide a testable mechanistic framework that explains the continued activation of an immune system in SCD. Although the concepts of functional recall responses, sustained metabolic, epigenetic, and progenitor cell reprogramming in trained immunity cannot yet be established as a therapeutic target without direct demonstration.

Abstract: This study explored how game based learning platforms influenced Indonesian EFL learners’ motivation in technology supported English learning. A qualitative case study design was employed to examine students’ experiences, perceptions, and responses to gamified English learning activities. Data were collected from purposively selected undergraduate EFL learners through semi structured interviews, classroom observations, and relevant learning documents. The data were analyzed using reflexive thematic analysis to identify recurring patterns related to students’ motivational experiences. The findings showed that game based learning increased students’ motivation by making English activities more enjoyable, interactive, challenging, and engaging. Students reported stronger willingness to participate when activities provided clear goals, immediate feedback, opportunities for collaboration, and visible evidence of progress. However, the motivational effects varied according to students’ English proficiency, confidence, previous digital experience, and perceptions of competition and rewards. The findings also indicated that lecturer support and task design played an important role in determining whether game based activities produced meaningful engagement. Activities that were closely connected to English learning objectives encouraged stronger participation, whereas excessive competition, repetitive tasks, or an emphasis on game mechanics could reduce motivation. The study concluded that gamification was most effective when game based technology was integrated with purposeful language learning and appropriate pedagogical support. The findings contribute to EFL research by providing a contextual understanding of how Indonesian university students experienced gamified learning and offer practical implications for lecturers seeking to design more motivating and learner centred English instruction.

Abstract: This explanatory sequential mixed-methods study examined pre-service science teachers’ self-efficacy for teaching science in diverse Indian classrooms. Quantitative data from 150 pre-service teachers using the SESSTD measured three dimensions: culturally responsive science teaching and inclusivity (CRSTI), instructional strategies and engagement (ISE), and teacher preparation and professional development (TPPD). Fifteen participants were purposively selected for a focus group discussion. Results showed moderately high self-efficacy across all subscales, with CRSTI marginally highest. Multiple regression indicated ISE significantly predicted CRSTI, whereas TPPD did not. Qualitative findings identified mastery experience as the most cited source of confidence; inconsistent or absent mentor feedback, linguistic diversity, and tension between teacher-education pedagogy and field practice emerged as challenges. The findings suggest general instructional and culturally responsive confidence are closely linked, while training/mentorship confidence is comparatively distinct. Implications concern mastery-oriented, practice-embedded teacher preparation for diverse science classrooms.

Abstract: Masters sprinters can retain remarkable straight-line speed into older age, creating the appearance of youthful movement despite continued biological aging. This hypothesis paper distinguishes outstanding task performance from restoration of the integrated neuromuscular system. The Dual-Barrier Model combines motor specificity with biological neuromuscular aging. First, improved straight-line speed does not automatically transfer to increasingly demanding change-of-direction tasks. Second, competitive Masters athletes can retain substantial muscle and sporting expertise while exhibiting age-associated differences in body composition, muscle quality, motor-unit organization, and power production. Human studies of rapid force development provide a further measurement window into function that maximal strength and visual observation may not capture. The model introduces whole-body reactive force-time capacity: the ability to organize, generate, absorb, redirect, and stabilize force across body segments when the required response is incompletely known in advance. It predicts that Masters sprinters will show larger age-associated differences relative to appropriately characterized young athletes as movement demands increase in multidirectional control and reactive uncertainty. Successful task completion need not preclude differences in force-time behavior, coordination, or stabilization. Existing evidence supports the component distinctions, but does not establish the proposed age-by-demand interaction in Masters sprinters. Body composition is one contributor, not a sufficient explanation, and residual impairment cannot automatically be assigned to neural degeneration. No evidence reviewed here demonstrates that training restores the integrated neuromuscular system of an older adult to its young-adult biological state. A preregistered, within-participant comparison of sprinting, planned change of direction, and matched reactive tasks is proposed to test or falsify the central prediction.

Abstract: Background/Objectives: Single-cell RNA sequencing enables reconstruction of developmental trajectories, but identifying regions of major transcriptional state reorganization remains challenging, particularly when no explicit dynamical model is available. We developed GDIS-Bio, a framework that applies the Generalized Dynamical Instability Score (GDIS) to pseudotemporally ordered single-cell state spaces to localize transition-associated instability. Methods: GDIS-Bio was evaluated in pancreatic endocrine differentiation (GSE114412) and externally validated in human induced pluripotent stem cell-derived cardiac differentiation (GSE175634). Biological transition landmarks and primary analytical settings were defined independently of GDIS. Robustness was assessed across alternative PCA dimensions and sliding-window configurations, and localization was benchmarked against total variance, Gaussian differential entropy, pseudotemporal step distance, and lag-1 pseudotemporal autocorrelation using structure-preserving null models and individual-level paired tests. Results: In GSE114412, GDIS peaks localized reproducibly near the NEUROG3-early transition across both endocrine lineages and differentiation replicates, with significant localization under circular-shift null testing. In GSE175634, significant localization was retained for MES→CMES, PROG→CM, and PROG→CF transitions without dataset-specific retuning. GDIS was not universally superior to conventional metrics; variance, entropy, and step distance were competitive or better in several settings, whereas GDIS showed its clearest comparative advantage over lag-1 pseudotemporal autocorrelation in the terminal cardiac transitions. Conclusions: GDIS-Bio provides a transferable, model-independent framework for localizing transition-associated dynamical instability in single-cell trajectories and is best interpreted as a complementary integrative measure rather than a universally superior early-warning statistic.

Abstract: Lean-oriented redesign is widely used to improve hospital flow and productivity, but the capabilities nurses need to implement and sustain change remain poorly defined. This critical narrative review integrates empirical evidence concerning nursing capability, organizational conditions, implementation, sustainment, and performance. Nursing-specific instruments assess perceived Lean implementation or service leanness, but none validates nursing improvement capability as an adaptive individual and collective capacity. The most credible candidate manifestations are practical knowledge and judgement, collective problem-solving, learning, professional agency, and enacted improvement leadership. Staffing, protected time, decision authority, data access, and infrastructure shape whether these capabilities can be expressed but are not equivalent measures of capability. Operational process improvements are reported most often, yet causal attribution is weak. Evidence for reallocated bedside time, net economic value, workforce benefit, patient safety, environmental benefit, and long-term sustainment remains limited or inconsistent. Evaluations should measure capability, context, implementation, sustainment, benefits, and harms separately and prospectively.

Abstract: Family-based treatment (FBT) is widely regarded as the leading evidence-based treatment for adolescents with anorexia nervosa and has demonstrated benefits, particularly in supporting weight restoration. FBT is organised around five central tenets: an agnostic view of illness causation, a non-authoritarian therapeutic stance, parental empowerment, externalisation of the eating disorder and a pragmatic focus on symptom reduction. However, evidence of group-level efficacy does not establish that treatment is appropriate, accessible or psychologically safe for every young person and family. This lived-experience-informed critical analysis brings treatment research into conversation with qualitative evidence, recovery-oriented scholarship and emerging understandings of treatment-related harm. It examines how the five tenets distribute authority, credibility and responsibility and how their enactment may shape psychological safety and recovery. Agnosticism may become incuriosity about the functions and contexts of eating-disorder behaviours; non-authoritarianism may redistribute rather than reduce clinical authority; parental empowerment may displace the young person’s voice; externalisation may support separation from the eating disorder for some while invalidating the testimony of others; and pragmatism may privilege physical restoration without adequately addressing psychological and relational needs. These tensions may be particularly consequential for young people whose presentations include neurodivergence, trauma, chronic illness or other intersecting needs. Rather than rejecting FBT, we propose five corresponding shifts: from agnosticism to explorative curiosity, from non-authoritarianism to meaningful patient choice, from parental empowerment to shared empowerment, from externalisation to individualised differentiation, and from pragmatism to person-centred responsiveness. These shifts may preserve the urgency of nutritional care while strengthening collaboration, dignity and psychological safety.

Abstract: Mapping host activity to the MITRE ATT&CK framework usually needs manual work or a cloud-hosted large language model, which raises privacy and cost concerns for small organisations that cannot send their logs off-host. We ask whether a small language model (SLM), running locally and without fine-tuning, can classify Linux auditd records at the technique level of MITRE ATT&CK. We built a deterministic cascade that captures, filters, scores, and aggregates auditd events into session narratives, discarding most records before any model call. Only these narratives reach a quantised SLM (Qwen 2.5 7B, served by Ollama). Candidate techniques are calibrated only on public sources (MITRE ATT&CK, GTFOBins, Sigma), never on the evaluation data. We evaluated the full pipeline on the CAM-LDS dataset, across 29 attack variants, with deterministic and reproducible model outputs under a fixed seed and a temperature of zero. The system reaches a macro-averaged incident-level F1 of 54.2%. Per-variant scores range from 19% to 78%, driven by how much of the attack auditd can observe: scripted attacks leave few visible events, while interactive ones expose far more. An initial pilot with Phi-3 Mini 3.8B produced invalid, hallucinated technique IDs and missed obvious techniques, motivating the switch to Qwen 2.5 7B, which gives the best accuracy–latency trade-off. Our central finding is where the loss happens: the deterministic cascade preserves almost all of the observable on-host activity, so the binding constraints are downstream. The model under-confirms techniques it is given 71% of missed techniques were already available to it and over-broad signatures, not hallucinations, cause most false positives. A local, fine-tuning-free SLM gives a usable technique-level baseline; the ceiling is the model and the catalogue, not the filtering stage.

Abstract: Psychological control — the extent to which an organization shapes employees’ inner thoughts, feelings, and self-expression rather than merely their outward behavior — is a pervasive but understudied feature of Korean workplace culture. This study examined how psychological control is experienced by Korean employees, how it is perceived to function (as a management tool) and dysfunction (as a source of psychological strain), and how these perceptions relate to the broader Korean organizational-cultural context. Using a descriptive-correlational design, a structured online questionnaire was completed by 403 Korean employees across a range of occupations and tenure levels. Respondents reported experiencing a high degree of psychological control at work (M = 4.00, “Agree”), most strongly reflected in having sacrificed personal values to meet organizational expectations and having hidden opinions for fear of negative consequences. Respondents also strongly endorsed the dysfunctional consequences of psychological control (M = 4.20, “Strongly Agree”) — increased competition and tension, suppressed emotion, reduced trust, and higher turnover intention — while agreeing only moderately that control brings functional benefits such as focus, responsibility, and efficiency (M = 3.54, “Agree”). Experienced psychological control was significantly and positively correlated with perceived dysfunctional outcomes (ρ = .569, p < .001) and with the perceived cultural normalization of organizational conformity (ρ = .307, p < .001), but only weakly correlated with perceived functional benefits (ρ = .240, p < .001), and functional and dysfunctional perceptions were themselves statistically unrelated (ρ = .080, p = .111). These findings suggest that, in the Korean workplace context studied, psychological control is experienced primarily as a source of strain rather than a motivational tool, and that beliefs about its benefits operate largely independently of beliefs about its costs.

Abstract: Robust Optimization Over Time (ROOT) addresses dynamic optimization problems where the goal is not to identify the best solution at each instant, but to find solutions that remain effective across multiple future environments. Despite recent algorithmic advances, the theoretical foundations of ROOT remain limited, especially regarding its formulation in terms of survival time. Additionally, discrete problem settings have received little attention. This paper addresses these limitations from a theoretical perspective by analyzing survival time in discrete ROOT under stochastic k-bit-flip environmental dynamics. Using drift analysis and martingale techniques, we derive tight analytical bounds and identify phase transitions for survival time on dynamic OneMax, capturing gradual fitness degradation. For dynamic LeadingOnes, which models catastrophic structural failure, we prove that survival time follows an exact geometric distribution. Monte Carlo simulations closely match all theoretical predictions. The results connect ROOT with classical runtime analysis and formalize the mechanisms governing solution durability, providing a mathematical foundation for predictive robustness models, survival-aware heuristics, and deployment policies tailored to combinatorial environments.

Abstract: We review what is known about finite-time singularity formation ("blow-up") in the unsteady Prandtl boundary-layer equations, from the numerical discovery of the van Dommelen--Shen singularity in 1980 to the rigorous description of its self-similar structure completed in 2018--2022. The survey is organized around five questions: (i) what the singularity is physically (unsteady separation and eruption of the boundary layer); (ii) where it is known to occur (the impulsively started cylinder, vortex-induced separation, colliding wall streams); (iii) what has been proved (the E--Engquist theorem, the Kukavica--Vicol--Wang theorem, the Collot--Ghoul--Ibrahim--Masmoudi description of the stable blow-up pattern, the classification of inviscid singularities); (iv) how blow-up relates to the ill-posedness of the Prandtl equations without monotonicity and to the inviscid limit of the Navier--Stokes equations; and (v) how the reduced one-dimensional system on the symmetry axis, which carries the rigorous theory, sits inside the recent similarity transformation of Sun [Phys.\ Fluids \textbf{36}, 083616 (2024)] as its \(m=1\) member. We also record the explicit affine blow-up solution \(u=-x/(t_*-t)\), \(v=y/(t_*-t)\), which is exact for both Prandtl and Navier--Stokes, and explain why Prandtl blow-up bears no relation to the finite-energy Navier--Stokes blow-up announced in September 2026. A list of open problems closes the survey.

Abstract: The Rubin survey is expected to extend the halo white-dwarf luminosity function into a regime where current data neither establish nor exclude remnants with cooling ages beyond the standard cosmic age. Public Montreal thick-hydrogen DA tracks give dwell times in the window M_bol = 17–20 from 4.84 Gyr at 0.5 M_☉ to 0.70 Gyr at 1.2 M_☉. Under an illustrative uniform cooling-age density on [T₀, 2T₀], with T₀ = 13–14 Gyr, the Montreal-only occupancy is 0.10–0.19 at 0.6 M_☉, at most 0.21 on the grid, and zero at 0.95 M_☉ and above. BaSTI-calibrated bright-edge shifts widen the 0.6 M_☉ range to 0.10–0.27; no analyzed channel exceeds 0.3720. A robust-within-set candidate whose conservative cooling-age lower bound exceeds the standard ceiling under the youngest age assignment in the declared model set is a chronology anomaly under that set, regardless of abundance. A null remains parametric: the population inputs are underived, and the frozen two-stage Rubin operator has not been executed on Rubin observations. Supplementary Material 1 regenerates the calculations and figure.