Aug 2026· Zenodo (CERN European Organization for Nuclear Research)
Abstract
The real part 1/2 occurs in the theory of the Riemann zeta function as the symmetry axis of its non-trivial zeros. This monograph asks a narrower question than the Riemann Hypothesis itself: can the distinguished role of the half-axis be explained by a common structural mechanism joining binary complementarity, information balance, two-channel interference, spinorial phase, and the anti-linear symmetry of the completed zeta function? The exact part of the programme is developed first. Binary Shannon entropy has its unique maximum at σ = 1/2, with value ln 2. A normalized equal-gain two-channel amplitude A(σ, ϕ) = √ σ + e iϕ√ 1 − σ vanishes if and only if σ = 1/2 and ϕ ≡ π (mod 2π). The involution J (s) = 1 − s has fixed set ℜs = 1/2. If the spinorial sign is parameterized by e 2πiσ, then the sign −1 also selects σ = 1/2 in the open unit interval. These statements combine into an exact “triple coincidence” theorem inside the explicitly defined binary-spinor model. A non-metaphorical bridge to zeta theory is provided by the Dirichlet eta function, η(s) = X n≥1 (−1)n−1n −s = (1 − 2 1−s )ζ(s), with η(1) = ln 2. Within the open critical strip, the eta and zeta zero sets coincide because the binary prefactor has no zeros there. This establishes a genuine relation among alternating binary sign, ln 2, and the non-trivial zeta zeros. It does not determine the horizontal location of those zeros. The central conditional theorem is then stated. If there exists a canonical, involution- covariant Hilbert-space state map whose fixed readout vanishes exactly with ξ(s) and whose normalized channel weights are ℜs and 1 − ℜs, then every non-trivial zero lies on ℜs = 1/2. The theorem is short; the construction of such a map is the entire unresolved burden. Several tempting shortcuts are shown to fail: symmetry alone produces zero quartets rather than fixed points, eta alternation adds a separate line of prefactor zeros, unequal channel metrics move the balance point away from one half, and a pointwise normalized factorization can be engineered non-canonically. The monograph closes by formulating operator, positivity-kernel, de Branges, Li-coefficient, and theta-kernel routes as concrete research programmes. Numerical calculations are used only as regression tests for identities and software, never as substitutes for proof.
MAGE explains how externalized knowledge, bounded action, independent evaluation, and retained human authority can compose into a governed engineering environment, and proposes tests of when that environment turns commodity intelligence into durable engineering progress.
James C. Davis, Kelechi G. Kalu, Huiyun Peng et al.· 1 citation
LLMs are increasingly used for code generation, yet they frequently hallucinate non-existent software packages, creating exploitable entry points into the software supply chain. We make four contributions to this problem. First, we show that prior evaluation methodologies systematically inflate hallucination rates by misclassifying standard-library modules as hallucinations in some languages. For Python, the overestimation reaches 9.4 percentage points. Second, we evaluate seven inference-time defenses for mitigating package hallucinations, including five guided decoding strategies (Greedy, Contrastive, DoLa, Nudging, and Active Layer-Contrastive Decoding), an iterative self-refinement approach (Self-Refine), and a Retrieval-Augmented Generation (RAG)-based defense.. Across eight models spanning five families and four programming languages (Python, JavaScript, Ruby, Rust), RAG reduces the package hallucination rate (PHR) in 18 of 32 model--language configurations. Third, we introduce Package Utility (PU) to assess whether defenses preserve valid and task-relevant recommendations. Among strategies evaluated, Greedy decoding provides the strongest average mitigation--utility trade-off. Fourth, we stress-test all strategies under adversarial prompts seeded with fabricated package names and find that PHR surges by up to 45 percentage points relative to standard prompts, with Ruby consistently the most vulnerable language (80.9--95.2\%). Under adversarial conditions, RAG and Self-Refine outperform all decoding-only strategies, indicating that robust defense requires either external grounding or iterative self-verification when prompts are actively hostile. Our results recast package hallucination as both a measurement problem and a decoding-time control problem, and they demonstrate that the choice of defense must be matched to the threat model and recommendation utility.
Albérick Euraste Djiré, Iyiola E. Olatunji, Melissa Tessa et al.· 1 citation
HawkEye is introduced, a modular, web-based vulnerability auditing platform designed to streamline security analysis by integrating multiple scanning tools within a unified dashboard and illustrates how consolidated reporting improves vulnerability prioritization for development teams.
D. R. Patil, Varad Salgare, Devaj Arya et al.· International Journal for Re...· 0 citations
By streamlining workflows and fostering collaboration, this platform offers a scalable, cost- effective solution for SMEs and contributes to software engineering by demonstrating how integrated technologies can modernize development processes in resource limited contexts, with potential for broader adoption in Albania and beyond.
OBJECTIVE
To prospectively evaluate whether modifying DSL version 5-based hearing aid (HA) fittings by adjusting gain on HA fitting software so that measured functional gain (FG) approached a one-third gain (1/3G) target could provide appropriate fitting outcomes in patients with sensorineural hearing loss.
METHODS
Twenty-four patients (48 ears) with bilateral sensorineural hearing loss underwent initial HA fitting using the DSL version 5 prescription formula. FG was measured at 250-4000 Hz, and HA gain was adjusted on HA fitting software so that FG approached the target 1/3 G. Speech discrimination scores at 65 and 80 dB SPL were evaluated after a two-week trial period using the 67-S Japanese monosyllable word list. Based on speech discrimination test results, ears were classified as well-fitting or non-well-fitting. FG values were compared between the two groups.
RESULTS
Twenty-one patients (42 ears) completed the study. Thirty-one ears (73%) were classified as well-fitting. Although HA gain was adjusted toward the target 1/3 G, measured FG values at 250 and 500 Hz remained lower than the target values. In well-fitting ears, low-frequency FG values were lower than the target 1/3 G, whereas FG at 2000 Hz was close to the target value. In contrast, non-well-fitting ears showed low-frequency FG values closer to the target 1/3 G, whereas FG values at 2000 and 4000 Hz remained below the target values.
CONCLUSIONS
Although HAs adjusted toward a 1/3 G target did not achieve the intended FG values, particularly at low frequencies, relatively favorable fitting outcomes were obtained in approximately three-quarters of the ears. In well-fitting ears, low-frequency FG remained below the target 1/3 G, whereas FG in the mid-frequency range around 2000 Hz was close to the target value. These findings provide a basis for future prospective studies to clarify how these FG characteristics should be applied to optimize HA adjustment.
A USAF cadet and a Lincoln Laboratory researcher found AI chatbots can help nontechnical service members produce viable software applications for their unique problems.
