Abstract: Biofilm formation by Staphylococcus hominis in pharmaceutical environments can promote microbial persistence on surfaces and hinder cleaning and disinfection, posing a risk to product quality and safety. This study aimed to standardize an in vitro adaptive methodology to evaluate biofilm for-mation on surfaces of interest to the pharmaceutical industry and analyze the impact of different interpretation criteria. Fifty-four S. hominis strains isolated between 2014 and 2022 from a pharma-ceutical production chain were evaluated. Biofilm formation was analyzed on stainless steel, acrylic, and vinyl coating using the Cell Counting Kit-8 (CCK-8) assay to quantify bacterial cell viability, as well as on polystyrene using the crystal violet method. Qualitative and quantitative interpretations applied different equations to define the negative control cutoff. Vinyl coating showed the highest formation, with 31 (57.41%) strains classified as moderate or strong producers, followed by stainless steel (n=20; 37.01%), acrylic (n=16; 29.63%), and polystyrene (n=2; 3.70%). Quantitative analysis identified surface-dependent hyper-producing strains, reaching maximum values from 49.75 to 61.60%. Applying three standard deviations to the negative control generated reclassifications without statistically significant differences between criteria. The proposed standardized method supports the CCK-8 assay as an adaptive methodology to evaluate biofilm formation by different bacterial strains and surfaces.

Abstract: Objective. Deep brain stimulators, cardiac pacemakers, cochlear implants and transcutaneous nerve stimulators all deliver the same rectangular industrial pulse across target tissues that differ by several orders of magnitude in electrical conductivity. This shape was inherited from 1970s electronics rather than being chosen on physiological grounds. This paper establishes a quantitative electrical benchmark for comparing candidate waveforms on spectral, energetic and hardware axes, which is a prerequisite to any fibre-level analysis. Approach. Eight waveforms, including the industrial rectangle and its clinical asymmetric variant, as well as a smooth curve, are driven through equivalent circuit models of eight target tissues, which cover the clinical conductivity range. Each tissue is represented by a linear passive network fitted to its measured dielectric spectrum, and every waveform-tissue pair is solved in the time domain under voltage- and current-driven modes. Main results. The smooth curve outperforms the industrial rectangle by two to three orders of magnitude on spectral leakage, and requires approximately ninety times less peak current per unit of delivered charge. On peak tissue voltage, tissue impedance dominates the ordering. The asymmetric rectangle sits at the opposite end of the ordering. Spectral rankings are invariant to drive mode, while peak tissue voltage varies in magnitude across tissues at a fixed clinical dose. Significance. Smooth-waveform alternatives to the industrial rectangle could reduce the peak current, thermal and battery demands of neural implants by up to two orders of magnitude, while maintaining the delivered charge. This would open up a design margin that is currently unavailable to clinicians and device makers. For patients receiving a chronic implant, this translates directly into longer intervals between battery-replacement surgeries at equal clinical dose.

Abstract: Spaza shops are central to food access and livelihoods in South African townships, yet little is known about how they combine digital payments with persistent cash use and partial formalisation. This convergent mixed-methods study surveyed a stratified random sample of 150 spaza owners in Tlhabane Township, Rustenburg, and conducted 19 semi-structured interviews with owners and key informants. Immigrant entrepreneurs owned 86.7% of shops. Respondents reported 2.25 payment device or platform mentions per shop, led by Flash (63.3%) and Yoco (54.0%), yet 95.9% preferred cash, 87.8% received most sales in cash, and 76.3% of employers paid wages in cash. Customer preference (96.0%) and convenience (95.3%) dominated reasons for cash use, and 50.7% also cited tax avoidance. Interviews suggested that owners use vending platforms and card terminals for different purposes, and that cash-only supplier deliveries and slow card settlement keep cash floats essential. Registration was selective: 91.3% were registered with municipal or provincial authorities and 78.7% with protection associations, but only 10.7% each with the tax authority and the companies registry. The findings reveal a hybrid cash–digital ‘dual operational reality’ and selective formalisation. Digitalisation policy should combine supplier-side instant payments, simplified tax and transparent engagement with associational governance.

Abstract: Charging infrastructure for battery electric bus (BEB) fleets must be sized against the timing of demand, not only its magnitude: an accurate per-trip energy estimate cannot on its own establish whether a depot’s chargers, contracted grid connection, and dispatch schedule can recover the fleet’s energy deficit without breaching demand-based tariff thresholds. This is especially consequential in resource-constrained settings, where notified-maximum-demand penalties and steep time-of-use differentials turn a mistimed charging load into a direct commercial liability rather than an operational inconvenience. Yet pre-investment planning tools typically treat vehicle energy consumption, dispatch scheduling, and charging infrastructure as separate problems, so a validated demand estimate rarely translates into a validated depot load profile. This paper presents an operational digital twin that converts the per-trip arrival state-of-charge predicted by a companion rolling stock twin into a depot-level charging load profile for the Golden Arrow Bus Services (GABS) electric fleet at the Arrowgate depot in Cape Town, South Africa. The twin reconstructs each bus’s daily duty chain from scheduling data to determine its available charging window, then simulates session initiation, power draw, and duration against these windows using charging behaviour parametrised from depot Open Charge Point Protocol (OCPP) records, including the smart charging constraints already enforced at the depot. Each bus’s state of charge is carried from one depot visit to the next, so an undercharged departure reappears as a lower arrival rather than disappearing from the model. The simulated load profile is validated against 968 OCPP session records from two periods with different depot hardware, achieving energy-per-session agreement of 4.3 to 7.3 % and load-shape correlation of 0.95 to 0.99, and is evaluated against the depot’s contracted notified maximum demand of 3 000 kVA. Scenario analysis quantifies how the charging schedule, charger rate, and site pool limit shift the load profile relative to this threshold and to time-of-use cost exposure, showing that scheduling charging into off-peak windows without a site-wide limit can raise peak demand above uncontrolled charging and beyond the contracted threshold (3 167 against 1 832 kW), that a site pool limit controls peak demand and monthly cost together, and that a 30 kW per-charger cap leaves buses unable to complete up to 15 % of their trips. By coupling a validated, condition-aware demand layer to depot dispatch and charging logic, this work supports capital-efficient charging infrastructure decisions for transit operators in the Global South, where undersized infrastructure risks service disruption and oversized infrastructure diverts capital from wider electrification.

Abstract: Background: Although the corpus callosum is the principal commissure connecting the cerebral hemispheres, it remains unclear whether its macrostructure and microstructure are associated with greater structural symmetry between the hemispheres. Objective: To examine associations of callosal macrostructure and microstructure with left–right symmetry of cortical thickness in healthy developing children. Methods: In 8,131 children aged 9 to 10 from the Adolescent Brain Cognitive Development Study (ABCD), we related 16 callosal measures to per-child hemispheric similarity indices computed across 75 paired cortical regions. Degree-of-symmetry indices are based on the mean absolute left-minus-right difference, reversed so that higher values denote greater symmetry; pattern indices express the correlation between the two hemispheric profiles. Results: All 16 callosal measures were positively associated with cortical thickness symmetry and 15 reached significance, the strongest at r = −.096. The probability that 16 measures would share a direction by chance is 3.1 × 10⁻⁵. Across 128 tests of callosal structure against hemispheric similarity, 51 reached significance against 6.4 expected. The yield was concentrated in magnitude indices rather than pattern indices. Conclusions: A larger and more myelinated corpus callosum accompanies hemispheres whose cortical thickness is more symmetrical. The association concerns the degree of symmetry rather than its regional pattern.

Abstract: FLOSS mailing lists record how newcomers learn, and earlier process-mining studies recognised learning activities in their messages with a-priori keyword models. This paper asks whether the architectures that now dominate natural language processing can perform that recognition step better, and what the language of contributions reveals about how participants mature. In Git and the Linux kernel every contribution is an e-mail that, once accepted, becomes a commit whose trailers (Reviewed-by, Helped-by, Mentored-by) name those who helped. This yields a corpus of 1,432,256 accepted patch e-mails with a learning clock for each author and a graph of helper-learner interactions. On author-disjoint partitions we compare an a-priori phase lexicon, TF-IDF with logistic regression, a Transformer trained from scratch and a Transformer pretrained by masked language modelling on 210,802 e-mails. Newcomers' e-mails (AUROC 0.789 in Git and 0.768 in Linux) and mentored work (0.688) are recognised best by TF-IDF with logistic regression. Pretraining improves the Transformer over training from scratch but leaves it 0.02 to 0.04 AUROC behind, and the a-priori lexicon is weakest (0.644, 0.575, 0.549). A fixed-cohort analysis shows that contributors' language moves towards a collective voice and explicit rationale as they mature, as the a-priori model predicts, whereas help received on the first patches is not associated with retention. A protocol for evaluating large language models on the same test sets is provided.

Abstract: A probe R², a judge-human agreement rate or a cross-validated correlation is often read as evidence of fine-grained structure. When the target is grouped, a predictor that knows only the group can attain such a score. Building on conditional probing (Hewitt et al., 2021), we compare selected published headlines H with training-only group baselines B in the paper's own metric and, for nested comparisons, quantify the conditional predictive gain (CPG): the out-of-sample reduction in squared error from adding the representation to the group predictor, split exactly into group-mean and within-group parts. The aim is to quantify what a published score allows one to infer about the resolution of prediction. In our worked example, the space and time probes of Gurnee & Tegmark, country, state or borough means match or exceed the published space scores, and resolution oracles built from the target exceed the time scores. Beyond country and state means, residual readouts from four 6-7B models remove 20-34% of the remaining coordinate error (an increase in total R² of .008-.013); for one of them the CPG point estimates met thresholds frozen before evaluation, although with whole countries resampled the World interval reaches zero. On the eligible USA subset with counties observed in training, the saved readouts' net gain over state means comes from between-county differences, and a cross-fitted linear recalibration within counties yields gains near zero. Below the century, decade or year the gains are small. The same diagnostic applies to a language-model probe of political ideology, a Twitter prediction of county heart-disease mortality and LLM judges: on retained non-tie votes, a model-identity baseline calibrated from other human votes in the same collection attains much of the judges' agreement with humans, while the judges reduce its disagreement rate by 12-28%. We recommend reporting both numbers, at more than one grouping level, whenever a salient grouping could plausibly attain much of the reported performance.

Abstract: The acid dissociation constant (pK_a) is a fundamental property reflecting the local propensity of a chemical species to release a proton. While graph neural networks excel at predicting global properties, accurate pK_a prediction requires a shift toward atomic mapping. We introduce hydrogen-centered graph machines (HGM), specifically designed for pK_a prediction, by incorporating within the graph the mobile proton involved in the acid-base equilibrium. To support this approach, we refined over 2,300 metrologically validated data points to guarantee fidelity to aqueous species. By calibrating the parametric complexity of HGM across an ensemble of 50 models, we ensured generalization capabilities for robust predictions. As a result, HGM achieved root mean square errors (RMSEs) between 0.6 and 0.7 pK_a units on the SAMPL6, Jensen, and EuroSAMPL1 test sets. However, 2D topological representations remain localized and thus fail to capture charge delocalization—where present—across an entire chemical species, particularly within complex poly-nitrogen systems. To bridge this gap, we introduce a mesomeric weighting strategy that complements the initial structure with relevant resonance forms. This approach significantly enhances predictive accuracy, driving the RMSE down to 0.5 pK_a units for the more complex SAMPL6 and EuroSAMPL1 challenges. Beyond proven accuracy, HGM acts as an automated metrological filter to establish an applicability domain. Thus, HGM identifies structural anomalies—such as complex tautomers and 3D interactions like charge-assisted hydrogen bonds—via statistical warnings that confirm their pK_a prediction falls beyond the actual scope of the HGM framework. As a definitive proof of concept, we deployed HGM to investigate four complex therapeutics (prednisolone, amoxicillin, azithromycin, and pristinamycin I_A). We successfully pinpointed the exact ionization sites and attributed the measured pK_a values to their corresponding equilibria. Benchmarking against the eight available experimental pK_a values yields a mean absolute error of 0.4 pK_a units. Fundamentally, for such complex systems, it is the synergy between the mapping of multiple speciation pathways and the chemist's critical evaluation that resolves the attribution ambiguities inherent to standard commercial databases. We release a standalone Docker container for result verification and out-of-the-box predictions of new compounds.

Abstract: Current editorial guidelines from organizations such as the International Committee of Medical Journal Editors (ICMJE) treat generative artificial intelligence (AI) primarily as an administrative assistant or text manipulator, relegating its contributions to footnotes or acknowledgments. This policy framework misinterprets the operational reality of modern biomedical research, where advanced language models function as active intellectual partners capable of logical stress-testing, data synthesis, and hypothesis generation. Conflating operational cognitive contribution with legal and ethical accountability creates unnecessary opacity in scholarly publishing. To resolve this tension, this paper examines four structural credit frameworks—ranging from the institutional status quo to dual-track independent lists and expanded contributor taxonomies. We propose that medical publishing must evolve beyond obsolete binary definitions, establishing transparent attribution models that separate human regulatory liability from the recognition of machine-assisted scientific co-creation.

Abstract: Background: Artificial intelligence (AI) is increasingly reshaping administrative systems in higher education; however, evidence regarding the differential effects of specific AI technologies on institutional performance remains limited. Understanding whether Optical Character Recognition (OCR), Chatbots and Virtual Assistants (CVA), and Robotic Process Automation (RPA) contribute differently to administrative outcomes is essential for evidence-informed digital transformation. Objectives: This study aimed to comparatively assess the effects of OCR, CVA, and RPA on administrative efficiency and effectiveness (AEE), decision-making (DM), and job redesign (JR), and to determine whether organizational culture moderates these relationships in Nigerian tertiary institutions. Methods: A cross-sectional quantitative study was conducted among 323 respondents from Nigerian tertiary institutions. Composite measures of OCR, CVA, RPA, AEE, DM, JR, and organizational culture were analysed using descriptive statistics, Pearson correlation, multiple regression, relative importance analysis, dominance analysis, and hierarchical moderation regression. Results: OCR demonstrated the highest mean AI score (mean 3.882, SD 0.831), followed by CVA (mean 3.849, SD 0.873) and RPA (mean 3.811, SD 0.905). Correlation analysis showed generally weak associations, with the strongest relationship observed between RPA and AEE (r = 0.161). The regression model predicting AEE was statistically significant (R² = 0.031; F = 3.410; p = 0.018), with RPA emerging as the only significant predictor (β = 0.148, p = 0.004). Models predicting DM (R² = 0.007; p = 0.524) and JR (R² = 0.002; p = 0.920) were not significant. Relative importance analysis showed that RPA contributed 83.1% of explained variance in AEE, while CVA contributed 85.1% in DM. Dominance analysis identified RPA as dominant for AEE (incremental R² = 0.0258) and JR (0.0009), and CVA for DM (0.0059). Organizational culture did not significantly moderate AI relationships across AEE (β = −0.109, p = 0.376), DM (β = 0.120, p = 0.323), or JR (β = 0.018, p = 0.891). Conclusion: AI technologies demonstrate outcome-specific rather than uniform effects within tertiary administrative systems. RPA showed the strongest empirical association with operational efficiency, whereas CVA demonstrated greater relative contribution to decision-support functions. Broader effects on decision-making, job redesign, and culture-dependent transformation remain limited. Recommendation: Tertiary institutions should adopt differentiated AI implementation strategies that align specific technologies with targeted administrative objectives, while strengthening infrastructure, workforce capacity, and governance frameworks to support sustainable digital transformation. Thus, this study provides empirical evidence that AI adoption in tertiary institutions should move beyond technology availability towards function-specific deployment. Identifying which AI applications contribute to particular administrative outcomes can support more effective, equitable, and context-responsive digital transformation policies.

Abstract: The Internet of Things (IoT) has become embedded in everyday consumer environments through smart home devices, wearables, connected appliances, and related technologies. These devices offer substantial convenience and functionality while creating persistent privacy and security concerns. This exploratory study examines how consumer IoT familiarity, usage, privacy and security concerns, awareness of data practices, and self-reported protective behaviors relate to one another. The study is interpreted through Protection Motivation Theory (PMT), the Technology Acceptance Model (TAM), and Risk Perception Theory (RPT). A cross-sectional survey was distributed to 423 members of the University at Albany community and yielded 30 complete responses (7.1%). Quantitative analyses used descriptive statistics, correlations, and a t-test, while open-ended responses were summarized to provide qualitative context. Respondents reported high familiarity and frequent IoT use alongside substantial privacy and security concern, but many demonstrated limited knowledge of the data collected by their devices and inconsistent protective practices. The hypothesis tests were not statistically significant at the .05 level: privacy concern and IoT usage were weakly negatively correlated (r = -0.167, p = .377); perceived risk and awareness were weakly positively correlated (r = .121, p = .525); the awareness-group comparison was nonsignificant (t = .717, p = .479); and trust in vendor privacy protection showed a moderate positive association with IoT usage that did not reach conventional significance (r = .334, p = .071). The results therefore provide exploratory rather than confirmatory evidence of an adoption concern paradox: participants often continued to use IoT technologies despite privacy and security concerns. The findings are consistent with the possibility that perceived usefulness, convenience, risk appraisal, self-efficacy, and trust jointly shape consumer behavior, but the small nonprobability sample and cross-sectional design preclude causal inference and broad generalization. Importantly, this study measures perceived risk and awareness; it does not independently conduct technical vulnerability assessments of participants' devices. This study contributes by integrating PMT, TAM, and RPT to interpret the coexistence of IoT adoption and privacy/security concern; documenting mismatches among concern, awareness, and self-reported protective behavior in an exploratory university sample; and identifying implications for user education, secure-by-default product design, vendor transparency, and future research that combines behavioral measures with objective device-security assessments.

Abstract: Membraneless compartments assembled by liquid–liquid phase separation have moved rapidly from a curiosity of in vitro biophysics to a working explanation for how crop plants sense temperature, water, ions and pathogens. In this review, we synthesize the physicochemical rules that govern condensate assembly in plant cells, trace how those rules are deployed across the horticultural pathosystems and stress physiologies that matter for food production and evaluate the emerging engineering and chemical toolkits — synthetic scaffolds, optogenetic phase regulators, condensate-targeting phytovirucides and condensate-aware breeding alleles — that aim to convert condensate biology into agronomic gain.

Abstract: “Tertulias” (Spanish for “conversational gatherings”) was a study to test a novel peer support group intervention with the purpose of reducing depression and social isolation, and increasing empowerment and resilience, for participants who were women immigrants from Mexico. Tertulias integrated group shared reading (SR) and arts-based research (ABR) activities as novel components of the peer support model being tested. Tertulias was a large, randomized control trial involving 252 participants followed over 12 months, which fills a key gap in SR and ABR research. Results demonstrate that these two practices resulted in unique outcomes that would not have been obtained using traditional health promotion approaches and they revealed novel insights that would not have been able to be discerned using standard research techniques, including using standard community-engaged research techniques. Here, we describe SR and ABR in the outcomes of the study and what we learned about them as novel community practices. The experience of Tertulias with using and integrating SR and ABR demonstrates the valuable potential of these two approaches, used alone or together, for enhancing social connectedness among participants, deepening our understanding of the process and outcomes, and for strengthening community practice in the context of Community-Engaged Research.

Abstract: Bilateral strategic partnerships (BSPs) have become a pivotal instrument of interstate cooperation, yet the concept remains undertheorized and systematic cross-case analysis of partnership structure and resilience is scarce. This study constructs a four-axis analytical framework distinguishing BSPs from cognate forms of cooperation and applies it, through reflexive thematic analysis and structured focused comparison, to four paradigmatic models—Franco-German, U.S.–Japan, Sino-Russian, and Saudi–U.S.—drawing on treaty texts, joint communiqués, official policy documents, institutional statistics, and peer-reviewed scholarship from 2015 to 2025. Three findings emerge. Partnership durability rests on four interdependent enabling conditions, of which institutional architecture alone discriminates among outcomes and alone compensates for weakness elsewhere in the system. Dimensional balance is analytically distinct from dimensional depth, and balanced partnerships absorb shocks that skewed partnerships do not. Typological placement is dynamic rather than fixed: the Saudi–U.S. case demonstrates how a partnership anchored historically in a single functional domain can be deliberately broadened into a multidimensional framework through a national transformation strategy, exercising strategic agency over the terms of its most consequential external relationship. The study concludes that BSPs function not merely as bilateral instruments but as constitutive building blocks of a polycentric international order, while cautioning against the inflationary deployment of the partnership label.

Abstract: Prickly pear (Opuntia ficus-indica) fruits are recognized as valuable sources of bioactive compounds with potential health-promoting properties. However, the relationship between phytochemical composition and antidiabetic activity among different cultivars remains insufficiently characterized. This study evaluated the chemical composition, antioxidant capacity, and anti-hyperglycemic effects of juices obtained from three Mexican prickly pear cultivars (San Martín, Mandarina, and Vigor). Organic acids, sugars, total phenolic and total flavonoid content, betalains, and antioxidant capacity were determined using chromatographic and spectrophotometric methods. The antihyperglycemic activity of the juices was evaluated in healthy Wistar rats using oral glucose tolerance tests (OGTT), and the antidiabetic potential of the San Martín cultivar was assessed in a neonatal streptozotocin-induced type 2 diabetes (T2D) model. Ascorbic acid, oxalic acid, and malic acid were identified in all cultivars, with ascorbic acid being the predominant organic acid in San Martín and Mandarina cultivars juices. Mandarina cultivar exhibited the highest concentration of total phenolic compounds, whereas San Martín cultivar contained significantly greater levels of flavonoids and betalains. Antioxidant activity assessed by ABTS and FRAP assays confirmed the presence of highly active hydrophilic antioxidant compounds. Among the cultivars evaluated, only Mandarina and San Martín juices significantly attenuated postprandial hyperglycemia in healthy animals. Interestingly, freeze-drying abolished the antihyperglycemic effect of San Martín cultivar juice, suggesting degradation or modification of bioactive constituents during processing. In diabetic rats, sub-chronic administration of fresh San Martín cultivar juice significantly reduced blood glucose levels but failed to restore glucose tolerance. Altogether, these findings demonstrate that San Martín prickly pear cultivar juice represents a promising source of bioactive compounds with antihyperglycemic activity. The observed effects are likely associated with the synergistic action of flavonoids, betalains, phenolic compounds, and ascorbic acid. Further mechanistic studies and clinical investigations are warranted to elucidate the molecular pathways involved and evaluate its potential as a functional food for the management of T2D.

Abstract: Varying the probabilities of the branches in a massive spatial superposition provides a controlled way to test gravitational response models. We develop this comparison for fixed source configurations and calibrated probe measurements. The between-branch covariance obeys a pairwise-distance law on the probability simplex and has rank at most one less than the number of occupied branches. Higher cumulants and ensemble-size scans constrain the same response model, although their statistics can also be produced by classical branch mixtures. Coherence recovery adds information when its permitted operations and accessible records are specified independently. For a branch-preserving measurement that produces an irreversible classical record and drives a common feed-forward response, we derive an upper bound on recovered source coherence in terms of record overlaps. A calibrated response diameter converts this into a response--recovery inequality. A second bound relates recovery to the conditional response variances and remains applicable to unbounded feedback with finite second moments. An explicit binary model saturates both inequalities. Coherent momentum transfer provides a contrasting example in which the probe statistics remain branch resolved while an eraser measurement restores source coherence. These comparisons require separate measurements of conditional probe noise, trajectories, and calibration parameters. The bounds apply to the stated classical-record channel; their application to a gravitational theory requires a derivation of that channel from the theory. Branch-weight scans therefore support quantitative tests of specified models without providing a theory-independent criterion for quantized gravity.

Abstract: We study the odd open spin-1 antiferromagnetic Heisenberg chain with positive endpoint fields through its reversible ground-state transform. The main results are two unconditional all-length obstructions to standard proof strategies. First, a high-magnetization projection recursion gives an explicit product bound on the fully polarized ground-state probability. For every positive field sequence \( h_N=o(N) \) this yields \( \alpha_N(h_N)\to 0 \), \( \qquad \limsup_{N\to\infty}\alpha_N(h_N)\log(N/h_N)\leq \frac{30}{7} \), for the ordinary logarithmic Sobolev constant of the ground-state process, with logarithmic tail coefficient at least (7/6). This does not imply collapse of either the Hamiltonian gap or the modified logarithmic Sobolev constant. Second, for the Diaconis–Stroock/Sinclair length-weighted congestion functional used in this paper, every routing with unit edge lengths has congestion at least linear in N; the same conclusion holds for uniformly comparable edge lengths, while routings forced through a polarized configuration obey a stronger rare-state obstruction. These are limitations of that comparison certificate, not upper bounds on the physical gap.As a complementary exact calculation, transfer matrices for the open AKLT ground space give both the singlet/triplet compression of \( W_m=\sum_{i=1}^{m-1}P_{1,i} \) and its coupling to the orthogonal complement. The compressed spectral diameter is \( O(m3^{-m}) \), whereas \( ||Q_mW_m\mathsf P_m||\sim\sqrt{2(m-1)}/3 \). This finite-block statement quantifies why the bare compressed splitting alone does not control the perturbation at the Heisenberg point; it is not a replacement for a locality-sensitive AKLT stability theorem. Exact rational inertia and interval arithmetic then provide supporting finite-volume certificates: full gaps and the complete AKLT–Heisenberg interpolation are certified for \( N=3,5 \), and at \( N=5,h=1 \) one obtains both a negative pointwise Bakry–Émery curvature witness and [ 27/25<\Delta_5(1)<567/500. \( 27/25<\Delta_5(1)<567/500 \)These finite-volume statements have no asserted local-to-global consequence. The fixed-field uniform boundary-gap problem remains open.

Abstract: Within the derivative-coupled effective action shared with the three-epoch model, we analyze the neutral, symmetric, shift-symmetric background branch and derive \(X\propto a^{-6}\), the mass zero-crossing slope \(\alpha=-\dot m_{\rm eff}^{\,2}(t_c)=6H_c|b|\), and the instability band \(p/a<\mu=\sqrt{-b-\gamma X}\). We construct transverse-traceless (TT) sources from non-collinear scalar gradients and show that, within the stated approximation, each tensor wavenumber \(0<K<2\mu\) admits a nonzero two-mode source. In the short-time constant-coefficient model of single real mode, zero initial data, no post-source impulse, a finite-duration exponential source leaves strictly positive residual wave energy. These results establish a conditional radiation mechanism and a continuous frequency band, but do not select a unique spectral peak; the companion contains conditional proof bodies. At the neutral origin, the composite branch of the neutrino-condensation model shares the instability structure through \(b_N=(G_0^{-1}-C)/Z_m\) and \(\gamma_N=\eta/Z_m\); a conserved nonzero time-charge branch cannot originate from an exactly vanishing condensate and requires a separate perturbation analysis. The present-day frequency is \(f_0=(a_*/a_0)K_*/(2\pi\hbar)\). For radiation domination with an adiabatic benchmark, \(f_0\simeq2.6493\times10^{-8}\,q_*(T_*/\mathrm{GeV})\,\mathrm{Hz}\), where \(q_*=K_*/H_*\) must be computed from the source. Emission before reheating also depends on the pre-reheating expansion and entropy history. The three cosmological epochs provide, respectively, early statistical and background conditions, possible intermediate-era inhomogeneous sources, and late-time propagation under conditional vacuum domination; their number fixes neither the number of emission events nor the number of spectral peaks. We derive a composite-parameter upper band bound, an explicit Gaussian spatial UETC with independent temporal coherence, and a tensor-work energy budget. Continuous-time covariance and finite-wave-packet positivity complement the earlier single-mode result. We formulate a unified unequal-time-correlator (UETC) and Green-function response framework, audit the legacy frequency estimates, and exhibit explicit examples of frequency non-uniqueness. The companion Lean file formalizes selected parts of this evidence chain under explicit assumptions; the physical matching, source statistics, and thermal history remain to be determined.

Abstract: Cohn and Rajagopal conjectured that no six-dimensional kissing configuration with Szöllősi's configuration Q₅ or with their configuration R₅ as a cross section can contain 72 or more points. We prove that such a configuration has at most 70 points, and we exhibit configurations with 64 points. The argument combines three ingredients: an elementary bound on the heights of points above a cross section in terms of its covering constant; a positive-kernel bound on each side of the section, together with its equality case; and explicit polar and deep-hole certificates. The upper bound 70 and a manual polar certificate also appear in a manuscript of Iuzhakov and Vetrov; we incorporate their certificate with attribution, so the proof of this bound and the 64-point constructions can be checked without exhaustive computation. The same method shows that every 72-point kissing configuration in R⁶ with a D₅ or L₅ cross section is isometric to one of the four classical configurations, and that a seven-dimensional kissing configuration with an E₆ cross section has at most 126 points, with exactly two configurations attaining 126 up to isometry. We also prove explicit neighborhood bounds of 40, 72 and 126 in dimensions five, six and seven; for E₆ the radius is \( \sqrt{113/448}-1/2>1/450 \).

Abstract: This study tackles high power generation costs and emissions in power systems with Line Commutated Converter-based High Voltage Direct Current (LCC-HVDC) integration. Although LCC-HVDC reduces costs and emissions, it demands substantial reactive power support. To address this, three shunt capacitors (SCs) are added to lower costs and improve performance. An optimization model minimizes generation costs and emissions under varying load levels using the Backtracking Search Algorithm (BSA) for its robust global search and constraint-handling capabilities. The IEEE 30-bus system is used under three different load levels to evaluate performance. The study examines three cases: the base system, the system with HVDC, and the system with HVDC and SCs. Results show that integrating HVDC and SCs reduces generation costs and emissions considerably. For nominal load, the cost dropped by 15.28% with HVDC and SCs. The BSA was more efficient in optimization than the Artificial Bee Colony (ABC) algorithm.