CENTAUR: Multidisciplinary Insights in Science & Tech

• CENTAUR in astronomy defines small bodies on unstable orbits between Jupiter and Neptune, acting as transitional objects from trans-Neptunian zones to comets.
• In cognitive science and AI, Centaur refers to a foundation model that simulates human behavior and a hybrid human-algorithm system enhancing decision-making.
• In computing and fusion, CENTAUR represents a privacy-preserving transformer inference framework and a compact negative triangularity tokamak design achieving 40 MW fusion power.

Centaur, and in acronymic form CENTAUR, denotes several distinct research objects. In planetary science, Centaurs are minor Solar System bodies on unstable orbits in the giant-planet region and are generally treated as transitional bodies between trans-Neptunian reservoirs and Jupiter-family comets. In contemporary AI literature, Centaur can denote either a foundation model of human cognition or a broader human-algorithm paradigm based on symbiotic learning. In computer systems, CENTAUR names a privacy-preserving transformer-inference framework, and in fusion engineering it names the Compact Experimental Negative TriAngUlarity Reactor, a compact high-field breakeven tokamak concept (Peixinho et al., 2019, Binz et al., 2024, Saghafian et al., 2024, Luo et al., 2024, Collaboration et al., 26 May 2026).

1. Planetary-science meaning and historical emergence

In astronomy, Centaurs are small bodies orbiting in the giant-planet region on dynamically unstable trajectories. Multiple operational definitions appear in the literature. A common strict definition uses perihelion beyond Jupiter and semimajor axis inside Neptune, $q > 5.2$ AU and $a < 30.1$ AU; other studies use $5.2 < q, a < 30$ au and exclude bodies in long-term stable $1{:}1$ resonance with a planet (Peixinho et al., 2019, Cabral et al., 2018, Lilly et al., 2021). Across these formulations, the central idea is the same: Centaurs inhabit the region between Jupiter and Neptune and occupy a transitional dynamical state between trans-Neptunian populations and comets.

The modern class begins with the discovery of (2060) Chiron in 1977 as 1977 UB, the first recognized object in this intermediate orbital region. Chiron was subsequently found to be active, which made it simultaneously asteroid-like in orbital cataloging and comet-like in physical behavior. The discovery of (5145) Pholus in 1992, extremely red and inactive, established immediately that Centaurs are not a homogeneous class (Peixinho et al., 2019).

Population counts depend on definition and epoch. A 2019 census cited 292 Centaurs under the strict $q>5.2$ AU, $a<30.1$ AU definition, of which 26 were also classified as comets, and 360 under the Deep Ecliptic Survey definition (Peixinho et al., 2019). More recent review chapters emphasize that the observed census remains strongly incomplete at smaller sizes and at larger perihelion distances, so the cataloged population is a biased sample of the underlying distribution (Fernandez et al., 4 Jun 2025).

2. Dynamical evolution, source regions, and resonant states

Centaurs are dynamically short-lived. The canonical evolutionary picture is TNO/Kuiper Belt object $\rightarrow$ scattered object $\rightarrow$ Centaur $\rightarrow$ Jupiter-family comet, although not all bodies follow the same path and some are ejected, temporarily captured, or routed into other reservoirs (Peixinho et al., 2019, Kokotanekova et al., 24 Nov 2025). Review work identifies the dynamically excited trans-Neptunian population, especially the scattered disk, as the main source, while also allowing contributions from resonant populations, the Oort cloud, Jupiter and Neptune Trojans, Quasi-Hildas, Haumea-family members, and possibly escaped inner Solar System asteroids (Volk et al., 2012, Kokotanekova et al., 24 Nov 2025).

Repeated encounters with the giant planets strongly reshape Centaur orbits. One numerical study found that each Centaur experiences on average $\sim 420$ planetary encounters over its lifetime, and that almost any plausible initial Kuiper-belt inclination distribution evolves toward a Centaur inclination distribution peaked near $a < 30.1$0–$a < 30.1$1. In this framework, low-inclination source signatures are largely erased, while only distinct high-inclination structure is partly retained. The same study concluded that the Kuiper belt is an extremely unlikely source of the observed retrograde Centaur and that an Oort-cloud or other intrinsically retrograde reservoir is more plausible for such objects (Volk et al., 2012).

Specific Centaurs display resonant behavior of unusual complexity. 2013 VZ70 is currently trapped in a horseshoe resonant state with Saturn, is dynamically transient, and in the nominal solution can transition into a quasi-satellite phase for nearly 200 yr beginning about 975 yr into the future. The same simulations allow brief temporary irregular-moon capture, with negative Saturnocentric relative binding energy occurring twice for about 3 years each (Marcos et al., 2021). For retrograde orbits near Saturn’s semimajor axis, clone-based integrations identified four potential $a < 30.1$2 resonant candidates; 2006 RJ2 was described as the best current candidate and 2017 SV13 as another important one (Li et al., 2018).

Centaur evolution also links the outer and inner Solar System. A long-integration impact study estimated that 53% of Centaurs can enter the terrestrial-planet region and 7% can interact with terrestrial planets. The same work inferred that 43.4% become near-Earth objects during their lifetimes and that Centaurs contribute about $a < 30.1$3 of the current NEO population, about 9\% of Potentially Hazardous Objects, and at least $a < 30.1$4 of short-period comets (Galiazzo et al., 2018).

3. Activity, volatile chemistry, and physical structure of astronomical Centaurs

Centaur activity is a central observational problem because ordinary water-ice sublimation is inefficient at giant-planet distances. Published activity fractions vary with sample definition and census epoch: one survey notes roughly $a < 30.1$5 of Centaurs as active, another gives about 10–20%, and a historical review counts about 29 active objects among roughly 290–360 known Centaurs, or about 8–9\% (Lilly et al., 2021, Cabral et al., 2018, Peixinho et al., 2019). The literature therefore treats activity as real but episodic, selective, and not uniformly distributed across the population.

Several mechanisms are discussed in the observational and thermo-dynamical literature. These include crystallization of amorphous water ice, release of trapped gases, sublimation of subsurface CO or CO$a < 30.1$6, and surface failure or landslides that expose buried volatile-rich layers. Surveys finding no activity among newly discovered Centaurs are typically interpreted not as evidence that the class is inert, but as evidence that many objects are dormant, weakly active, or between outbursts, even when orbital histories show that they have passed through thermal regimes where activity could in principle be triggered (Lilly et al., 2021, Cabral et al., 2018, Kokotanekova et al., 24 Nov 2025).

A major spectroscopic milestone was the JWST detection of CO$a < 30.1$7 in 39P/Oterma. Observed with NIRSpec IFU PRISM mode on 2022 July 27 at 5.82 au, 39P showed a clear 4.26 $a < 30.1$8m emission feature identified as the CO$a < 30.1$9 $5.2 < q, a < 30$0 band. The detection was 7-sigma, with a production rate

$5.2 < q, a < 30$1

described as the first detection of CO$5.2 < q, a < 30$2 emission in any Centaur and the lowest CO$5.2 < q, a < 30$3 detection yet reported for any comet or Centaur. CO and H$5.2 < q, a < 30$4O were not detected, giving $5.2 < q, a < 30$5 and $5.2 < q, a < 30$6, consistent with CO$5.2 < q, a < 30$7 and/or CO as important drivers of the activity and inconsistent with water as the dominant driver at that epoch (Pinto et al., 2023).

The 39P result also sharpened the contrast with 29P/Schwassmann-Wachmann 1, a highly active Centaur in the Jupiter-family-comet “Gateway” region. At similar heliocentric distance, 29P shows a very different volatile pattern, with $5.2 < q, a < 30$8 and $5.2 < q, a < 30$9, implying a CO-dominated coma rather than the CO$1{:}1$0-favored chemistry inferred for 39P. Long radio monitoring of 29P further showed that CO and dust outbursts are not always well correlated: a factor-of-two CO outburst on 2016 Feb 28.6 UT did not trigger detectable dust brightening for at least 10 days, while two dust outbursts in 2018 occurred with CO production at quiescent levels (Pinto et al., 2023, Wierzchos et al., 2020).

Occultations and light curves have become central to Centaur structural studies. The first-ever observed stellar occultation by 29P yielded a solid-body occultation lasting about 3.65 s, a chord length of about 54.2 km, and a lower limit on the nucleus radius of $1{:}1$1 km. The light curve also showed gradual ingress dimming interpreted as a localized dust cloud or jet at least 23.4 km above the surface with optical depth $1{:}1$2 (Pereira et al., 2024). For (54598) Bienor, three occultations and rotational photometry gave a triaxial ellipsoid with

$1{:}1$3

a refined period of $1{:}1$4 h, a geometric albedo of $1{:}1$5, and the first determination of a Centaur’s rotational sense as prograde by this combined method (Rizos et al., 2024). For (60558) 174P/Echeclus, occultations gave

$1{:}1$6

an area-equivalent radius of $1{:}1$7 km, albedo $1{:}1$8, and non-detection limits sufficient to state that a Chariklo-like ring would have been seen (Pereira et al., 2023).

Review chapters on Centaur nuclei emphasize that most measured light curves have low amplitudes, suggesting many Centaurs are near-spherical or only moderately elongated, but they also stress strong observational biases from unknown pole orientation, unresolved coma, rings, and unresolved secondaries. This suggests that the current structural taxonomy remains provisional and that occultations are the most reliable route to shape, ring, and binarity constraints (Fernandez et al., 4 Jun 2025, Kokotanekova et al., 24 Nov 2025).

4. Centaur as a foundation model of human cognition

In cognitive science, Centaur is the name of a foundation model trained to predict and simulate human behavior across many psychological tasks. Binz and collaborators introduce it as a computational model that can predict and simulate human behavior in any experiment expressible in natural language, motivated by Newell’s program of a unified theory of cognition (Binz et al., 2024). The model starts from Llama 3.1 70B and is fine-tuned with QLoRA, inserting rank-8 low-rank adapters into all non-embedding layers. The adapters add only 0.15% trainable parameters, training runs for one epoch, and the loss is masked so that only human responses, not instructions, contribute (Binz et al., 2024).

The enabling corpus is Psych-101, a natural-language transcription of trial-by-trial human behavior containing 160 psychological experiments, 60,092 individual participants, 10,681,650 human choices, and 253,597,411 text tokens. The tasks span multi-armed bandits, decision making, memory, supervised learning, Markov decision processes, categorization, exploration/exploitation, reasoning, and related paradigms (Binz et al., 2024). On held-out participants, the reported average pseudo-$1{:}1$9 values are 0.50 for Centaur, 0.36 for the base Llama model, and 0.32 for domain-specific cognitive models. The paper also reports generalization to a magical-carpet two-step task with pseudo-$q>5.2$0 versus 0.10 for Llama and 0.12 for a cognitive baseline, to Maggie’s farm with 0.62 versus 0.43 and 0.11, and to an excluded logical-reasoning domain with 0.18 versus 0.05 (Binz et al., 2024).

The same study argues that Centaur is not only predictive but also neurally informative: after fine-tuning, its internal representations become more aligned with human neural activity in two-step-task fMRI and sentence-reading fMRI, despite never being trained on neural data (Binz et al., 2024). This is presented as evidence that behavioral fine-tuning can move a LLM toward a more brain-like representational geometry, at least in the restricted sense of linear decodability.

That interpretation has been challenged. “Not Yet AlphaFold for the Mind” argues that Centaur is promising as a predictor of human choices but not yet a reliable synthetic participant. The critique distinguishes sharply between predictive performance, measured by next-trial negative log-likelihood under human histories, and generative performance, measured in open-loop simulation when the model must respond to its own past behavior (Namazova et al., 11 Aug 2025). In reversal learning, Centaur shows only a weak reversal effect and in some random seeds no adaptation after the contingency switch. In a horizon-dependent bandit task it fails to capture the horizon effect, and in the Wisconsin Card Sorting Test it exhibits too many perseveration and set-loss errors. The critique therefore concludes that Centaur is presently closer to a powerful next-response predictor than to a behaviorally faithful autonomous simulator (Namazova et al., 11 Aug 2025).

5. Human-algorithm “centaurs” in generative AI

A separate AI literature uses centaur as a generic term for a hybrid human-algorithm system. In this usage, centaurs are defined as hybrid human-algorithm AI models that combine formal analytics and human intuition in a symbiotic manner within their learning and reasoning process (Saghafian et al., 2024). The core distinction from standard human-in-the-loop methods is that the human is not merely an external annotator, oracle, or fallback reviewer; instead, human knowledge, preferences, or behavior are treated as a coequal component of the learning objective.

The formalism in this literature separates a machine model, a human-preference model, and a symbiotic model constrained not to drift too far from either source. The paper identifies five implementation routes: preference-based augmented covariate space, human-guided rewards, human-preference-based supervised fine-tuning, human-machine ensembles, and preference-constrained cost functions (Saghafian et al., 2024). In this framework, reinforcement learning with human feedback, supervised preference tuning, and adapter-based alignment of LLMs are interpreted as practical centaur-building methods.

This literature also argues that centaurs are not universally preferable. They are presented as most valuable when objectives are fuzzy, behavioral alignment matters, data are imperfect, or there are multiple technically acceptable solutions. Traditional AI is described as preferable when the objective is clearly specified and human intuition is likely to inject bias or noise (Saghafian et al., 2024). A plausible implication is that the cognitive-science Centaur model can be understood as a specific instantiation of a broader centaur paradigm, although the two literatures use the term at different abstraction levels.

6. CENTAUR as privacy-preserving transformer inference

In privacy-preserving machine learning, CENTAUR is a hybrid Privacy-Preserving Transformer Inference framework designed to reconcile privacy, efficiency, and performance in cloud inference. The system considers three parties: $q>5.2$1, the model developer owning a private Transformer $q>5.2$2; $q>5.2$3, the cloud platform; and $q>5.2$4, the client owning private input $q>5.2$5. The threat model is semi-honest, and the technical objective is to protect both model parameters and inference data while retaining accurate and efficient inference (Luo et al., 2024).

The framework’s central idea is to combine random permutations with SMPC / secret sharing. Random permutations protect model parameters and allow most linear and nonlinear computations to be carried out efficiently in plaintext on permuted representations; secret sharing protects user inference data and selected intermediate states. The algebraic basis is that for linear layers,

$q>5.2$6

and for element-wise nonlinearities, $q>5.2$7, so correct computation can proceed on permuted values (Luo et al., 2024).

CENTAUR is motivated by weaknesses in earlier approaches. Pure SMPC can protect both model and data, but nonlinear Transformer components such as Softmax, GeLU, and LayerNorm dominate runtime; the paper notes that these account for over 90% of runtime in some SMPC-based systems and cites earlier GPT-2$q>5.2$8 inference at over 25 minutes per token. Pure permutation-based approaches achieve near-plaintext efficiency and preserve accuracy, but may leak embeddings, attention scores, or other intermediate results (Luo et al., 2024).

The framework uses CrypTen-style 2-out-of-2 additive secret sharing over $q>5.2$9, together with transformer-structure-aware protocols that convert many share-share matrix multiplications into communication-free plaintext-share multiplications and evaluate nonlinear layers by reconstructing only permuted plaintext locally before re-sharing the outputs (Luo et al., 2024). Experimentally, the paper reports resistance to three reconstruction attacks, SIP, EIA, and BRE, plaintext-level inference accuracy, and speedups of $a<30.1$0–$a<30.1$1 over prior PPTI systems (Luo et al., 2024).

7. CENTAUR as the Compact Experimental Negative TriAngUlarity Reactor

In fusion engineering, CENTAUR stands for the Compact Experimental Negative TriAngUlarity Reactor, a design study for a compact, affordable, breakeven tokamak (Collaboration et al., 26 May 2026). The concept is explicitly organized around negative triangularity (NT), high magnetic field, and reactor-relevant power exhaust in a device sized to target an overnight cost below $a<30.1$2B. The stated performance point is 40 MW of fusion power with scientific gain $a<30.1$3 (Collaboration et al., 26 May 2026).

The principal design point has major radius $a<30.1$4 m, minor radius $a<30.1$5 m, edge elongation $a<30.1$6, triangularity $a<30.1$7, on-axis toroidal field $a<30.1$8 T, plasma current $a<30.1$9 MA, and pulse length $\rightarrow$0 s (Collaboration et al., 26 May 2026). The magnet system employs REBCO high-temperature superconductors in 18 toroidal field coils, an hourglass-shaped central solenoid, and six poloidal field coils. Neutronics calculations indicate that a 12 cm $\rightarrow$1 shield keeps superconducting magnet heating below the 33 K quench limit during 10 s, 40 MW DT pulses, and that the modeled fluence allows HTS components to survive more than ten times the 3000-pulse design lifetime (Collaboration et al., 26 May 2026).

The NT choice is physically important because the design study associates it with natural ELM-free operation and improved edge power handling. Ballooning-stability calculations place the pedestal within the first stability regime, consistent with the expected ELM-free behavior. Edge and divertor modeling gives a 13.5% radiated-power fraction between separatrix and plasma-facing components and a peak divertor heat flux of 7.9 MW/m$\rightarrow$2, below the quoted tungsten limit of 10 MW/m$\rightarrow$3 (Collaboration et al., 26 May 2026).

Economically, the paper reports an overnight cost estimate of $\rightarrow$4B target (Collaboration et al., 26 May 2026). In this usage, **CENTAUR is therefore neither astronomical nor algorithmic; it is a reactor concept in which physics design, magnet design, edge power handling, neutronics, and costing are optimized jointly around a compact NT tokamak architecture.