The sum nobody bounded: an optimal 15j inequality, a directional decay law, and the one direction in which absolute majorants fail for the Lorentzian EPRL vertex
Sep 2026· Zenodo (CERN European Organization for Nuclear Research)
Noncommutative and Quantum Gravity Theories
Abstract
Every Lorentzian spinfoam amplitude computed numerically truncates the sum over virtual SU(2) spins l_f >= j_f at a shell depth Delta l; the convergence of that sum has not been proved. This paper bounds the sum by the direct absolute-value route and reports how far it reaches. (1) For the first-kind 15j symbol of the vertex assembly we prove |15j| <= J, a closed form in the fifteen labels, with constant 1 proved optimal (saturated at a doubled-label tuple where both sides equal sqrt(3)/6). (2) Assembling J with rigorous booster envelopes under one shared rapidity, and under the explicit hypothesis that the internal 15j label and the four auxiliary intertwiners carry no growth rate, we derive an exact direction-resolved decay law for the envelope: coordinate directions decay with exponent at least 17/6, the law is piecewise affine on a 13-hyperplane arrangement (7,377 cells), and the envelope fails to be summable on a proper subcone around the isotropic diagonal with maximal deficit 7/18. (3) Over every choice the construction admits (1,458 members per booster) the best achievable exponent coincides with the realized one. VERSION 2 CORRECTS THE SCOPE OF (2)-(3): the auxiliary intertwiners have key-bounded cardinality but their values track the shell, so the decay law describes the envelope under the stated hypothesis and not the vertex tail; on the tail's actual support the absolute route fails by more than stated (crude exponent at the isotropic point at most -1/3 rather than 11/3), and the summand is supported only on the cone where, at each edge, the largest virtual spin is matched by at least one other. Theorem 1 is unaffected. All results are exact rational or symbolic statements at the stock convention rho = gamma (j+1), gamma = 6/5.
Agile - denoting "the quality of being agile, readiness for motion, nimbleness, activity, dexterity in motion" - software development methods are attempting to offer an answer to the eager business community asking for lighter weight along with faster and nimbler software development processes. This is especially the case with the rapidly growing and volatile Internet software industry as well as for the emerging mobile application environment. The new agile methods have evoked substantial amount of literature and debates. However, academic research on the subject is still scarce, as most of existing publications are written by practitioners or consultants. The aim of this publication is to begin filling this gap by systematically reviewing the existing literature on agile software development methodologies. This publication has three purposes. First, it proposes a definition and a classification of agile software development approaches. Second, it analyses ten software development methods that can be characterized as being "agile" against the defined criterion. Third, it compares these methods and highlights their similarities and differences. Based on this analysis, future research needs are identified and discussed.
P. Abrahamsson, O. Salo, Jussi Ronkainen et al.· arXiv.org· 728 citations· ⚡54
Context: Software startups are newly created companies with no operating history and fast in producing cutting-edge technologies. These companies develop software under highly uncertain conditions, tackling fast-growing markets under severe lack of resources. Therefore, software startups present a unique combination of characteristics which pose several challenges to software development activities. Objective: This study aims to structure and analyze the literature on software development in startup companies, determining thereby the potential for technology transfer and identifying software development work practices reported by practitioners and researchers. Method: We conducted a systematic mapping study, developing a classification schema, ranking the selected primary studies according their rigor and relevance, and analyzing reported software development work practices in startups. Results: A total of 43 primary studies were identified and mapped, synthesizing the available evidence on software development in startups. Only 16 studies are entirely dedicated to software development in startups, of which 10 result in a weak contribution (advice and implications (6); lesson learned (3); tool (1)). Nineteen studies focus on managerial and organizational factors. Moreover, only 9 studies exhibit high scientific rigor and relevance. From the reviewed primary studies, 213 software engineering work practices were extracted, categorized and analyzed. Conclusion: This mapping study provides the first systematic exploration of the state-of-art on software startup research. The existing body of knowledge is limited to a few high quality studies. Furthermore, the results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
What if pathology foundation models could do more with less? GigaPath-Flash and GigaTIME-Flash cut computational demands while maintaining strong performance, opening the door to larger studies and broader exploration. The post GigaPath-Flash and GigaTIME-Flash: Toward population-scale discovery with efficient pathology foundation models appeared first on Microsoft Research.
MIT News · Artificial Intelligence· news.mit.eduAug 31, 2026
With millions of users across the world, Julia has been used to conduct cutting-edge research and to design new drugs, jet engines, heat pumps, and more.
MIT News · Artificial Intelligence· news.mit.eduAug 27, 2026
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
