Another Dark Matter v. MOND Comparison Paper

MOND still looks respectable good compared to various dark matter particle models in the SPARC database of galaxies.

The observed rotation velocities of spiral galaxies at large scales exceed those predicted by their baryonic components, motivating the need for dark matter (DM) or Modified Newtonian Dynamics (MOND). We fit the rotation curves of 147 late-type galaxies from the SPARC database, using a suite of models including Cold Dark Matter (CDM) models with and without baryonic feedback, Warm DM, Fuzzy DM, and MOND. We also combine SPARC kinematics with weak-lensing data to extend the mean rotation curves to ~1 Mpc. On a galaxy-by-galaxy basis, the inner SPARC rotation curves marginally favour CDM models with baryonic feedback, although accounting for the uncertainties in distances and inclinations increases the degeneracy among DM-based models and MOND. All DM models predict host halo masses larger than abundance-matching expectations, with only the CDM model with baryonic feedback reducing the scatter around the mean luminosity-halo mass relation. MOND is able to reproduce the flatness of the mean galactic rotation curves on scales up to 1 Mpc, providing stellar mass-to-light ratios within observational uncertainties. In contrast, all DM models, without the contribution of mass external to the bound halo, struggle to explain the flat rotation curves. The inclusion of the current weak-lensing data tends to favour MOND over DM models, at least at the largest scales. Future observations from BIG-SPARC, the Square Kilometre Array, and most importantly, upcoming weak-lensing surveys such as EUCLID and Rubin will provide more stringent and independent tests of these competing frameworks.

Amy Smith, et al., "Dark Matter and MOND successes and degeneracies in reproducing SPARC rotation curves and weak lensing data" arXiv:2610.33157 (October 23, 2026) (Accepted at MNRAS).

Triton Station also has a new post comparing dark matter particle theories and MOND. The summary is as follows:

How Significant Was The LZ Event?

A dark matter detection experiment, Lux Zepplin (LZ) has seen one event that could be dark matter. 

How likely is it that it could just be an extreme outlier of the background?

A new preprint attempts to quantify that better than the original note reporting the detection. The paper doesn't reach a final conclusion which is highly model dependent, but points the way to determining if the LZ event could be just a fluke of ordinary physics rather than a singular dark matter detection, and points the way to how to clarify the matter.

This is mandatory reading for anyone proposing a beyond the Standard Model explanation of this result.

We reconstruct the continuum electron-recoil contribution to the LZ background expectation from the collaboration's released simulation configuration. The released model specifies a definite response tail, but the published calibration information supplies no bound on how far the physical tail may depart from it at the probabilities the expectation depends on. 

Distributions reproducing the executable model's mean, variance, and standardised skewness exactly, and its event-conditioned 10, 50, and 90% (N_e) quantiles to about one per cent, differ in the relevant tail probability by more than five orders of magnitude. 

The ladder is short: a tail agreeing with that central characterisation to 0.14% in the quantiles lifts the electron-recoil contribution out of the negligible range, and one agreeing to 0.47% makes it comparable to the entire background quoted for the comparison region. We go on to identify the measurements that would settle it.

Triparno Bandyopadhyay, Rajarajeswari Ramasamy, Nishitha TP, "The Electron-Recoil Response Tail and the LZ High-Energy Event Background" arXiv:2610.27105 (October 19, 2026).

Thoughts On The Riemann Hypothesis

AI has purported to prove two new and improved versions of the quasi-Riemann hypothesis, as discussed at Quanta magazine and a Twitter thread discussing additional proofs (by humans) that flow from the new quasi-Riemann hypothesis proof.

What is the Riemann Hypothesis?

The Riemann hypothesis can be explained as follows (from the first link):

The Riemann hypothesis is about which values of s will make the zeta function equal zero.

But it is also about far more than how this particular function behaves. As Bernhard Riemann realized when he first made the conjecture in 1859, the function relates to patterns in the prime numbers — integers divisible only by 1 and themselves that many mathematicians call the “atoms of arithmetic.”

It’s long been known that as you move along the number line, the primes thin out. Riemann showed that exactly how the primes thin out is, in a sense, governed by the zeta function — in particular by the places where it equals zero.

It’s straightforward to prove that if s is a negative even number (−2, −4, −6, …), then ζ(s) = 0. These are called trivial zeros. The Riemann hypothesis says that the only other zeros of the zeta function, called nontrivial zeros, occur when s has a real part of 1/2. That is, they should all be located on a vertical line:

If any nontrivial zero were to be found somewhere away from that vertical line, it would imply that the primes must form an extremely surprising pattern, one that has never been observed to date.

Just narrowing the area where the nontrivial zeros can appear has had huge ramifications. Riemann himself proved that nontrivial zeros of the zeta function can only be found in a vertical strip between zero and 1. Then, in 1896, two mathematicians showed that zeros could not lie on the edges of the strip. As a direct consequence, they were able to prove an important result called the prime number theorem, a formula for how quickly, on average, the primes thin out.

If the Riemann hypothesis holds, then mathematicians can guarantee that any deviations from the average given by the prime number theorem will always be small.

Mathematicians have numerically verified(opens a new tab) that the first 12 trillion nontrivial zeros are on the 1/2 line. But they can’t be sure the hypothesis holds for all the zeros, and even one solitary outlier would land like an earthquake. As Enrico Bombieri(opens a new tab) wrote in the paper(opens a new tab) laying out the Millennium Prize formulation of the problem: “The failure of the Riemann hypothesis would create havoc in the distribution of prime numbers.”

The connection between the zeta function and the primes was known before Riemann. In 1737, Leonhard Euler showed that for any complex number s, the zeta function is equivalent to another function that can be written entirely in terms of primes:

This brings us to the quasi-Riemann hypothesis. Where the Riemann hypothesis posits that all the nontrivial zeros are on the vertical line at 1/2, the “quasi” version just asks one to prove that they are all contained in a vertical strip that’s narrower than the known strip between zero and 1. The narrower the strip, the more one can say about how the primes are distributed.

What did AI recently prove? 

OpenAI announced two different versions of their quasi-Riemann hypothesis proof. The first version, dated September 30, 2026(opens a new tab), claimed to show that all nontrivial zeros must be between 1/8 and 7/8, and was formally verified using the Lean programming language. The second version, which was completed almost a week later(opens a new tab) (and is not yet formally verified), claimed to prove a weaker result: that the zeros must have a real part between 1/12 and 11/12. But while the first paper is 199 pages long, the second weighs in at a comparatively modest 49 pages.

More background

The Euler version makes it more obvious, but the zeta function is undefined and at s=0, and approaches a limit of infinity close to s=0.

Even this simple explanation for a relatively simple hypothesis (all the good ones are) begs the question of what a complex exponent of an integer even means (and I won't try to explain that here). Suffice it is say that this isn't trivially intuitive in the way that an integer exponent is, and that it is less intuitive than a non-integer real exponent is.

Commentary on the AI proof

First off, consider that the new proofs are less impressive than they seem. We already knew that the real part of the exponent s in a zeta function zero has to be more than 0 and less than  1. We knew that in 1896, one hundred and thirty years ago. Narrowing that range to greater than 1/12 and less than 11/12, or greater than 1/8 and less than 7/8 improves on that result, but it isn't that Earth shaking of an improvement over the status quo.

Ideas for breaking down the Riemann Hypothesis into subparts

Next, lets break this down and consider some points that would help prove the overall Riemann hypothesis. Some of them may already have been proven. All of them must be true if the Riemann Hypothesis is correct, which numerical methods strongly suggest.

* It would be nice to prove that for any given value of the imaginary part of s that there is only one zero.

* It would be nice to prove that for any given value of the real part of s that there are either zero or an infinite number of zeros.

* It would be nice to prove that, to produce a zero, the real part of s must be a rational number (a subset of the real numbers).

* It would be nice to prove that, to produce a zero, the imaginary part of s must be a whole number (i.e. a positive, non-zero, integer), or failing that, that it must be a positive rational number, or in between, a positive rational number related by some rule to the rational number that is the real part of s, or better still, a whole number related by some rule to the rational number that is the real part of s.

* It would be nice to prove that the imaginary part of s must be an odd number to produce a zero.

* It would be nice to prove that all values of s with a real part of 1/2 and an imaginary part which is a prime number of zeros. Keep in mind that the Riemann Hypothesis is an if and only if conjecture: it says that non-trivial zeros have a real part of 1/2 and an imaginary part that is prime, and it also says that there are no other non-trivial zeros. Proving the affirmative part standing alone would be a big deal, even without a proof that there are no other non-trivial zeros, but requires consideration of far fewer possibilities.

* Proof of the affirmative part of the Riemann Hypothesis would likely require that the term in the Euler infinite series definition of the zeta function where integer in the imaginary part of s is equal to the number that it is the exponent of is special somehow, because it cancels out all of the other terms of the infinite series (I don't think that a single term of either infinite series definitions of the zeta function can be zero by itself, but proving that would itself be a step).

* Proof of the negative part of the Riemann Hypothesis might start with a determination that the imaginary part of s can't produce a zero if it is even. 

* Proof of the negative part of the Riemann Hypothesis might establish that the imaginary part of s can't produce a zero if it has exactly two, or better yet, an even number, of prime factors.

* Proof the the negative part of the Riemann Hypothesis might establish that the imaginary part of s can't produce a zero if it has an odd number of prime factors greater than one.

* Proof of inability to produce a zero, in a given case, amounts to showing there are one or more terms of the infinite series that don't cancel out at that value.

* It would be nice to tie in the conclusion about trivial zeros of the zeta function to the conclusion about non-trivial zeros of the zeta function somehow.

Post Script

Of course, I'm not going to prove (or disprove) the Riemann Hypothesis. Complex analysis (i.e. the calculus of imaginary numbers) was my weakest subject as a math major in college, and I never formally studied number theory at all. 

And, I only scratch the surface of the most obvious ideas in a deeply reached and explored corner of mathematics.

But I had a long dentist appointment this morning and needed a distraction, so I thought about it then, and that's why I'm writing about it now.

A New Anomaly

There are four sets of valence quarks that produce kaons, two of which are charged and two of which are electromagnetically neutral: 

K⁺ (positive charge: up quark + anti-strange quark)

K⁻ (negative charge: anti-up quark + strange quark)

K⁰ (neutral: down quark + anti-strange quark)

K̄⁰ (neutral antiparticle: anti-down quark + strange quark)

In certain heavier atom collisions, there are more charged kaons than expected relative to the number of neutral kaons observed, which means that there are more up quarks (and anti-up quarks) relative to down quarks (and anti-down quarks) than expected.

Isospin symmetry is the concept that particles with up quarks substituted for down quarks (and vice versa) are identical in strong force interactions (in part, due to their similar mass and the indifference of the strong force to electromagnetic or weak force charge).

For some reason, however, more charged kaons are seen in argon-scandium collisions and also in some other particle collisions. The paper below fails to come up with a good explanation for why this is the case and calls for further study. The introduction to the paper explains that:

This paper focuses on hadron–nucleus and nucleus–nucleus collisions at center-of-mass (cms) energies of the order of 10 GeV per nucleon pair. Such processes are governed by (mostly) non-perturbative strong interactions, and result in the production of a large number– tens, hundreds– of new particles in the final state (multiparticle production). 

Isospin symmetry (IS) which can be considered as a remnant of the QCD flavor symmetry between u and d quarks, remains an essential even if approximate feature of the production process. 

At energies equal (or higher) to those specified above, the bulk features of multiparticle production (inclusive spectra, total multiplicities, etc) are widely believed to obey IS up to a very good accuracy, of the order of 3−4%. Nevertheless, the simultaneous measurement of inclusive spectra and yields of charged (K+, K−) and neutral (K0 S) mesons reported by the NA61/SHINE experiment in central Ar+Sc collisions at √ sNN = 11.9 GeV [1] reveals an unexpectedly large IS violation (18 ±6% at kaon mid-rapidity). 

As will be discussed below, measurements from other experiments over a wide range of collision energy appear consistent with this observation. At the present moment (Oct., 2026), the origin of this effect remains unclear.

The paper and its abstract are as follows: 

The NA61/SHINE experiment at the CERN SPS reports an unexpectedly large excess in the inclusive production of charged over neutral kaons in 0-10% central Ar+Sc collisions at sNN‾‾‾‾√=8.8 and 11.9 GeV. This effect corresponds to an unexpectedly large violation of isospin symmetry, that cannot be explained by known mechanisms contained in the present theoretical models. 

The comparison of the NA61/SHINE results to data from other experiments reveals, within sizeable uncertainties, a consistent isospin symmetry-violating excess of charged kaon production in the energy regime 2.6<sNN‾‾‾‾√<200 GeV. At LHC energies (0.9<sNN‾‾‾‾√<13 TeV) the charged-over-neutral kaon ratio appears consistent with unity, but the uncertainties remain sizeable. 

A similar excess of charged over neutral kaon yields is observed by NA61/SHINE in minimum bias π−+C reactions at sNN‾‾‾‾√=17.3 and 25.7 GeV, also in disagreement with model predictions. 

No clear theoretical explanation of these phenomena has been provided so far. An unexpectedly large violation of isospin symmetry brings potential heavy consequences for our understanding of particle production, and calls for a concentrated experimental and theoretical effort.

Andrzej Rybicki for the NA61/SHINE Collaboration, "Unexpectedly large violation of isospin symmetry in nucleus-nucleus collisions at CERN SPS energies" arXiv:2610.23498 (October 16, 2026) (18th International Workshop on Meson Physics (MESON 2026), Kraków, Poland).

I'm personally confident that ultimately an explanation consistent with Standard Model physics will be found. But it is a fairly recent anomaly that hasn't gotten a lot of attention yet, so it deserves a post here.

Milgrom's Latest MOND Paper

Mordehai Milgrom, who invented MOND, has long been ambivalent about whether this is really a modification of gravity or a modification of inertia. In his latest paper, he considers the possibility that it could be both.

It is plausible that in a more fundamental theory of MOND both gravity and inertia will differ from their Newtonian versions. Such theories, if they embody the basic tenets of MOND, will share its primary predictions with existing theories, which modify either gravity or inertia. But they are expected to differ in their structure and in their secondary predictions. 

Here, I discuss families of nonrelativistic MOND theories that modify both the kinetic and the gravitational actions of Newtonian dynamics. Each family is spanned by one parameter 0≤η≤1, which is the scaling dimension of the deep-MOND limit of all terms in the action. Pure modified gravity (η=0) and pure modified inertia (η=1) are the end cases in each family. I speak of families, since the modified action terms themselves are not strictly specified, but are treated in rather general terms. 

These theories are artificial in that they are not based on a single unifying idea that dictates the modification of the two components. But they are still useful in pinpointing some idiosyncracies of such theories. 

For example, neither of the two modified terms, by itself, leads to MOND phenomenology; only their combined effect does. I show how the two combine to make some of the primary MOND predictions, such as asymptotic flatness of rotation curves, the mass-asymptotic-speed relation, and the deep-MOND, virial, mass-velocity-dispersion (M−σ) relation. 

Another idiosyncracy of such theories is the emergence of different interpolating functions in the kinetic equations of motion and in the gravitational field equations, each relevant under different circumstances, and neither of which have the standard deep-MOND limit. Such examples alert us to the wide range of theories that can lead to MOND phenomenology.

Mordehai Milgrom, "Mixed modified-gravity--modified-inertia MOND theories" arXiv:2610.21699 (October 15, 2026).

Gallium Non-Anomaly Confirmed

The Gallium Anomaly had been used to support the idea of sterile neutrinos. But it turns out that the anomaly was just a result of a flawed calculation of the Standard Model expectation. The correct calculation shows no anomaly in independent experimental measurements.

The Gallium Anomaly is the disagreement between the measured capture rate of neutrinos by 71Ga and the rate theoretically expected from the electron capture decay of 71Ge. The experimental measurements were performed with intense artificial sources. 

In the present work we consider the sun as a neutrino source that can be calibrated via the fundamental, standard-model neutrino-electron elastic scattering reaction in terrestrial detectors. The result is found to be not anomalous, with good agreement between the measured value of 66.1 ± 3.1 SNU from SAGE and Gallex/GNO, and the total measured source strengths of solar sources, 67.5 +1.4 −1.1 SNU. It may be concluded that neither the 71Ga charged-current cross section nor gallium experiment extraction and counting efficiencies account for the Gallium Anomaly.

Steven R. Elliott, R. G. Hamish Robertson, "Gallium Anomaly and Solar Neutrinos"arXiv:2610.22219 (October 15, 2026).

Another paper confirms again that muon g-2 doesn't show a discrepancy between theoretical predictions of it and experimental measurements of it at extreme precision. The muon g-2 anomaly was also due to a flawed calculation of the Standard Model expectation. 

Progress is also being made in the tau g-2 calculation, but the experimental measurements of tau g-2 are too imprecise to meaningfully compare them to the theoretical calculation.

More On MOND And Mach

More exploration of one possible "fundiMOND" explanation for why MOND/dark matter phenomena are observed appears in a new preprint. 

Mach's principle is the hypothesis that inertia is a consequence of the collective gravitational pull of everything in the Universe on matter, rather than just an assumption that goes into the Newton's laws of motion and modern derivations of them, without any mechanism or cause.

The physical origin of Modified Newtonian Dynamics (MOND), which predicts galaxy rotation curves via a single empirical acceleration constant a(0) without the need for dark matter, remains unknown. I propose a modified-inertia origin for both MOND's interpolating function and a(0) within a framework closely related to Gravitoelectromagnetism, the linearized limit of General Relativity. Following Sciama's model unifying gravity and inertia, which implements Mach's principle and the relativity of acceleration through gravitoelectric induction, I consider an idealized homogeneous universe undergoing constant Hubble expansion. 

I identify a(0) ∼ H(0)^2*R(u) ∼ c^2/R(u) with the relative recession acceleration of cosmic matter near the horizon, which dominates the cosmological contribution. I show that this scale enters local inertial dynamics only when the relative acceleration of the universe becomes anisotropic and the Rindler horizon is comparable to or larger than the cosmic Hubble horizon, at accelerations of order a(0) and below. 

By the simplest Ansatz for the observer's acceleration-dependent causal volume, accounting for the interplay between the cosmic and Rindler horizons, I derive MOND's simple interpolating function as a modified inertia law without the need to insert it by hand or make any further ad hoc adjustments. Physically, the region brought into causal connection ahead of the accelerating observer by the deformation of the cosmic horizon contributes less inertial drag than is lost from the region removed behind him by the Rindler horizon. This proof of concept motivates the possibility that MOND arises from large-scale linear inertial frame-dragging induced by the expanding universe within General Relativity.

Manuel Uruena Palomo, "Is MOND an effect of cosmic frame-dragging à la Mach?" arXiv:2610.09987 (October 7, 2026).

A previous paper from the same author was discussed here and has been accepted for publication in a peer reviewed journal (see that comments to that post).

AI Revolutionizes Math Research

The year 2026 will be remembered as the year that AI revolutionized mathematics research.

In August, AI made some real breakthroughs in some notable unsolved problems in mathematics, mostly involving disproof of conjectures by counterexample. But this week, Open AI published more than three hundred proofs of unsolved problems by various methods, that were significant although not quite as notable, across all major areas of mathematics on a single day (although a few of those proofs have been withdrawn or revised in response to comments).

Its single day results (rumored to be from an initial set of 400 problems), that probably took several months to put together and were just released all at once for drama. 

But its productivity on mathematical problems of this medium level of significance which are what the best human mathematics researchers might solve once every few years, rivals the productivity of the entire global mathematical research community over a time frame somewhere between many months and a few years.

The announcement this week leaves no doubt that AI will forever and profoundly change how mathematical research is done. We can expect a surge of mathematical breakthroughs for a few years as the backlog of AI solvable unsolved problems in mathematics are conquered and human mathematicians have to come up with new mathematics problems for humans and AI to solve together, in many cases probably building on the findings made in a new surge of proofs.

“If a human did this, it would be an instant Fields Medal, no questions asked.”

That’s how Alex Kontorovich, chair of the department of mathematics at Rutgers, responded to an A.I.-generated proof that OpenAI, the artificial intelligence giant, released on Tuesday.

And that single proof — worthy, in Dr. Kontorovich’s assessment on social media, of arguably the highest honor in the field of mathematics — was just one among more than 350 findings that the firm released that day, all at once.

Not all of them were quite so remarkable. But Martin Bridson, a mathematician at Oxford and the president of the Clay Mathematics Institute, which established the coveted Millennium Prize Problems, called OpenAI’s release “breathtaking.”

“Until very recently, it would have been impossible to imagine that the frontiers of mathematics could move so far in one day,” Dr. Bridson said.

If there had been any doubt that the leaps achieved by artificial intelligence this year would transform the discipline of mathematics, the tens of thousands of pages let loose on Tuesday have put that doubt to rest. The puzzles apparently conquered by OpenAI include crucial open questions in nearly every subfield of math, including algebra, number theory, theoretical computer science, mathematical logic and topology.

None of the proofs fully resolve any of the five remaining Millennium Prize Problems, which were designated at the turn of the century as a way of celebrating mathematics and its vast frontier of mysteries. But the trove of findings seemed to include results that make tangential or related progress on all of them. Perhaps the most significant result — the one Dr. Kontorovich was responding to — was a proof of the “quasi-Riemann hypothesis,” a conjecture related to the best known of the Millennium problems, the Riemann hypothesis, and a possible steppingstone of sorts to its resolution.

Ken Ono, a professor at the University of Virginia and the founding mathematician at Axiom Math, a math-focused artificial intelligence firm, wasn’t sure whether the quasi-Riemann solution would be a springboard for solving the original hypothesis. But he said that, as is expected with the original Riemann hypothesis, an encyclopedia of consequences would flow from this result, providing rich fodder for future breakthroughs. . . .

(As of Thursday, OpenAI had made a number of updates to the public online repository; withdrawing three papers and making fixes to several others. A spokeswoman said: “Where errors are identified, we will work to correct them promptly and withdraw papers if no fixes can be found. As with other research manuscripts, this is an iterative process.”) . . . .

For Bryna Kra, a mathematician at Northwestern University, problem No. 145 on the list was of great interest — “the Rokhlin problem on mixing implying higher order mixing,” which answers a question from the 1940s. “The writing, however, makes it impossible to understand,” said Dr. Kra, former president of the American Mathematical Society, who is among a group of mathematicians who are proactively working to chart a course for the field through this period of “uncertainty and seismic change,” as she described it. . . .

The French mathematician Jean-Pierre Serre, an emeritus professor at the Collège de France in Paris — who has won two of math’s top prizes, the Fields Medal and the Abel Prize, and celebrated his 100th birthday last month — was naturally attracted to finding No. 46 in OpenAI’s list, which solves positively a conjecture he made almost 70 years ago.

But Dr. Serre is conflicted about doing math with A.I. He uses the technology for things like references, and, with the help of friends, for chasing down hunches about errors. “Mathematicians take pleasure in doing maths in two different ways: learning and finding new things,” Dr. Serre said. “Hence a conflict: A.I. increases the first pleasure and lowers the second one. The problem is it may lower the pleasure too much; that is especially serious for young mathematicians.”

From the New York Times.

More analysis from Woit (a math professor at Columbia who blogs about and researches math, particle physics, and academic life) can be found here and here. Reacts from others are compiled here.

3.3 Sigma Support For Normal Neutrino Mass Ordering

A combined analysis of multiple neutrino experiments strongly favors a normal rather than inverted ordering of the neutrino masses at the 3.3 sigma level, echoing the preference from almost all previous observational indications including JUNO's new most precise measurement of some neutrino oscillation parameters.

We present a combined analysis of the latest publicly available atmospheric neutrino data from Super-Kamiokande including all data-taking stages previous to the gadolinium phase, IceCube-DeepCore, and the six-detection-unit configuration of KM3NeT/ORCA. Our fit uses all event samples simultaneously and treats the systematic uncertainties shared among experiments as fully correlated, while detector-response uncertainties are modeled independently for each experiment. 

The combined data constrain the atmospheric oscillation parameters to Δm(31)^2 = 2.44 +0.06 −0.04 × 10^−3 eV^2 and sin^2(θ23) = 0.52 +0.03 −0.04, with a precision of 2.2% and 6.1%, respectively, which is competitive with current accelerator-based measurements, and independently constrain the CP-violating phase to δCP = 1.30 +0.24 −0.28 π. 

Finally, comparing the orderings of the neutrino mass spectrum, we find a preference for the normal ordering with Δχ2 = 11.0; further calibrated with pseudoexperiments, we exclude the inverted ordering at 99.95% confidence level (3.3σ).

Miaochen Jin, et al., "Evidence for Normal Neutrino Ordering with Combined Atmospheric Neutrino Experiments" arXiv:2610.12208 (October 8, 2026).

Inferred Dark Matter Distribution Interpreted As Non-Equilibrium

Honestly, this is a plausible interpretation under any model. But, of course, the predisposition is to treat any deviation from the LambdaCDM model as a non-equilibrium system, rather than a flaw in the model.

We present a combined strong and weak gravitational lensing mass model of the massive merging galaxy cluster Abell 2744 (z = 0.308). The mass reconstruction combines strong-lensing constraints in the cluster core with weak-lensing measurements derived from deep imaging with the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST), enabling a reconstruction of the projected mass distribution from the core to the cluster outskirts. 

Using the resulting mass map, we identify cluster substructures and construct the subhalo mass function (SHMF) for Abell 2744. To interpret the observed substructure population, we apply identical detection methods to projected mass maps of massive galaxy clusters from the BAryons and HAloes of MAssive Systems (BAHAMAS) simulations. We observe a systematic excess of detected substructures in Abell 2744 compared to BAHAMAS. 

We interpret this excess as likely reflecting Abell 2744's exceptionally disturbed dynamical state, characterised by complex ongoing mergers, rather than tension with ΛCold Dark Matter (ΛCDM) or self-interacting dark matter (SIDM) predictions. Although confirming this interpretation will require extending the analysis to a larger sample of clusters spanning a range of dynamical states.

Nency R. Patel, et al.,"The BUFFALO Survey : The Subhalo Mass Function for Abell 2744 with Strong+Weak Gravitational Lensing" arXiv:2610.08919 (October 6, 2026).

Nobel Prize In Physics (2026) Announced

This year's Nobel Prize in physics was awarded for the relatively uncontroversial first discovery in 2013 of high energy neutrinos from space at the IceCube Neutrino Observatory that Francis Halzen spearheaded.

Francis Halzen was awarded the Nobel Prize in Physics on Tuesday for pioneering a telescope that paved the way for a new kind of astronomy. Scientists used this telescope, embedded deep in the ice at the South Pole, to detect ghostly particles known as neutrinos whizzing in at high energies from the far reaches of the universe.

“It’s a way of bringing us information about distant cosmic sources, which we are unable to acquire in other ways,” Mark Pearce, chair of the Nobel Committee for Physics, said at the prize announcement. In a statement following the announcement, he added that Dr. Halzen had “provided us with a fantastic instrument.”

Dr. Halzen conceptualized the IceCube Neutrino Observatory in the late 1980s as a way to observe the natural particle accelerators of the cosmos, such as supermassive black holes. These objects generate neutrinos at far higher energies than what can be produced on Earth.

The IceCube team, which today consists of more than 400 scientists around the world, completed construction of the telescope in 2011 and announced the discovery of high-energy neutrinos originating from far beyond our solar system two years later.

Aurelien Breeden, Katrina Miller, "Nobel Prize in Physics Is Awarded for the Advent of Neutrino Astronomy: The Nobel Committee honored Francis Halzen for his “vision and scientific leadership” of a telescope within the ice at the South Pole." New York Times (October 6, 2026).

A New Phenomenological Relationship Of Neutrino Masses

A new phenomenological relationship of the neutrino mass differences is interesting, and close matches to simple formulas like this one are rare.

In the standard three-flavor paradigm, two of the three neutrino mass-squared differences are independent. The existence of an additional dependence between these oscillation parameters was recently predicted on empirical grounds, taking the form

The JUNO Collaboration has now reported the most precise measurements to date of both Δm(21)^2 and Δm(31)^2. We demonstrate that this relation is in excellent agreement with the experimental data, which yield 1.4143 +0.0036 −0.0038 corresponding to a relative precision of 0.27%. Remarkably, the central value differs by less than 0.03 standard deviations from the prediction (2‾√≈1.4142). This provides strong experimental support for the novel constraint and thereby suggests an underlying symmetry governing the neutrino mass spectrum, rather than purely independent parameters.

I. Alikhanov, "Novel dependence between neutrino mass splittings strongly supported by initial JUNO results" arXiv:2610.06738 (October 5, 2026). This updates:

I. Alikhanov, "Another relation among the neutrino mass-squared differences?", arXiv:2601.18781 (January 26, 2026).

There are more comparisons along this line from a different author, Vernon Barger, at https://arxiv.org/html/2603.00810v2.

An Attempt To Compare MOND v. CDM

A preprint finds a draw between MOND and CDM, with each having issues in some domains.

The rotation curves of the 175 disk galaxies in the SPARC database are confronted, one by one and under identical conditions, with the two mass models that have dominated the missing-mass debate for four decades: a cold dark-matter halo of Navarro-Frenk-White (NFW) form, and Milgromian dynamics (MOND) with the acceleration constant held at a0=1.2×10^−10 m s^−2. Stellar mass-to-light ratios, distances and inclinations are treated as nuisance parameters with priors set by the 3.6 μm photometry and by the SPARC error budget, and every galaxy is sampled with a Markov-chain Monte Carlo. 

Three findings emerge. 

(i) Judged by the Bayesian information criterion, the free NFW halo is preferred in 96 galaxies and MOND in 79; once the halo is required to obey the ΛCDM concentration-mass relation the score becomes 86 to 89, i.e. a draw. The two theories fail in different places: MOND loses in massive, high-surface-brightness, bulge-dominated systems, NFW loses in slowly rising dwarf rotation curves. 

(ii) The NFW concentrations demanded by the data sit a median 0.24 dex below the ΛCDM expectation, and 53% of the sample lies more than 2σ below it, independent of halo mass; this is the core-cusp problem expressed as a scaling-relation offset rather than as a handful of anecdotes. 

(iii) The radial acceleration relation built from the full sample has a0= (1.13 ±0 .02) × 10^−10 m s^−2 and an observed scatter of 0.14 dex, yet the value of a0 preferred by individual galaxies spans more than a decade and correlates with surface brightness. The two statements are not in contradiction: the population-level relation is tight because it averages over exactly the degeneracies with mass-to-light ratio and distance that make a0 ill-determined galaxy by galaxy. The full table of fits is provided.

Mikhael Da Silva, "Cusps, cores, and one acceleration: dark-matter haloes versus modified dynamics across the full SPARC sample" arXiv:2610.05871 (October 5, 2026).

Gallium Anomaly Solved Without New Physics

The gallium anomaly as a 20% deviation from the expected number of neutrino interactions with a gallium atom, which was pointed at as evidence of sterile neutrinos. Only, it turns out that what was wrong was a 20% error in the calculation of the theoretically expected value by ignoring parts of the calculation that were too important to ignore. When calculated correctly, theory and experiment were consistent (in what has become, by now, a familiar pattern).

For more than 30 years, scientists have found that roughly 20% fewer electron neutrinos are captured by gallium nuclei than expected. Dubbed the gallium anomaly, this discrepancy has raised the possibility that something fundamental might be missing from our understanding of neutrinos or atomic nuclei. Now Matteo Cadeddu at the National Institute for Nuclear Physics (INFN) and the University of Cagliari, both in Italy, and his colleagues have shown that this mismatch may instead originate from the way the electron-neutrino capture rate is calculated [1]. . . . 

When an electron neutrino is captured by a gallium nucleus, an electron is created and a neutron turns into a proton, transforming gallium into germanium. In the standard capture-rate calculation, the behavior of the nucleus is treated separately from that of the neutrino and electron. This approximation simplifies the calculation but may overlook key aspects of the capture process. Cadeddu and his colleagues instead developed a more rigorous approach that fully accounts for the interplay between the nucleus, neutrino, and electron. Using this technique, the researchers predicted a capture rate about 20% lower than previous estimates, closely matching the experimental results. This finding offers a solution to the gallium anomaly without requiring new physics. It disfavors one of the previously leading explanations: the existence of so-called sterile neutrinos. . . . 

[1] M. Cadeddu, et al., "Possible solution to the gallium anomaly moving beyond the leptonic wave-function factoriziation," 137 Phys. Rev. Lett. 131805 (September 24, 2026). 

From here.

Are Neutrinos Really Massive? (And Top Quark Mass Technicalities)

Neutrino oscillation is the primary evidence for the conclusion that neutrinos have mass. And, this paradigm has been pretty successful so far (although, with six degrees of freedom, fitting the data isn't necessary too difficult). The short (five page) paper below makes the provocative argument that neutrino oscillation arises from the curvature of space-time rather than from massive neutrinos.

This would solve the problem of how neutrinos acquire mass, which is a major unsolved problem in physics, in an unexpected way: they don't. I'm skeptical, and this isn't a fully worked out idea that explains neutrino oscillation in full yet. But it is at least notable and deserves serious exploration by other researchers to see if this idea really has merit.

The Dirac equation in stationary curved spacetime implies that describing two-flavor neutrino oscillations requires treating the invariant mass and conserved energy of each propagating state distinctly, as gravity affects energy differently than mass. 

By re-analysing the publicly released KamLAND dataset, we show that modeling flavor states of massless neutrinos as two-level quantum states with energy-dependent level splitting, analogous to modified Jaynes-Cummings models, results in a higher-likelihood fit to the observed data than the standard massive-neutrino paradigm.

Golam Mortuza Hossain, Pushpit Kumar, "Neutrino Oscillations without Mass: A Re-analysis of KamLAND Data following the Dirac Equation in Curved Spacetime" arXiv:2609.39638 (September 30, 2026).

In other physics news, a preprint suggests corrections to the formula used to determine the top quark mass in one of the approaches used to do so (the introduction to the paper is also a good background discussion of the general issue addressed):

We calculate the three-loop O(αα2s) mixed QCD-EW corrections to the top quark mass and obtain the relationships between the pole (Mt) and MS bar (mt(μ)) masses at this order. 

In performing our calculation, we express the three-loop self-energies as a function of three-loop master integrals (MIs). These MIs are defined so as to solve a differential equation in ϵ-factorized form, allowing for their solution to be expressed as iterated integrals. We discuss the types of differential forms that we encounter, which include periods of elliptic curves, and their role in the final physical result. 

Using our results, we calculate the shift in mt(Mt) arising at this order. For Mt = 172.3 GeV, the shift is -216 MeV, which is comparable to the currently quoted experimental uncertainty.

Daniele Gaggero, Ciaran Williams, "O(αα2s) corrections to the Top Quark mass" arXiv:2609.40229 (September 30, 2026).

The Treaty of Kadesh

 

The Treaty of Kadesh signed around 1269 BCE is the oldest known peace treaty, and a new fragment of it found recently relates to the treatment of refugees.

The manga Red River portrays the Battle of Kadesh which occurred several years earlier and gave rise to it, and also alludes to some of its provisions (such as treating prisoners of war decently).

Do Galaxy Rotation Curves Decline Or Are They Indefinitely Flat?

Other studies have strongly suggested that galaxy rotation curves remain flat indefinitely for as far as they can be observed. This study claims that they decline in a Keplerian manner at the extremes of their outer portions.

Jeans-based measurements of the Milky Way (MW) rotation curve (RC) have revealed a declining outer RC. The interpretation, however, depends sensitively on the tracer selection, the tracer density profile, gradient terms in the Jeans equation, and non-axisymmetric perturbations in the outer disk. 

We present a more self-consistent Jeans analysis of the MW RC and reassess whether the outer decline remains after a revised treatment of the main Jeans terms and their associated systematic uncertainties, including those related to non-axisymmetric perturbations. We select a kinematically homogeneous disk tracer sample designed to retain stars on nearly circular disk orbits, removing only 12% of the original sample. We estimate the tracer density profile from the same stars used for the kinematic moments, rather than adopting an external scale length. 

We find that the tracer density profile is better described by a double exponential over the validated range 12.5 < R < 21 kpc. We also assess the main systematic uncertainties associated with the fiducial Jeans equation terms, including the often neglected cross term, and account for different rotational velocities in the outer disk substructures. The derived RC remains nearly flat in the inner disk and declines at large radii. Over the adopted outer interval, R≳16kpc, the RC slope is consistent with a Keplerian decline even after accounting for the systematic uncertainties. The corresponding mass modeling gives an extrapolated dynamical mass of 2.01 +0.10 −0.08 × 10^11M⊙.

Yongjun Jiao, Francois Hammer, Istiak Akib, Yanbin Yang, Haifeng Wang, "A Self-Consistent Jeans Analysis of the Milky Way Rotation Curve" arXiv:2609.30364 (September 24, 2026) (accepted by The Astrophysical Journal, September the 19th 2026).

What Is Fundamental In Physics?

This is a question and my answer from the Physics Forums (officially written at the graduate school level, but dumbed down since the question indicates that the person asking isn't actually that sophisticated and knowledgable. The question is in a block quote, but my answer is not, for ease of reading.

Wiktorius I said:

TL;DR: Does physics establish that mass, particles, and fields are fundamental, or could they be emergent properties of a deeper physical structure?

Are mass, particles, and fields fundamental physical entities, or could they be observable consequences of a deeper physical structure? I am particularly interested in what experimental evidence allows us to distinguish between these possibilities.They aren't necessarily fundamental, but we have no real idea what kind of deeper physical structure could cause what we see and there are no experiments or observations that are likely to take place in the next few decades that can tell us.

Generally, going as deep as we possibly can, we think of particles in the context of an effective field theory as local excitations of fields.

But, most popular accounts, because it is more intuitive to understand, talk in terms of particles, with fermions corresponding to what we think of as matter in a colloquial sense, and bosons corresponding to "force fields" for the fundamental forces of the Standard Model.

Generally speaking, the mass of particles (both fundamental and composite) is not understood as fundamental. Massive Standard Model fundamental particles like electrons, muons, tau leptons, and quarks and W bosons and Z bosons and the Higgs boson (with the probable exception of the neutrinos whose mechanism for acquiring mass isn't well understood at this point) get their mass from their interactions with the Higgs field. Massive composite particles (like protons and neutrons) get their mass from a combination of the masses of the fundamental Standard Model particles that they are made up of (to a small extent) and from the energy of the gluon fields that bind them together (to a great extent). But the sometimes elusive concept of mass-energy is something that is fundamental and conserved.

There is no real consensus over whether gravity is something that arises from the exchange of massless spin-2 gravitons (which are bosons) in a way analogous to the way that electromagnetism arises from the exchange of massless spin-1 photons, or whether gravity is a property of space-time itself which is either classical and smooth, or as in the quantum gravity approach of loop quantum gravity, in which case space-time itself is discrete at some ultra-fine scale.

There is no consensus on this because we don't have any observational tools sufficiently powerful to distinguish between the hypotheses, and because while the math behind classical general relativity is hard, we haven't cracked the math behind quantum gravity theories of various kinds outside some very specific isolated cases in theories that don't hold true for all circumstances and have internal mathematical issues with them that make quantum gravity theories in the general case intractable.

We don't have any well accepted theories that explain why the couple dozen plus experimentally measured physical constants of the Standard Model plus general relativity have the values that they do, although electroweak theory does establish that a few of the Standard Model physical constants are not actually mathematically independent of each other, so the number of independent degrees of freedom in the experimentally measured physical constants of the Standard Model is a few less than the number of experimentally measured physical constants (e.g. the electromagnetic coupling constant, weak force coupling constant, W boson mass, and Z boson mass are related to each other by a formula which has fewer than four independent degrees of freedom).

There are some theories out there that go part of the way, providing a road map for possible ways to explain more of the experimentally measured physical constants of the Standard Model and general relativity. But while these are bit more than speculative, none of them are established in a settled way that can secure a scientific consensus or anything close to that. Moreover, as impressive as our scientific methods are, imprecision in measuring some of these experimentally measured physical constants limits the degree to which we can distinguish one explanation for their values from another. Many key physical constants are measured only to percent or part per thousand levels.

But the failure of scientists so far to find any meaningful deviations from the Standard Model in particle accelerator experiments and other terrestrial tests of it (like ultra-precise measurements of the anomalous magnetic moment of the muon) profoundly constrains any alternatives that would predict anything experimentally different from what the Standard Model predicts.

I can't recall ever meeting a physicist who thinks that there isn't some deeper theory that could explain why those physical constants have the values that they do. But most physicists, having seen the parade of physicists before them who have failed to find that deeper theory, are content to not go looking for it very seriously.

As a practical matter, even if you found the deeper theory that explained why most of those physical constants have the values that they do, it wouldn't necessary change much for most physicists, because we've already measured those physical constants to high precision in most of the cases where precise values are important to precise calculations. Having the deeper theory might allow you to assign more precise values to the physical constants whose values are hardest to measure, which would be a helpful thing on the margins as a practical matter and very personally satisfying, but that might be just about it.

Of course, if we knew why those physical constants had the values that they do, we would probably also rule out all sorts of beyond the Standard Model theories and models in a way that would be more satisfying than the way that we do now. But it wouldn't have many very practical consequences.

There are a variety of reasons why the most naively obvious alternative to the list of Standard Model particles being fundamental, which would be that they are composite particles of a smaller number of more fundamental particles (generically called preons), is unlikely to be an explanation. The reasons are a bit technical (e.g. the binding energy necessary for this to be the case is too great to be consistent with the hypothesis), but the consensus is that this is pretty much a dead end.

String theory, at first, seemed to be another path to a more fundamental explanation of the laws of nature than the Standard Model plus general relativity (which aren't themselves compatible with each other which implies that one or the other or both aren't truly fundamental) but this research agenda in the many decades since it was first introduced has turned out to be a quagmire that even many of its leading theorists don't claim is an accurate description of the world we actually live in, even though the things we learned along the way investigating it may have value.

So, while our core theories, the Standard Model and general relativity, probably aren't the most fundamental and complete explanations of the laws of nature that are possible, we really have no solid leads on alternatives.

Perhaps the most promising area where we might gain a better understanding is from astronomy where ill-understood concepts summarized as dark matter and dark energy might be better understood with more observational astronomy evidence. But we are far from reaching a consensus understanding of them, and are less confident about the baseline explanation of them called Lambda CDM (for cold dark matter) theory now than we have been since Lambda CDM was formulated.

The prospects for something more fundamental didn't always seem so bleak. In the late 1980s and early 1990s, a group of theories called "supersymmetry" and their gravitational extension, "supergravity" looked very promising. It would have explained many of the fundamental constants in an overall framework (although not all of them), it would have provided a path to unifying the Standard Model coupling constants at higher energies into a single force, it would have provided a candidate for dark matter particles that was sufficient to fit the astronomy and particle physics data available at the time, there was no evidence that the cosmological constant wasn't constant, it would have provided a bridge between the Standard Model and string theory, and a path to a workable theory of quantum gravity.

But bit by bit, that fell apart. Supersymmetry predicted particles with well defined properties, but when particle collider scientists looked for those predicted particles they weren't were they were assumed to be. Better data showed that the Standard Model coupling constants weren't on a path to converging at high energies. Better astronomy observations found that dark matter phenomena behaved differently than it would have if the supersymmetry candidates were what explained it. Better astronomy observations found that the cosmological constant might not be constant after all. The discovery that neutrinos had mass complicated the situation and the failure to detect neutrinoless beta decay complicated one of the most elegant explanations of neutrino mass that might fit better into the supersymmetry/string theory framework. The math necessary for string theory and quantum gravity turned out to be much more problematic than early researchers in these fields had hoped or expected at a very fundamental level. Strong experimentally confirmed anomalies that would deviate from the Standard Model to prove that supersymmetry was correct, instead failed to materialize. The experimental anomalies that seemed to potentially support supersymmetry went away as theoretical predictions and experimental measurements grew more precise.

Supersymmetry isn't definitively ruled out yet, but any version of it that is discovered won't solve the problems that a large share of the physics community hoped and believed that it would in the late 1980s and early 1990s, before they had enough experimental data and mathematical understanding to realize that their beautiful solution to all of the unsolved problems in fundamental physics with a deeper theory wasn't going to hold together.

A generation or two later, we have bits and pieces of ideas - MOND, entropic gravity, axion-like ultralight dark matter particles, Koide's rule and extrapolations of it, multiple Higgs doublet theories, see saw theories of neutrino mass, and more. There are many more partial theories to explain one little thing that surfaced as an anomaly or possibility for a while that were later ruled out. But we have no real solid agenda for developing a deeper theory.

Who knows?

Maybe we're just a genius or three away from ending a period of non-consensus and confusion about a way forward and finding the deeper theories we need to explain the outstanding unsolved problems of fundamental physics. But I'm not that genius and there aren't a lot of good candidates among living physicists today for people who could be that genius.

POST SCRIPT (not in the original post):

It is notable that MOND and Koide's rule, two of the most successful enduring beyond the Standard Model theories, albeit both phenomenological only, both date to the early 1980s, before supersymmetry and string theory had become dominant trends in fundamental physics.

Neutrino physics

Neutrino mass was first discovered in 1998. This finding was replicated and confirmed in 2001. In 2015 Nobel prizes were awarded for the discovery that neutrinos are massive. Experimental determination of some of the parameters of neutrino oscillation (such as the CP violating phase) is still very crude and the absolute neutrino masses are still also not tightly established.

Supersymmetry and string theory advocates tend to strongly favor Majorana mass for neutrinos. The absolute masses of the neutrinos are still not known, only their mass differences. But there are strong hints from cosmology and from the magnitude of the mass differences, that neutrino masses are so small that we wouldn't expect to have observed definitive neutrinoless beta decay signals that would be proof of Majorana mass in neutrinos yet even if that was the source of neutrino mass. I personally find the hypothesis that neutrinos are their own antiparticles to be highly unlikely given that the main reason that they were hypothesized in the first place was to provide particle-antiparticle balance that conserves lepton number. There is a good chance that the bounds on absolute neutrino mass and the non-discovery of neutrinoless double beta decay will exclude a vanilla version of the Majorana mass hypothesis for neutrinos in my lifetime.

This said, I'm also not very impressed with see saw models, in which neutrinos have a Dirac mass arising from oscillations with one to three otherwise undetectable right handed neutrinos that are much more massive than their Standard Model active neutrino counterparts. 

The most plausible alternatives that I imagine, with only thin support from academic research, are that neutrinos either acquire their mass through a combination of their self-interactions via the weak force and their interactions with W bosons more generally, or acquire their mass through a second neutral scalar boson analogous to the Higgs boson.

More generally, I suspect that the role of the W boson in imparting mass to fundamental particles is underrated relative to the rule of the Higgs boson in doing so.

Higgs physics

The Higgs boson was discovered in 2012, although it was predicted about forty years earlier and efforts continue at the Large Hadron Collider (LHC), and in reanalysis of Tevatron collider data, to confirm that its properties are actually fully consistent with the Standard Model Higgs boson predicted in the early 1970s (so far no experimental data disproves this hypothesis and the extent to which it could deviate from that hypothesis is heavily constrained by the data that we do have). The measured mass of the Higgs boson according to the Particle Data Group, which is 125.11  ± 0.11 GeV/c², significantly constrains that parameter space of many supersymmetry (a.k.a. SUSY) theories.

One largely back burner issue is that a global electroweak fit would favor a Higgs boson mass of 90 + 21 -18 GeV/c², which is consistent at the two sigma level with the measured Higgs boson mass, but has a best fit value 1.7 sigma below the measured value which is still a bit puzzling.

There are exclusions of additional Higgs bosons (neutral, charged) proposed by some beyond the Standard Model theories, which the Particle Data Group also underplays, but which are indeed not quite as insurmountable as the exclusions for supersymmetric particles.

Supersymmetry

While supersymmetry papers are still being published, this line of beyond the Standard Model physics inquiry has greatly fallen out of favor from its heyday. A large share of physicists expected it to be discovered at the LHC but that didn't happen.

The Particle Data Group has a full page of supersymmetry exclusions from experiments, which in my humble opinion is too conservative. But it is a difficult set of experimental data points to present because many of the exclusions of model dependent. The three linked review articles on that page, however, are helpful.

The main reasons that supersymmetric particles are disfavored as dark matter candidates (called WIMPs) now are that: 

(1) direct dark matter detection experiments (such as Lux-Zepplin which detected a single first candidate for a direct dark matter detection signal earlier this month mostly like with a mass of about 1 TeV/c² which is six times the top quark mass and four times the mass of a uranium atom) imply a far smaller cross-section of interaction that the cross-section of interaction predicted by supersymmetry theories;

(2) galaxy dynamics (particularly the core-cusp problem) disfavor a dark matter candidate in the 1 TeV/c² or more mass range (even though plenty of preprints hypothesizing that the LZ candidate is a WIMP are out there) and really favor dark matter particle candidates in the 10 keV/c² or less mass range; and

(3) particle collider bounds on the minimum mass of supersymmetric particles that could plausibly be dark matter candidates are generally in the hundreds of GeV/c² or more range.

The consistency of the experimentally measured value of the anomalous magnetic moment of the muon (muon g-2) and the Standard Model predicted value of that quantity, strongly disfavors the existence of supersymmetry below very high energies. 

Population Replacement In Pre-Columbian Columbia

UPDATE: I previously blogged this same paper closer to when it came out in 2025.

The "old world" is full of examples of hunter-gatherers being demographically replaced by farmers. The pre-Columbian New World was no different. The paper below explores a specific example of this happening in what is now the country of Columbia around 0 CE. In the "old world" this generally happened at the time that the Neolithic Revolution reached a region, and sometimes again when a civilization transitioned to the Bronze Age.

Also, to be clear, the extinct population is not outside the overall range of New World genetic diversity, it just doesn't correspond to any particular population that survived to the present that had been previously sampled. As the ancestry model chart below illustrates, it is within the range of South American specific ancestry.

Geographically, however, the location is notable. The modern DNA samples sometimes described as having Papuan affinity come from an area in the Amazon more or less due south of the highlands areas where the deceased subjects in this study, shown in the map below, were found. 

It is so geographically close, indeed, that the absence of any Papuan-like DNA in the hunter-gatherer samples in this study is itself notable, and tends to contradict the hypothesis that Papuan-like DNA seen in relict populations of living subjects nearby has a source older than the main New World founder population of ca. 14,000 years ago. I summed up a lot of the Paleo-Asian DNA in the New World discussion in a 2021 post, although I have made more posts since then on the subject.

Genetic studies on Native American populations have transformed our understanding of the demographic history of the Americas. However, a region that has not been investigated through ancient genomics so far is Colombia, the entry point into South America. Here, we report genome-wide data of 21 individuals from the Bogotá Altiplano in Colombia between 6000 and 500 years ago. 

We reveal that preceramic hunter-gatherers represent a previously unknown basal lineage that derives from the initial South American radiation. These hunter-gatherers do not carry differential affinity to ancient North American groups nor contribute genetically to ancient or present-day South American populations. 

By 2000 years ago, the local genetic ancestry is replaced by populations from Central America associated with the Herrera ceramic complex and survives through the Muisca period despite major cultural changes. These ancient Altiplano individuals show higher affinities to Chibchan speakers from the Isthmus of Panama than to Indigenous Colombians, suggesting a dilution of the Chibchan-related ancestry through subsequent dispersal events.

Krettek, K. L., Casas-Vargas, A., Mas-Sandoval, A., & Posth, C. "A 6000-year-long genomic transect from the Bogotá Altiplano reveals multiple genetic shifts in the demographic history of Colombia." 11(22) Science Advances (May 28, 2025) (open access). https://www.science.org/doi/10.1126/sciadv.ads6284