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DOE OSTI2024

Improving Cost and Efficiency of the Scalable Solid Oxide Fuel Cells Power System

The objective of this project was to design and develop a 20kW range small-scale solid oxide fuel cells (SOFC) power system for applications such as data centers and commercial buildings. The original plan included a 5,000 hours demonstration and a Techno-Economic Analysis (TEA) which were dropped as part of project termination. The original project plan was to use a stack with a cross-flow cell design which had previously been tested for 500 hours at a community college in Malta, NY. However, it was decided to move to the advanced R-SOFC co-flow cell developed under Department of Energy Award DE-FE0031971. The advanced cell design has the advantage of a larger active area for the same manufacturing footprint which results in fewer required cells for the same stack power, hence a higher volumetric power density (kW/L) and lower cost per kW than the original cross-flow cell design. A full SOFC system Simulink model was developed and calibrated with testing data from a fuel cell stack and BOP (balance of plant) components. The simulation results from the calibrated model showed an acceptable match with the experimental data. A structural analysis conducted for various load scenarios indicated no high stress areas for all spatial directions. Major electrical system components were acquired, built and successfully tested. System sensors were verified and validated against controls. Safety checks, a diagnostic check, PID tuning, and control software commissioning tasks were also conducted. The power electronics prototype was delivered and trial testing completed. Balance of Plant component testing and simulation work was conducted to characterize Reformer-Heat Exchanger heat transfer and backpressure and reformer catalyst methane conversion and product selectivity. Simulations were conducted to design the Anode and Cathode fluid passages and size the air-air and fuel-fuel heat exchangers. A Burner operation map was created from test data and the Anode Gas Recirculation blower was tested to evaluate its durability. The SOFC system used a horizontal style design where components sit directly on a casting with a direct connection to the skid. This design has efficient packaging and a small footprint with approximate dimensions of 750 mm x 700 mm x 1700 mm. An SOFC system was built and successfully tested at the Malta, NY facility The system for over 500 hours under load of which over 300 hours was at full load of 20 kW.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2024

Fiscal Year 2024 Software Quality Assurance Activities for the ARC Software

The continued goal of the ARC SQA project in the Advanced Reactor Technologies program of DOE is to resolve the QA gaps for the ARC software that limit, or prevent, commercialization of the software for industry users. This project started in earnest in fiscal year 2023 which saw the entire code system moved from a SVN repository to a GitLab repository and an associated software quality assurance plan (SQAP) developed and ratified. Most of the QA gaps in the ARC software were identified in collaboration with industry partners and work begin in fiscal year 2023 and continued in 2024. The primary documentation that is missing includes user manuals, user guides, software verification reports, and code coverage assessments. The SUMMAR manual was completed this fiscal year and work was started on creating manuals for SE2ANL, SE2RCT, and DASSH. Software verification work was carried out for DIF3D and REBUS in a previous program and the current fiscal year saw the completion of software verification reports for GAMSOR, GAMSRC, VARPOW, EvaluateFlux, and SUMMAR. The goal for the next fiscal year is to complete the PERSENT software verification work and begin planning the software verification work for DASSH, SE2ANL, and SE2RCT. The code coverage reports for DIF3D and MC2-3 were completed in the previous fiscal year and the goal is to generate code coverage reports for REBUS, GAMSOR, PERSENT, and DASSH in the coming fiscal year. A considerable amount of effort was spent in the current fiscal year working on the continuous integration capability for automated regression testing in GitLab. The first version of the testing was created in the previous fiscal year and applied to DIF3D and its utility programs. That testing was extended this year to cover GAMSOR, REBUS, and PERSENT. To accomplish this, the first version of the new testing methodology had to be updated to make a single output checking methodology viable for all of the ARC software. This will result in a single document to detail the automated regression testing methodology and minor documents to detail the tolerance settings that have been applied to the output for each ARC code. The previous methodology put into place with SVN would have required a separate document for each ARC code to detail the output checking methodology and the tolerance settings for the output from each code. Because some of our industry partners are providing funds to add new capabilities to the ARC software to meet their needs, all of which must be reviewed and approved by the SQA program funded by this project, a summary of that development work is detailed in this report. Overall progress on resolving the QA gaps has been good this year with the most impactful improvement for our industry partners in capability being the creation of a threaded version of DIF3D-VARIANT that allows the DIF3D, REBUS, and GAMSOR run times to be reduced by a factor of 4-6. The most impactful QA gap that was resolved was the software verification of GAMSRC and VARPOW.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Sierra/SolidMechanics Verification Tests Manual (V.5.24)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Sierra/SolidMechanics 5.28 Verification Tests Manual

Presented in this document is a small portion of the tests that exist in the Sierra/SolidMechanics (Sierra/SM) verification test suite. Most of these tests are run nightly with the Sierra/SM code suite, and the results of the test are checked versus the correct analytical result. For each of the tests presented in this document, the test setup, a description of the analytic solution, and comparison of the Sierra/SM code results to the analytic solution is provided. Mesh convergence is also checked on a nightly basis for several of these tests. This document can be used to confirm that a given code capability is verified or referenced as a compilation of example problems. Additional example problems are provided in the Sierra/SM Example Problems Manual. Note, many other verification tests exist in the Sierra/SM test suite, but have not yet been included in this manual.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2026

Hydropower Infrastructure - LAkes, Reservoirs, and RIvers (HILARRI), v4

HILARRI is a database of links between major datasets of operational hydropower dams and powerplants, and inland water bodies. These connections are critical for conducting large-scale analysis of hydropower infrastructure and their associated natural and engineered water systems. Features include: – Dams from the National Inventory of Dams (2025) and the Global Reservoir and Dam Database (GRanD v1.3) – Hydropower plants from the Existing Hydropower Assets dataset (EHA 2025) – Power plants that are listed in the 2025 U.S. Hydropower Development Pipeline Data or were listed in previous versions of the dataset These hydropower infrastructure features are linked to several major datasets that provide hydrologic and hydraulic information relevant for analysis of hydropower systems that includes the integral water resources. That information comes from: – Products from the National Hydrography Dataset (NHD) – NHDPlusV2 Medium Resolution river network flowlines, – NHD waterbodies (limited to lakes and reservoirs), – NHD Watershed Boundary Dataset (HUC12-level for the Conterminous United States (CONUS)) – NHD High Resolution waterbodies – HydroLAKES water bodies (lakes and reservoirs) – LAGOS-US lakes and reservoirs – EPA National Lakes Assessment (2007, 2012, 2017, and 2022) – The Reservoir Sedimentation Database (RESSED) – EPA SuRGE sampling locations Unique identifiers are used to facilitate joining to the original full datasets. For example, characteristics of NHD flowlines such as estimated average flow rate can be joined from the NHDPlusV2 dataset to a dam or power plant listed in HILARRI based on the ID field, “COMID”, that is common to both datasets. HILARRI only includes basic information about identifiers, location, and data quality or usage notes. It does not contain the attributes or time series data associated with these sites. The HILARRI dataset incorporates information from several datasets to facilitate more effective and accurate analysis of hydropower infrastructure and their associated waterbodies. For example, dams were checked against the most recent American Rivers Dam Removal Database to identify and flag facilities that may no longer exist. Additionally, dams that are listed multiple times in the NID are identified and flagged to avoid double-counting when analyzing and summarizing information. Other quality flags include certainty of operational hydropower (i.e., if one or more datasets indicates hydropower at a particular location), whether an associated water body is accurate or composed of multiple polygons, or whether there is a known issue with reported characteristics in one of the underlying datasets. These additional data flags are designed to increase confidence in data usage for individual to large-scale analyses.

Hansen, Carly [ORNL] (ORCID:0000000193280838)↗

DOE OSTI2025

Diffusion Codes: Self-Correction from Small(er)-Set Expansion with Tunable Non-locality

Optimal constructions of classical LDPC codes can be obtained by choosing the Tanner graph uniformly at random among biregular graphs. We introduce a class of codes that we call ``diffusion codes'', defined by placing each edge connecting bits and checks on some graph, and acting on that graph with a random SWAP network. By tuning the depth of the SWAP network, we can tune a tradeoff between the amount of randomness -- and hence the optimality of code parameters -- and locality with respect to the underlying graph. For diffusion codes defined on the cycle graph, if the SWAP network has depth $\sim Tn$ with $T> n^{2β}$ for arbitrary $β>0$, then we prove that almost surely the Tanner graph is a lossless ``smaller set'' vertex expander for small sets up size $δ\sim \sqrt T \sim n^β$, with bounded bit and check degree. At the same time, the geometric size of the largest stabilizer is bounded by $\sqrt T$ in graph distance. We argue, based on physical intuition, that this result should hold more generally on arbitrary graphs. By taking hypergraph products of these classical codes we obtain quantum LDPC codes defined on the torus with smaller-set boundary and co-boundary expansion and the same expansion/locality tradeoffs as for the classical codes. These codes are self-correcting and admit single-shot decoding, while having the geometric size of the stabilizer growing as an arbitrarily small power law. Our proof technique establishes mixing of a random SWAP network on small subsystems at times scaling with only the subsystem size, which may be of independent interest.

Combinatorics (math.CO)↗

DOE OSTI2024

EPCAPE-PT-LANL Measurements: Humidified Cavity Attenuated Phase Shift Spectroscopy

Coastal cities offer a unique environment for studying aerosol-cloud interactions and the effects of urban emissions on cloud properties. As part of the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE), the Partitioning Thrust by Los Alamos National Laboratory (EPCAPE-PT-LANL) was conducted. Our campaign focused on measuring the optical and chemical properties of aerosols and their interactions within marine stratocumulus clouds in La Jolla, California. EPCAPE-PT-LANL enhances the primary goals of EPCAPE through innovative observations of vapor-phase transitions between aerosols and cloud droplets, the impact of black carbon on aerosol-cloud dynamics, and the effects of cloud processing on aerosol optical properties. Instrument: Humidified Cavity Attenuated Phase Shift Particulate Matter Single Scattering Albedo (H-CAPS-PMSSA, Aerodyne Inc) Data Notes: The scattering truncation correction was not applied to Bsca. The Bext needs no correction. Files: data_10sec_CAPS.csv, data_10min_CAPS.csv Header: - Bext_wet_CAPS_450nm[1/Mm]: Wet aerosol extinction coefficient measured at 450 nm by the CAPS, in inverse megameters (Mm⁻¹). - Bsca_wet_CAPS_450nm[1/Mm]: Wet aerosol scattering coefficient measured at 450 nm by the CAPS, in inverse megameters (Mm⁻¹). - Temp_wet_CAPS[K]: Temperature inside the wet CAPS measurement chamber, in Kelvin. - Bext_dry_CAPS_450nm[1/Mm]: Dry aerosol extinction coefficient measured at 450 nm by the CAPS, in inverse megameters (Mm⁻¹). - Bsca_dry_CAPS_450nm[1/Mm]: Dry aerosol scattering coefficient measured at 450 nm by the CAPS, in inverse megameters (Mm⁻¹). - Temp_dry_CAPS[K]: Temperature inside the dry CAPS measurement chamber, in Kelvin. - Wet_RH_preCAPS[%]: Relative humidity before entering the wet CAPS, in percent. - Wet_RH_postCAPS[%]: Relative humidity after exiting the wet CAPS, in percent. - Humidifier_RH_CAPS[%]: Relative humidity inside the humidifier used with the CAPS, in percent. - dualCAPS_inlet_RH[%]: Relative humidity at the inlet of the dual (wet/dry) CAPS setup, in percent. - Wet_Temp_preCAPS[C]: Temperature before entering the wet CAPS, in degrees Celsius. - Wet_Temp_postCAPS[C]: Temperature after exiting the wet CAPS, in degrees Celsius. - Humidifier_Temp[C]: Temperature inside the humidifier used with the CAPS, in degrees Celsius. - dualCAPS_inlet_Temp[C]: Temperature at the inlet of the dual (wet/dry) CAPS setup, in degrees Celsius. - Zero_dry_CAPS: 1 is a calibration check for the dry CAPS to ensure zero reading under filter air conditions. - Zero_wet_CAPS: 1 is a calibration check for the wet CAPS to ensure zero reading under filter air conditions. - CVI_Flag[bool]: A boolean flag indicating whether the Counterflow Virtual Impactor (CVI) was active (true) or inactive (false) during the measurement.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

BSEC flux towers: CSAT3B and TRH

The data were collected as part of the BSEC project, during the period from June 2025 to May 2026. Directory "broadway" contains data collected on a multi-level flux tower (US-BWf) in the Broadway East neighborhood (1808 North Patterson Park Ave., Baltimore City, MD 21213; LAT: 39o18'40.31'' N; LONG: 76o35'12.43'' W). At each of the four measurement heights (8.5 m, 11.1 m, 13.4 m, 15.9 m), a Campbell Scientific CSAT3B sonic anemometer was operated at 50 Hz to measure virtual temperature (tc) and three velocity components (u: 270 degrees; v: 180 degrees; w: vertical), and a RM Young temperature sensor (model 41382VC) was operated at 1 Hz inside a compact aspirated radiation shield (model 43502) to measure absolute temperature (T) and relative humidity (RH). Inside directory "broadway", directory "netcdf" contains data collected each day in 5-minute chunks that have been converted to NetCDF format (before quality checking), while "4hr" contains data arranged into 4-hour chunks (also in NetCDF format) that have been through basic quality checking steps (treating data points with nonzero diagnostic codes as missing data; fixing six or fewer consecutive missing data points using linear interpolation). Users are recommended to start with data in directory "4hr", while data in directory "netcdf" can be used for reference purposes.

Baltimore↗

DOE OSTI2025

The DESI DR1 Peculiar Velocity Survey: Fundamental Plane Catalogue

Measurements of peculiar velocities in the local Universe are a powerful tool to study the nature of dark energy at low ($z < 0.1$) redshifts. Here we present the largest single set of $z<0.1$ peculiar velocity measurements to date, obtained using the Fundamental Plane (FP) of galaxies in the first data release (DR1) of the Dark Energy Spectroscopic Instrument (DESI). We describe the photometric and spectroscopic selection criteria used to define the sample, as well as extensive quality control checks on the photometry and velocity dispersion measurements. Additionally, we perform detailed systematics checks for the many analysis parameters in our pipeline. Our DESI DR1 catalogue contains FP-based distances and peculiar velocities for $98,292$ unique early-type galaxies, increasing the total number of $z < 0.1$ FP distances ever measured by a factor of $\sim2$. We achieve a precision of $26\%$ random error in our distance measurements which is comparable to previous surveys. A series of companion DESI papers use the distances and peculiar velocities presented in this paper to measure cosmological parameters.

Ross, C. E. [Queensland U.]↗

DOE OSTI2026

Design and Characterization of the 162.5 MHz RF Component Layout for Fermilab's PIP-II Reference Line

The Proton Improvement Plan II (PIP-II) Reference Line at Fermi National Accelerator Laboratory distributes phase-stable radio-frequency (RF) signals throughout the accelerator. PIP-II requires stable timing and phase reference signals so its accelerating cavities transfer energy to the particle beam at the correct point in each RF cycle. The full system includes 162.5, 325, and 650 MHz sections corresponding to the frequency sections of the PIP-II Linac, with this project focusing on the 162.5 MHz section. The Reference Line must provide a phase stable source signal while responding to phase changes caused by environmental conditions or system drift. Its RF components will be mounted on aluminum heat plates inside a temperature controlled enclosure to further limit temperature-driven phase changes. To prepare the system for manufacture, the project reviewed component functions and dimensions, developed a computer-aided design (CAD) model, and arranged the hardware to support short cable paths, grounding, fastener access, and maintenance. Several full scale, three dimensional printed prototypes allowed the available components to be mounted and inspected. These fit checks revealed mechanical conflicts and guided revisions to component placement, countersink geometry, labeling, and plate thickness. Electrical characterization was also performed on selected RF hardware to compare its measured behavior with the performance metrics that were set for our design. Overall, the project produced a manufacturable 162.5 MHz layout, physical fit-check prototypes, and documented electrical measurements that support review before metal fabrication. The 325 and 650 MHz layouts remain future work because they require additional minor mechanical changes.

Subedi, Harsheet [Unlisted, US, CA] (ORCID:0009000↗

DOE OSTI2024

Globus service enhancements for exascale applications and facilities

Many extreme-scale applications require the movement of large quantities of data to, from, and among leadership computing facilities, as well as other scientific facilities and the home institutions of facility users. These applications, particularly when leadership computing facilities are involved, can touch upon edge cases (e.g., terabyte files) that had not been a focus of previous Globus optimization work, which had emphasized rather the movement of many smaller (megabyte to gigabyte) files. We report here on how automated client-driven chunking can be used to accelerate both the movement of large files and the integrity checking operations that have proven to be essential for large data transfers. In conclusion, we present detailed performance studies that provide insights into the benefits of these modifications in a range of file transfer scenarios.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Report on the AAPM grand challenge on deep generative modeling for learning medical image statistics

Abstract Background The findings of the 2023 AAPM Grand Challenge on Deep Generative Modeling for Learning Medical Image Statistics are reported in this Special Report. Purpose The goal of this challenge was to promote the development of deep generative models for medical imaging and to emphasize the need for their domain‐relevant assessments via the analysis of relevant image statistics. Methods As part of this Grand Challenge, a common training dataset and an evaluation procedure was developed for benchmarking deep generative models for medical image synthesis. To create the training dataset, an established 3D virtual breast phantom was adapted. The resulting dataset comprised about 108 000 images of size 512 512. For the evaluation of submissions to the Challenge, an ensemble of 10 000 DGM‐generated images from each submission was employed. The evaluation procedure consisted of two stages. In the first stage, a preliminary check for memorization and image quality (via the Fréchet Inception Distance [FID]) was performed. Submissions that passed the first stage were then evaluated for the reproducibility of image statistics corresponding to several feature families including texture, morphology, image moments, fractal statistics, and skeleton statistics. A summary measure in this feature space was employed to rank the submissions. Additional analyses of submissions was performed to assess DGM performance specific to individual feature families, the four classes in the training data, and also to identify various artifacts. Results Fifty‐eight submissions from 12 unique users were received for this Challenge. Out of these 12 submissions, 9 submissions passed the first stage of evaluation and were eligible for ranking. The top‐ranked submission employed a conditional latent diffusion model, whereas the joint runners‐up employed a generative adversarial network, followed by another network for image superresolution. In general, we observed that the overall ranking of the top 9 submissions according to our evaluation method (i) did not match the FID‐based ranking, and (ii) differed with respect to individual feature families. Another important finding from our additional analyses was that different DGMs demonstrated similar kinds of artifacts. Conclusions This Grand Challenge highlighted the need for domain‐specific evaluation to further DGM design as well as deployment. It also demonstrated that the specification of a DGM may differ depending on its intended use.

Radiology, Nuclear Medicine & Medical Imaging↗

DOE OSTI2025

Correlating processing variables to material properties in recycled polypropylene: A data‐driven approach

Abstract Polypropylene (PP) is one of the most widely used plastics, yet its recycling remains limited, with less than 1% of solid waste PP being reprocessed. Mechanical recycling through extrusion is the most practical method, but inconsistent reprocessing conditions introduce variability in material properties. While temperature, screw speed, and residence time influence the thermomechanical stress applied during reprocessing, there are no standardized guidelines for optimizing these parameters. This study examines how these factors shape the properties of recycled PP, using conditions designed to mimic post‐industrial recycled (PIR) scrap. Residence time was measured using colorimetric tracking and correlated with molecular weight, viscosity, and mechanical properties over multiple extrusion cycles. Data‐driven modeling, including response surface methodology, support vector machines, and artificial neural networks, identified processing temperature as the dominant factor in material degradation, followed by residence time. Mechanical properties remained stable, while viscosity decreased predictably with increasing residence time. By linking reprocessing conditions to property evolution, this study provides a method to optimize processing parameters and reduce variability in recycled PP. These findings help manufacturers improve process control, making recycled PP more predictable for reuse in manufacturing. Highlights Study of PIR‐quality PP without additives or compatibilizers. Residence time analysis shows processing temperature drives PP property changes. Mark‐Houwink enables quick molecular weight checks for quality control. Models predict mechanical and rheological shifts in reprocessing. Optimized processing parameters minimize property degradation in recycling.

Estela‐García, John E. [Polymer Engineering Center↗

DOE OSTI2025

Threshold resummation for double-deeply virtual Compton scattering

The threshold region for double-deeply virtual Compton scattering (DDVCS) is discussed. I derive a resummation formula for the (partonic) threshold logarithms in the flavor non-singlet case. The resummations can be done by using (re)factorization theorems for the coefficient functions near the partonic thresholds. As a byproduct, we obtain the leading term in the threshold limit of the two-loop coefficient function in double-deeply-virtual Compton scattering, which agrees with the recent result from explicit calculation, providing a highly non-trivial cross-check.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Updated constraints from electric dipole moments in the MSSM with R-parity violation

We revisit the electric dipole moments (EDMs) of quarks and leptons in the Minimal Supersymmetric Standard Model (MSSM) with trilinear R-parity violation (RPV). In this framework, EDMs are induced at the two-loop level via RPV interactions. We perform a comprehensive recalculation of several classes of Barr-Zee type diagrams in a general Rξ gauge. While we find general agreement with previous analytic results in the literature, our work provides a valuable independent cross-check of the complicated calculations. We also point out some subtleties in the intermediate steps and in the choice of the flavor basis for the numerical evaluation of the expressions. By confronting the theoretical predictions with the latest experimental limits on EDMs, we derive updated constraints on combinations of RPV couplings. We highlight an approximate, testable correlation between the proton and neutron EDM that emerges within the considered class of RPV models, offering a distinctive signature for future EDM experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Scalar-scaffolded gluons and the combinatorial origins of Yang-Mills theory

We present a new formulation for Yang-Mills scattering amplitudes in any number of dimensions and at any loop order, based on the same combinatorial and binary-geometric ideas in kinematic space recently used to give an all-order description of Tr Φ 3 theory. We propose that in a precise sense the amplitudes for a suitably “stringy” form of these two theories are identical, up to a simple shift of kinematic variables. This connection is made possible by describing the amplitudes for n gluons via a “scalar scaffolding”, arising from the scattering of 2n colored scalars coming in n distinct pairs of flavors fusing to produce the gluons. Fundamental properties of the “u-variables”, describing the “binary geometry” for surfaces appearing in the topological expansion, magically guarantee that the kinematically shifted Tr Φ 3 amplitudes satisfy the physical properties needed to be interpreted as scaffolded gluons. These include multilinearity, gauge invariance, and factorization on tree- and loop-level gluon cuts. Our “stringy” scaffolded gluon amplitudes coincide with amplitudes in the bosonic string for extra-dimensional gluon polarizations at tree-level, but differ (and are simpler) at loop-level. We provide many checks on our proposal, including matching non-trivial leading singularities through two loops. The simple counting problem underlying the u variables autonomously “knows” about everything needed to convert colored scalar to gluon amplitudes, exposing a striking “discovery” of Yang-Mills amplitudes from elementary combinatorial ideas in kinematic space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Split-helicity tree amplitudes and flag cluster algebras

Recent work has uncovered a connection between the symbol letters of general massless scattering and (permutations of) cluster variables of partial flag varieties. In this paper we explore the cluster adjacency of tree-level gluon amplitudes, specifically focusing on split-helicity amplitudes which can be written in closed form in terms of zigzag diagrams. We check in several cases, and conjecture in general, that the poles in each term satisfy cluster adjacency under a set of permutations that is built from arc permutations of the corresponding zigzag.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Multi-invariants and bulk replica symmetry

In this paper, we analyze the question of replica symmetry in the bulk for multi-partite entanglement measures in the vacuum state of two dimensional holographic CFTs. We first define a class of multi-partite local unitary invariants, multi-invariants , with a given replica symmetry that acts freely and transitively on the replicas. We look for a subclass of measures such that the dual bulk geometry also preserves replica symmetry. We obtain the most general solution to this problem if we require the bulk to preserve replica symmetry for general configurations of the regions. Orbifolding the bulk solution with the replica symmetry gives us a bulk geometry with a network of conical singularities. Our approach makes it clear that there are infinitely many infinitely large families of multi-invariants such that each family evaluates identically on the holographic state. Geometrically, these are equalities involving volumes of handlebodies, possibly of different genus, at particular points in the moduli space. In certain cases, we check our bulk computation with an explicit calculation in CFT. Finally we comment on the generalization to higher dimension.

AdS-CFT Correspondence↗