It is worth noting that none of the complexities below involve anything more sophisticated that pre-calculus study and logs and trig functions, and perhaps the early part of a first course in calculus, both of which are often taught at the high school level.
We combine the current experimental muon g−2 world average, which incorporates the final Fermilab result, with the latest electron g−2 determinations based on cesium and rubidium measurements to set 95% CL exclusion contours for a pure vector mediator coupled to leptons. We explicitly test the assumption that the electron and muon coupling magnitudes are equal by comparing this restricted case with the case of independent electron and muon couplings and quantify the impact on the allowed parameter space.
In the minimal visible dark-photon model, both leptons constrain the same kinetic mixing and are analyzed through a combined χ2 analysis. We compare the resulting g−2 bounds with existing accelerator direct-search exclusions and model-dependent astrophysical and cosmological constraints. From the accelerator comparison, we identify a region in the (mA′,|ϵ|) parameter space near 17~MeV, close to the reported X17 mass, that remains allowed by the direct-search contours displayed here but is excluded by the cesium-based electron g−2 constraint. The rubidium-based fit does not exclude this interval.
For an X17 boson with independent lepton couplings, we constrain the electron and muon couplings separately. Electron-only direct searches leave two disconnected allowed regions near the reported X17 mass: a newly reopened low-coupling interval and a higher-coupling region above the NA64 excluded band. The cesium-based electron g−2 constraint closes the higher-coupling region, while the rubidium-based constraint reduces its extent; neither affects the newly reopened low-coupling interval.
Using the current experimental muon g−2 world average, we obtain a new g−2-based exclusion region for the muon coupling, with no significant preference for a nonzero coupling.
Artificial intelligence programs have recent disproved some famous mathematical conjectures by finding counter-examples.
Most mathematical proofs are deductive. They reason, point by point, from axiom, to lemma, to theorem, in a straight forward, X implies Y, Y implies Z, fashion.
Some mathematical proofs, arguably more elegant ones, are inductive. A common structure of an inductive proof is roughly speaking: imagine that this theorem is not true. Then, X could imply Y, and if X implies Y, then Z must have a certain value, but Z can have a different value. Therefore, the theorem must be true.
Another form of inductive proof shows that if proposition X is true that proposition X+1 is true by deduction. Then, it shows that proposition X is true in a separate proof for a particular early case of X (and possibly by other separate proofs for several other early cases of X that come before the one you use to validate the rest of the cases). Thus, for the early case or cases, and all subsequent cases, the conjecture must be true.
Many theorems are also almost always true, but have some "trivial" exceptions, typically for things like values of variables that are equal to zero or one, or for the first few iterations of a series, with the theorem holding only after those iterations.
One of the most elegant and efficient ways to prove that a theorem is not true is with a counterexample. The theorem may be true for every situation or set of values considered, sometimes millions of them, but it takes only one counterexample to show that the theorem is not always true, and hence, is false.
For example, in the case of Fermat's Last Theorem, before it was prove to be true, one could have imagined a counterexample disproving it with just three whole numbers that defied it's rule, that could be stated in a line or two, even thought it has been numerically tested for millions of numbers and in the end, it it would take a proof hundreds of pages long to rigorously establish that it was true deductively.
Disproof of longstanding mathematical conjectures by counterexample is rare, but it has happened, even in the pre-computer era, for theorems that held in vast numbers of examples, with no flaws identified for many decades by extremely smart people trying hard to do so.
I haven't very exactly described this kind of conjecture, although I'm sure that a clever mathematician could do so, but let's assume for sake of argument that this kind of conjecture is susceptible to precise definition, and call this kind of conjecture a "near miss conjecture".
Disproof of a near miss conjecture by counterexample, however, in and of itself, while it is efficient, indeed elegant, is also dissatisfying in the case of conjectures the hold true for so many examples and which defied logical reasoning to show that they are true or false for long periods of active efforts to do so. Disproof of a near miss conjecture by counterexample is dissatisfying because, while they do show that the conjecture is not true, they don't tell why the conjecture doesn't always work, even though it does work for so many cases and logically feels like it should work in every case.
Maybe the near miss conjecture is true for all but a finite set of counterexamples that is well defined, and can be used to modify the conjecture in much the same way as many theorems are modified to exclude a handful of trivial exceptions.
Maybe the near miss conjecture could be true if some other assumption so obvious that even smart people don't recognize that it needs to be made, add it.
For example, a conjecture about the probability of heads or tails in a coin toss may need to be supplemented with the assumption that the coin doesn't land on its side and thus doesn't generate either a heads or a tails result, rescuing the near miss conjecture, which remains very useful, despite not being perfectly true without the added assumption.
Knowing why a disproof by counterexample is possible adds insight that the counterexample itself often does not.
A generation ago, we imagined that Homo sapiens, “thinking man,” emerged fully formed in Africa over 100,000 years ago and swept away all our monstrous kin before us through dint of our sheer genius. Today, it seems more likely that it was we who were the monsters out of the dark, the demons about which Neanderthal mothers would tell their little-ones.In 2002’s The Dawn of Human Culture, Stanford paleoanthropologist Richard Klein presented what at that time was the standard model of the recent origins of humanity. Some time before 50,000 years ago, a new form of human arose through some sort of mutational jump. Klein posited that our genius, our superiority, was because of a macromutation that enabled us to generate fully articulate language. Before the emergence of this new species of human, there were many varieties of human, or, more precisely, hominin. Neanderthals in Europe and Central Asia, various “archaic” lineages in eastern Eurasia, and also descendants of other Homo forms in Africa.
Ω humans, whom many popular slogans would refer to as “Africans,” rapidly swept away all these varieties of humanity after 50,000 years.And so it was for a decade. There were dissents; in 2006 Jeffrey Wall and Michael Hammer published Archaic admixture in the human genome. This paper reflected suspicion among many evolutionary geneticists that the orthodoxy promulgated was too pat and simplistic (see also Magnus Nordborg’s 1998 On the Probability of Neanderthal Ancestry). But despite an underground counter-consensus, very few evolutionary geneticists were vocal on this issue in public. . . . This all changed in 2010, when Svante Paabo and colleagues reported that Neanderthal whole genomes yielded strong evidence of several percent admixture into non-Africans, as well as the discovery of a new human lineage in eastern Eurasia, the Denisovans, who also contributed about 5% of the ancestry of Papuans.Previous work had almost entirely been a matter of inference derived from contemporary populations. You looked at genetic variation in people alive today and worked backward to plausible models of how that variation could have arisen. In the 1980s, geneticists examined mitochondrial lineages, which represent the direct matrilineal genealogy. Geneticists noticed that all non-African populations nested within African genetic variation. They soon replicated this result with the Y chromosome, passed only through males, and the autosomes (markers on chromosomes 1 through 22) representing the whole genetic heritage. These results neatly dovetailed with the findings of paleoanthropologists like Chris Stringer of the British Museum of Natural History, who argued that modern human morphology, mostly exemplified by traits in human skulls, reflected continuity with African Homo, and not Neanderthals. Following the molecular genetic results, researchers applied similar phylogenetic methods to morphometric traits and discovered the same pattern of non-Africans nesting within African variation.It was an immaculate and tidy story. . . . And that still seems to be much of the story. But not the entire story.
Over the last few years, geneticists have concluded that a much higher fraction of non-African DNA was originally Neanderthal. In an interview with Dwarkesh Patel Harvard’s David Reich asserted that as much as 10-20% of the overall heritage of early non-Africans, just as they were expanding out of the Near East 50,000 years ago, may have been Neanderthal.
How then is that today we detect only about 2% Neanderthal genes outside of Africa?
The genome rapidly sheds genetically incompatible segments within a few thousand years via purifying selection. Because Neanderthals diverged from our predominantly African ancestors 600 to 700,000 years ago, their overall genetic makeup exhibited much more striking incompatibilities with the expanding Africans than occurs when different branches of our own species mix (the deepest division in our own lineage dates to about 200,000 years, when Khoisan ancestors diverged from everyone else). No doubt the same phenomenon applied to Denisovan admixture, which today in some Oceanian populations, like those in New Guinea or the indigenous populations of the Philippines, approaches 5% or so.What does this all mean?
Because natural selection changes allele frequencies in ways that are out of step with the overall genome, the signatures that we get from modern and ancient DNA are deceptive as to the demographic dynamics of early anatomically modern humans and the Neanderthals (and Denisovans) whom they encountered. All the evidence, both ancient and modern, points to a tiny non-African ancestry population between 50 and 60,000 years ago, a few thousand individuals at most (some models posit a bottleneck of 200 breeding individuals!). If 10-20% of the ancestry of the early modern human expansion, also known as the Initial Upper Paleolithic (IUP), was Neanderthal, that implies the integration of hundreds of Neanderthals, as opposed to ten or twenty.
Admixture between modern humans and extinct hominins has shaped the genomes of present-day individuals, but reconstructing this history has been constrained by the scarcity of archaic samples and unadmixed outgroup populations.
We introduce TRACE, a reference- and outgroup-free approach that uses features of ancestral recombination graphs to identify archaic ancestry. Simulations show TRACE has high precision and low false discovery rates.
Applied to 1000 Genomes, TRACE recovers known Neanderthal and Denisovan introgression and uncovers ghost admixture from uncharacterized hominins in both Africans and non-Africans. Ghost ancestry persists in Neanderthal and Denisovan ancestry deserts, challenging their interpretation as Homo sapiens–specific regions. In Oceanians, TRACE finds deep lineages are enriched in Denisovan compared to Neanderthal regions, supporting super-archaic introgression. TRACE enables mapping archaic introgression without archaic genomes.
We argue that effects of the quantum spin-connection foam, which describes quantum gravity according to the precanonical quantization of General Relativity, may already be observed in the form of the small cosmological constant and a modification of Newtonian dynamics at small accelerations, manifested in the flat rotation curves of galaxies.
We obtain a modification of the Newtonian potential that takes into account the existence of a fundamental small acceleration scale, a∗ = 8πGℏϰ, where ϰ is a parameter with the dimensions of inverse spatial volume that appears on dimensional grounds. The connection between ϰ and the hadronic scale of the mass gap in the pure Yang-Mills sector of the Standard Model leads to an estimated value of a∗ compatible with the Milgromian acceleration scale in MOND. The connection between a*^2 and the cosmological constant leads to a realistic value of the latter. Milgromian MOND, together with a theoretically distinct interpolating function, is derived under the assumption that classical dynamics is modified by the mean-field acceleration calculated from the simplest solution of precanonical quantum gravity in the nonrelativistic approximation.
We also indicate that the effects of Newtonian dynamics modified by the spin-connection foam may be observable in the Solar System and even in laboratory experiments.
The anomaly of the day is an anomaly in a certain kind of B meson decay. I'm very skeptical and think it will go away and is probably due to poor modeling of the Standard Model prediction, but I'll note its existence in this post for further analysis.
The decays B→PP, where the pseudoscalar P is a π or K, have been studied under the assumption of flavour SU(3) symmetry [SU(3)F]. The global fit shows a 3.6σ discrepancy with the Standard Model (SM).
Separate fits for ΔS=0 and ΔS=1 decays find parameter sets that differ by a factor of 10, suggesting 1000% SU(3)F breaking, significantly larger than the ∼ 30% breaking expected in the SM. This study has been extended to include final states with η and η′ mesons. The resulting global fit, once again under the assumption of SU(3)F symmetry, is worse, with a 4.1σ deviation from the SM. When theoretical constraints |C˜/T˜| = 0.2 or A˜ = 0 are imposed, the fits worsen, with the discrepancy approaching 5σ. These results hint at new-physics contributions to these decays.
A Covarying Coupling Constant theory performs similarly to, but not better than MOND. Both are much better at explaining galaxy rotation dynamics than a Cold Dark Matter theory using an NFW dark matter distribution (which is theoretically necessary for truly sterile dark matter particles).
The Covarying Coupling Constants (CCC) framework, developed to account for high-redshift JWST observations, contains a mechanism -- a covarying-constant effective mass field keyed to local density -- that modifies galactic dynamics without particle dark matter.
We test it against the full Spitzer Photometry and Accurate Rotation Curves (SPARC) sample of 175 disc galaxies, extending an earlier study of a few objects. Working in an inverse formulation, in which each model predicts the baryonic rotation curve from the observed one, we compare CCC against Modified Newtonian Dynamics (MOND) and one- and two-parameter Navarro-Frenk-White (NFW) haloes on identical footing, using the reduced χ2ν. We show that the published sharp density turn-off in the earlier study is unphysical and replace it with a smooth transition -- the density-space analogue of the MOND interpolating function, introducing no new parameter. One-parameter smooth-CCC then performs comparably to galaxy-by-galaxy fitted MOND (the lower χ(ν)^2 in 56 per cent of galaxies, mean χ(ν)^2 of 2.58 versus 2.65; the paired difference is not significant), while two-parameter NFW shows a substantially broader fit-quality distribution and a larger tail of poor or boundary-limited fits (mean χ(ν)^2≈7). The CCC turn-off density is not universal (scatter 0.82 dex) and correlates with galaxy size, qualitatively consistent with a spherical reconstruction applied to flattened disc systems. Recast as an acceleration, however, a(t) = V(flat)^2/R(t) has scatter 0.33 dex (on the 91-galaxy resolved subset) -- matching the MOND scale a0 (0.34 dex) -- and comparable magnitude of order 2×10^−10 m/s^2, with its size correlation removed. Though not designed for galactic dynamics, CCC describes rotation curves as well as galaxy-by-galaxy fitted MOND.
Not long ago, we were finally able to find decent sized bones that proteins provided proteomic evidence (rather than DNA evidence which was not available) were able to match to Denisovans, which were found on the coast of the main island of Taiwan, finally putting a body together with the ghost population implied by DNA evidence. Two more leg bones were recently found.
Earlier dating had suggested an age for the Taiwanese Denisovan remains of about 160,000 years ago, long before modern humans arrived in the region and overlapping with Homo erectus. Analysis of the new leg bones by a more reliable and credible method, however, reveals that they are actually just 45,000 years old, contemporaneous with a modern human presence in the region.
At one level this isn't a surprise. Modern humans in Southeast and East Asia and Oceania have genetic admixture from Denisovans, so they had to overlap at some point. But it is surprising that the two different dating methods differed from each other by a factor of four.
The chemical analysis also suggests that these Denisovans, like Neanderthals, had a diet heavy in meat from large mammals.
We ask whether any one-parameter structural correction to the radial acceleration relation (RAR) can be uniquely recovered from SPARC rotation curves, and answer with an identifiability audit: each candidate is benchmarked against per-galaxy nuisance freedom, with predictive scoring against mass-only and data-quality baselines.
In the full sample (N = 126) the answer is no: a hybrid compactness term improves the fit, but zero-point freedom absorbs the gain, and in cross-validation the model fails to out-predict a mass-only baseline and loses to a quality-flag baseline.
One regime retains structural information: in gas-dominated, low-acceleration disks -- where MOND's strict locality and ΛCDM feedback models diverge most sharply -- the RAR residual correlates with compactness (r = 0.46, p = 1.3×10^−4), remains significant under hierarchical partial pooling (β = 0.23, p = 1.7×10^−5; N = 63), and survives canonical joint control for quality, sampling, mass, inclination error, and first-order pressure support (r = 0.30, p = 0.02). All significant results pass a Benjamini-Hochberg correction over the declared 27-test family.
Three limits temper that survival: it is not significant under rank-based control over the widest proxy set; it resides in faint dwarfs independent surveys do not reach; and after mass control it is shared across the mass-size manifold. Pressure support brackets the interpretation -- isotropic drift correction absorbs a quarter of the amplitude, while a Jeans treatment overcorrects resolved cases -- leaving the physical origin undetermined. The audit's product is the extraction limit: claimed corrections must clear the 0.106 dex per-galaxy nuisance floor, a mass-only baseline, and data-quality stratification.
Modified Newtonian Dynamics (MOND) generally resolves the need for dark matter in galaxy rotation curves introducing a single new constant of acceleration a(0). It is well known that increasing a(0) by a factor of a few can alleviate the residual mass discrepancies that MOND leaves in galaxy clusters.
Within a parameter-free Machian interpretation of MOND, in which a(0) ∼ GM(u)/R(u)^2 arises from the scalar sum of inverse-square distance gravitational mass contributions in the universe, we promote a(0) to a variable influenced by mass external to a locally enclosed region in the spherically symmetric case.
Instead of a boost of a(0) in terms of gravitational potentials as in EMOND, we show that a boost in terms of this directionless inverse-square field roughly amounts to the boost needed to accommodate the mass discrepancies of MOND in galaxy clusters. We conclude by beginning to generalize the proposed formulation beyond spherical symmetry.
A hydrogen gas cloud, called Cloud-9, that has been observed in deep space in the radio wave frequency, which cannot be seen in the visible light spectrum provides a way to distinguish between different dark matter hypotheses and while the paper below doesn't consider it, between modified gravity theories and dark matter hypotheses.
Starless gas clouds provide a new way to test gravitational dynamics and this is just the first examination of many to come.
Between cold dark matter and self-interacting dark matter, the observations strongly favor self-interacting dark matter, although neither hypothesis is a great fit.
Recently, the Five-hundred-meter Aperture Spherical Telescope discovered a gas-rich hydrogen cloud near M94 in the 21cm band. Lacking an optical counterpart, this object, dubbed Cloud-9, has been identified as a compelling Reionization Limited H Cloud (RELHIC). RELHICs provide exceptionally clean laboratories for probing dark matter, free from the baryonic complexities associated with star formation and feedback.
We show that the observed hydrogen column density profile of Cloud-9 is consistent with a gas cloud embedded in either a cuspy halo predicted by the standard cold dark matter (CDM) model or a cored halo produced by self-interacting dark matter (SIDM).
In both cases, the halo must have an unusually diffuse central density. The best-fitting CDM halo lies around 7σ below the cosmological concentration--mass relation, whereas SIDM core-forming halos reduce the tension to only around 3σ.
We further identify Cloud-9 analogs in the Concerto suite of cosmological zoom-in simulations with velocity-dependent SIDM, demonstrating that RELHICs provide a promising new probe of dark matter self-interactions.
The Baryonic Tully-Fisher relation (BTFR) is one of the tightest scaling relations for disk galaxies in the local Universe, and therefore is an important tool for studying the fomation and evolution of galaxies. . . .
A random forest classifier is used to investigate the origin of the outlier component. We find that low signal significance and inaccurate inclinations are the key factors that contribute to the outlier population, indicating that observational effects are the dominant origin.
Evolutionary trends are examined in three different redshift bins. Both the slope and zero point show consistency within 1-σ uncertainty in the two low redshift bins, indicating no significant evolution.
A glueball is a strong force bound system without any valence quarks that binds gluons, the carrier bosons of the strong force instead of quarks. A well-established resonance seen in experiments at discovery level significance since 2011, whose internal structure is unclear, is shown in a new preprint to be consistent with a nearly pure pseudoscalar glueball state (i.e. a spin-0, electromagnetically neutral boson with odd parity and no valence quarks).
The properties of glueballs (which depend primarily on a single experimentally measured physical constant, the strong force coupling constant), have been calculated from the very early days of quantum chromodynamics (QCD), which is the Standard Model theory of the strong force. And, there are only a modest number of theoretically possible glueballs. This resonance is on the low end of, but consistent with, the mass predicted for a pseudoscalar glueball.
But distinguishing a glueball resonance from a non-glueball resonance is difficult, and because glueballs are always bosons and share quantum numbers with bosons that include valence quarks, they have a natural tendency to blend with similar bosons making a mere glueball component in a resonance rather than a pure glueball, something that is probably common in reality.
There have only been a few resonances that have been convincingly interpreted as a near pure glueball, and this is one of them. But the fact that this is an analysis of a lone author which has not yet been published in a peer reviewed journal bodes caution in accepting this conclusion as definitive. But to the extent that this analysis holds up, it confirms an important qualitative prediction of QCD (i.e. the existence of glueballs with various quantum numbers that have their predicted masses).
In this work, we take the X(2370) with J^PC = 0−+ as a glueball consists of three valence gluons, and construct a six-quark current based on rigorous current-field duality to obtain the glueball-quark Lagrangian. Then we perform Fierz transformation to bosonize the quark current into a series of three pseudoscalar mesons. At last, we obtain ratios among the partial decay widths of the glueball to three pseudoscalar mesons in a model-independent way, which are compatible with the experimental data from the BESIII Collaboration and support assigning the X(2370) as a glueball.
Observations of high energy out space sourced neutrinos from an Earth based neutrino detector further constrain the parameter space of possible sterile neutrinos in a way that the LHC, reactor experiments, and an Antarctica based cosmic ray observatory do not.
While the sterile neutrino mass range probed (1-100 TeV) is vastly greater than the active neutrino mass range, this is a sterile neutrino mass range frequently considered in see saw neutrino mass models, so it is relevant for discriminating between hypotheses.
The money chart, below, is a bit difficult to explain, but the key point is that it adds new constraints that rule out sterile neutrinos with certain properties with masses ca. 12-120 TeV, that other experiments can't probe.
We investigate the sensitivity of the Pierre Auger Observatory to physics beyond the Standard Model arising from magnetic-moment-induced transitions between active and heavy sterile neutrinos. Such dipole portal interactions can enhance neutrino-nucleon cross sections above a kinematic threshold set by the sterile neutrino mass, leading to observable modifications of neutrino detection rates at ultrahigh energies (UHE).
We estimate the impact of these interactions on both down-going and Earth-skimming neutrino detection channels, the contrasting responses of which enable discrimination between an enhanced neutrino flux and a modified interaction cross section. Using the non-observation of UHE neutrino candidates, we derive neutrino-flux-dependent constraints with 90% confidence-level on the transition magnetic moment for sterile neutrino masses in the range 1 TeV-100 TeV. Under the assumed flux scenarios, the resulting flavor-independent limits extend existing bounds into previously unexplored parameter space.