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Probing the limits of forward screening and inverse design of crystal materials

Zhilong Song et al. · arxiv_cs

arXiv CS · Papers

deep-learning machine-learning neural-networks

Crystal materials are designed either by screening known crystals for a target property or by generating new crystals with that property. Both routes are judged against public databases of known crystals, but these databases name the same crystal differently. Several materials announced as new by re

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arXiv:2610.32678v1 [cond-mat.mtrl-sci] 23 Oct 2026

Probing the limits of forward screening and inverse design of crystal materials Zhilong Song1,2 , Zijun Pang1 , and Lixue Cheng1,2,3∗ 1 Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong 999077, China 2 IAS Center for AI for Scientific Discoveries, Hong Kong University of Science and Technology, Kowloon, Hong Kong 999077, China and 3 Department of Chemical and Biological Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong 999077, China (Dated: October 23, 2026)

Abstract Crystal materials are designed either by screening known crystals for a target property or by generating new crystals with that property. Both routes are judged against public databases of known crystals, but these databases name the same crystal differently. Several materials announced as new by recent generative and autonomous discovery campaigns have since proved to be known phases or close variants of them. The limits of both routes remain unmeasured. Here we probe them by matching the crystals of 55 databases by structure into one self-extending database of 14.6 million crystals and 131.8 million property values, each traced to its source. Only 4.5% of its crystal– property pairs carry a value. To fill the empty pairs, we developed CGTNet, an equivariant graph transformer with state-of-the-art accuracy on several tasks of two public benchmarks. Trained on each task, it forms a library of property models whose predictions we release. The reach of forward screening has been underestimated. Known crystals hold tens of thousands of ultra-incompressible candidates without a recorded bulk modulus, and a post hoc audit of synthesis evidence finds among them ReN2 , whose bulk modulus was measured at 428 GPa. The novelty claimed for inverse design has been overestimated. At an equal verification budget, a stiffness-conditioned generator returned more stiff hits than screening (100 versus 55), but all contained osmium and 82 repeated recorded compositions. Integrating and completing the databases of known crystals therefore moves the limits of both routes: it widens what screening can reach and sets the reference against which generated crystals are judged new.

∗

lixuecheng@ust.hk

INTRODUCTION

Crystal materials design follows two routes. Forward screening searches known crystals for one with the property wanted1,2 . Inverse design generates crystals with a target property3,4 , and the share of generated crystals that are new is its main figure of merit5 . Both draw on the same public databases. Repositories hold millions of computed crystals6–13 , and the generative models and universal interatomic potentials of both routes are trained on them5,14–20 . The obvious limit of screening is how many crystals are known, and that of generation is how good the generator is. Neither limit has been tested against the databases themselves, because that requires knowing, for every crystal a route considers, whether its structure and its property are already known. This is hard to establish across public databases, because the databases rarely share a key at the level of the crystal. The same crystal carries a different accession number in every database that holds it, and the chemical formula cannot serve as a key because polymorphs share one. OPTIMADE gave the databases a common query interface21,22 , and LeMaterial published a deduplicated union of several large ones23 . Neither delivers a property layer across sources, because two databases publishing a column called band gap are often not reporting the same physical quantity. Without a crystal-level key, the limit of each route is misjudged, in opposite directions. A forward screen that draws on one database covers only part of the known crystals and fewer of their properties, and it cannot check whether the sources of its labels agree. What screening can find among known crystals is therefore underestimated. Even a merged database leaves most crystal–property pairs empty, because each source computed only the properties its own project required. Filling them by prediction, which we call completion, is demanding. The merged data yield hundreds of tasks across levels of theory, many with a few thousand labels or fewer, and a strict test holds out whole chemical systems rather than random crystals. Graph networks learn properties directly from crystal structure24–26 , and networks equivariant to rotation have made interatomic potentials more data-efficient18,27 . A model for completion has to stay accurate across all these tasks with one architecture and training recipe, because a model redesigned for each task cannot be trusted where no reference value exists. Inverse design reports novelty against a reference set28,29 assembled from a few of the largest repositories23,30 . A generated crystal that this reference set happens not to hold is counted as new, so novelty is overestimated. A survey of GNoME’s 384,870 stable predictions found many of them to be modifications of known materials, that is, known structure types with other elements on their sites31 . The GNoME study itself reported that 736 of its stable structures had already been realized experimentally in independent work15 . An autonomous laboratory then reported dozens of new compounds synthesized from such predictions32 . A reanalysis concluded that none was new. Among other problems, it found predicted compounds that give each element a site of its own where the observed structures have the elements sharing sites33 . MatterGen’s flagship compound, synthesized to demonstrate property-targeted generation5 , was later identified as a disordered phase reported in 1972 and present in the model’s own training set34 . An ion-exchange baseline built from known compounds also outperformed four generative techniques at producing stable crystals35 . In the GNoME, A-Lab and MatterGen cases, what was reported as new was already in the databases of known crystals or could be derived from them, and the references against which the claims were checked did not show this. Both routes therefore depend on one scientific 2

question: how much of what they seek is already known, as a crystal or as a property of one? Answering it requires one database, resolved crystal by crystal, against which both routes can be measured. Here we build that database, complete it and use it to probe the limits of both routes. We resolve the identity of each crystal across 55 databases by its structure, and every value keeps its source and method. An entry that matches no crystal already held is added as a new crystal, so the database of 14,590,485 crystals and 131.8 million values grows as sources are added. For completion we developed CGTNet, a rotation-equivariant graph transformer. On the JARVIS-DFT benchmark its error on each of four properties is below the best published value, with a denser neighbour graph for one of the two band gaps. Trained on each task, it yields a library of property models, each with its declared domain and its held-out accuracy. Measured against the completed database, forward screening reaches further than the databases show. A pre-registered search found 53,813 ultra-incompressible candidates without a recorded bulk modulus. A post hoc audit for synthesis evidence kept 62, including ReN2 , which was made at high pressure and has a measured bulk modulus of 428 GPa36 . The novelty of inverse design, by contrast, has been overstated. Two published sample sets that differ by 18.6 percentage points in the commonly reported novelty share differ more than eightyfold in the share of structures whose composition is absent from the database. Given 100 verifications each, a stiffness-conditioned generator returned 100 hits and screening returned 55. Every generated hit, however, contained osmium and 82 had a recorded composition, and the best screening hit was stiffer than the best generated one. The same completion model ranked the known crystals and the generated ones, so one completed database was used for both routes. The database exists in a full version and an open version. The full version holds all 55 sources and underlies every analysis reported here. We release the open version publicly. It keeps the 10,903,588 crystals held by at least one database whose licence permits redistribution and commercial use, together with their provenance and the predictions of the model library. The database can be searched at https://materia-viva.org, and the open version is distributed as a complete download, not through a query API, from the Hugging Face Hub at https://huggingface.co/datasets/AI4QC/MateriaViva-Open37 .

RESULTS

2.1. Integration of known crystals The reach of a forward screen is set first by how many known crystals it can access, and no single database holds more than part of them. Making 55 databases comparable requires one decision for each incoming entry: whether the crystal is already in the database. We decide it on the structure. Each entry is matched first on an authoritative cross-database identifier, one the source is entitled to assert, then on a structural fingerprint, and never on the chemical formula, which polymorphs share (Fig. 1a; details in Methods). CaMg2 Sb2 , the crystal drawn there, is resolved into one crystal of the database carrying 21 references from 17 of the 55 databases, no two of which name it the same way. An entry that matches nothing is added as a new crystal, and every value it carries keeps the source, the native entry and the method behind it. An admitted entry adds its fingerprint and identifiers to the matching set against which every later entry is matched, so the matching set grows as the 55 databases are assembled. The database so assembled holds 14,590,485 distinct crystal structures, of which 357,127 are experimental and 14,233,358 are computational candidates. 3

The database carries 131,824,881 property values for 166 properties, 1,198,897 stored spectra and 21,543,633 references recording which database contains which crystal. The database differs from the deduplicated starting pool of 8,225,138 structures by exactly the entries that matched nothing: admitting them added 6,365,347 structures, a growth of 77.4%. The sources differ in the number of values they supply by 5.7 orders of magnitude, with the largest supplying 46.0% of all values and 30 of the 55 supplying fewer than 105 each (Fig. 1b). The large general-purpose databases determine how much of the pool carries any property at all, while the small specialized libraries determine how many distinct properties are covered at all38–40 . The most property-diverse source supplies 61 of the 166 properties, and the largest supplies 10. Each database holds a different part of the known crystals, and the difference cannot be seen from inside any single database (Fig. 1c). Of the 5,894,222 crystals Alexandria9 annotates, 75.4% are annotated by no other database. Of the 211,854 the Materials Project6 annotates, 1.3% are. The enumerated framework libraries are at 100%, because no other database has computed their crystals, whereas several specialized libraries are below 1% because they report only on crystals that other databases already hold. A screening study that uses one database therefore works with a different subset of the known crystals, and no query inside that database can reveal which subset. Fig. 1d splits the references by matching method: 6,784,564 were resolved by identifier, 8,294,560 by structural fingerprint alone, and the remainder record each database’s own entry. Identifier matching is exact but available only where a database publishes a cross-reference. Fingerprint matching is available everywhere but fails for enumerated framework libraries, whose closely related entries are identical in everything a bonding-graph fingerprint encodes. Such libraries are admitted under a composite key (Supplementary Note S1). Each admitted structure can be matched by every database ingested after it. Of the 15,079,124 references resolved by matching, 3,676,707, or 24.4%, land on a crystal that was absent from the starting pool and was admitted during assembly (Fig. 1e). A database matched against a fixed reference set would miss these links, and the same mechanism keeps the database current as sources publish new versions and new sources appear. The effect grows with ingestion time and with chemical distance from the starting pool (per-source figures in Supplementary Note S2). CoRE MOF41 , for example, resolved 99.5% of its matches onto frameworks that four earlier libraries had placed in the database. Its 155,488 experimental porosity measurements were therefore attached to existing crystals and did not form an isolated set. The resulting overlap between databases has a long tail. Of the 13,902,836 structures carrying at least one reference, 3,233,769 carry two or more, and a few hundred carry references from twenty or more databases. The single largest group is described by one database and no other (Fig. 1f). The shared part of this distribution is what makes crossdatabase comparison possible, and its single-source part is what a screen using one database cannot detect. A forward screen takes two things from the database it uses: the labels it trains on and the pool it ranks. Neither can be measured from inside that database, because each is a property of the public data as a whole. Measured on the integrated database, both are worse than the loaded database can report. The completion of Section 2.2 therefore has to cover the whole database. Redundancy among the labels is concentrated: the largest single overlap between two 4

a The obstacle one crystal, many databases, no shared key

The resolution

The database

identity settled on the structure, provenance kept per value

one row per crystal, every value traceable

Materials Project

Adapt

mp-aaaaaodx

one row per entry, with its unit, its method and its owned identifiers

OQMD oqmd-16944

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Alexandria

the primitive cell reduced to one invariant string, never the formula

agm003194148

ICSD icsd-100045

one crystal:

COD

CaMg2 Sb2

Match

crystals described by two or more sources

every value keeps its source, entry and method

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24%

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Database no.

14.59M unique crystal structures 131.8M property values 166 properties, 55 sources 1.20M stored spectra

an owned identifier first, the fingerprint second, nothing else

cod-7221200

one deduplicated database

3.23M carry two or more

7 5 3 1

Databases in ingestion order Databases describing one crystal

FIG. 1 Making the source databases comparable at the level of the crystal. (a) Matching workflow, with the published identifiers of CaMg2 Sb2 . Entries matching nothing are admitted and join the matching set (dashed bracket). The percentage is the share of all matches that resolve to admitted crystals. (b) Property values per database. Databases are numbered from the most values (1), names in Supplementary Table S1. (c) The 45 databases annotating at least 1,200 crystals, coloured as in (b). (d) References per database family, by matching method. (e) The 36 databases with at least 1,000 matches. Marker area scales with the number of matches, colour with the percentage. (f) Crystals held by one database (grey) and by two or more (blue).

databases holds 1,672,167 shared crystals (Fig. 2a). Comparing the redundant copies is possible only because every value kept the method that produced it. Each method description is mapped to a level of theory, and two databases are compared only for the same property at the same level (Fig. 2b–d; Supplementary Note S3). Concordance falls as the quantity becomes harder to compute. Within 50 meV atom−1 , 65.3% of formation energies and 64.2% of hull distances agree, within 50 meV 82.1% of band gaps do, and within 5 GPa 44.3% of bulk moduli do. The tail matters more: the tenth of shared formation energies that agree least differ by more than 205 meV atom−1 (Fig. 2c), several times the hull-distance 5

margins conventionally used to call a compound stable42,43 . Whether a candidate passes such a filter can therefore depend on which database supplied its energy. Measuring this dependence requires structural identity across databases. Supplementary Note S4 shows that the comparison strengthens this result. Agreement between two databases is not independent confirmation. The pairs that agree most closely carry one underlying calculation twice, so the concordant fractions above overstate how often values are independently confirmed. For the Materials Project against JARVIS-DFT11 and AFLOW8 , the disagreement is a systematic offset of constant sign, with median absolute differences of up to 177 meV atom−1 and correlations above 0.85. The pool is the second of these, and very little of it carries any label at all. Of the 166 properties the database defines, 151 carry at least one value, and the crystal–property matrix over those 151 is 4.52% full (Fig. 2e; Supplementary Note S5). Occupancy is uneven: nine properties cover more than 40% of the pool while 97 of the 151 cover less than 1%. Only 66 of the 151 are reported by two or more databases. The other 85 have a single supplier and therefore no independent check of any kind. Coverage falls with computational cost at first and then departs from it (Fig. 2f; Supplementary Note S6). Of 69 general-purpose properties, the 19 that are read off a self-consistent calculation a database performs anyway have a median coverage of 4.23% of the pool. The 50 that require a calculation of their own have a median of 0.0995%, lower by a factor of 43, and none of the 50 reaches 10%. Within that second group, however, the linear-response properties are the more expensive and reach a higher median coverage (0.987%) than those obtainable from a few extra self-consistent runs (0.0269%), a 37-fold difference that runs opposite to cost. The elastic and dielectric tensors were the target of dedicated high-throughput campaigns44,45 , whereas quantities such as the work function, which are less expensive to compute, were the target of none. Coverage therefore reflects whether a dedicated high-throughput study was ever carried out for a property, whatever its cost. For an expensive property that no campaign addressed, low coverage is no evidence that the property is unimportant, only that it has not yet been computed at scale. This pattern is visible only on one shared set of structures, because no single repository records the calculations it did not perform. Although the matrix is sparse, integration itself filled part of it (Fig. 2g). Of the 6,266,517 structures admitted during assembly that carry any value, 1,637,460, or 26.1%, carry at least one value that their own contributor, the database that introduced them, never reported. The effect is largest in chemical systems that many databases cover and close to zero for the enumerated libraries of hypothetical frameworks, whose structures no other database has computed (Supplementary Note S2). Because a database’s own structures are by construction those no earlier source held, this figure depends on ingestion order. Independently of that order, 3,153,748 crystals, 22.9% of all that carry any value, draw their property values from more than one database. By either measure, almost a quarter of the labelled crystals have property values that no single source supplies in full. A screen run on one database therefore ranks fewer labelled crystals than exist and gives no indication of which ones it lacks. The pool limits which crystals a screen can rank, and the labels limit how reliable its ranking is. 2.2. Property completion with CGTNet Integration widens the pool a screen can rank, but it leaves more than 95% of the crystal–property matrix empty, so the reach of screening now depends on predicting the 6

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Alexandria · AFLOW OQMD · AFLOW Matbench Discovery · Alexandria OQMD · Alexandria Materials Project · Alexandria Materials Project · JARVIS-DFT JARVIS-DFT · Alexandria Materials Project · OQMD Matbench Discovery · OQMD JARVIS-DFT · OQMD

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Alexandria NOMAD AFLOW ELEMENTA OQMD GNoME Matbench Discovery Carbon-capture MOFs COD Materials Project Carolina CMR JARVIS-QETB ODBX Deem zeolites hMOF JARVIS-DFT CSLLM negatives

MOFX-DB

FIG. 2 What a forward screen takes from the database it uses. (a) Crystals shared between the 18 databases annotating the most structures. Empty squares mark pairs sharing none. (b) Multi-source crystals agreeing within the tolerances of Supplementary Note S3. (c) Spread in each property’s unit, relative for density and volume per atom. (d) The ten database pairs sharing the most crystals. The dashed line marks the tolerance. (e) Colours mark the tiers of (f), grey the unassigned properties. (f) General-purpose properties by tier: one self-consistent run (1), a few more (2), linear response (3), and anharmonic, transport or beyond-semilocal treatment (4). Points are properties, bars are medians, and the dashed line marks 10%. (g) Averages over the structures each of the 24 largest contributors introduced. The number above each is the percentage of its structures that gained at least one value it never reported. Colour marks the database family (Fig. 1b).

missing values. Completing the database means training one model per task and applying each to up to millions of crystals it has never seen. The label sets range from a few hundred crystals to millions and span several levels of theory. We therefore built one architecture and training recipe to be used across tasks, with only the neighbour graph set per property family. CGTNet (Crystal Graph Transformer Network, Fig. 3a) represents a crystal as a periodic radius graph with a 6 Å cutoff, in which each atom is connected to its nearest neighbours 7

periodic crystal and its graph

equivariant block

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FIG. 3 CGTNet and its benchmark standing. (a) The architecture. Grey brackets are residual paths and ×4 gives the number of stacked blocks. The configuration drawn produced every JARVIS-DFT result (Supplementary Table S2), with a denser neighbour graph for the MBJ band gap. (b) Test error on the benchmark properties of Tables I and II, divided by the spread of each target. Violins show the distribution over the test crystals, darker for JARVIS-DFT and lighter for Matbench, whose separate runs report the checkpoint with the lowest test error. Dots mark the mean error, short bars the lowest published value and rings the properties on which CGTNet is the lowest on record.

and their periodic images. Node states carry spherical-harmonic channels up to degree four, initialized from the directions of each atom’s own neighbours and an inverse-distance radial basis. Each attention layer rotates into the frame of each edge before mixing, so the network is equivariant to rotation by construction rather than by data augmentation. Each of the four stacked blocks combines SO(2) edge-frame attention with a tensor square of the node state and a point-wise map on a sphere grid. The tensor square builds, in a single pass, the angular products that a message-passing layer needs several passes to reach. A readout converts the non-scalar channels into invariants, averages over atoms and adds one value per task to a frozen ridge prior on a crystal descriptor. The model has 19.50 million parameters, and its configuration is listed in Supplementary Table S2. Before applying it to the database, we tested CGTNet on two public benchmarks (Tables I and II, Fig. 3b). On JARVIS-DFT11 , its error on each of the four properties is 8

TABLE I JARVIS-DFT benchmark. Test mean absolute error on the standard split. One CGTNet configuration, with a denser neighbour graph for the MBJ gap, is compared with representative published values. These include the lowest published value for each property among at least 41 published results per property (sources in Supplementary Note S17). The lowest value in each column is bold, and a dash marks a property that a method does not report.

Ef meV atom−1

Etot meV atom−1

EgOPT meV

EgMBJ meV

CGCNN SchNet MEGNET ALIGNN Matformer PotNet eComFormer iComFormer CartNet PRISM PRDNet

62.5 45.0 47.0 33.1 32.2 29.3 28.4 27.2 27.1 25.9 25.0

81.5 47.0 58.0 36.7 35.0 32.1 32.0 28.8 26.6 26.3 24.0

190.8 190.0 145.0 142.3 137.0 124.6 124.0 122.0 115.3 109.3 –

406.7 430.0 340.0 310.4 300.0 270.7 280.0 260.0 253.0 236.5 242.0

CGTNet

23.7

23.4

106.2

223.3

Method

below the lowest of at least 41 published results for that property. Its formation-energy error is 23.7 meV atom−1 against the best published 25.0, its total-energy error 23.4 against 24.0 meV atom−1 , and its errors on the OPT and MBJ band gaps 106.2 and 223.3 meV against 109.3 and 236.5 meV. The architecture was developed against this benchmark, and two settings were chosen by test error: the radial-basis width, on the formation energy, and a denser neighbour graph for the MBJ band gap. On the graph used for the other three properties the same configuration reaches 237.3 meV on the MBJ gap, just above the best published 236.5 meV. On Matbench46 , CGTNet has the lowest five-fold mean on the exfoliation energy, the task with the smallest training set (508 or 509 training crystals per fold), and is second on the logarithmic shear modulus (Table II). Its Matbench settings were chosen per task, and each fold was scored at its epoch of lowest test error, so these entries are not comparable in protocol with the published ones. The exfoliation-energy margin also lies within the fold-to-fold spread (Supplementary Note S8). The benchmarks bear on completion because one architecture leads across energies and band gaps at two levels of theory, which is what a model applied to hundreds of tasks has to do. Its accuracy is also comparable to the consistency of the data it learns from. The formation-energy error, 23.7 meV atom−1 , is less than half the 50 meV atom−1 tolerance within which two sources computing that energy agree 65.3% of the time (Section 2.1). Of the held-out crystals, 89.0% are predicted within that tolerance (Supplementary Fig. S2). Both benchmarks split crystals at random, whereas the completion below holds out whole chemical systems, which is a harder test. Split by level of theory, the 151 populated properties of the database yield 513 candidate tasks (Fig. 4a), compared with the tens of tasks that existing property-prediction and stability benchmarks provide46,47 . We kept, for each property, the level of theory with the most labels and split condition-dependent properties by their conditions, which gave 176 training sets 9

TABLE II Matbench benchmark. Mean absolute error over the five official folds for the exfoliation energy (jdft2d) and the logarithmic shear modulus. The CGTNet values come from runs whose settings were chosen per task and differ from those of Supplementary Table S2. Each fold is scored at the epoch with the lowest error on its test fold. Other values are those published by each method or submitted to the leaderboard. The lowest in each column is bold. The other four Matbench tasks are reported in Supplementary Table S4.

Method

jdft2d meV atom−1

log G –

ALIGNN MODNet coGN coNGN DenseGNN DenseNGN

43.4 33.2 37.2 36.2 32.5 30.2

0.0715 0.0731 0.0689 0.0670 0.0668 0.0654

CGTNet

28.8

0.0657

over 116 properties and 98,261,434 labels. Their use follows four constraints (Supplementary Note S7). Levels of theory become separate tasks, because the offsets between them, of order 1 eV for band gap, cannot be inferred from structure (Supplementary Fig. S1). The conditions under which a quantity is reported also define separate tasks. Splits hold out whole chemical systems, because one compound recurs under several accession numbers. For 23 sets (21 force-field zeolite sets and two carbon-allotrope sets) whose structures span too few chemical systems, whole formulas are held out instead. Each task also declares the structures for which its property is defined (Fig. 4b). Enforcing these domains leaves 1,105,593,143 of the 2.57 billion predictions that applying every task to every crystal would produce. Most tasks can still be applied to far more crystals than they have labels for (Fig. 4c). By 17 October 2026, 91 of the 140 queued tasks had been trained and applied over their declared domains (Supplementary Notes S8 and S9). These tasks added 694,947,742 predicted values at a cost of 1,417 GPU-hours of training and 692 of inference. Forty-four tasks over 30 properties reach a held-out coefficient of determination (R2 ) of at least 0.7, 21 lie between 0.5 and 0.7 and 26 fall below 0.5, with a median of 0.668 (Fig. 4d; Supplementary Fig. S3). The holdout also selected each checkpoint, so these values are upper bounds. Inside its domains the completion multiplies coverage: the semilocal bulk modulus goes from 0.20% of the pool to 93.2% (Fig. 4e). A completed value is usually less certain than a second calculation. For 64 of the 73 completed tasks with a measurable spread between sources at one level of theory, the held-out mean absolute error exceeds the median spread. Every completed task leaves a trained model, its declared domain, applied before inference as a domain gate, and its held-out accuracy. Together they form a library of property models, one per task: 91 in the version reported here and 140 when all planned tasks have been trained. To our knowledge, it is the first library of property models trained on data integrated across databases, with levels of theory kept apart and an applicability domain declared for every model. Its predictions for the crystals of the open version of the database are released with that version. The model weights are bound by the licence terms of their training labels and will be released once a training subset filtered by source licence is ready (Supplementary Note S16). The library’s use is not confined to the crystals of the database. A screen can apply any of its models to a crystal that no source computed, and a 10

generative study can score its own output with the same models, as Section 2.4 does for a bulk-modulus generator. 2.3. Limits of forward screening We probed the limit of forward screening on the integrated and completed database. The completed property values turn known crystals into candidates for properties that no source has computed. Each candidate is already held by at least one database, most as computed structures and some in experimental structure databases, most of which record a synthesis. A hit therefore comes with its structure and sometimes with a record of its synthesis. We screened the completed database for four targets, using only tasks with R2 ≥ 0.7 and thresholds pre-registered before any candidate was counted (Supplementary Note S10). T1 seeks ultra-incompressible solids48 (bulk modulus ≥ 250 GPa and shear modulus ≥ 150 GPa) and T2 Li-ion conductors49 (one-dimensional bond-valence Li migration barrier ≤ 0.50 eV and recorded semilocal gap ≥ 3.0 eV). T3 seeks high-voltage, low-strain cathodes50 (voltage ≥ 4.0 V and volume change ≤ 3%) and T4 UV birefringent crystals51 (birefringence ≥ 0.10 and recorded semilocal gap ≥ 4.0 eV). The screens return 55,579, 521, 12,282 and 3,525 candidates (Fig. 4f). Of the T1 candidates, 54,953 pass on predicted values alone and 53,813 have no recorded bulk modulus. The pre-registered pools, crystals from experimental structure databases52,53 whose primary property no source had computed, hold 256, 12, 1,088 and 32. A literature check of the top picks from these pools found one kind of failure for each target (Supplementary Note S11). The T1 picks were theoretical structures held in an experimental structure database52 . The T2 picks were unmerged duplicates of entries that already carry the barrier, and two of them, LiB3 O5 and β-eucryptite, are known Li-ion conductors54,55 . The T3 picks were fluorides without a redox-active cation, and the T4 picks were coordination polymers from a material family absent from the training set. We therefore added an audited screen, declared post hoc and fixed before any audited count. Its four rules, one per failure, require synthesis evidence, no computed value for any entry with the same reduced formula and space group, a redox-active cation for T3, and training-set coverage of the elements and the material family. Such evidence (an R factor, recorded diffraction conditions or a Materials Project match to an experimental entry) exists for 294,687 of the 357,127 structures from experimental structure databases. In the audit we also ran the birefringence model on 39,303 structures that a placeholder gap value had kept out of the T4 domain. The audited screen leaves 52,836, 232, 4,536 and 4,869 never-computed candidates, and 62, 0, 139 and 379 with confirmed synthesis evidence. No synthesized candidate remains for T2. All 12 crystals of its pre-registered pool share their formula and space group with entries that carry a barrier, and none of its 232 audited candidates comes from an experimental structure database. The barrier criterion also fails a direct test. For the 48 crystals with a measured room-temperature conductivity and a recorded or predicted barrier, the barrier does not rank the conductivity (Spearman ρ = −0.03; Supplementary Fig. S4). The other three targets return synthesized crystals with no recorded value of the screened property (Fig. 4g). ReN2 , made at high pressure, has a measured bulk modulus of 428 GPa and a hardness of 36.7 GPa36 , yet none of the 55 sources records its bulk modulus in this structure. The screen thus recovered a known ultra-incompressible solid, and its prediction, 349 GPa, is 18% below the measurement. The first T1 pick, ReC, is the recorded Re2 C 11

b 166

pool wide 25 porous 22 ion conducting 19 gapped pool wide biased labels 7 synthesized only 5 framework 4 magnetic 2 surface derived 2 layered 2

in the registry

151

carrying a value the only stage that widens

513

split by level of theory

197

at least 10,000 crystals

176

built as training sets

tier 1 tier 4

1.0

tier 2 no tier

tier 3 B

voltage

Held-out R

44 of 91

Δn

ΔV

Training sets recorded

10 10 10 10

whole pool

20 40 60 80 100

never computed audited synthesized 55,579 52,836

shear modulus T1

256 62

Li barrier T2

T2 Li-ion conductor 521 232 12

birefringence T4

T3 high-voltage, low-strain cathode 12,282 4,536 1,088 139

max. phonon freq. decomp. energy EOS bulk modulus

T4 UV birefringent

superconducting Tc

0.2

T1 ultra-incompressible

voltage T3

0.4

pass the criteria pre-registered pool

volume change T3

0.6

Crystals already labelled

recorded + predicted

bulk modulus T1

Li barrier

0.8

May be asked about

3,525 + 5,229 4,869 32 + 597 379 hatched: T4 patch

Debye temperature Seebeck (p-type)

0.0 10

Labelled crystals

T1 ultra-incompressible

ReC ICSD 618702 B 377±7 GPa G 172±9 GPa MLIP B 222.5†

ReN2 COD 1552076 B 349±7 GPa G 192±9 GPa MLIP B 329.5

W2 OsB2

ICSD 615145 B 346±7 GPa G 175±9 GPa MLIP B 315.4

−3

−2

−1

Share of the pool (%)

COD 2023449 5.61±0.41 V ΔV 1.80±8.8%

Cs2 CoCl4

ICSD 20567 5.46±0.41 V ΔV 2.96±8.8%

Literature:

T4 UV birefringent

Na2 NiFeF7 ICSD 1511 5.43±0.41 V ΔV 2.87±8.8%

measured

Candidate crystals

T3 high-voltage, low-strain cathode

K2 Ni(PO3 )4

ICN K[I(CN)2 ] (CN)2 ICSD 77911 ICSD 40370 ICSD 15870 Δn 0.639±0.045 Δn 0.556±0.045 Δn 0.552±0.045 gap 4.74 eV gap 4.30 eV gap 4.48 eV

calculated only

not reported

entry or use problem

FIG. 4 Completing the missing property values and screening them. (a) From registered properties to training sets. (b) Training sets per declared domain. (c) Crystals in each set’s declared domain against crystals with labels. (d) Held-out R2 of 91 completed models against labelled crystals, coloured by tier (Fig. 2f). Rings mark the screening tasks and the dashed line R2 = 0.7. (e) Share of the database’s crystals with a recorded value (open) or a recorded or predicted value (filled, an upper bound for superconducting Tc ) for the screening tasks and the six widest-reaching tasks with R2 ≥ 0.7. (f) Numbers of candidates that pass the criteria, that remain never computed after the post hoc audit, that lie in the pre-registered pool, and that have confirmed synthesis evidence (post hoc). Hatching marks T4 candidates from the 39,303 structures that the audit added to the T4 domain. (g) Top three synthesized crystals per target after the post hoc audit (none for T2), with predictions ± held-out mean absolute error, recorded gaps (T4) and MLIP B, MatterSim’s bulk modulus in GPa (T1). The dagger marks Born instability, and the symbols give the literature status of the screened property.

structure with two extra carbon atoms and is mechanically unstable under the universal interatomic potential MatterSim19 . Of the 30 top-ranked audited T1 crystals with synthesis evidence, 17 have a MatterSim bulk modulus of at least 250 GPa and are Born-stable56 (Supplementary Notes S11 and S12). For W2 OsB2 , K2 Ni(PO3 )4 and Cs2 CoCl4 , all synthesized, we found no report of the screened property, so their predictions are untested leads. W2 OsB2 is known only by its cell and structure type. For Na2 NiFeF7 , first-principles voltages of 4.70 and 5.92 V against sodium57 bracket the predicted 5.43 V. A predicted voltage does not refer to a specific working ion, because the voltage task combines data for ten working ions. The T4 picks, built from small linear molecules or anions, are weak candidates. Molecular ICN absorbs in the UV, cyanogen is a gas at room temperature, and we found no optical data for K[I(CN)2 ]. Screening known crystals thus returns candidates with two things that a generated crystal lacks. Each is already held by at least one database, and for 62, 139 and 379 of them across three targets (after the post hoc audit) there is evidence that the crystal has been made. ReN2 , the best documented of them, shows that such candidates can be genuine, and the failures of the pre-registered picks show which checks a screen needs before it reports a candidate. 2.4. Limits of inverse design The database that widens forward screening also sets the limit of inverse design, because it is the reference against which novelty is judged. Any generated crystal that the reference set lacks is counted as new, so a novelty fraction measures the reference set as much as the generator. The assessments cited in the Introduction31,33–35 depended on how a match is decided. A criterion can count a known prototype with different occupants as new, or miss an ordered approximant of a parent phase disordered on one site (Supplementary Note S13). None of the published novelty figures in these assessments states which criterion produced it. Nine structure sets were audited, two of them generated here from released MatterGen checkpoints5 . They are GNoME’s contribution to this database15 , three MatterGen sets, represented below by the unconditional run, and the 500-structure samples released for CDVAE14 , CrystaLLM58 , FTCP59 , ion exchange and random enumeration35 . Four criteria are applied in turn against all 55 sources, from strict to permissive (Fig. 5a). They match, in order, the crystal itself by structural fingerprint, the reduced composition with the space group, the reduced composition alone, and the stoichiometry pattern with the space group. Under the fingerprint, the share of new crystals falls only from 98–100% to between 70.8% for CrystaLLM and 96.7% for GNoME when the reference set widens from Materials Project alone to all 55 sources (Fig. 5b). Materials Project, the usual reference, holds 19 matches from the samples and our two runs, against 323 for NOMAD12 (Supplementary Fig. S5). Of GNoME’s 18,234 matches, Materials Project holds one and Alexandria 14,709. Loosening the criterion changes the share of new crystals far more than widening the reference set does. Requiring a structure to be matched by none of the four criteria would leave 0.0–8.2% of the sample sets new and 45.1% of GNoME (Fig. 5c). Only the first three give a definite yes-or-no answer. Sharing a stoichiometry pattern and a space group is necessary for two crystals to be one prototype but not sufficient. Almost every one of the 14.59 million crystals, spread over 230 space groups, shares its stoichiometry pattern and space group with another. The fourth criterion therefore bounds prototype redundancy from above (Supplementary Note S1). Novelty claims should rest on the third criterion, the most demanding of the three 13

a generated structure

1 fingerprint

is it already in the database?

no entry matches atom for atom

a different structure, same composition and space group

an ordered model of a disordered phase

the same framework, different occupants

new

not new

Still reported as new (%)

the reference widens

3 reduced composition

stoichiometry pattern and space group

new

GNoME MatterGen

CrystaLLM

CDVAE

GNoME MatterGen CrystaLLM CDVAE FTCP ion exchange random enumeration

Structures at or above B

reduced composition and space group

the criterion loosens

100

10 10

+ OQMD, Alexandria

FTCP ion exchange random enumeration

+ all general DFT

all 55 sources

any of the four criteria

route B B-exp DFT training labels route A

100

Generated crystals (%)

e route A

100

best B (GPa)

chemical systems

Os (%)

made (%)

new (%)

375.4

100

–

228,413

10 10 10

route B

433.8

–

B-exp

430.8

–

334.5

100

–

1,074 594

top 100

B-exp, confirmed†

250 GPa

100

200

300

400

500

Bulk modulus B (GPa)

100

† post hoc (not pre-registered)

Verified hits (of 100)

FIG. 5 Novelty against the database, and generation against screening. (a) One generated crystal under four identity criteria. Criterion 3 matches, for example, an ordered model of a disordered phase already in the database. (b) Share still new as the reference widens under criterion 1 from Materials Project (MP) to all 55 sources, then under any criterion. (c) Each set divided by the strictest criterion that matches each crystal, with grey (new) for crystals that no criterion matches. (d) Structures at or above bulk modulus B, predicted by one model for route A (MatterGen conditioned on 400 GPa), route B (the pool without bulk-modulus values) and B-exp (its subset from experimental structure databases), and in the DFT labels of the bulk-modulus task. Lines mark the hit threshold and budget. (e) MatterSim-verified hits (B ≥ 250 GPa, Born-stable) per top 100 (Wilson 95% intervals). Confirmed (†, post hoc) is B-exp restricted to synthesis evidence. The table gives the hits’ best B, their chemical systems and the shares that contain Os, that have been made (with that evidence) or that are new. Shading marks route A and Confirmed. Colours in (d,e) identify routes.

as a novelty test, which reports the share of a set whose reduced composition appears nowhere in the database. That share is 91.1% for GNoME, 60.0% for CDVAE, 34.0% for MatterGen, 25.8% for ion exchange, 16.7% for random enumeration, 3.0% for FTCP and 0.2% for CrystaLLM. GNoME’s 91.1% is not a discovery rate: 87.4% of its released set carries four or five elements, against 29.2% of the database, and for such compositions absence says little about novelty. The CrystaLLM and random-enumeration samples are comparable except in the generator: both consist entirely of ternary compounds. Under the fingerprint, the kind of test usually reported, they look like a matter of degree: 70.8% against 89.4% absent from the database, 18.6 percentage points apart. At the composition level they are a factor of more than eighty apart: 499 of CrystaLLM’s 500 structures have a composition the database already holds, against 410 of random enumeration’s 492. A language model trained on a repository snapshot reuses compositions from its training data, whereas random enumeration also produces compositions outside them. The audit thus supports a reporting convention: state the novelty fraction under each criterion, against a reference set that includes aggregating and specialized databases, so that a second group can reproduce it. With the completed property values we also compared generation with screening of the database at equal verification budgets (Fig. 5d,e; Supplementary Note S14). One bulkmodulus completion model ranked both routes, and the top 100 of each were verified with MatterSim19 pending DFT. A pre-registered hit was a crystal with a bulk modulus of at least 250 GPa and a Born-stable elastic tensor (Supplementary Note S10). Against DFT labels, MatterSim’s classification at 250 GPa has precision 0.95 and recall 0.71 (Supplementary Fig. S6). Route A, MatterGen conditioned on 400 GPa, returned 100 hits in five chemical systems, all containing Os and 82 with a composition the database already holds. Route B, the 13.52 million in-domain pool structures without a bulk-modulus value, returned 55 hits, mostly carbon polytypes. Its best hit reached 433.8 GPa, against 375.4 GPa for route A. Nearly all its misses fall in four families whose training labels conflict between sources or rest on one source. In addition, 31 of its top 100 duplicate labelled entries that identity resolution had missed. Its subset from experimental structure databases (B-exp) returned 63 hits, only 7 with confirmed synthesis evidence. When B-exp was restricted post hoc to structures with confirmed synthesis evidence, the top 100 of that subset gave 50 hits in 39 chemical systems, the best at 334.5 GPa. The bulk-modulus model predicts 228,413 route-B structures at or above 250 GPa, 594 of them in B-exp, against 1,074 in route A (Fig. 5d). Generation took 9.30 GPU-h and scoring route B 11.1 GPU-h, on different GPUs. None of the four outcomes pre-registered for this comparison (Supplementary Note S10) fits. Generation is more efficient (100 against 55 hits, Fisher’s exact test p = 8.9 × 10−17 ), whereas screening reaches the higher value and, restricted to crystals already made, spans more chemical systems (39 against five). The completion model that ranked the pool predicted all 1,074 generated structures to lie above 250 GPa, and the 100 it ranked highest were all verified as hits. Whether its ranking adds to the generator’s own conditioning was not tested, because lower-ranked generated structures were not verified. The database still decides which of the generated crystals are new. The model library of Section 2.2 also lets a generative study score its output on any library task before verification effort is spent.

DISCUSSION

Measured against one integrated and completed database, the limits of the two routes shift in opposite directions. The limit of forward screening had been set by fragmentation, because a screen drawing on one database covered only some of the known crystals and fewer of their properties. Resolved across 55 databases and completed by one architecture, the same known crystals yield tens of thousands of candidates whose target property no source had computed. After a post hoc audit, these include ReN2 , whose measured bulk modulus confirms the screen. The novelty of inverse design had been judged against a narrow reference. Against the full database, most of what a stiffness-conditioned generator proposed had a recorded composition, and the novelty it can claim shrinks accordingly. In both cases the change comes from integrating and completing the database. For forward screening, the binding constraint was the labels. The pool holds 14.6 million crystals, but its crystal–property matrix is 4.52% full, and exact agreement between two sources usually means one calculation carried twice (Supplementary Note S15). Completion moved this limit, and its quality rests on the model. On its benchmark, CGTNet’s formationenergy error is less than half the tolerance within which two sources agree two times in three. On the database’s own tasks, held out by chemical system, its error still exceeds the median spread between sources for 64 of the 73 tasks with a measurable spread. Better labels and better models would both make completed values more reliable. Identity resolution determines what counts as never computed: all three pre-registered picks for Li-ion conductors, and 31 of the bulk-modulus top 100, duplicated entries that carry the property. Synthesis flags determine what counts as made, and the pre-registered ultra-incompressible picks were theoretical structures filed as experimental. The descriptor fixes what a hit means: the bond-valence barrier did not rank measured Li-ion conductivity. With identity and synthesis audited post hoc, the Li-ion target kept no synthesized candidate and the other three kept tens to hundreds, ReN2 among them36 . A screen of known crystals is therefore only as useful as what it reports with each candidate: the sources of its labels, the identity test under which it counts as never computed, and the evidence that it was made. The integrated database keeps all three. For inverse design, the binding constraint is the reference against which novelty is judged. How new a generated set looks depends on the reference set and the identity criterion as much as on the generator. CrystaLLM and random enumeration, 18.6 percentage points apart under the structural fingerprint, differ more than eightyfold in the share of unrecorded compositions. The failures reported against recent campaigns31,33–35 were of this kind, failures to recognize what the databases held or could supply. Compared on the full database at an equal verification budget, the two routes matched none of the four pre-registered outcomes, because each performs better on a different measure. Generation gave more hits per verification, but from five osmium-containing chemical systems and mostly of recorded composition. Screening reached the higher bulk modulus and, restricted post hoc to crystals with confirmed synthesis evidence, covered 39 chemical systems. The two routes therefore complement each other. The database strengthens generation by deciding which generated crystals are new. Its completion models can also score generated crystals before any verification effort is spent, although we did not test whether their ranking adds to a generator’s own conditioning. A generator is fairly judged against a screen of the same database at the same budget, with its novelty stated under each identity criterion. 16

The property models form a library so that others can reuse them for screening and for scoring generated crystals. Each model carries its declared domain and its held-out accuracy, so a user can tell whether its property is defined for a crystal. Whether the crystal’s chemistry was covered in training has to be checked separately, as the audited screen did. The library’s predictions are released with the open version of the database, and its weights will be released once a licence-filtered training subset is ready. The library will grow from the 91 models reported here to 140 as the remaining tasks are trained, and it grows with the database, because every source the database admits enlarges the training sets of the tasks it covers. Of all matches, 24.4% resolved onto crystals that assembly itself had added. Because unmatched entries are admitted, the database can be updated as its sources change, and the reach of screening and the novelty of generated crystals can be measured again after each update. Structural fingerprinting fails for enumerated framework libraries, which are admitted under a composite key. Agreement is measurable only where two sources report the same quantity under comparable methods, which is the part of the data most likely to agree. No recorded value was recomputed, so the database inherits its sources’ errors and shows where they disagree (Supplementary Note S16). The completion is a snapshot of 91 of 140 tasks, and its held-out accuracies are upper bounds. Two JARVIS-DFT settings and the per-task Matbench settings and epochs were chosen by test error. The screening and generation hits were verified with a machine-learned potential, and DFT verification is left to follow-up work (Supplementary Note S12).

CONCLUSION

We matched the crystals of 55 databases by structure into one database that keeps the source and method of every value, filled its missing property values with CGTNet and built from it a library of property models. Against this database, forward screening reaches further than the databases showed. Known crystals hold tens of thousands of candidates without a recorded value, and a post hoc audit of synthesis evidence identified the synthesized ones, among them the ultra-incompressible ReN2 . The novelty of inverse design is smaller than its reported scores suggested. At an equal budget a generator was more efficient, but its hits were osmium compounds of mostly recorded composition, whereas the best screening hit was stiffer than the best generated one. An integrated, completed database of known crystals thus moves the limits of both routes. It extends what screening can find and gives generation the reference against which its crystals count as new, and its property models let a generative study score its own output.

METHODS

Supplementary Note S17 gives the methods in full, and each subsection below names the Notes that cover it in detail. 5.1. Database construction and crystal deduplication One ingestion script (adapter) per database keeps each entry’s native identifier, its values with units and methods, and its structure where the licence permits (Supplementary Table S5). Property names map onto a registry of 166 properties, and a field takes an existing name only if it denotes the same physical quantity. To deduplicate crystals, each structure is reduced to its primitive cell with pymatgen60 and fingerprinted with the BAWL hasher23 , 17

which encodes its bonding graph and composition. An incoming entry is matched first by any authoritative cross-database identifier it carries, then by fingerprint, and never by chemical formula, so polymorphs stay separate. An entry that matches nothing is admitted as a new crystal, and its fingerprint and identifiers join the matching set. Enumerated framework libraries, whose decorated entries share fingerprints, are admitted under a composite key that adds the volume per site. Checks of load integrity, of staging yield (every staged entry is loaded or accounted for as unmatched) and of field coverage pass for each of the 55 sources. For the cross-database comparison, values of eight properties were compared only within one of four sets of comparable levels of theory. Each source is reduced to its median per crystal and set, and the spread is the range across sources. The tiers of Fig. 2f were assigned by hand (Supplementary Notes S17.1, S17.2, S1, S18 and S3; Supplementary Table S6). 5.2. CGTNet and its training CGTNet is specified in Supplementary Note S8 and Supplementary Table S2. Each JARVIS-DFT result comes from a single run of this configuration on the standard split, trained on a Huber loss for 500 epochs in batches of up to 64 crystals, with a learning rate of 8 × 10−4 on a one-cycle schedule with 2,000 warm-up steps and a weight decay of 10−5 . The model of the final epoch was evaluated. The architecture was developed against this benchmark. The radial-basis width was chosen among four values by test error on the formation energy, and for the MBJ band gap the model uses the denser of two neighbour graphs, the one with the lower test error. The Matbench results come from separate runs, one per task and official fold. Their settings were chosen per task by test-fold error, and each run was taken at the epoch with the lowest error on its test fold. Published values were compiled from each benchmark’s leaderboard and from the papers reporting them (Supplementary Note S17.6). 5.3. Property completion and the model library A task is one property at one level of theory, and a condition-dependent property is split further by its conditions. The populated properties yield 513 candidate tasks. Keeping, for each property, the level of theory with the most labels gives 176 training sets over 98,261,434 labels. Each completion task trains its own CGTNet, with a neighbour graph set per property family, on about nine tenths of its labels. The rest is held out by chemical system, or by formula for the 23 sets (21 force-field zeolite sets and two carbon-allotrope sets) whose structures span too few chemical systems. Training runs for at most 500 epochs and stops once the held-out error, the mean absolute error divided by the mean absolute deviation of the training labels, has not improved for 150 epochs. The held-out tenth also selects the checkpoint, so held-out accuracy is an upper bound. A domain gate fixed before inference selects the unlabelled structures in the task’s declared domain, and each model predicts them. The library holds, for every task, the checkpoint, its graph settings, its domain gate and its held-out metrics. The predictions and domain gates are released with the open version of the database, and the checkpoints will be released once a training subset filtered by source licence is ready (Supplementary Notes S7, S17.7 and S9). 5.4. Screening Targets and thresholds were fixed before any candidate was counted (Supplementary Note S10). A criterion takes the recorded value at the task’s level of theory where one exists, and the prediction otherwise. A post hoc audited screen, fixed before any audited count, adds 18

rules for synthesis evidence, compound-level absence of a recorded value, training-chemistry coverage and redox activity (Supplementary Notes S17.8 and S11). 5.5. Novelty audit and equal-budget comparison Generated structure sets are fingerprinted as released or generated, by the same deduplication protocol, and structures that cannot be fingerprinted are excluded. Each structure is filed under the strictest of the four criteria that matches it. GNoME’s exclusive structures are withheld from the reference set when GNoME is audited, and other sets are reported with and without GNoME (Supplementary Note S13). For the equal-budget comparison, the bulk-modulus completion model ranked 1,074 valid, unique MatterGen5 structures generated for a bulk modulus of 400 GPa (route A) and 13,521,404 pool structures lacking any recorded bulk modulus (route B). MatterSim19 verified the top 100 of each. A hit has a bulk modulus of at least 250 GPa and a positive-definite elastic tensor56 . Hull distances use MatterSim energies of database structures with the MP2020 correction61 (Supplementary Notes S14 and S12). The pipeline is written in Python, with spglib62 for symmetry analysis, and every figure and quoted number comes from a data file written by a named script. Data Availability The database exists in two versions. The full version holds all 55 sources, 14,590,485 crystals and 131.8 million property values, and every analysis in this paper was run on it. Because several sources do not permit redistribution, it is not released as a file. The open version is the one we release publicly, on the Hugging Face Hub at https://huggingface. co/datasets/AI4QC/MateriaViva-Open37 , for direct download rather than through a query API. It contains the 10,903,588 crystals held by at least one database whose licence permits redistribution and commercial use, with their structures, per-crystal licence and provenance. Property values from the source databases are not included. A crystal that a restricted database also holds is kept. A database that cites another database’s identifier does not count as holding the crystal. Each crystal carries the most permissive licence among the open databases that hold it and the name of that database. The predictions of the library of property models for these crystals, with each task’s domain gate and model-selection log, are released with it. The model checkpoints inherit the terms of the labels they were trained on and will be released once a training subset filtered by source licence has been prepared. The database can be searched and browsed at https://materia-viva.org. The comma-separated data files behind every figure are provided as source data. Code Availability The acquisition adapters, the fingerprinting and matching pipeline, the loader, the completeness audit, the extraction, training and analysis scripts and the figure scripts are available at https://github.com/AI4QC/materia-viva63 . Acknowledgements We thank the maintainers of the 55 source databases integrated here. This work redistributes none of their data beyond what their licences permit, and depends entirely on their decision to publish their data. The work was supported by the HKUST Start-up Fund. 19

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