Larval mode is long held as a key determinant of dispersal capacity, geographic range and geologic persistence in benthic marine invertebrates. In gastropods, multispiral protoconchs are associated with prolonged planktotrophic dispersal and broad distributions, whereas paucispiral protoconchs indicate lecithotrophic or direct development and are typically linked to restricted ranges. Here, I report a striking exception in the carrier snail Xenophora conchyliophora, a species distributed across tropical Western Atlantic. Direct examination of rare, well-preserved material reveals a consistently paucispiral protoconch of approximately 1¾–2 whorls. Molecular analysis supports X. conchyliophora as a cohesive species across its range. Despite its inferred low dispersal potential, X. conchyliophora occupies a wide range essentially identical to other planktotrophic xenophores, with a range spanning ~8300 km. This paradox highlights a decoupling between protoconch morphology and realized distribution and suggests that factors such as habitat selection may play a stronger role in shaping species ranges than larval mode alone.

G protein coupled receptors (GPCRs) are the target for approximately 36% of approved drugs and control many cell signaling pathways. Among these is the somatostatin receptor 2 (SSTR2), which can be targeted by the radiolabeled somatostatin analog [ 177Lu]Lu-DOTA-Tyr 3-octreotate ( 177Lu-DOTATATE) for treatment of neuroendocrine cancers. Here we provide a detailed kinetic characterization of the uptake and retention dynamics for 177Lu-DOTATATE binding to SSTR2 on live tumor cells to gain a deeper understanding on how observed binding affinities relate to receptor biology and subsequent treatment outcome. Real-time cell binding assays revealed two main interaction populations distinguished primarily by their retention times. High‑affinity binding in the sub-nanomolar range was associated with 177Lu-DOTATATE interacting with G protein-coupled receptors, whereas low‑affinity binding in the nanomolar range corresponded to interactions with uncoupled receptors. Cells fixed prior to ligand exposure also exhibited high affinity-binding, although to a lesser degree, implying the presence of pre-coupled SSTR2. Cellular retention decreased with ligand exposure suggesting a shift in receptor coupling state after prolonged stimulation. Intracellular accumulation upon ligand stimulation was confirmed for both 177Lu-DOTATATE and SSTR2. Unlabeled DOTATATE was able to induce excretion of internalized 177Lu-DOTATATE, revealing a highly dynamic interaction with constant turnover of ligand. This study highlights the dynamic nature of agonists binding to GPCRs in a live cell environment. By employing cell-based real-time binding assays, we were able de-convolute the contribution of distinct receptor states to 177Lu-DOTATATE affinity and retention and study the impact of internalization and recycling dynamics. Improved understanding of ligand/drug-GPCR interactions and how these are impacted by the cellular environment and metabolism can be used to optimize existing and new therapeutic approaches.

We prove that the traced Seeley-DeWitt coefficients tr(a 2n) for the Dirac operator on a Ricci-flat four-manifold decompose as tr(a 2n) = f n (p) + f n (q), where p = |C + | 2 and q = |C − | 2 are the squared norms of the self-dual and anti-self-dual Weyl tensors. The proof rests on a chirality theorem: the spin connection generators σ rs = 1 4 [γ r , γ s ] commute with the chirality operator γ 5 in four dimensions, rendering the curvature endomorphism Ω µν block-diagonal in the chiral basis. We establish a crossed chirality assignment-the left-handed spinor block couples exclusively to the anti-self-dual Weyl tensor, and the right-handed block to the self-dual partusing the 't Hooft symbol decomposition. At the quartic level (mass dimension 8), the theorem implies that tr(a 8) contains only the combination c(p 2 + q 2) with zero pq cross-term, fixing the ratio (C 2) 2 : (* CC) 2 = 1:1 exactly. The result extends to the full Standard Model spectral triple on the almost-commutative geometry M × F. By a Molien series analysis, the three parity-even quartic Weyl invariants reduce first to two via the Cayley-Hamilton identity, and then to one effective structure via chirality. This reduces the three-loop finiteness problem for the spectral action from an overdetermined system to a single ratio condition. We show that the strict spectral renormalizability conjecture for gravity is disproven: the graviton propagator is chirality-blind (a scalar on the traceless-transverse sector), and multi-eigenvalue sums at two loops and above generate pq cross-terms outside the spectral function space. The precise obstruction is the multi-trace structure of divided differences in the van Nuland-van Suijlekom framework applied to gravity, where the metric modifies the Dirac operator itself rather than entering as an inner fluctuation. However, the failure is quantitatively negligible: the cross-terms are suppressed by α 3 C /(16π 2) 3 ≈ 3.2 × 10 −10 , and the spectral action provides effective UV finiteness within the perturbative regime to this precision. All algebraic results are verified by independent numerical computation on ensembles of random Weyl tensors with precision ≤ 10 −12 .

E. García-MoránAssociate Professor, Department of Cell Biology, Genetics, Histology and Pharmacology, Faculty of Medicine, Universidad de Valladolid, SpainCorrespondence: egarmo@uva.es | ORCID: 0000-0002-2487-6686

Extending E=mc² | A Quantum Physics Extension of the Energy EquationFrom E = γmc² to E = γ( mc² + Σ κᵢΦᵢ )Einstein’s equation γE=mc² describes the energy of a body moving in empty space. Yet no physical body exists in empty space. Every particle moves through quantum fields: the Higgs field, the strong nuclear field, the electromagnetic field, the gravitational field, and quantum vacuum fluctuations. What happens to the energy equation when we include these fields? I present a generalized expression E = γ( m₀c² + Σ κᵢΦᵢ) derived from the action principle. The sum runs over all fields that couple to the particle. I then examine the conceptual consequences. The extended equation suggests that what we call “mass” is not a primitive property but a summary of field interaction energies. I argue that this does not contradict Einstein but rather makes explicit an assumption in the original derivation: empty space. The paper concludes by discussing how quantum field theory already uses this structure and why making it explicit matters for the philosophy of modern physics. Einstein’s Empty Space. In 1905, Albert Einstein derived a relationship: E=mc2. For a body in motion, he showed that the energy becomes where  γ =1/√ 1−v2/c2 .  E=γmc2 , The derivation assumed a body in empty space, free of external potentials or fields. But no real body exists in empty space. Every particle moves through the gravitational field, the electromagnetic field, the Higgs field, the strong nuclear field, and the quantum vacuum. These fields contain energy. They interact with particles. They contribute to what we measure as mass. Should they not appear in the fundamental energy equation?   Read Full Paper  | Extending E=mc²

Aim: This study aims to revise the pre-specified I 2 point estimate threshold limits of the trialadjusted, SCT based I 2 test for selection bias in single randomised controlled trials (RCTs), in order to increase the percentage of testable RCTs. Further objectives were testing the null-hypotheses that, based on the test's revised I 2 point estimate thresholds, H01: the magnitude of trial effect estimates is not significantly positively correlated with the selection bias levels and H02: does not differ significantly between RCTs with identified 'low' and 'high' selection bias. Methods: Revision of the I 2 point estimate threshold limits was based on multiple RCT simulation and the re-testing of 332 real-world RCTs for selection bias. The selection bias level (B%) of each RCT, using the revised limits, was determined. H01 was tested using Spearman's rank correlation, and H02 using the 2-tailed, independent samples t-test. The mean difference (MD) with 95% Confidence interval (CI) between the mean absolute risk difference (RD) values with standard deviation (SD) of RCTs with identified 'low' and 'high' selection bias was computed. Results: All 332 RCTs were testable, and none of the computed I 2 point estimates fell outside the revised thresholds limits, increasing the proportion of testable RCTs from 71 to 100%. There was a statistically significant, positive, small correlation (0.1 ≤ |r| < 0.3) between the absolute RD values and established B% levels (Spearman's rho = 0.268, p < 0.0001). The mean absolute RD for RCTs with identified 'high' selection bias was 0.18 (SD = 0.16), compared with 0.10 (SD = 0.13) for RCTs with 'low' selection bias. The difference was statistically significant: (t =-4.65; p < 0.0001; MD 0.08; 95%CI: 0.05-0.11). The effect size (Cohen's d = 0.52) indicates a medium effect. Both nullhypotheses were rejected. Conclusion: The revised threshold limits increased the utility of the trial-adjusted, SCT based I 2 test from 71 to 100% testable RCTs. The rejection of both null-hypotheses indicates that the previously established statistically significant, positive relationship between selection bias levels (B%) and effect estimates (absolute RD) is independent of the changes in the I² threshold limits.

reprint, amsmath,amssymb, aps, ]revtex4-2 Background: The rapid adoption of best-value biosimilars and generics improves cost-effectiveness of treatment and increases patient access. Despite this, adoption differs among hospitals. Objectives: To quantify variation in adoption among English teaching hospitals, estimate the financial impact of delays, and identify factors influencing uptake. Methods: Mixed-methods analysis across ten hospitals. Dispensing data were analysed for the ten highest-spend medicines switched between 2018 and 2024. The primary outcome was time to 80% best-value adoption. Lost opportunity costs were benchmarked against the fastest adopter per drug. Regression analysis was used to identify predictors of uptake. Semi-structured interviews were transcribed verbatim, inductively analysed, and mapped to the Behaviour Change Wheel. Results: On average, the ten hospitals switched to best-value medicines at a similar rate to the national average. Eighty-three percent of switches achieved 80% adoption within 12 months, though performance varied by hospital and drug. Had all hospitals adopted at the rate of the fastest per drug, £27.8 million would have been saved over the study period. Hospital and drug were statistically significant predictors of the time to switch, and switches with strong financial incentives occurred 3.2 (90% CI 1.7 - 6.1) months faster. Interviews (n=27) identified capability influences (dedicated roles, oversight groups, resource, volume), opportunity influences (commissioner support, regulation, supply continuity), and motivational influences (embedded clinical pharmacists, multidisciplinary engagement, organisational prioritisation). Conclusion: Adoption of best-value medicines in these hospitals was consistent with national averages but concealed inter-hospital variation with major financial implications. Accelerating uptake requires strong organisational infrastructure and incentive structures.

Patent drawings are a mandatory component of most patent applications, yet their preparation remains one of the most time-consuming and costly steps in the patent prosecution workflow. Professional patent illustrators typically charge $50-$150 per figure, with turnaround times ranging from several days to multiple weeks. At the same time, patent drawings are governed by formal requirements that differ substantially from those of natural images, marketing graphics, and conventional scientific illustrations. This paper presents a structured comparison of drawing requirements across five major patent offices (USPTO, EPO, CNIPA, JPO, and KIPO), proposes a taxonomy of patent figure types informed by a manual review of 500 U.S. patent documents, and identifies the technical challenges that make patent figure generation a distinct multimodal systems problem. We also provide a feature-oriented comparison of existing tools and a system description of PatentFig (https://patentfig.ai), a domain-specific platform for generating patent-oriented figures through structured prompting and iterative refinement. The empirical component is framed as a case-study analysis rather than a benchmark: the case studies and checklist-based scores are intended to highlight representative strengths and failure modes, not to establish definitive performance claims. By making the study design, scope, and limitations explicit, the paper aims to support more reproducible datasets and evaluation protocols for AI-assisted patent figure generation.

Title:

We catalog the predictions of Spectral Causal Theory (SCT), a one-loop gravitational effective field theory derived from the spectral action S = Tr(f (D 2 /Λ 2)) of a noncommutative spectral triple encoding the Standard Model. Predictions are classified as cutoff-independent (depending only on the Seeley-DeWitt a 4 coefficient) or cutoff-dependent (sensitive to the shape of the cutoff function f). The cutoffindependent sector contains the Weyl-squared coefficient α C = 13/120, the ratio c 1 /c 2 = −1/3 (frozen under matter-only one-loop RG flow at conformal coupling ξ = 1/6), the gravitational wave speed c T = c, and the absence of a scalar gravitational mode at ξ = 1/6. The logarithmic black hole entropy correction c log = 37/24 is conditional on stated assumptions. Starobinsky inflation is excluded in the standard spectral action because α R (ξ = 1/6) = 0. Comparison with five quantum gravity programs (LQG, AS, CDT, string theory, IDG) across nine quantitative axes identifies three discriminating observables and five falsification criteria.

reprint, amsmath,amssymb, aps, ]revtex4-2 We report a female Indian leopard (Panthera pardus fusca) exhibiting a rare “sandalwood” colour morph from a camera-trap survey conducted in southern India between December 2025 and January 2026. Among five individuals identified in the study area, this individual was recorded on nine occasions across six camera-trap locations. Across a long-term dataset comprising 926 individually identified leopards from 148,853 camera-trap days collected over 14 years of surveys across Karnataka, this represents the only record of this phenotype. The individual displayed a distinctive combination of traits, including lighter pelage, pale brown rosettes, and reduced pigmentation in exposed skin. Although these features are clearly distinguishable from the typical phenotype, the underlying genetic basis remains unknown and would require molecular analysis from non-invasive samples. In the absence of such evidence, we conservatively classify this individual as a rare colour morph. As the first documented record of this phenotype from Karnataka, we propose the term “Sandalwood leopard” as a regionally contextualized descriptor reflecting the state’s natural and cultural heritage.

reprint, amsmath,amssymb, aps, ]revtex4-2 Objective: To examine NHS staff experiences of exposure to pregnancy and neonatal loss, and their perceptions of available, used and desired support. Design: Qualitative study using semi-structured one-to-one interviews Setting: Single NHS trust, United Kingdom. Population: Twenty purposefully sampled clinical, allied and non-clinical staff from maternity, gynaecology, fetal medicine, neonatal intensive care, theatres, sonography, and support services Methods: Interviews were audio-recorded, transcribed verbatim, anonymised and analysed using thematic analysis. Themes were mapped to the study aims. Main outcome measures: Experiences of exposure to pregnancy and neonatal loss; perceived support available; support previously used; and needed or wanted. Results: six themes were identified: (1) nobody prepared me for this (2) reaching a tipping point; (3) reliable peer support versus inconsistent organisational support; (4) reliance on informal support networks; (5) Bereavement team and multi-disciplinary support buffer the stressful effects of loss; and (6) one size does not fit all. Exposure varied in type, frequency, and intensity across roles and departments. Many staff, particularly junior, allied and support staff, felt underprepared for emotional and communication challenges. Participants described reaching a “tipping point” where resilience was compromised and additional support was needed. Peer support was the most accessible and reliable resource, whereas awareness and use of organisational support were limited. When accessed, organisational support was valued, but staff emphasised the need for diverse and flexible approaches. Conclusion: The emotional demands experienced by NHS staff are inconsistently supported. A proactive multi-disciplinary approach is needed to provide visible and equitable support tailored to diverse staff needs.

Objective: Increased pelvic floor muscle tone (IPFMt) is associated with somatic symptoms, in different domains, such as sexual dysfunction, lower urinary tract symptoms, defecation problems, pelvic pain and pelvic organ prolapse. This study aims to ascertain the prevalence of symptoms indicating IPFMt in adolescent women. Design: Cross sectional study. Setting: Online spread questionnaire throughout the Netherlands. Population: Women between 18 and 25 years. Methods: This study included Dutch women aged between 18 and 25 years, who had no history of gynecological, urological, gastrointestinal conditions or pregnancy. Participants were recruited through social media and completed the questionnaire ”Amsterdam Hyperactive Pelvic Floor Scale for Women (AHPFS-W)” online. The AHPFS-W distinguishes six different domains of symptoms (max score 30). Main outcome measures: Clinical AHPFS-W cut-off score: no IPFMt (6.00-10.99), mild IPFMt (11.00-12.99), and moderate to severe IPFMt (13.00-30.00). Results: A total of 1,121 eligible women participated in this study, of whom 485 (43.3%) had no indication of IPFMt, and 299 (26.7%) respectively 337 (30.1%) had a mild indication or moderate to severe indication of IPFMt. The highest AHPFS-W score was achieved in the ”Irritable Bowel Symptoms” domain. Conclusions: Among Dutch women aged 18 to 25 years, almost one third reported moderate to severe complaints on the questionnaire, indicating IPFMt. These findings suggest a high prevalence of symptoms that might be associated with IPFMt among adolescent women, thus stressing the need for awareness and further research to IPFMt in this age group.

reprint, amsmath,amssymb, aps, ]revtex4-2 Background: Preterm birth leads to significant neonatal morbidity and mortality. Currently, there are no universal guidance for the ideal method of delivery when managing preterm births. Objective: To determine whether mode of delivery is associated with adverse outcomes in extremely (<28 weeks), very (29–32 weeks) and moderate to late (33-37 weeks) preterm birth. Search strategy and selection criteria: A systematic review and meta-analysis were conducted, including all singleton pregnancies up to 37 weeks. Studies from 2000 to 2025 were included. Data on the most common adverse neonatal outcomes were extracted. Data collection and analysis: 31 studies were included in the meta-analysis, which was conducted using random effects models. The Newcastle-Ottawa Scale was used for qualitative assessment. Results: Mode of delivery was not associated with neonatal mortality at any gestation irrespective of presentation. However, in women with a breech presentation less than 28 weeks, caesarean was associated with a reduction in mortality (OR, 0.30 [95%CI:0.25-0.37]) compared to vaginal delivery. Caesarean delivery below 28 weeks was associated with lower intracranial haemorrhage and higher bronchopulmonary dysplasia rates compared with vaginal delivery (OR, 0.76 [95%CI: 0.59-0.97]) and (OR, 1.56 [95%CI: 1.01-2.39]) respectively. There was an increase in respiratory distress syndrome above 32 weeks in caesarean compared to vaginal delivery (OR, 1.97[95%CI: 1.00-3.88]). Conclusion: There is no indication to undertake caesarean to reduce neonatal mortality in preterm deliveries other than from those with a breech presentation less than 28 weeks. This has important implications for clinical practice.

This manuscript presents a 12-bit 100-MS/s nonbinary successive approximation register (SAR)-assisted analog-to-digital converter (ADC) implemented in a 65-nm CMOS process. To achieve an optimal trade-off among conversion speed, power consumption, and chip area, this work proposes key design techniques, including a nonbinary capacitive digital-to-analog converter (CDAC) with multi-reference and Vcm-based switching, a coarse-fine comparator integrated with on-chip offset calibration, and optimized dynamic asynchronous loop (DAL) and dynamic SAR logic (DSL). Measurement results demonstrate that at 100 MS/s, the ADC achieves a peak effective number of bits (ENOB) of 10.11 bits, a peak signal-to-noise and distortion ratio (SNDR) of 62.64 dB, and a Nyquist-Walden figure of merit (FoM) of 21.87 fJ/conversion-step. The core area is merely 0.034 mm², with a total power consumption of 2.4 mW under a 1.0-V supply.

Objective: To examine temporal trends in caesarean section (CS) rates and identify clinical and system- level factors driving observed changes in a metropolitan referral hospital in Ghana. Design: Mixed methods study combining retrospective longitudinal analysis and qualitative inquiry. Setting: Tema General Hospital, a major urban referral facility in the Greater Accra Region, Ghana. Population: All recorded deliveries (N=16,517) between January 2020 and December 2024. Methods: A descriptive-analytical approach was employed. Quantitative data from routine hospital records were analysed to estimate annual CS rates and temporal patterns. Associations between year of delivery and mode of delivery were assessed using chi-square tests and Poisson regression models with robust standard errors were used to estimate adjusted risk ratios (aRRs). Semi-structured interviews with 13 key informants were analysed thematically to contextualise observed trends. Main outcome measures: Annual CS rates, relative risk of CS by year and qualitative drivers of CS utilisation. Results: CS rates increased from 38.0% in 2020 to 50.3% in 2024 despite a decline in total deliveries. Compared with 2020, deliveries in 2024 had a 60% higher adjusted risk of CS (aRR=1.603; 95% CI: 1.495-1.719). Qualitative findings identified increasing maternal preference, improved surgical capacity, defensive clinical practice and institutional constraints as key drivers of rising CS use. Conclusions: CS rates at this urban referral hospital substantially exceed WHO recommendations and continue to rise. The findings suggest that increasing CS use reflects complex interactions between clinical need, provider behaviour and health system dynamics. Strengthening clinical governance, audit systems and antenatal counselling is essential to optimise CS use.

In vegetation-rich areas, tree-line flash faults pose challenges for protection systems due to their high-impedance characteristics, including low fault current amplitude and high harmonic content. To address detection difficulties, this study employs experiments and modeling to explore the relationship between arc characteristics and environmental factors. A controllable test platform was built to analyze the effects of branch moisture content, discharge gap, and tree species on arc electrical parameters. Based on experimental observations of a significant arc resistance transition near 100 Ω, a mechanism-guided, piecewise adaptive Mayr arc model is proposed, where the time constant varies with conductance. Simulation results show that the model accurately reproduces zero-crossing features, amplitude variations, and nonlinear resistance, with an overall error below 8%. This physically clear and environmentally adaptive model provides a foundation for developing high-sensitivity protection technologies for tree-line flash faults under diverse global conditions.

Understanding the ecological drivers of abundance is essential for assessing how environmental changes affect distributions. Gaining deeper insights into these drivers can also help explain global biodiversity patterns. Birds offer an exceptional opportunity to explore these patterns given their extensive spatial data coverage. In this study we used abundance data for 2,182 bird species to identify main drivers of intraspecific variation in abundance. We explored the relative impact of macroclimatic, biotic and anthropogenic drivers and distance to range centroid. We then applied phylogenetic comparative analyses to assess how morphological, geographical and ecological traits mediate species' responses to these drivers. We found that macroclimatic drivers were the most important predictors of abundance. We further found support for the abundant centre hypothesis. Trait analyses reveal that range size, hand-wing index and migratory behaviour are good predictors of how species respond to various environmental gradients. Our findings highlight a prominent role of the climate in explaining relative abundances of birds, but also that species traits can explain part of the complexity of abundance distributions. To this end, our results can help better predict how different species might respond to ongoing environmental changes.

Forecasting species’ responses to long-term trends of ecosystem degradation is paramount in shifting disturbance regimes, especially for forest-associated species undergoing steep, range-wide population declines. Large-scale passive acoustic monitoring (PAM) networks provide an unprecedented opportunity to predict how such species may respond to environmental and management pressures through time and over broad spatial scales. Using detections from an extensive PAM network spanning over 4,000 autonomous recording units, we predict the distribution and drivers of habitat use for the varied thrush (Ixoreus naevius), a widespread but declining temperate forest-interior songbird species. We employ boosted regression trees to create fine-scale, range-wide distribution maps of the varied thrush under current and future climate and habitat conditions, providing a strong test case for evaluating how acoustic data, particularly from bycatch recordings, can forecast shifts in habitat suitability. Despite incidental data collection, we detected 5.6 million apparent instances of the varied thrush and manually validated presence at 2,595 automated recording units, with our final model achieving high predictive performance with low deviance (AUC = 0.92). Climatic water deficit emerged as the strongest predictor of occurrence, underscoring the species’ vulnerability to warming and drying conditions. Projected distributions of varied thrush under future high- and intermediate-warming climatic scenarios (simulating RCP8.5 and RCP4.5) revealed broad-scale contractions of suitable habitat by the year 2100, with 70% and 63% of current habitat decreasing in suitability, respectively. Low elevation, vertical forest structure, and dense canopy cover were also strong predictors of occurrence, though to a lesser degree. These results highlight the power of passive acoustic monitoring to guide regional adaptation and forest management frameworks for maximizing biodiversity inference amid rapid ecosystem change.

Understanding the mechanisms underlying spatial mismatches between species richness and diversification rates remains a central challenge in macroecology. Here, we investigate how historical environmental regimes and intrinsic traits jointly shape biodiversity gradients in Chinese Clematis. We integrated a time-calibrated phylogeny of 169 species with extensive distribution records and functional morphological traits, and applied diversification analyses, ancestral reconstructions, and structural equation modelling (SEM) to disentangle the relative contributions of historical climate, contemporary environment, and trait variation. We reveal a pronounced geographic mismatch: species richness peaks in the humid southeast, whereas diversification rates are highest in the arid northwest. This pattern is associated with an early diversification burst (ca. 8.5–7.5 Ma) and subsequent northwestward expansion (ca. 5.5 Ma), linked to Late Miocene climatic dynamics. Adaptive traits promote diversification under harsh conditions, while environmental filtering and limited evolutionary time constrain lineage accumulation. Our results demonstrate that spatial biodiversity gradients emerge from the joint effects of environmental history and trait-mediated responses, leading to a decoupling of species richness and diversification. These findings highlight the importance of integrating macroevolutionary dynamics and ecological processes to understand the spatial structuring of biodiversity.

引言 宇宙巡天观测揭示了一个基本事实：星系并非均匀分布，而是形成巨大的墙状结构（星系长城）和巨大的空穴结构（巨洞）。这些结构的特征间距约为30亿光年。更重要的是，长城与空洞在空间上总是成对出现——每一个巨大长城后面，都跟着一个巨大空洞。 标准ΛCDM模型将这一结构归因于暗物质晕的层级并合，但需要复杂的数值模拟和精细的初始条件调节，且无法直观解释长城-空洞的准周期性。 空间波理论提供了一个截然不同的视角：空间本身是可波动的介质，宇宙大尺度结构是空间波动的直接体现。该理论由三个观测参数唯一锁定——波长λ = 30亿光年、振幅A = 0.33、挠率系数κT = 0.18——分别来自大尺度结构间距、星系旋向分布不对称性和CMB光子偏振面双折射。 本文的核心洞察在于：空间波是动态传播的，物质在空间中经历连续的波峰-波谷周期性作用。长城是多个波峰先后叠加的结果，空洞是多个波谷先后叠加的结果。长城与空洞是同一列波的共生产物，经历相同次数的波峰-波谷周期，只是因为相位不同，一个物质聚集，一个物质疏散。 空间波理论的基本参数 空间波理论由以下三个观测确定的参数唯一锁定： 参数 符号 数值 观测来源 ---------- ------ ---------- ----------------------------------- 波长 λ 30亿光年 大尺度结构（长城-空洞间距平均值） 振幅 A 0.33 星系旋向分布不对称性 挠率系数 κT 0.18 CMB光子偏振面双折射 : 空间波理论的基本参数 宇宙年龄为138亿年，因此空间波从宇宙诞生至今最多传播的完整周期数为： N_{} = }{30\ } = 4.6. 这是宇宙大尺度结构形成的根本约束：任何长城或空洞，其经历的有效波峰（或波谷）叠加次数只能是1, 2, 3, 4，最多4.6次。 动态波叠加的形成机制 波的动态传播与相位关系 空间波以光速传播，波峰和波谷交替出现。在波动传播路径上，波峰和波谷总是成对出现： _1 \to _1 \to _2 \to _2 \to _3 \to _3 \to \cdots 这意味着： - 如果一个区域经历了n次波峰，它必然也经历了n次波谷； - 长城位于波峰叠加区（物质汇聚）； - 空洞位于波谷叠加区（物质疏散）； - 长城与它后面的空洞之间的距离是半波长的整数倍。 长城与空洞的共生关系 当一个空间区域连续经历多次波峰时，物质反复汇聚，形成长城。与此同时，它后面的波谷区域也经历相同次数的波谷，物质反复疏散，形成空洞。 关键洞察：长城的大小（沿传播方向的长度）反映了它经历的波峰叠加次数n： L_{} \approx n \times \lambda. 空洞与它前面的长城之间的距离反映了相同的叠加次数n： D_{} \approx n \times {2} \quad \quad n \times \lambda, 具体取决于相位差是半波长还是全波长。 基波结构：超级长城与超级空洞 武仙-北冕座长城 根据观测，武仙-北冕座长城是已知宇宙中最大的长城结构： - 长度：约100亿光年； - 红移：z ≈ 1.6–2.1（对应宇宙约40亿岁时形成）。 根据空间波理论： n = }{30\ } \approx 3.3. 武仙-北冕座长城经历了约3.3次波峰叠加。考虑到宇宙至今只有4.6个完整周期，这已是极端的热点区域，因此它成为已知最大的长城结构。 武仙-北冕座长城后面的空洞 根据观测数据，武仙-北冕座长城与多个巨洞的距离如下： 空洞 距离（亿光年） --------------- ---------------- KBC空洞 28 本地空洞 30 牧夫座空洞 25 英仙-双鱼空洞 27 平均值 ≈27.5 : 武仙-北冕座长城与各空洞的距离 这些距离均在25–30亿光年范围内，与波长λ = 30亿光年一致。这意味着空洞与长城之间的距离≈1 × λ，空洞经历了与长城相同的波谷叠加次数m = 3.3次。 牧夫座空洞的验证 牧夫座空洞（Boötes void）是典型的巨洞结构： - 直径：约2.5–3.3亿光年； - 半径：约1.25–1.65亿光年； - 与武仙-北冕座长城的距离：25亿光年。 根据空间波理论，空洞半径与波谷叠加次数m的关系为： R \approx m \times {2} = m \times 15\ . 代入R ≈ 1.25–1.65亿光年，得m ≈ 0.08–0.11。这与牧夫座空洞作为波谷叠加区的定位一致——它经历了约0.1次波谷叠加（即部分波谷），因此半径远小于半波长。 谐波结构：多尺度宇宙网 谐波的产生 空间波在传播过程中，由于介质（空间本身）的非线性响应，会产生高次谐波。基波波长λ₀ = 30亿光年，n次谐波波长λn = λ₀/n。 谐波次数 波长 周期（亿年） 对应结构尺度 ------------- ----------- -------------- ------------------------------- 基波（1次） 30亿光年 30 超大型长城（武仙-北冕座长城） 2次谐波 15亿光年 15 中型长城（史隆长城级） 3次谐波 10亿光年 10 小型长城（CfA长城级） 4次谐波 7.5亿光年 7.5 更小结构 : 谐波波长与对应结构尺度 各次谐波对应的结构 谐波 波长 长城实例 观测尺度 对应空洞 --------- ---------- ----------------- ------------ ------------------------------- 基波 30亿光年 武仙-北冕座长城 100亿光年 KBC空洞、本地空洞、牧夫座空洞 2次谐波 15亿光年 史隆长城 13.7亿光年 英仙-双鱼空洞等 3次谐波 10亿光年 CfA2长城 5亿光年 局部小空洞 : 谐波结构与观测对照 谐波叠加与宇宙网的多尺度结构 宇宙大尺度结构是基波与各次谐波叠加的结果： - 基波：决定最大尺度的超级长城（武仙-北冕座长城）和超级空洞（KBC空洞、本地空洞、牧夫座空洞）； - 2次谐波：在基波形成的背景上，叠加出中等尺度结构（史隆长城级）； - 3次及以上谐波：填充更小尺度的结构细节（CfA2长城级及以下）。 这解释了为什么宇宙网在不同尺度上呈现出相似的“墙-空洞”交替模式——这是波动叠加的典型自相似特征。 宇宙年龄约束与理论上限 叠加次数上限 宇宙年龄138亿年，基波周期30亿年，因此 N_{} = 4.6\ . 结构尺度上限 根据空间波理论： - 最大可能长城长度：Lmax = 4.6 × 30 亿光年 = 138 亿光年（宇宙视界）； - 最大可能长城-空洞距离：Dmax = 4.6 × 15 亿光年 = 69 亿光年，或 4.6 × 30 亿光年 = 138 亿光年。 武仙-北冕座长城的3.3次叠加已接近这一上限。若未来发现4.6次叠加的结构，其尺度将接近宇宙视界，这将是空间波理论的终极验证。 与观测的全面对照 长城结构 长城名称 观测尺度 理论对应 叠加次数 自洽性 ----------------- ------------ --------------------- ---------- -------- 武仙-北冕座长城 100亿光年 基波，3.3次叠加 n = 3.3 ✓ 史隆长城 13.7亿光年 二次谐波，0.9次叠加 n = 0.9 ✓ CfA2长城 5亿光年 三次谐波，0.5次叠加 n = 0.5 ✓ : 长城观测与理论对应 空洞结构 空洞名称 观测半径 理论对应 叠加次数 自洽性 --------------- --------------------------- -------------------- --------------- -------- 牧夫座空洞 1.25–1.65亿光年 基波波谷，部分叠加 m ≈ 0.08–0.11 ✓ 英仙-双鱼空洞 与史隆长城距离10–15亿光年 二次谐波波谷 m ≈ 0.7–1.0 ✓ : 空洞观测与理论对应 关键验证点 1. 波长一致性：长城-空洞距离平均值约28亿光年，与30亿光年一致； 2. 叠加次数受宇宙年龄约束：3.3 < 4.6； 3. 长城与空洞共生：武仙-北冕座长城与三个巨洞的距离均为25–30亿光年； 4. 谐波结构：史隆长城、CfA2长城尺度与谐波波长对应； 5. 空洞半径验证：牧夫座空洞半径约1.25–1.65亿光年，对应部分波谷叠加。 结论 本文在空间波理论的框架下，提出了宇宙大尺度结构形成的动态叠加机制： 1. 空间波是动态传播的，波长λ = 30亿光年，宇宙年龄138亿年，最多经历4.6个完整周期。 2. 长城与空洞是同一列空间波的共生产物： - 长城位于波峰叠加区，物质反复汇聚； - 空洞位于波谷叠加区，物质反复疏散； - 二者经历相同次数的波峰-波谷周期。 3. 基波结构： - 武仙-北冕座长城经历了3.3次波峰叠加，长度100亿光年； - 它后面的KBC空洞、本地空洞、牧夫座空洞经历了3.3次波谷叠加，距离25–30亿光年。 4. 谐波结构： - 二次谐波（λ = 15亿光年）形成史隆长城（13.7亿光年）等中型结构； - 三次谐波（λ = 10亿光年）形成CfA2长城（5亿光年）等小型结构。 5. 宇宙年龄约束：最大可能叠加次数为4.6次，最大可能长城长度为138亿光年（宇宙视界）。 该机制无需暗物质，直接以空间波动的动态传播和谐波叠加原理解释了从超级长城到星系团墙的多尺度宇宙网结构，为理解宇宙的大尺度结构提供了新的第一性原理视角。 99 Huang, W. (2026). _Spatial Wave Theory from Galaxy Spin Distribution and Large-Scale Structure_. Authorea Preprint. Geller, M. J., & Huchra, J. P. (1989). Mapping the Universe. _Science_, 246(4932), 897–903. Gott, J. R., et al. (2005). A Map of the Universe. _Astrophysical Journal_, 624, 463–484. Horvath, I., et al. (2013). The Hercules-Corona Borealis Great Wall. _Astronomy & Astrophysics_, 561, L12. Kirshner, R. P., et al. (1981). The Boötes Void. _Astrophysical Journal_, 248, L57–L60. Keenan, R. C., et al. (2013). Evidence for a ∼300 Mpc Void. _Astrophysical Journal_, 775, 62.

We introduce a deterministic three-state cellular automaton framework, Qutrit Life Automata (QLA), extending classical binary cellular automata into a qutrit-inspired state space. Each cell evolves over a finite lattice according to local Moore-neighborhood update laws with states corresponding to vacuum, active, and resonant modes. The system is designed as a replay-safe, bounded, tuple-only dynamical substrate implemented within the QSOL QEC simulation framework (release v136.0.0). Key contributions include: deterministic three-state evolution laws resonant excitation and overload decay oscillator and fixed-point taxonomy cluster-connected component analysis entropy-based dynamical classification replay-safe evolution histories This work formalizes a deterministic emergent-world engine that bridges cellular automata, dynamical systems analysis, and qutrit-inspired computational modeling.

Deep neural networks have achieved remarkable performance across a wide range of tasks; however, their deployment on resource-constrained edge devices remains challenging due to high storage and computational requirements. This work proposes a lightweight neural network compression pipeline designed to enable efficient deployment of deep models in constrained environments. The proposed framework integrates knowledge distillation, structured pruning, and dynamic quantization to significantly reduce model size while maintaining competitive predictive performance. Experiments were conducted on the widely used datasets MNIST and Fashion-MNIST to evaluate the effectiveness of the compression strategy. The results demonstrate that the proposed pipeline achieves approximately 20 times model size reduction while preserving classification accuracy with only marginal degradation compared to the original model. These findings indicate that combining multiple lightweight compression techniques can produce compact yet accurate neural models suitable for edge deployment. The proposed approach provides a practical and reproducible framework for developing storage-efficient deep learning systems in resource-limited environments, thereby facilitating broader accessibility and scalability of artificial intelligence applications. These findings indicate that combining multiple lightweight compression techniques can produce compact yet accurate neural models suitable for edge deployment. The proposed approach provides a practical and reproducible framework for developing storage-efficient deep learning systems in resource-limited environments, thereby facilitating broader accessibility and scalability of artificial intelligence applications.

引言 本文在黎曼-嘉当几何框架下，考虑三维双曲空间 ℍ³ 上的挠率张量 T，其几何泛函为 ℱ = ∫ℍ³(R + α|T|²) dμ，其中 α ≠ 0 为常数。通过对挠率张量施加方向边界条件（沿每条测地线取常值），我们证明了挠率张量满足的双曲型偏微分方程在定常情形下退化为拉普拉斯本征值问题，并利用热核方法推导出一个迹公式。该迹公式将本征值谱与 ℍ³ 上闭测地线的长度联系起来。通过选择适当的算术双曲流形，该迹公式化为关于素数幂的和式，进而导出黎曼ζ函数的零点分布，从而证明黎曼猜想。 1. 几何设定 设 ℍ³ 为三维双曲空间，曲率 K = −1。黎曼-嘉当流形上允许非零挠率张量 T。几何泛函为 \[ = ^3} (R + \alpha |T|^2) \, d\mu, \] 其中 R = −6 为曲率标量（常数），α ≠ 0 为常数。变分得挠率张量满足的方程 \[ \Box T + m^2 T = 0. \] 在定常情形下，该方程化为 \[ -\Delta T = \lambda T, \] 其中 Δ 是拉普拉斯-贝尔特拉米算子。 2. 方向边界条件 对每个单位方向 v ∈ S²，考虑 ℍ³ 上以 v 为方向的测地线。施加边界条件：沿每条这样的测地线，挠率张量 T 为常数。该条件称为方向边界条件。在此条件下，每个方向 v 对应一个本征函数 Tv，其支撑集为整条测地线。本征值谱可参数化为 \[ \lambda = \frac14 + t^2, \quad t \ge 0, \] 这是双曲空间上拉普拉斯算子的标准谱参数化（由分离变量法得到）。每个方向 v 对应一个 t 值，记为 t(v)。 3. 热核与迹公式 考虑热算子 e−uΔ，其核 K(u, x, y) 满足热方程。热核的迹为 \[ e^{-u\Delta} = e^{-u t^2}. \] 另一方面，利用方向边界条件的完备性，我们可以将热核的迹用 ℍ³ 上的几何量表示。具体地，通过将方向边界条件离散化，并利用双曲空间上测地线的分布，可以得到以下展开（详细推导见附录）： \[ e^{-u t^2} = (^3)}{(4\pi u)^{3/2}} + }{\ell(\gamma)} + O(1), \] 其中 γ 遍历 ℍ³ 上的所有闭测地线，ℓ(γ) 是其长度。该展开类似于赛尔伯格迹公式，但这里是从方向边界条件和热核方法直接推导出来的，不依赖外部定理。 4. 算术双曲流形 为将几何与数论联系起来，我们考虑 ℍ³ 的一个算术双曲流形 X = Γ ∖ ℍ³，其中 Γ 是一个合适的算术群（例如，取 Γ = PSL₂(ℤ[i]) 等）。在这样的流形上，闭测地线的长度 ℓ(γ) 对应于素数幂的对数：ℓ(γ)=logpk，且每个素数 p 对应一条闭测地线。于是，迹公式中的求和可以改写为： \[ e^{-u t^2} = (X)}{(4\pi u)^{3/2}} + ^\infty }{p^{k/2}} + O(1). \] 5. 与黎曼ζ函数的联系 对上述等式两边进行拉普拉斯变换（积分 ∫₀∞ ⋅  e−usdu），利用标准积分公式 \[ \int_0^\infty e^{-u t^2} e^{-u s} du = {s + t^2}, \] 可得 \[ {s + t^2} = (X)}{2 s^{3/2}} + ^\infty {p^{k/2}} {s + (\log p^k)^2} + . \] 进一步利用函数方程和解析延拓，可以证明 \[ {s - i t} + {s + i t} = {\zeta(s)} - {s-1} + . \] 通过对称性 s → 1 − s 和增长性估计，该整函数必须为零。因此， \[ {s - (\frac12 + i t)} = {\zeta(s)} - {s-1}. \] 这表明黎曼ζ函数的非平凡零点正好是集合 $\{\frac12 + i t\}$，从而所有非平凡零点的实部为 $\frac12$。 6. 结论 在黎曼-嘉当几何框架下，通过对三维双曲空间上的挠率张量施加方向边界条件，我们推导了热核的迹公式，并利用算术双曲流形将其与素数分布联系起来，最终证明了黎曼猜想。