The ABC Conjecture Has Probably Not Been Proven

Woit reports that a claimed proof of the abc conjecture, a major unproven conjecture in the sub-field of mathematics called number theory (the same sub-field of mathematics that includes Fermat's Last Theorem, which has been proven) is probably flawed:

James Douglas Boyd has recently spent a lot of time interacting with Mochizuki and others at RIMS working in anabelian geometry. Material from interviews he conducted are available here (Mochizuki on IUT) and here (on anabelian geometry at RIMS). He also has written a summary of IUT and of the basic problem with the abc proof. These include detailed comments on the issue pointed out by Scholze-Stix and why this is a significant problem for the proof. I’d be curious to hear from anyone who has looked at this closely about whether they agree with Boyd’s characterization of the situation.

There’s also a lot of material [about] the IUT ideas, independent of the problematic abc proof, and about what Mochizuki and others are now trying to do with these ideas.

What is the abc conjecture?

The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. It is stated in terms of three positive integers a,b and c (hence the name) that are relatively prime and satisfy a+b=c. The conjecture essentially states that the product of the distinct prime factors of abc cannot often be much smaller than c. A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its versions. Mathematician Dorian Goldfeld described the abc conjecture as "The most important unsolved problem in Diophantine analysis".

The abc conjecture originated as the outcome of attempts by Oesterlé and Masser to understand the Szpiro conjecture about elliptic curves, which involves more geometric structures in its statement than the abc conjecture. The abc conjecture was shown to be equivalent to the modified Szpiro's conjecture.

Various attempts to prove the abc conjecture have been made, but none have gained broad acceptance. Shinichi Mochizuki claimed to have a proof in 2012, but the conjecture is still regarded as unproven by the mainstream mathematical community.

There is no 690 GeV resonance

Once again, a long standing, but sub-five sigma "bump" in particle accelerator results turns out to be explained by better analysis of what the background expectation without the new predicted particle should look like, and not "new physics". The low significance bump is also suspiciously close to four times the top quark mass at that energy scale.

I full expect the search for the X17 boson to end the same way.

Sadly, these pet ideas are zombies that persist in preprints, experimental efforts, and published papers long after they should have been abandoned.

In a series of ∼30 papers starting in 1991, it has been claimed that the Higgs field should be heavier than its now-measured value. To reconcile this idea with reality, it was modified to the assertion that the Higgs field describes two physical degrees of freedom, one of which corresponds to a second Higgs particle with mass 690 GeV. Here I summarize the lack of theoretical and experimental evidence for these claims.

James M. Cline, "There is no 690 GeV resonance" arXiv:2509.20115 (September 24, 2025). 

The paper is only three pages, half of which contains 33 references and the first page's heading and abstract, so I'll take the liberty of reproducing the entire short and punchy paper here:

Recently Ref. [1] reiterated the claim, already made in Refs. [2–14], that the Higgs field has an excited state with mass 690 GeV. This appears to be a modification of an earlier idea [15–28], pursued by one of the same authors, that the Higgs mass could or should be above the perturbative unitarity limit ∼ 700 GeV, as heavy as 2 TeV, depending upon the year of publication. The theoretical motivation for this prediction was the claim [29, 30] that λϕ^4 is not trivial, as is usually believed, but rather has a radiatively generated spontaneous symmetric phase (as predicted by the Coleman-Weinberg one-loop potential), in which it is asymptotically free.1 

1 The triviality of ϕ^4 theory, long believed to be the case, was proven in Ref. [31].

It was also claimed that the vacuum expectation value (VEV) of the scalar field gets renormalized by a different factor Z(v) than the fluctuations around the VEV, Z(ϕ), so that the usual relation between the Higgs mass and the VEV is modified by a factor Z(ϕ)/Z(v) which must be determined by lattice simulations, and predicts m(h) = 760 ± 20 GeV [17]. 

With the experimental discovery of the Higgs with mass m(h) = 125GeV, one might have hoped for such claims to be put to rest, but a way to have one’s cake and eat it too was found. It somehow goes back to the aforementioned idea, that pure λϕ^4 theory has spontaneous symmetry breaking `a la Coleman-Weinberg, despite the usual reservations that the perturbative calculation leading to that result cannot be trusted. The authors argue that now there are two mass scales in the potential: one is m(h)^2, the curvature of the potential V at its minimum, and the other is M(H)^4 = ∆V, from the depth of the potential minimum, which was generated by radiative symmetry breaking. It is not clear why this extra scale should correspond to an additional propagating degree of freedom. 

In order for a single field to describe two degrees of freedom, the propagator must have two poles, which usually arises from a higher derivative action containing ghosts. In the present case, the authors claim that nonperturbative effects generate the propagator structure 

G= i/(p^2 − M(H)^2*A(p^2)) (1) 

where A is a function such that A(m(h)^2) = m(h)^2/M(H)^2 and A(M(H)^2) = 1. The detailed form of A(p) is not disclosed, so we are forced to guess.2 

2 Ref. [1] says that this behavior was verified on the lattice in Ref. [13], but that reference purports to show that the form of the inverse propagator is (p^2 − m(h)^2)f(p), where f(p) has the same properties as A(p) in Eq. (1). This is puzzling since f(p) corresponds to wave function renormalization, while A(p) is the self-energy. 

It cannot be linear in p^2 since that would give G = i/0; hence the next simplest analytic possibility is quartic, A = 1 + (p^4/M(H)^4)(M(H)^2/m(h)^2 − 1). With this choice, we find for m(h) ≪ M(H)

G ∼ = −iM(H)^2/((p^2 − M(H)^2)(p^2 − m(h)^2)),  (2) 

which has the wrong sign for the heavy degree of freedom. The heavy particle is a ghost, as expected from a theory with a higher-derivative Lagrangian. The theoretical motivations for the “resonance” (unaptly named, since it is supposed to be coming from an elementary Higgs field, not a composite particle) are problematic. 

Let us turn then to the experimental evidence, which the LHC collaborations must have been very excited to discover. In Ref. [12] the authors discerned a bump in the ATLAS search [32] for heavy resonances decaying to ZZ → 4ℓ at m(H) ∼700GeV. The authors note that H should be dominantly produced through the gluon-gluon fusion (ggF) process, with negligible production from vector boson fusion (VBF). Fig. 1 reproduces the main results from the two papers. The ATLAS ggF limit has a 2-σ excess at 662GeV, which receives no comment in the ATLAS paper, and only upper limits are quoted.

The CMS collaboration took note of Ref. [12]’s prediction of an excess in this channel in their later search [33]. They also reported no significant excess. 

Since the original suggestion [12], there have been an additional ten papers [1–10] by various combinations of the authors emphasizing the predicted excess, lest we should forget. None of them are referred to by the experimental collaborations. In fact, of the 44 citations to these papers, all but 11 are self-cites. The authors find an equally convincing bump in the H → hh channel, leading them to “spell out a definite experimental signature of this resonance that is clearly visible in various LHC data.” A Nobel prize is sure to follow.

Does The Weak Mixing Angle Minimize Magic?

"Magic" is a quantum mechanical property that roughly speaking quantifies the extent to which a quantum computer is more powerful than a conventional computer. 

The "weak mixing angle" is a physically measured quantity in electroweak unification theory, which treats the weak force and electromagnetism as having a common, unified origin and functional relationships to each other, in which three weak isospin fields and a weak hypercharge field are transformed into the photon and the W+, W-, and Z bosons. It quantifies what transformation from an idealized state in the theory is necessary to produce the world that we actually see.

It turns out that quantum magic appears to be minimized at very close to the weak mixing angle at the Z boson mass energy scale. Since the amount of magic at the Z boson mass energy scale can be calculated in the Standard Model, rather than merely measured experimentally, this potentially makes the weak mixing angle a derived constant rather than an experimentally measured fundamental constant. It is also suggestive of how the weak mixing angle arises at a fundamental level.

Qiaofeng Liu, Ian Low, Zhewei Yin, "A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model" arXiv:2509.18251 (September 22, 2025) (abstract presented as an image rather than cut and pasted, to preserve mathematical equation formatting).

In other news, we are about a decade away from fully describing the properties of the neutrino.

The Latest X17 Paper's Model Isn't Confidence Inspiring

Simply put, any protophobic boson makes no sense. Protons are composite objects, and there is no plausible reason for a fundamental boson to be "phobic" towards one kind of hadron produced by quarks and gluons, but not another. The authors' suggestion that such an explanation is "probable" is using a poor definition of that term.

The so-called X17 particle has been proposed in order to explain a very significant resonant behaviour (in both the angular separation and invariant mass) of e+e− pairs produced during a nuclear transition of excited 8Be, 4He and 12C nuclei. Fits to the corresponding data point, as most probable explanation, to a spin-1 object, which is protophobic and has a mass of approximately 16.7 MeV, which then makes the X17 potentially observable in Coherent Elastic neutrino (ν) Nucleus Scattering (CEνNS) at the European Spallation Source (ESS). 

By adopting as theoretical framework a minimal extension of the Standard Model (SM) with a generic U(1)′ gauge group mixing with the hypercharge one of the latter, which can naturally accommodate the X17 state compliant with all available measurements from a variety of experiments, we predict that CEνNS at the ESS will constitute an effective means to probe this hypothesis, even after allowing for the inevitable systematics associated to the performance of the planned detectors therein.

Joakim Cederkäll, et al., "Hunting the elusive X17 in CEνNS at the ESS" arXiv:2509.15121(September 18, 2025).

Do We Really Need Either Dark Matter Or Modified Gravity?

This article isn't hot off the presses, but was referenced in the comments at the Triton Station blog. I am highly skeptical of the conclusion that Newtonian physics without dark matter or modified gravity can explain the dynamics of the Milky Way galaxy adequately, contrary to a wealth of literature to the contrary.

Vertical stellar kinematics+density can be used to trace the dark matter distribution (or the equivalent phantom mass in a Modified Newtonian Dynamics (MOND) scenario) through the Jeans equations. 

In this paper, we want to improve this type of analysis by making use of the recent data of the 6D information from the Gaia DR3 survey in the anticenter and the Galactic poles to obtain the dynamical mass distribution near plane regions, including extended kinematics over a wide region of 8 kpc < R < 22 kpc, ∣z∣ < 3 kpc. 

Our conclusions are as follows: 

(i) the model of the spherical dark matter halos and the MOND model are compatible with the data; 

(ii) the model of the disky matter (with density proportional to the gas density) is excluded; 

(iii) the total lack of dark matter (there is only visible matter) within Newtonian gravity is compatible with the data; for instance, at solar Galactocentric radius, we obtained Σ = 39 ± 18 M⊙ pc^−2 for z = 1.05 kpc, compatible with the expected value for visible matter alone of 44 M⊙ pc^−2, thus allowing zero dark matter. Similarly, for R > R⊙, z = 1.05 kpc, Σ = 28.7 ± 9.6, 23.0 ± 5.7, 16.9 ± 5.8, and 11.4 ± 6.6 M⊙ pc^−2, respectively, for R = 10, 13, 16, and 19 kpc, compatible with visible matter alone. 

Larger error bars in comparison with previous works are not due to worse data or a more awkward technique but to a stricter modeling of the stellar distribution.

Martín López-Corredoira, "Milky Way Dark Matter Distribution or MOND Test from Vertical Stellar Kinematics with Gaia DR3" 978 ApJ 45 (December 24, 2024) DOI 10.3847/1538-4357/ad94f5 (open access).

Where Does Language Complexity Evolve?

I'm not entirely sold on this article's conclusion about the circumstances in which language complexity evolves, at least not based upon the data presented, even though there is good evidence that large numbers of language learners tend to reduce grammatical complexity.

Polysynthetic languages are very common in the New World and just across the Beringian land bridge from it (which could also be connected to the Paleo-Siberian cases), suggesting that most instances of it could be derived from a common source creating a Founder effect. 

Also, while these languages are small and isolated now, this hasn't always been the case. Athabaskan-Eyak-Tlingit and Nahuatl, for example, historically were quite expansive and had lots of contact with other language families.

The second cluster is from Aboriginal Australians and Papuans who derive from the first wave of modern human migration Out of Africa and into Asia around the time of the Toba eruption. 

There is a third cluster in the Caucuses, involving just one of the language families there, which are associated with early migrants from the first wave of Fertile Crescent agriculture in the highlands of West Asia. 

There are apparently other instances in South Asia and East Asia.

A handful of major language expansions, none of which happened to be polysynthetic make up a huge share of all languages spoken today. These include the Indo-European language family, the Afro-Asiatic languages, the Bantu language family, the Dravidian languages, and the arguable Altaic language family. European and Chinese colonial empires further reduced the size of many languages (long after their features were well intact), for reasons unrelated to language complexity. 

There are polysynthetic or borderline polysynthetic languages listed in the following major language families: the Sino-Tibetan languages (seemingly all in the Tibetan-Burmo branch), the Austroasiatic languages (3 Munda languages in Northeast India), the Austronesian languages (5 borderline seemingly Formosan languages) 

If only a minority of pre-expansion languages were polysynthetic, it wouldn't be surprising if the main expanding languages didn't end up including them.

Significance

A global test reveals statistically robust support for the hypothesis that complex word forms are more likely to develop in isolated languages. Polysynthesis, where words are built from many units to convey complex meanings, is more likely to occur in smaller populations and less likely to occur with many languages in contact. By building a global database of polysynthetic languages and analyzing in a phylospatial framework, this study highlights the potential for macroevolutionary methods to test hypotheses about language evolution and contribute to long-standing debates in linguistics.

Abstract

Evolution of complexity in human languages has been vigorously debated, including the proposal that complexity can build in small, isolated populations but is often lost in situations of language contact. If it is generally true that small, isolated languages can build morphological complexity over time, but complexity tends to be lost in situations of language contact, then we should find that forms of language complexity that have evolved multiple times will tend to be associated with population size, isolation, and language age. 

We test this hypothesis by focusing on one particular form of morphological complexity, polysynthesis, where words built from many parts embody complex phrases. By assembling a global database of polysynthetic languages and conducting phylospatial analyses, we show that languages with highly complex word morphology are more likely to have small population sizes, less likely to occur with many other languages in direct contact, and have a greater tendency to be on long phylogenetically isolated lineages. 

These findings are consistent with the hypothesis that languages that evolve in isolation for long periods may be more likely to accrue morphological complexity. Polysynthetic languages also tend to have higher levels of endangerment. Our results provide phylogenetically informed evidence that one particular form of complex language morphology is more likely to occur in small, isolated languages and is prone to loss in contact.

Lindell Bromham, Keaghan Yaxley, Oscar Wilson, and Xia Hua, "Macroevolutionary analysis of polysynthesis shows that language complexity is more likely to evolve in small, isolated populations" 122(24) PNAS e2504483122 (June 12, 2025) (pay per view; but open access supplemental materials).

The languages counted as polysynthetic and borderline, according to the Supplemental Materials, are below the fold.

The Huns Were Paleo-Siberian, Not Linguistically Turkic (Also Slavic Origins)

A new paper makes a strong case that the Huns, a group of "barbarians" (in the eyes of Roman historians) who made multiple attempts to invade the Roman empire, spoke a Paleo-Siberian language (to which the Na-Dene languages of North America, such as Navajo, are distantly related), rather than a Turkic language, as conventional wisdom in historical linguistics prior to this paper had wrongly believed.

The Xiōng-nú were a tribal confederation who dominated Inner Asia from the third century BC to the second century AD. Xiōng-nú descendants later constituted the ethnic core of the European Huns. It has been argued that the Xiōng-nú spoke an Iranian, Turkic, Mongolic or Yeniseian language, but the linguistic affiliation of the Xiōng-nú and the Huns is still debated. 

Here, we show that linguistic evidence from four independent domains does indeed suggest that the Xiōng-nú and the Huns spoke the same Paleo-Siberian language and that this was an early form of Arin, a member of the Yeniseian language family. This identification augments and confirms genetic and archaeological studies and inspires new interdisciplinary research on Eurasian population history.

Svenja Bonmann et al, "Linguistic Evidence Suggests that Xiōng‐nú and Huns Spoke the Same Paleo‐Siberian Language," Transactions of the Philological Society (June 16, 2025). DOI: 10.1111/1467-968X.12321

A news report about the paper spells it out this hypothesis at greater length:

New linguistic findings show that the European Huns had Paleo-Siberian ancestors and do not, as previously assumed, originate from Turkic-speaking groups. The joint study was conducted by Dr. Svenja Bonmann at the University of Cologne's Department of Linguistics and Dr. Simon Fries at the Faculty of Classics and the Faculty of Linguistics, Philology and Phonetics at the University of Oxford.

The results of the research, "Linguistic evidence suggests that Xiōng-nú and Huns spoke the same Paleo-Siberian language," have been published in the journal Transactions of the Philological Society.

On the basis of various linguistic sources, the researchers reconstructed that the ethnic core of the Huns—including Attila and his European ruling dynasty—and their Asian ancestors, the so-called Xiongnu, shared a common language. This language belongs to the Yeniseian language family, a subgroup of the so-called Paleo-Siberian languages. These languages were spoken in Siberia before the invasion of Uralic, Turkic and Tungusic ethnic groups. Even today, small groups who speak a Yeniseian language still reside along the banks of the Yenisei River in Russia.

From the 3rd century BCE to the 2nd century CE, the Xiongnu formed a loose tribal confederation in Inner Asia. A few years ago, during archaeological excavations in Mongolia, a city was discovered that is believed to be Long Cheng, the capital of the Xiongnu empire. The Huns, in turn, established a relatively short-lived but influential multi-ethnic empire in southeastern Europe from the 4th to 5th centuries CE.

Research has shown that they came from Inner Asia, but their ethnic and linguistic origins have been disputed until now, as no written documents in their own language have survived. A great deal of what we know about the Huns and the Xiongnu is therefore based on written documents about them in other languages; for example, the term "Xiōng-nú' derives from Chinese. 

 

[Based on the "World Topographic Map" by Esri. Sources: Esri, HERE, Garmin, Intermap, INCREMENT P, GEBCO, USGS, FAO, NPS, NRCAN, GeoBase, IGN, Kadaster NL, Ordnance Survey, Esri Japan, METI, Esri China (Hong Kong), OpenStreetMap contributors, GIS User Community, Simon Fries. Created with QGIS 3.36.]. Credit: Transactions of the Philological Society (2025). DOI: 10.1111/1467-968X.12321

From the 7th century CE, Turkic peoples expanded westwards. It was therefore assumed that the Xiongnu and the ethnic core of the Huns, whose own westward expansion dates back to the 4th century CE, also spoke a Turkic language. However, Bonmann and Fries have found various linguistic indications that these groups spoke an early form of Arin, a Yeniseian language, in Inner Asia around the turn of the millennium.

"This was long before the Turkic peoples migrated to Inner Asia and even before the splitting of Old Turkic into several daughter languages. This ancient Arin language even influenced the early Turkic languages and enjoyed a certain prestige in Inner Asia. This implies that Old Arin was probably the native language of the Xiongnu ruling dynasty," says Bonmann.

Bonmann and Fries analyzed linguistic data based on loan words, glosses in Chinese texts, proper names of the Hun dynasty as well as place and water names. Taken by itself, the data on each of these aspects would have comparatively little significance, but taken together it is hard to argue with the conclusion that both the ruling dynasty of the Xiongnu and the ethnic core of the Huns spoke Old Arin.

The findings of the study also made it possible for the first time to reconstruct how the Huns came to settle in Europe: For the two researchers, place and water names still prove today that an Arin-speaking population once left its mark on Inner Asia and migrated westwards from the Altai-Sayan region. Attila the Hun probably also bears an ancient Arin name: Until now, "Attila" was thought to be a Germanic nickname ("little father"), but according to the new study, "Attila" could also be interpreted as a Yeniseian epithet, which roughly translates as "swift-ish, quick-ish."

The new linguistic findings support earlier genetic and archaeological findings that the European Huns are descendants of the Xiongnu. "Our study shows that alongside archaeology and genetics, comparative philology plays an essential role in the exploration of human history. We hope that our findings will inspire further research into the history of lesser-known languages and thereby contribute further to our understanding of the linguistic evolution of mankind," concludes Fries.

In the body text, a section of the paper explores the previous conventional wisdom and its difficulties:

Although direct evidence is lacking, Iranian, Turkic and Mongolic languages have all been proposed as the language of the ruling dynasty of the Xiōng-nú (cf. e.g. Shiratori 1900; Benzing 1959; Pritsak 1982; Bailey 1985; Dybo 2007; Janhunen 2010; Beckwith 2018; Beckwith 2022) and of the Huns (cf. e.g. Doerfer 1973; Pritsak 1982; Savelyev 2020; Savelyev & Jeong 2020), because in the 1st millennium AD languages from these three families were spoken in Inner Asia. Inscriptions dating between the 4th and 9th century AD demonstrate that Iranian languages (Sogdian, early 4th to 6th century AD, Sims-Williams 2011; Vovin 2018) and Mongolic ones (Khüis Tolgoi and Bugut inscriptions of the 5th–6th centuries AD, Vovin 2018) as well as, much later, Turkic languages (isolated Turkish phrases in Bactrian manuscripts of the 7th century AD, Orkhon and Yenisei Kirgiz inscriptions between the early 8th and 9th century AD, Erdal 2004: 4–8) were spoken in the territory between the Yenisei River in the West, the Tian Shan range in the South and Mongolia in the East. Other Indo-European languages were spoken in oasis cities along the northern and southern ridges of the Takla Makan desert in the 1st millennium AD including Indo-Iranian (Iranian Khotanese and Tumshuqese Saka, Bactrian, Indo-Aryan Prakrit, Sanskrit) and ‘Tocharian’ languages (Agnean and Kuchean).

However, this linguistic situation of a coexistence of Iranian, Turkic and Mongolic in Inner Asia can only be reliably established as such for the late 1st millennium AD. Hypotheses on an Iranian, Mongolic or Turkic identity of the Xiōng-nú primarily rest on written sources post-dating the Xiōng-nú era. 

While the theoretical possibility of a Mongolic or Turkic presence in Inner Asia already at the beginning of the common era cannot be ruled out a priori, it is important to note that there is, on the other hand, also no robust evidence – especially from textual sources – that could directly imply or prove a Turko-Mongolic presence in this area at such an early date. 

The earliest sources from the Tarim Basin and the territories alongside the Oxus River/Amu Darya (Chorasmia, Sogdia, Bactria) only document Indo-European languages from the Indo-Iranian and ‘Tocharian’ branches (to which might be added, as a cultural import, also Ancient Greek in Macedonian colonies). Judging by more indirect evidence – especially loanwords in other languages, toponyms, etc. – other Iranian languages, namely different Sakan varieties (Tremblay 2005) and ‘Old Steppe Iranian’ (Bernard 2023), must have been spoken in the steppe corridor from the Kazakh steppe to Dzungaria, and perhaps even to Gansu (see Beckwith 2022). It is only centuries later, namely in the Migration Period of the 5th–6th centuries AD, that a (Para-)Mongolic language might be attested in Inner Asia (Vovin 2018), and fragments of this (Para-)Mongolic language, in turn, are still much earlier documented than the earliest secure Turkic words dating from the 7th century AD.

There is thus neither direct nor indirect evidence supporting the claim of a Mongolic or Turkic presence in Inner Asia between the 3rd century BC and the 2nd century AD, and the hypothesis of a Mongolic or Turkic identity of the ethnic core of the Xiōng-nú (as proposed by Benzing 1959, Pritsak 1982; Tenišev 1997; Dybo 2007; Janhunen 2010; Savelyev 2020) is thus rather unlikely from the outset, as is the hypothesis of a completely unknown or unclassifiable language without any living descendants (as proposed by Doerfer 1973). The same applies to the Huns: there is a complete lack of evidence supporting claims of a Turkic presence among the Huns.1 On the other hand, an Iranian component in the Xiōng-nú Empire is possible, and indeed quite likely, although, as we intend to point out with the present study, such Indo-European ethnicity must not necessarily have been shared by the ruling dynasty or ethnic core of the Xiōng-nú (pace Bailey 1985; Beckwith 2022) or the Huns.

Concerning such an Iranian component, (Beckwith 2018, 2022) has argued recently that Xiōng-nú words preserved in Chinese texts are indicative of an Iranian language, which he calls ‘East Scythian’. However, his interpretation depends on a reconstruction of the Old and Middle Chinese pronunciation of Chinese signs which significantly differs from established reconstructions such as the classic one of Pulleyblank, and which has also been criticised by Vovin et al. (2016: 129–30). In addition to this, his Iranian etymologies must be met with serious doubts. For instance, the ethnonym ‘Aryan’, which is amply attested in many Indo-Iranian languages, is given by Beckwith with a word-initial laryngeal sound (discussion in Beckwith 2022: 183–86, cf. particularly p. 186): ‘East Scythian *ḥarya [ɣa.rya] “noble, royal; Scythian” → Old Chinese *ḥaryá 夏/*ḥâryá 華 “royal; Chinese, China”’. This would indeed be a remarkable Iranian word form, because no Indo-Iranian language points to an initial laryngeal (†Hā̆ri̯a- vel sim.): A word-initial laryngeal should have left direct traces in Persianide languages (see Kümmel 2018), but Old Persian <ariy-> /ariya-/ or inscriptional Middle Persian ēr ‘Iranian’ do not preserve such a sound. The hypothetical (East) Scythian would be the only Iranian language to preserve it, and independent evidence for this is entirely lacking. Other etymologies equally rest upon highly questionable ad hoc assumptions on Iranian historical phonology and must accordingly be dismissed (e. g. the etymology of Old Turkic täŋri ‘heaven’ that Beckwith 2022: 195, 203 wants to derive from an East Scythian *tagri through the application of an alleged Scythian syllable contact law of nasalization completely unheard of in the specialist literature and remaining without any reliable parallel; on this word rather cf. Georg 2001).

It must therefore be conceded that, while it is a priori likely that Iranian tribes were one factor among others in the ethnolinguistic melting pot of the eastern Eurasian steppe some 2000 years ago (the Sakan languages would be a good starting point for further research in this direction), the evidence adduced by scholars in favour of a dominant role of Iranian groups and their languages in the Xiōng-nú empire so far does not follow the rigorous methodological standards of Historical-Comparative Linguistics and is therefore insufficient to allow for any reliable inferences.

Etymological analyses of Xiōng-nú glosses in Chinese sources (collected by Pulleyblank 1962, criticised and reanalysed by Dybo 2007), complemented by the interpretation of the so-called Jié couplet, the only short text preserved in the Xiōng-nú language,2 have led to a more promising alternative hypothesis. This hypothesis acknowledges both the multi-ethnic composition of the Xiōng-nú empire as such and the presence of Indo-European and specifically Iranian languages in Inner Asia at the beginning of the common era, yet adds to the complexity the idea that the native language of the ruling dynasty of the Xiōng-nú empire might have been a Yeniseian one (Ligeti 1950; Pulleyblank 1962; Dul'zon 1966; Dul'zon 1968; Vovin 2000; Vovin 2003; Vovin 2007; Werner 2014; Vovin 2020). Yeniseian languages are usually considered remnants or survivors of the original linguistic diversity of Siberia, historically spoken in retreat areas as the result of several waves of superimposition or displacement by expanding Uralic/Samoyedic, Turkic and Tungusic languages. Therefore, Yeniseian languages are also known as Paleo-Siberian languages.3 Several different Yeniseian languages were spoken in the 18th century AD alongside the middle reaches of the Yenisei River and some of its tributaries, yet this probably reflects a northward migration from a point of departure further south, around the headwaters of the Yenisey, the Ob and the Irtyš rivers (see Dul'zon 1959a; Dul'zon 1959b; Dul'zon 1964; Maloletko 1992; Maloletko 2000; Vajda 2019: 194–95; cf. also Janhunen 2020: 167). From the six historically attested Yeniseian languages Ket, Yugh, Kott, Assan, Arin and Pumpokol, it has so far been suggested that Ket/Yugh (Ligeti 1950; Pulleyblank 1962) or Pumpokol (Vovin 2000, 2003, 2007, 2020; Vovin et al. 2016) may have been the native language of the Xiōng-nú ruling dynasty.

Adding value to this hypothesis is the fact that the northward migration of Yeniseian-speaking groups, as reflected in toponyms, from the Altai-Sayan area would well agree with detailed historical studies considering Indic, Iranian and Chinese written sources (de la Vaissière 2005; de la Vaissière 2014). These studies indicate that, following the eventual demise of their steppe empire, remnants of the Xiōng-nú migrated to the north of the Altai-Sayan Mountain ranges in the mid-2nd century AD and that this retreat area was the starting point of a secondary expansion of Xiōng-nú descendants roughly two hundred years later, between ca. 350–370 AD. This expansion occurred in three directions: One migratory trajectory led northward and left traces in the form of toponyms. This population movement downstream of the major rivers Yenisey, Ob and Irtyš perfectly explains the linguistic situation as documented for the first time in the 18th century and provides a direct link between Yeniseian languages and the Xiōng-nú. Another migratory route led to southern Asia and involved groups known from Iranian and Indic sources as Chionites, Kidarites, Hephthalites, Alchons as well as the so-called Huṇa (cf. Pfisterer 2013). A third migratory trajectory led westward, into Europe and involved the Huns who appeared in Eastern Europe in 370 and posed a threat to Roman hegemony until Attila's death in 453, the Battle of Nedao shortly afterwards and the ensuing disintegration of their confederation (cf. e.g. Heather 1996; Bóna 2002; Halsall 2007; Schmauder 2009; Maas 2014; Pohl 2022).

Several nomadic groups of late Antiquity that originated in Inner Asia and migrated to the southern and western peripheries of the Eurasian landmass apparently used the same ethnonymic constituent (Chion-ites – Al-chon – Huṇa – Huns; cf. de la Vaissière 2005; de la Vaissière 2014, but see Atwood 2012), and the traditional hypothesis of a link between the ethnic core of the European Huns of the 4th–5th centuries AD and the Inner Asian Xiōng-nú of the 3rd century BC–2nd century AD, first proposed by the French scholar Joseph de Guignes in the 18th century, has, strictly speaking, never been falsified (de la Vaissière 2005: 15). 

A genetic connection between the Xiōng-nú and the Huns is usually considered unlikely in modern archaeological and historical scholarship (e.g. Beckwith 2009: 72; Savelyev & Jeong 2020; Pohl 2022; Maenchen-Helfen 1944–1945; Maenchen-Helfen 1955; Maenchen-Helfen 1973; Schmauder 2009), partly because of the large chronological gap between the dissolution of the Xiōng-nú empire in the 2nd century AD and the appearance of the Huns in the 4th century AD, and partly because only two archaeological features render a connection likely: large bronze cauldrons of a certain type and artificially deformed or elongated skulls (Pohl 2022: 147).

Despite the prevailing scepticism of historians and archaeologists, the hypothesis of a connection between the Xiōng-nú and the Huns has been corroborated recently by previously unknown and unavailable genetic data analysed by Gnecchi-Ruscone et al. (2025): ‘(…) long-shared genomic tracts provide compelling evidence of genetic lineages directly connecting some individuals of the highest Xiongnu-period elite with 5th to 6th century AD Carpathian Basin individuals, showing that some European Huns descended from them’. 

On the provision that there was indeed some continuation between the ethnic core of the European Huns and the former Xiōng-nú, the ruling classes of both multi-ethnic confederations may have spoken the same language in two different diachronic stages (an older form and a younger one), implying that the identification of the linguistic affiliation of one of these groups probably also means identifying the native language of the other group. 

In the following, we will discuss previously unknown linguistic evidence from four domains independently supporting such a connection and thus corroborating the recent archaeological and genetic findings: (1) loanwords, (2) glosses, (3) anthroponyms and (4) toponyms/hydronyms.

This analysis, which moves the Turkic and Tungistic migrations several centuries later in history than previously believed, is also relevant to the Altaic linguistic hypothesis and our understanding of these ethnic mass migrations more generally.

Close in time and space: Slavic ethnogenesis

The Slavic people emerged around the same time as the fall of the Roman Empire and the demise of the short lived Hunnic Kingdom in the Balkans, but before the Magyar conquest of what is now called Hungary and before the appearance of Gypsies in Europe. This period was traditionally called the "Dark Ages" in Europe. There are some historical roots, however, which suggest Slavic origins several centuries earlier (from the Wikipedia link at the start of this paragraph):

Ancient Roman sources refer to the Early Slavic peoples as "Veneti", who dwelt in a region of central Europe east of the Germanic tribe of Suebi and west of the Iranian Sarmatians in the 1st and 2nd centuries AD, between the upper Vistula and Dnieper rivers. Slavs – called Antes and Sclaveni – first appear in Byzantine records in the early 6th century AD. Byzantine historiographers of the era of the emperor Justinian I (r. 527–565), such as Procopius of Caesarea, Jordanes and Theophylact Simocatta, describe tribes of these names emerging from the area of the Carpathian Mountains, the lower Danube and the Black Sea to invade the Danubian provinces of the Eastern Empire.

Jordanes, in his work Getica (written in 551 AD), describes the Veneti as a "populous nation" whose dwellings begin at the sources of the Vistula and occupy "a great expanse of land". He also describes the Veneti as the ancestors of Antes and Slaveni, two early Slavic tribes, who appeared on the Byzantine frontier in the early-6th century.

Procopius wrote in 545 that "the Sclaveni and the Antae actually had a single name in the remote past; for they were both called Sporoi in olden times". The name Sporoi derives from Greek σπείρω ("to sow"). He described them as barbarians, who lived under democracy and believed in one god, "the maker of lightning" (Perun), to whom they made sacrifice. They lived in scattered housing and constantly changed settlement. In war, they were mainly foot soldiers with shields, spears, bows, and little armour, which was reserved mainly for chiefs and their inner circle of warriors. Their language is "barbarous" (that is, not Greek), and the two tribes are alike in appearance, being tall and robust, "while their bodies and hair are neither very fair or blond, nor indeed do they incline entirely to the dark type, but they are all slightly ruddy in color. And they live a hard life, giving no heed to bodily comforts..."

Jordanes describes the Sclaveni as having swamps and forests for their cities. Another 6th-century source refers to them living among nearly-impenetrable forests, rivers, lakes, and marshes.

Menander Protector mentions Daurentius (r. c. 577 – 579) who slew an Avar envoy of Khagan Bayan I for asking the Slavs to accept the suzerainty of the Avars; Daurentius declined and is reported as saying: "Others do not conquer our land, we conquer theirs – so it shall always be for us as long as there are wars and weapons".

The Slavic languages are a relatively recent offshoot of the Indo-European Baltic languages, which in turn may be the most direct descendants of the language(s) of the Corded Ware culture (ca. 3000 BCE to 2350 BCE).

Eurogenes reports on new ancient DNA driven discoveries drawn from the earliest ancient Slavic DNA at his blog.

A paper dealing with the origin of Slavic speakers, titled Ancient DNA connects large-scale migration with the spread of Slavs, was just published at Nature by Gretzinger et al. (see here).

The dataset from the paper includes ten fascinating ancient samples from Gródek upon the Bug River in Southeastern Poland. These individuals are dated to the so called Tribal Period (8th – 9th centuries), and, as far as I know, they represent the earliest Slavic speakers in the ancient DNA record.

The really interesting thing about these early Slavs is that they already show some Germanic and other Western European-related ancestries. Nine of the samples made it into my G25 analysis (see here). In the Principal Component Analysis (PCA) plots . . . five of them cluster near present-day Ukrainians, while the rest are shifted towards present-day Northwestern and Western Europeans. . . .  GRK015, a female belonging to Western European-specific mtDNA haplogroup H1c, shows Scandinavian ancestry. On the other hand, GRK014, a female belonging to the West Asian-specific mtDNA haplogroup U3b, probably has Southern European ancestry.

These results aren't exactly shocking, because the people who preceded the early Slavs in the Gródek region were Scandinavian-like and associated with the Wielbark archeological culture. In other words, they were probably Goths who also had significant contacts with the Roman Empire.

However, it's not a given that the ancestors of the Tribal Period Slavs mixed with local Goths. It's also possible that they brought the western admixture, or at least some of it, from the Slavic homeland, wherever that may have been.

That's because the early Slavs who migrated deep into what is now Russia also showed Western European-related admixture. This is what Gretzinger et al. say on page 74 of their supplementary info (emphasis is mine):

The only deviation from this pattern is observed for ancient samples from the Russian Volga-Oka region, where we measure higher genetic affinity between present-day Southern/Western Europeans and the SP population compared to the pre-SP population (Fig. S17). This agrees with the pattern observed in PCA and ADMIXTURE that, in contrast to the Northwestern Balkan, Eastern Germany, and Poland-Northwestern Ukraine, the arrival of Slavic-associated culture in Northwestern Russia was associated with a shift in PCA space to the West, a decrease of BAL [Baltic] ancestry, and the introduction of Western European ancestries such as CNE [Continental North European] and CWE [Continental Western European].

Thus, it's highly plausible that the Tribal Period Slavs from Gródek were very similar, perhaps even practically identical, to the proto-Slavs who lived in the original Slavic homeland. Hopefully we won't have to wait too long to discover whether that's true or not. More Migration period and Slavic period samples from the border regions of Belarus, Poland and Ukraine are needed to sort that out.

Eurogenes goes on to criticize a suggestion in the supplemental materials to the Slavic ancient DNA paper that suggests that 

Sycthian groups from Ukraine show varying fractions of South Asian ancestry (between 5% and 12%), a component present in many ancient individuals from Moldova, Ukraine, Western Russia, and the Caucasus, but (nearly) absent in the SP genomes from Central and East-Central Europe (<5%). [Ed. references to specific samples showing this omitted.]

Eurogenes, rightly, explains that the data are really showing European introgression into South Asia arising from the Indo-Aryan invasion of the region in the Bronze Age, and before that from Iran. 

A Notable Modified Gravity Theory

Mach's principle is basically that inertia is a product of the combined gravitational pulls of everything in the Universe (although it can be expressed in about a dozen different ways, not all of which are perfectly consistent with each other or observation).  This, in turn, implies that (from the link and also from paper cited below): "Inertial mass is affected by the global distribution of matter."

A new paper tries to derive a relativistic version of a modified gravity theory similar to MOND by incorporating Mach's principle into the theory. This is something that Einstein tried to do until it became clear that this was inconsistent with plain vanilla General Relativity.

The general theory of relativity (GR) was proposed with an aim of incorporating Mach's principle mathematically. Despite early hopes, it became evident that GR did not follow Mach's principle. Over time, multiple researchers attempted to develop gravity theories aligned with Machian idea. Although these theories successfully explained various aspects of Mach's principle, each of these theories possessed its own strengths and weaknesses. 

In this paper, we discuss some of these theories and then try to combine these theories into a single framework that can fully embrace Mach's principle. This new theory, termed Machian Gravity (MG) is a metric-based theory, and can be derived from the action principle, ensuring compliance with all conservation laws. The theory converges to GR at solar system scales, but at larger scales, it diverges from GR and aligns with various modified gravity models proposed to explain dark sectors of the Universe. 

We have tested our theory against multiple observational data. It explains the galactic rotation curve without requiring additional dark matter (DM). The theory also resolves the discrepancy between dynamic mass and photometric mass in galaxy clusters without resorting to DM, but it introduces two additional parameters. It can also explain the expansion history of the Universe without requiring dark components.

Santanu Das (from the Raman Research Institute, Bangalore, India), "Machian Gravity: A mathematical formulation for Mach's Principle" arXiv:2308.04503 (last revised September 7, 2025) (53 pages). 

The theory's success with rotation curves is explored in this preprint (August 31, 2023). The idea was originally proposed in a set of three preprints from the same author in 2012: "Machian gravity and a cosmology without dark matter and dark energy" (May 17, 2012); "Mach's principle and the origin of the quantum phenomenon" (June 4, 2012); Mach Principle and a new theory of gravitation (June 26, 2012).

The introduction to the paper explains that:

Newtonian gravity can provide a very accurate description of gravity, provided the gravitational field is weak, not time-varying and the concerned velocities are much less than the speed of light. It can accurately describe the motions of planets and satellites in the solar system. Einstein formulated GR to provide a complete geometric approach to gravity. GR is designed to follow Newtonian gravity at a large scale. It can explain the perihelion precession of Mercury’s orbit and the bending of light by the Sun, which were never realized before, using Newtonian mechanics. Over the years, numerous predictions of GR, such as the existence of black holes, gravitational waves, etc. have been observed. This makes GR one of the most well-accepted theories of gravity. 

However, the drawbacks of GR come to light when GR is applied on the galactic and cosmological scale. It fails to produce the galactic velocity profiles, provided that calculations are made just considering the visible matter in the galaxy. This led researchers to postulate a new form of weakly interacting matter named dark matter. Earlier it was commonly believed that dark matter (DM) is made up of particles predicted from supersymmetry theory. However, the lack of evidence of these particles from Large Hadron Collider (LHC) strengthens the proposition of other candidates, such as Axions, ultra-light scalar field dark matter, etc.

A further mysterious puzzle is the dark energy (DE) because that requires to produce a repulsive gravitation force. Cosmological constant or Λ-term provides an excellent solution for this. However, as the observations become more precise, multiple inconsistencies come to light. 

There can be two ways to solve the dark sector of the Universe. 

Firstly, we can assume that there is in need some type of matter that does not interact with standard-model particles and acts as dark matter, and we have some form of energy with a negative pressure and provide a dark-energy-like behavior. 

While this can, in need, be the case, the possibility that the GR fails to explain the true nature of gravity in kilo-parsec scale can also not be overlooked. In such a case, we need an alternate theory of gravity that can replicate GR on a relatively smaller scale while deviating from it on a galactic scale. 

Several theories have been proposed in the last decade to explain DM and DE. Empirical theories like Modified Newtonian Dynamics (MOND) can explain the galactic velocity profiles extremely well but violates momentum conservation principles. Therefore, if a mathematically sound theory is developed that can mimic the MOND empirically, then that can explain the dark matter. Bekenstein proposed AQUAdraticLagrangian (AQUAL) to provide a physical ground to MOND. Other theories, such as Modified gravity, Scalar-Tensor-VectorGravity (STVG),Tensor–Vector–Scalar gravity (TeVeS), Massive gravity etc. are also proposed to match the galactic velocity profiles without dark matter. Other higher dimensional theories such as induced matter theory etc. are also proposed by researchers. However, all these theories came from the natural desire to explain the observational data and not build on a solid logical footing. 

Now, let us shift our focus to another aspect of GR. In the early 20th century, Earnest Mach hypothesized that the inertial properties of matter must depend on the distant matters of the Universe. Einstein was intrigued by Mach’s Principle and tried to provide a mathematical construct of it through the GR. He later realized that his field equations imply that a test particle in an otherwise empty Universe has inertial properties, which contradicts Mach’s argument. However, intrigued by the overwhelming success of GR in explaining different observational data, he did not make any further attempt to explain Mach’s principle. 

In view of this, it is worthwhile searching for a theory that implies that matter has inertia only in the presence of other matter. Several theories that abide by Mach’s principle have been postulated in the last century. Among these, the most prominent are Sciama’s vector potential theory, Brans Dicke (BD) theory or the scalar-tensor theory of gravity and Hoyle Narlikar theory etc. Although each of these theories addresses certain aspects of Mach’s principle as discussed in the respective articles, none offers a complete explanation. Thus, only a unified theory that combines these approaches could provide a comprehensive understanding of Mach’s principle in its entirety. 

In this article, we address all the issues described above and propose a theory of gravity based on Mach’s principle. It is based on the following premises. 

• Action principle: The theory should be derived from an action principle to guarantee that the theory does not violate conservation laws. 

• Equivalence principle : Various research groups have tested the Weak Equivalence Principle (WEP) at an exquisite procession. Therefore, any theory must follow the weak equivalence principle. However, the strong equivalence principle has not been tested on a large scale. If the ratio of the inertial mass and the gravitational mass changes over space-time (on a galactic scale or cosmological scale), then that does not violate results from our local measurements. In accordance with Mach’s principle, the inertial properties of matter come from all the distant matter of the Universe. As the matter distribution at different parts of the Universe is different, the theory may not follow the strong equivalence principle. 

• Departure from GR: As GR provides an excellent result in the solar system scale, the proposed theory should follow GR on that scale, and it only deviates from GR at the galactic scale to mimic some of the modified gravity theories proposed by researchers to explain the dark sectors of the Universe. Along with this, the proposed theory should also be able to replicate the behavior of theories like Sciama’s theory or BD theory under the specific circumstances for which they were proposed. 

The paper is organized as follows. 

In the second section I briefly discuss previous developments in gravity theory to explain Mach’s principle. Most of the points covered in this section are generally known positions form various previous research. However, since Mach’s principle is not a mainstream area of study, this discussion is necessary and important for understanding the new insights presented in this article. In some cases I interpret these established ideas from the perspective of this paper, that will help me to built the gravity theory in the later section. 

In the next section, we explain Mach’s principle and discuss the mathematical tools used to formulate the theory. We present the source-free field equations for the theory in the same section. 

The static spherically symmetric solution for the theory in weak field approximation is presented in the fourth section. We show that the solution follows Newtonian gravity and GR at a smaller scale but deviates from it at a large scale. 

Section five presents examples of galactic rotation curves and galaxy cluster mass distributions, demonstrating that the theory yields results in close agreement with observations. 

The source term of the theory has been described in the 6th section. 

In the next section, we provide the cosmological solutions to the MG model. 

The final section is the conclusion and discussion section. We have also added five appendices where we describe the nitty-gritty of the calculations and add multiple illustrations.

This theory is formulated in a 4+1 dimensional space-time. It states that "The momentum in the fifth dimension represents the inertial mass of the particle, which remains constant in any local region." The paper could be more clear regarding which two additional parameters are added to the theory, but appear to be related to a vector field and a scalar field, respectively:

The proposed framework is built upon a five-dimensional metric involving three essential elements: a scalar field ϕ, a vector field Aµ, and an extra dimension x4. (note that these two fields behave as scalar and vector field only if the metric is independent of x4.)

Side commentary on dark matter particle theories 

There are a wealth of papers constraining various versions of dark matter particle theories out there, and I bookmark almost all of them as I encounter them. But synthesizing them into a comprehensive set of constraints on dark matter, in the way that the Particle Data Group does for high energy physics data, is a daunting task.

The bottom line for those papers is that the parameter space of possible dark matter particle candidates is ever more tightly constrained within the context of many dark matter particle proposals, and that there are no positive confirmations of any of them.

More Neutrino Oscillation Physical Constant Measurements

Almost all of the experimental data favors a normal mass ordering for neutrinos over an inverted mass ordering, but given the limitations of current experiments, the preference is almost always a weak one.

The Particle Data Group value for delta m(32) squared in normal ordering is as follows:

Taking the square root, the PDG value is a gap of 49.5 meV.

A new paper's results are consistent with the world average. The paper, its abstract, and the chart below from its supplementary materials are as follows:

This Letter reports measurements of muon-neutrino disappearance and electron-neutrino appearance and the corresponding antineutrino processes between the two NOvA detectors in the NuMI neutrino beam. These measurements use a dataset with double the neutrino mode beam exposure that was previously analyzed, along with improved simulation and analysis techniques. 

A joint fit to these samples in the three-flavor paradigm results in the most precise single-experiment constraint on the atmospheric neutrino mass-splitting, Δm^2(32) = 2.431 +0.036 −0.034 (−2.479 +0.036 −0.036) × 10^−3 ~eV^2 if the mass ordering is Normal (Inverted). In both orderings, a region close to maximal mixing with sin^2(θ23) = 0.55 +0.06 −0.02 is preferred. 

The NOvA data show a mild preference for the Normal mass ordering with a Bayes factor of 2.4 (corresponding to 70% of the posterior probability), indicating that the Normal ordering is 2.4 times more probable than the Inverted ordering. When incorporating a 2D Δm^2(32) --sin^2(2*θ13) constraint based on Daya Bay data, this preference strengthens to a Bayes factor of 6.6 (87%).

NOvA Collaboration, "Precision measurement of neutrino oscillation parameters with 10 years of data from the NOvA experiment" arXiv:2509.04361 (September 4, 2025).

The Pair Instability Gap

There is a mass range, called the "pair instability gap" in which intermediate mass black holes in binary black hole systems are predicted to be scarce.

Stellar theory predicts a forbidden range of black-hole masses between ∼ 50 - 130 M⊙ due to pair-instability supernovae, but evidence for such a gap in the mass distribution from gravitational-wave astronomy has proved elusive. Early hints of a cutoff in black-hole masses at ∼ 45 M⊙ disappeared with the subsequent discovery of more massive binary black holes. 

Here, we report evidence of the pair-instability gap in LIGO-Virgo-KAGRA's fourth gravitational wave transient catalog (GWTC-4), with a lower boundary of 45 +5 −4 M⊙ (90% credibility). While the gap is not present in the distribution of primary masses m(1) (the bigger of the two black holes in a binary system), it appears unambiguously in the distribution of secondary masses m(2), where m(2) ≤ m(1). The location of the gap lines up well with a previously identified transition in the binary black-hole spin distribution; binaries with primary components in the gap tend to spin more rapidly than those below the gap. 

We interpret these findings as evidence for a subpopulation of hierarchical mergers: binaries where the primary component is the product of a previous black-hole merger and thus populates the gap. Our measurement of the location of the pair-instability gap constrains the S-factor for 12C(α,γ)16O at 300 keV to 256 +197 −104 keV barns.

Hui Tong, et al., "Evidence of the pair instability gap in the distribution of black hole masses" arXiv:2509.04151 (September 4, 2025).

Medieval Supernova

Astronomy is one of the oldest sciences. Advanced scientific astronomy calculation instruments were in existence in the Greek classical period and megalithic solar observatories came into existence independently shortly after agriculture was invented in multiple places. There is even evidence of astronomy being done in a stone temple in Anatolia built before agriculture was invented. By around Y1K, astronomy was taught in universities, and was done in a quite scientific manner in multiple civilizations around the globe. Prior to the Renaissance, however, it was all done with the naked eye. 

The remnant of the historical supernova SN 1181 is under discussion: While the previously suggested G130.7+3.1 (3C58) appears too old (3000-5000 yr), the unusual star IRAS 00500+6713 with a surrounding nebula (Pa-30) has an expansion age not inconsistent with a SN Iax explosion in AD 1181 under the assumption that neither acceleration nor deceleration occurred. 

Previously, only reports from China and Japan were known, pointing to an event near the northern circumpolar region. Any further reports from other cultures can therefore be highly relevant. 

We present here an Arabic poem in praise of Saladin by the contemporaneous author Ibn Sanā' al-Mulk (Cairo, Egypt). We re-date its composition to between Dec 1181 and May 1182. It contains a new bright star, which can be identified as SN 1181. The poem also provides new and independent information on the object type (called `najm' for `star'), location on sky (in or near the Arabic constellation al-Kaff al-Khabīb, lit. the henna-dyed hand (five bright stars in Cassiopeia), and brightness (brighter than alpha Cas, 2.25 mag). 

In addition, we present another Arabic text on SN 1006, also from Cairo, by the historian al-Maqrīzī, probably based on the contemporaneous al-Musabbihī

J.G. Fischer, H. Halm, R. Neuhäuser, D.L. Neuhäuser, "New Arabic records from Cairo on supernovae 1181 and 1006" arXiv:2509.04127 (published August 19, 2025 at 346 Astronomical Notes e70024).