Gentzen's 1936 proof of the consistency of Peano Arithmetic was a significant result in the foundations of mathematics. We provide here a modified version of the proof, based on Gödel's reformulation, and including additional details and minor corrections which are necessary to definitively prove the well-foundedness of the cut-elimination argument in a constructive environment. All results have been verified using the Coq theorem prover. NOTE TO READERS 26 February 2026: this is a draft which we had intended to submit to the Journal of Automated Reasoning with no particular time-line in our minds as the work was completed as part of Aaron's honours project at ANU in 2023. For that reason, we have used the Springer style files. We are putting it on arxiv as there appears to be some interest in this work as indicated by a post to https://proofassistants.stackexchange.com/questions/6462/how-far-is-gentzens-consistency-proof-of-peano-arithmetic-from-being-formalized in early February 2026. The Coq code is available here: https://github.com/aarondroidbryce/Gentzen/tree/master
A new approach for deriving neutrino masses from the known masses of quarks, charged leptons, and the parameters of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix is proposed. This framework is based on the simultaneous diagonalization of the kinetic and mass terms in an extension of the Standard Model (SM) with massive Dirac neutrinos. Numerical results for the neutrino masses are obtained, which are consistent with experimental data through a new scaling parameter, $\anu$, introduced to adjust the mass splittings $Δm^2_{21}$ and $Δm^2_{31}$ in order to reach their precise experimental values, thereby reducing the number of flavor parameters in this SM extension. The proposed framework connects neutrino mass generation to the known masses of quarks and charged leptons, offering a unified perspective on the matter sector of the SM.
This Letter presents results of a search for the mixing of a sub-eV sterile neutrino with three active neutrinos based on the full data sample of the Daya Bay Reactor Neutrino Experiment, collected during 3158 days of detector operation, which contains $5.55 \times 10^{6}$ reactor \anue candidates identified as inverse beta-decay interactions followed by neutron-capture on gadolinium. The analysis benefits from a doubling of the statistics of our previous result and from improvements of several important systematic uncertainties. No significant oscillation due to mixing of a sub-eV sterile neutrino with active neutrinos was found. Exclusion limits are set by both Feldman-Cousins and CLs methods. Light sterile neutrino mixing with $\sin^2 2θ_{14} \gtrsim 0.01$ can be excluded at 95\% confidence level in the region of $0.01$ eV$^2 \lesssim |Δm^{2}_{41}| \lesssim 0.1 $ eV$^2$. This result represents the world-leading constraints in the region of $2 \times 10^{-4}$ eV$^2 \lesssim |Δm^{2}_{41}| \lesssim 0.2 $ eV$^2$.
The operation of the ANU 2.3m telescope transitioned from classically scheduled remote observing to fully autonomous queue scheduled observing in March 2023. The instrument currently supported is WiFeS, a visible-light low-resolution image-slicing integral field spectrograph with a 25''x 38'' field of view (offering precision spectrophotometry free from aperture effects). It is highly suitable for rapid spectroscopic follow-up of astronomical transient events and regular cadence observations. The new control system implements flexible queue scheduling and supports rapid response override for Target-of-Opportunity observations. The ANU 2.3m is the largest optical telescope to have been retro-fitted for autonomous operation to date, and it remains a national facility servicing a broad range of science cases. We present an overview of the automated control system and report on the first six months of continuous operation.
The proposed research aims to develop an innovative semantic query processing system that enables users to obtain comprehensive information about research works produced by Computer Science (CS) researchers at the Australian National University (ANU). The system integrates Large Language Models (LLMs) with the ANU Scholarly Knowledge Graph (ASKG), a structured repository of all research-related artifacts produced at ANU in the CS field. Each artifact and its parts are represented as textual nodes stored in a Knowledge Graph (KG). To address the limitations of traditional scholarly KG construction and utilization methods, which often fail to capture fine-grained details, we propose a novel framework that integrates the Deep Document Model (DDM) for comprehensive document representation and the KG-enhanced Query Processing (KGQP) for optimized complex query handling. DDM enables a fine-grained representation of the hierarchical structure and semantic relationships within academic papers, while KGQP leverages the KG structure to improve query accuracy and efficiency with LLMs. By combining the ASKG with LLMs, our approach enhances knowledge utilization and natural language understandi
Bright quasar samples at high redshift are useful for investigating active galactic nuclei evolution. In this study, we describe XQz5, a sample of 83 ultraluminous quasars in the redshift range $4.5 < z < 5.3$ with optical and near-infrared spectroscopic observations, with unprecendented completeness at the bright end of the quasar luminosity function. The sample is observed with the Southern Astrophysical Research Telescope, the Very Large Telescope, and the ANU 2.3m Telescope, resulting in a high-quality, moderate-resolution spectral atlas of the brightest known quasars within the redshift range. We use established virial mass relations to derive the black hole masses by measuring the observed Mg\,\textsc{ii}$λ$2799Å emission-line and we estimate the bolometric luminosity with bolometric corrections to the UV continuum. Comparisons to literature samples show that XQz5 bridges the redshift gap between other X-shooter quasar samples, XQ-100 and XQR-30, and is a brighter sample than both. Luminosity-matched lower-redshift samples host more massive black holes, which indicate that quasars at high redshift are more active than their counterparts at lower-redshift, in concordance
We report the discovery of a new Blue Large-Amplitude Pulsator, SMSS J184506-300804 (SMSS-BLAP-1) in Data Release 2 of the SkyMapper Southern Sky Survey. We conduct high-cadence photometric observations in the $u$ band to confirm a periodic modulation of the lightcurve. SMSS-BLAP-1 has a ~19-min pulsation period with an amplitude of 0.2 mag in $u$ band, and is similar to the classical BLAPs found by OGLE. From spectroscopic observations with the Wide-Field Spectrograph on the ANU 2.3m telescope, we confirm it as a low-gravity BLAP: best-fit parameters from the non-LTE Tlusty model are estimated as $T_\mathrm{eff}$ = 29,020$^{+193}_{-34}$ K, $\log g$ = 4.661$^{+0.008}_{-0.143}$ (cm s$^{-2}$), and $\log$ n(He)/n(H) = -2.722$^{+0.057}_{-0.074}$ dex. However, our BLAP exhibits a very He-deficient atmosphere compared to both low- and high-gravity BLAPs, which have $\log$ n(He)/n(H) in the range -0.41~-2.4.
We present results of a search for extremely metal-poor (EMP) stars in the Large Magellanic Cloud, which can provide crucial information about the properties of the first stars as well as on the formation conditions prevalent during the earliest stages of star formation in dwarf galaxies. Our search utilised SkyMapper photometry, together with parallax and proper motion cuts (from Gaia), colour-magnitude cuts (by selecting the red giant branch region) and finally a metallicity-sensitive cut. Low-resolution spectra of a sample of photometric candidates were taken using the ANU 2.3m telescope/WiFeS spectrograph, from which 7 stars with [Fe/H] $\leq$ -2.75 were identified, two of which have [Fe/H] $\leq$ -3. Radial velocities, derived from the CaII triplet lines, closely match the outer rotation curve of the LMC for the majority of the candidates in our sample. Therefore, our targets are robustly members of the LMC based on their 6D phase-space information (coordinates, spectrophotometric distance, proper motions and radial velocities), and they constitute the most metal-poor stars so far discovered in this galaxy.
Photoionization models frequently assume constant temperature or density within HII regions. We investigate this assumption by measuring the detailed temperature and density structures of four HII regions in the Large Magellanic Cloud and the Small Magellanic Cloud, using integral-field spectroscopic data from the Wide-Field Spectrograph on the ANU 2.3m telescope. We analyse the distribution of emission-lines of low-ionization species, intermediate-ionization species and high-ionization species. We present the complex electron temperature and density structures within HII regions. All four nebulae present a negative gradient in the electron density profile. Both positive and negative temperature gradients are observed in the nebulae. We create a series of nebula models with a constant ISM pressure and varying temperature and density distributions. Comparison of the line ratios between our HII regions and models suggests that none of the simple nebula models can reproduce the observed temperature and density structures. Comparison between the models and the data suggests that the ISM pressure of nebulae in LMC and SMC is between log(P/k)=6-7.5. Complex internal structures of the neb
Complex software systems, e.g., Cyber-Physical Systems (CPSs), interact with the real world; thus, they often behave unexpectedly in uncertain environments. Testing such systems is challenging due to limited resources, time, complex testing infrastructure setup, and the inherent uncertainties in their operating environment. Devising uncertainty-aware testing solutions supported with test optimization techniques can be considered as a mandate for tackling this challenge. This paper proposes an uncertainty-aware and time-aware test case prioritization approach, named UncerPrio, for optimizing a sequence of tests to execute with a multi-objective search. To guide the prioritization with uncertainty, we identify four uncertainty measures: uncertainty measurement (AUM), uncertainty space (PUS), the number of uncertainties (ANU), and uncertainty coverage (PUU). Based on these measures and their combinations, we proposed 10 uncertainty-aware and multi-objective test case prioritization problems, and each problem was additionally defined with one cost objective (execution cost, PET) to be minimized and one effective measure (model coverage, PTR) to be maximized. Moreover, considering time
The European Union is likely to introduce among the first, most stringent, and most comprehensive AI regulatory regimes of the world's major jurisdictions. In this report, we ask whether the EU's upcoming regulation for AI will diffuse globally, producing a so-called "Brussels Effect". Building on and extending Anu Bradford's work, we outline the mechanisms by which such regulatory diffusion may occur. We consider both the possibility that the EU's AI regulation will incentivise changes in products offered in non-EU countries (a de facto Brussels Effect) and the possibility it will influence regulation adopted by other jurisdictions (a de jure Brussels Effect). Focusing on the proposed EU AI Act, we tentatively conclude that both de facto and de jure Brussels effects are likely for parts of the EU regulatory regime. A de facto effect is particularly likely to arise in large US tech companies with AI systems that the AI Act terms "high-risk". We argue that the upcoming regulation might be particularly important in offering the first and most influential operationalisation of what it means to develop and deploy trustworthy or human-centred AI. If the EU regime is likely to see signif
This is a PhD thesis about generated Jacobian equations; our purpose is twofold. First, we provide an introduction to these equations, whilst, at the same time, collating some results scattered throughout the literature. The other goal is to present the author's own results on these equations. These results all concern solutions of generated Jacobian equations, usually paired with the second boundary value problem. We prove strict convexity and $C^1$ differentiability results under optimal hypothesis in two dimensions, and the same results in higher dimensions with some additional hypothesis. We also consider uniqueness results for the second boundary value problem, and the application of the uniqueness results to global regularity. We conclude with notes on the parabolic generated Jacobian equation. The arXiv version contains minor updates to the ANU open research repository version which is available from the listed DOI.
High-harmonic generation (HHG) normally requires a careful adjustment of the driving laser intensity (typically $10^{14} - 10^{15}$ W/cm$^2$) and gas medium parameters to enable good phase matching conditions. In contrast with conventional wisdom, we present experimental results indicating phase-matched HHG in all rare gases, using a high-density medium and a driver laser intensity of around $10^{16}$ W/cm$^2$. The experimental results are corroborated by theoretical simulations, which indicate that ionization-induced self-phase modulation and plasma defocusing self-regulate the driver laser intensity to a level that is appropriate for good phase matching. A ten-fold broadening of the NIR spectrum is observed, which results in the generation of continuous spectra from $18-140$ eV in spite of using 50-fs-long driving pulses. The presented scheme represents a simple and versatile concept for the generation of XUV and soft X-ray continua, which are ideally suited for transient absorption and reflection spectroscopy.
Scientists have pulled off a mind-bending quantum experiment that sounds almost impossible: they showed that tiny metal particles made of thousands of atoms can exist in multiple places at once。 Using advanced laser techniques, researchers at the University of Vienna observed quantum interference in sodium nanoparticles far larger than the kinds of
A new quantum physics study reveals that simply changing a magnetic field over time can unlock entirely new forms of matter that don’t exist under normal conditions。 By carefully “driving” materials with timed magnetic shifts, researchers created exotic quantum states that could be far more stable and resistant to errors—one of the biggest challeng
Astronomers have spotted something surprising in the far outer Solar System—a faint, short-lived atmosphere clinging to a tiny icy world that shouldn’t be able to hold one at all。 The object, called 2002 XV93, is far smaller than Pluto, yet observations during a rare stellar alignment revealed its presence through a subtle dimming of starlight。 Eve
A scorching, airless world just 48 light-years away is offering scientists a rare glimpse into the geology of distant planets。 Using the James Webb Space Telescope, researchers studied LHS 3844 b—a tidally locked “super-Earth” with a permanent dayside hot enough to melt metal—and discovered it’s a dark, barren rock with no atmosphere
Artemis II proved NASA’s deep space systems are ready for the next leap。 Orion survived its high-speed return with improved heat shield performance and pinpoint landing accuracy, while the SLS rocket nailed its trajectory。 Even the launch pad upgrades paid off, with minimal damage despite the powerful liftoff