SPLENDOR: Dark Matter Detectors, Graphs & More

• SPLENDOR is a multidisciplinary term defining both a dark matter detector platform and a theoretical framework in algorithmic economics.
• Its detector design employs narrow-gap semiconductors and cryogenic two-stage HEMT amplifiers to achieve near-single-electron charge resolution for sub-eV interactions.
• The framework leverages proportional-response dynamics on vertex-weighted bipartite graphs to optimize density decompositions and market equilibrium analysis.

SPLENDOR is a term used in multiple, technically unrelated research contexts. In astroparticle physics it denotes the collaboration and detector platform “Search for Particles of Light dark mattEr with Narrow-gap semiconDuctORs,” centered on narrow-gap semiconductor targets and low-noise cryogenic charge readout for sub-MeV dark matter searches (Anczarski et al., 2023, Abbamonte et al., 23 Jul 2025). In theoretical computer science and algorithmic economics, “Symmetric Splendor” denotes a named framework on vertex-weighted bipartite graphs that unifies density-friendly hypergraph decomposition, universally closest distribution refinements, and a symmetric special case of linear Fisher markets (Chan et al., 2024). In astronomy, the term is sometimes associated with a planned node-based visual programming environment around the SpeX Prism Library, but the underlying paper explicitly does not name that platform “SPLENDOR” (Burgasser, 2014). In AI and games research, the closely related term “Splendor” refers to the board game used as a benchmark in the Rinascimento framework for Statistical Forward Planning, event-value functions, and MAP-Elites-based behavioral-space analysis (Bravi et al., 2019, Bravi et al., 2020, Bravi et al., 2021).

1. Dark-matter collaboration and detector platform

In detector physics, SPLENDOR stands for “Search for Particles of Light dark mattEr with Narrow-gap semiconDuctORs” (Anczarski et al., 2023). The collaboration targets dark matter candidates in the sub-MeV mass regime, where typical kinetic energies are $\mathcal{O}(\mathrm{eV})$ or lower and detector energy deposits are sub-eV (Abbamonte et al., 23 Jul 2025). The program is motivated by the limitation of conventional ionization searches in wide-bandgap materials for such low-energy interactions, and therefore emphasizes narrow-bandgap semiconductors with electronic bandgaps on the order of $1$–$100~\mathrm{meV}$ (Anczarski et al., 2023).

The detector strategy combines materials development with low-noise charge readout. The collaboration’s stated present strategy entails the use of strongly correlated $f$-electron semiconductors with anisotropic electronic structures and custom charge readout based on cryogenic high-electron-mobility transistor amplifiers approaching single-electron resolution (Abbamonte et al., 23 Jul 2025). A central motivation is that near-single-electron charge resolution maps, through the average electron–hole pair creation energy, to meV-scale threshold energies in suitably small-gap substrates (Anczarski et al., 2023).

The platform is described as modular and scalable, able to accommodate different target materials and signal readout technologies (Abbamonte et al., 23 Jul 2025). This material-agnostic architecture is significant because it allows rapid prototyping across multiple candidate semiconductors without requiring target-specific wafer or device fabrication. A plausible implication is that SPLENDOR is designed not merely as a single detector realization, but as a general experimental infrastructure for comparative materials R&D in the sub-eV direct-detection regime.

2. Detector architecture, target materials, and readout chain

The hardware architecture centers on a split-stage cryogenic amplifier. A low-capacitance HEMT buffer stage is placed at approximately $10~\mathrm{mK}$, and a higher-capacitance HEMT gain stage operates at $4~\mathrm{K}$ (Anczarski et al., 2023, Abbamonte et al., 23 Jul 2025). In the two-stage design reported in 2023, the front-end HEMT has gate–source capacitance $\sim 1.6~\mathrm{pF}$ and acts as a common-drain voltage buffer, while the second stage has capacitance $\sim 200~\mathrm{pF}$ and provides the main voltage gain (Anczarski et al., 2023). The rationale is to capture the detector signal immediately at very low input capacitance, thereby mitigating stray capacitance and preserving charge sensitivity.

The first prototype detector platform selects Eu$_5$In$_2$Sb$1$0 as the target material (Abbamonte et al., 23 Jul 2025). The material is described as a stoichiometric Zintl phase with strong spin-orbit coupling and an orthorhombic, highly anisotropic crystal structure, with transport and AC Hall data indicating a transport gap of $1$1 above $1$2 (Abbamonte et al., 23 Jul 2025). First-principles calculations yield an indirect gap of approximately $1$3 after a scissor correction and a direct gap of approximately $1$4 (Abbamonte et al., 23 Jul 2025). Mobility is reported as $1$5 at $1$6, increasing to $1$7 at $1$8, while dark-current extrapolations to $1$9 suggest extremely small intrinsic rates (Abbamonte et al., 23 Jul 2025).

The signal path is capacitively coupled through a fuzz button to the front-end cryoHEMT, then amplified at $100~\mathrm{meV}$0, passed to room-temperature electronics, and digitized (Abbamonte et al., 23 Jul 2025). SPLENDAQ, a detector-agnostic Python package developed within the collaboration, provides continuous time-stream acquisition and offline matched-filter triggering and pulse analysis (Watkins, 2023, Abbamonte et al., 23 Jul 2025). This integration of cryogenic front-end electronics, room-temperature readout, and software-trigger infrastructure is central to the collaboration’s experimental workflow.

3. Noise performance, calibration, and projected sensitivity

The 2023 amplifier paper reports preliminary voltage-noise performance and an estimated charge resolution of $100~\mathrm{meV}$1 electrons for the two-stage cryogenic HEMT-based amplifier (Anczarski et al., 2023). The relevant scaling relation is summarized as

$100~\mathrm{meV}$2

with the low-temperature buffer intended to minimize both the effective noise contribution and parasitic capacitance (Anczarski et al., 2023). For a benchmark capacitive budget of $100~\mathrm{meV}$3, an optimal-filter calculation using the measured amplifier noise spectrum yielded the quoted one-sigma ENC of $100~\mathrm{meV}$4 electrons (Anczarski et al., 2023).

The 2025 platform paper reports a measured charge resolution of $100~\mathrm{meV}$5 electrons in silicon test samples, described as consistent with predicted performance (Abbamonte et al., 23 Jul 2025). The same paper gives a staged upgrade path: approximately $100~\mathrm{meV}$6 after vibration mitigation, approximately $100~\mathrm{meV}$7 with active reset, approximately $100~\mathrm{meV}$8 with parallel amplification, and a fiducial sub-electron target of $100~\mathrm{meV}$9 for planned quantum cCPT upgrades (Abbamonte et al., 23 Jul 2025). The 2025 calibration paper refines the amplifier characterization further, reporting input-limited voltage noise of $f$0 and current noise of $f$1 at $f$2, together with a photon-shot-noise calibration yielding a baseline resolution of $f$3 electrons (Anczarski et al., 1 Oct 2025).

These performance numbers are directly connected to SPLENDOR’s projected physics reach. The platform paper presents sensitivity estimates for athermally produced relic dark matter under high- and low-background environments and under several readout scenarios (Abbamonte et al., 23 Jul 2025). It states that a modulation-based low-threshold surface analysis extends sensitivity below $f$4 for the first time in a terrestrial direct search, while only the deep-site quantum scenario with sub-electron resolution fully reaches the freeze-in relic-density target curve (Abbamonte et al., 23 Jul 2025). This suggests that amplifier performance is not a peripheral subsystem metric but a primary determinant of the reachable parameter space.

4. Directionality and modulation as discrimination channels

A distinguishing feature of the detector-platform interpretation of SPLENDOR is the explicit use of anisotropic electronic structure for directional sensitivity (Abbamonte et al., 23 Jul 2025). In Eu$f$5In$f$6Sb$f$7, the dielectric tensor and electric susceptibility are reported to be anisotropic in both energy and momentum, and this anisotropy is used to predict direction-dependent response to the incoming dark matter flux (Abbamonte et al., 23 Jul 2025). The stated goal is signal-background discrimination through daily modulation.

The scattering-rate formalism is given in terms of the loss function and the time-dependent target velocity relative to the halo:

$f$8

with the modulation amplitude defined as

$f$9

For $10~\mathrm{mK}$0–$10~\mathrm{mK}$1, the total-rate modulation amplitude is reported as approximately $10~\mathrm{mK}$2–$10~\mathrm{mK}$3 (Abbamonte et al., 23 Jul 2025).

The background model includes amplifier noise, dark currents, Compton scattering, radiological activity, cosmogenic muons, thermal phonons, and microphonics (Abbamonte et al., 23 Jul 2025). The proposed discrimination strategy is to bin events into “DM day” and “DM night” aligned to maximal phase difference and thereby subtract unmodulated backgrounds (Abbamonte et al., 23 Jul 2025). This is methodologically important because the experiment does not rely exclusively on absolute background suppression; it also leverages sidereal-time structure as a signal observable. A plausible implication is that SPLENDOR is designed around a joint optimization of materials anisotropy, low-threshold charge readout, and time-domain analysis.

5. SPLENDAQ within the SPLENDOR collaboration

SPLENDAQ is the collaboration’s detector-agnostic data acquisition and offline analysis package (Watkins, 2023). The package is Python-based and offers two main features for offline analysis of continuous data: a threshold-triggering algorithm based on the time-domain optimal filter formalism and an algorithm for randomly choosing nonoverlapping segments for noise measurements (Watkins, 2023). Combined with the commercially available Moku platform, it forms a full pipeline of event building from raw data with minimal setup (Watkins, 2023).

The triggering formalism assumes a continuous data stream $10~\mathrm{mK}$4, a known signal template $10~\mathrm{mK}$5, and a measured noise power spectral density $10~\mathrm{mK}$6. The frequency-domain least-squares objective is

$10~\mathrm{mK}$7

leading to the optimal-filter amplitude estimator and its time-domain realization as a cross-correlation:

$10~\mathrm{mK}$8

SPLENDAQ implements this efficiently with scipy.signal.correlate and applies hysteretic thresholds in units of the expected resolution $10~\mathrm{mK}$9 (Watkins, 2023).

The package’s example workflow uses $4~\mathrm{K}$0 of Moku:Lab noise at $4~\mathrm{K}$1 sampling to estimate a baseline resolution of $4~\mathrm{K}$2 from random windows, then applies threshold triggering with a $4~\mathrm{K}$3 cut and optional event merging (Watkins, 2023). The example runtime is sub-second and reconstructs injected pulse amplitudes within $4~\mathrm{K}$4–$4~\mathrm{K}$5 (Watkins, 2023). Planned extensions include multi-channel triggering, coincidence merging, and support for more hardware platforms beyond Moku (Watkins, 2023).

Within the SPLENDOR detector program, SPLENDAQ functions as the software layer that translates continuous cryogenic readout into triggerable, analyzable events. Its detector-agnostic design is consistent with the collaboration’s broader substrate-agnostic philosophy.

6. Symmetric Splendor in theoretical computer science and economics

A separate usage of the name appears in “Symmetric Splendor,” a named framework rather than a formal acronym (Chan et al., 2024). The framework is defined on vertex-weighted bipartite graphs and is built around refinement pairs that satisfy two local optimality conditions: they are locally maximin and are proportional responses to each other (Chan et al., 2024). Its stated role is to unify density-friendly hypergraph decomposition, universally closest distribution refinements, and a symmetric special case of linear Fisher market equilibrium.

For a bipartite instance $4~\mathrm{K}$6, a refinement $4~\mathrm{K}$7 distributes vertex weights on one side over incident edges, inducing payloads and payload densities on the other side:

$4~\mathrm{K}$8

The local maximin condition is

$4~\mathrm{K}$9

and proportional response is defined by

$\sim 1.6~\mathrm{pF}$0

Among all refinement pairs satisfying these conditions, the induced payload and density vectors are unique (Chan et al., 2024).

The framework yields several notable results. In density decomposition, a locally maximin refinement recovers the canonical decomposition, and reversing the ground-set side yields the same sequence of pairs in reverse order (Chan et al., 2024). In the universally closest distribution refinements problem, any locally maximin/proportional-response pair minimizes $\sim 1.6~\mathrm{pF}$1 for all divergences satisfying the data processing inequality (Chan et al., 2024). In the symmetric Fisher market setting, SPLENDOR provides equilibrium tests through purely local conditions on either buyers or sellers, without explicit prices (Chan et al., 2024).

Algorithmically, the framework connects convex optimization, proportional-response dynamics, and first-order methods. For density-friendly hypergraph decomposition, the paper gives Frank–Wolfe and FISTA guarantees for approximating the density vector in absolute error and shows that proportional-response dynamics provide distributed multiplicative-error approximations (Chan et al., 2024). This cross-transfer of structure and algorithms is the principal significance of the mathematical SPLENDOR framework.

7. Terminological overlap, misattribution, and related usage in astronomy and AI

The name “SPLENDOR” is not uniformly used across all papers in which it has been informally associated. The 2014 SpeX Prism Library paper describes an online, node-based visual programming tool for spectral analysis, but the paper “does not explicitly name the planned node-based visual programming platform ‘SPLENDOR’” (Burgasser, 2014). What it does describe is a node-based, visual, dataflow programming model, drawing on resources such as SQL-searchable spectra, VO-compliant formats, and a Python toolkit called splat, intended to lower the barrier to ultracool-dwarf spectral analysis for students and citizen scientists (Burgasser, 2014). The acronymic or branded use of “SPLENDOR” in this astronomy context is therefore a later association rather than a term defined in that paper.

A further nearby usage concerns the board game Splendor in AI research. Rinascimento models Splendor as a parameterized, partially observable multiplayer game and uses it to study Statistical Forward Planning, event-value functions, and MAP-Elites illumination of behavioral space (Bravi et al., 2019, Bravi et al., 2020, Bravi et al., 2021). The game mechanics include five colored token types plus a joker type, development cards in three decks, nobles that award victory points, and an end condition at $\sim 1.6~\mathrm{pF}$2 victory points (Bravi et al., 2021). The behavioral-space study reports a consistent coverage ordering

$\sim 1.6~\mathrm{pF}$3

showing that event-value-function agents illuminate more of Splendor’s behavior space than point-based or linear state-value alternatives (Bravi et al., 2021).

This usage is orthographically close but conceptually separate from SPLENDOR as a dark-matter collaboration or as Symmetric Splendor. The overlap matters primarily for bibliographic disambiguation. In current arXiv usage, “SPLENDOR” most often denotes either the dark-matter program or the graph-theoretic framework, whereas “Splendor” in AI papers ordinarily refers to the tabletop game benchmark.