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$\text{GSF-}\chi$: Global Stereochemical Fields for Chiral Graph Transformers
Jiaqing Xie, Yuxin Wang, Xipeng Qiu
TL;DR
Enantiomers can share atoms, bonds, and distances but behave differently in chiral environments, creating a representation challenge. GSF-χ combines a global even field, signed rotary interactions, and a parity-aware ECD projection; it achieves strong benchmark results, with controlled studies supporting global signed support and the projection's mirror-consistency trade-off.
Problem
Enantiomers can share atoms, bonds, and pairwise distances yet behave differently in chiral environments, while encoders must preserve atom relabelings and proper rotations without identifying molecules with their mirrors.
Source: §1 · p. 1Method
GSF-χ uses a reflection-even field to locate all-pair interactions, a handedness pseudoscalar to direct Chiral-RoPE, and a parity projection for ECD outputs.
Source: §1 · p. 2Results
GSF-χ achieves state-of-the-art accuracy on standard chirality-classification benchmarks and outperforms all baselines on central and axial ECD prediction.
Source: §1 · p. 2, §7 · p. 10Takeaways & Limitations
Equal-budget controls show global support improves Rotation over query-anchor support by more than 10%, while the C2 projection gives exact enantiomer-pair complementarity and becomes predictive with scarce mirror supervision.
Source: §6 · pp. 7–8Replacing curated units with an automatic extractor costs about 6% of Rotation and 9% of Symbol accuracy, while parity-even targets remain unchanged.
Source: §6.3 · p. 9
Abstract
from arXiv · showhide
Enantiomers share atoms, bonds, and pairwise distances yet can behave differently in chiral environments, so molecular encoders must respect atom relabelings and proper rotations without becoming blind to reflection. We introduce GSF-$\chi$, a graph transformer in which stereogenic units modulate all pairwise interactions rather than single out one atom as special. Each central or axial stereogenic unit creates a reflection-even phase field over all atoms, a handedness pseudoscalar $\chi$ sets the direction of a relative rotation on latent query--key blocks, giving a \textbf{Chiral-RoPE} that reflection inverts rather than leaves fixed. A $C_2$ projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs. We prove the operator's even--odd decomposition and its annotation-inversion, permutation, and unit-order identities under explicit canonical-role conditions; property tests and a coordinate-reflection audit verify the laws end to end. GSF-$\chi$ leads every central-ECD output and improves axial Rotation and Symbol by $12.6\%$ and $7.9\%$ over the strongest baseline. Equal-budget controls attribute the Rotation advantage to global signed support rather than parameter or edge count; the $C_2$ projection yields exact enantiomer-pair consistency at a small raw-accuracy cost under complete supervision and becomes predictive when mirror supervision is scarce.
1 Introduction
Enantiomers can share molecular structure and pairwise distances while behaving differently in chiral environments, so encoders must preserve proper-motion and relabeling invariance without erasing reflection. GSF-χ introduces global signed interactions and a parity-aware ECD readout to address this gap.
1 Introduction
- Enantiomers can share atoms, bonds, and pairwise distances yet behave differently in chiral environments; (S)-thalidomide binds cereblon about tenfold more strongly than its (R)-enantiomer.Drug-development guidance calls for separate characterization when stereoisomers differ in pharmacology or toxicity.Source: §1 · p. 1
- Reflection leaves distances and unsigned angles unchanged, but ECD peak number and position are even while peak signs reverse, making readout parity consequential.An encoder invariant to the full Euclidean group removes orientation needed to distinguish enantiomers [6].Source: §1 · p. 1
- Prior approaches introduce orientation in several ways, but where chirality should enter attention remains open; anchor-query designs privilege one stereogenic center and may not suit axial or multiple units.The all-atom alternative is treated as a design choice evaluated by ablations.Source: §1 · p. 2
- GSF-χ uses a reflection-even phase field over all atoms and a handedness pseudoscalar to direct Chiral-RoPE, while keeping every atom in the same architectural role.Its parity projection separates mirror-even ECD peak number and position from mirror-odd peak signs.Source: §1 · p. 2
2 Related Work
Prior chirality-aware models use several orientation-bearing representations, while GSF-χ focuses on where signed information enters graph attention and how each output handles parity.
Molecular chirality representations
- Chirality-aware networks use ordered tetrahedral neighborhoods, permutation-sensitive aggregation, torsions, stereochemical graph features, or determinant kernels [7] [8] [9] [12].Related work also learns interpretable chiral kernels, pretrains Graph Transformers for handedness, and diagnoses poor chiral-token recognition in sequence Transformers.Source: §2 · p. 2
Rotary and geometric positional encodings
- Graphormer and Uni-Mol inject graph or 3D pair structure into attention, but those encodings remain reflection-even; Chiral-RoPE instead uses atom–stereogenic-unit phase and a pseudoscalar-reversed relative operator [17–19].Unlike descriptor injection in the Dual Graph Transformer, the rotation applies to every atom pair and obeys an exact inversion identity.Source: §2 · pp. 2–3
3 Preliminaries
The preliminaries define molecular inputs and symmetry requirements, then motivate replacing sequence-based rotary position with a parity-aware atom–unit relation.
3.1 Molecular Graphs and Stereochemical Prediction
- A conformer is represented by atoms, bonds, chemical features, and coordinates; atom relabeling must permute atom states consistently while leaving molecular outputs unchanged.The encoder maps the molecular graph to atom states and task predictions.Source: §3.1 · p. 3
3.2 Rigid-Motion Symmetry and Parity
- Proper motions preserve chirality, whereas reflections relate enantiomers; distances and unsigned angles are even, but oriented volumes and handedness are odd.ECD peak number and position are even, while optical rotation and ECD peak signs are odd.Source: §3.2 · p. 3
3.3 Relative Rotary Attention
- Chiral-RoPE retains relative rotary compatibility but replaces sequence position with an atom–unit phase and lets handedness reverse the operator under reflection.The ordinary query–key path remains explicit.Source: §3.3 · p. 3
4 Method
GSF-χ adds signed all-pair compatibility to a graph transformer using an even stereochemical field and a handedness-directed latent rotation, then constructs symmetry-aware guarantees and ECD readout.
4.1 A Global Reflection-Even Field
- Each valid central or axial stereogenic unit supplies reflection-even relations and descriptors plus handedness; a centered phase field is evaluated for every atom and unit.Canonical roles exclude handedness, so reflection preserves role tensors and reverses only the pseudoscalar, subject to the stated tie policy.Source: §4.1 · p. 4
4.2 Chiral-RoPE
- Chiral-RoPE adds a residual rotary correction to ordinary attention, allowing any atom pair, including remote pairs, to receive signed compatibility without rotating values.The heatmaps show pairwise angles rather than attention weights; reflection inverts the angles, while anchor queries restrict signed compatibility to one row.Source: §4.2 · p. 4, Figure 2 · p. 5
4.3 Structural Guarantees
- Handedness creates a first-order parity-odd compatibility signal while the even correction begins at O(θ^2); inversion reverses blocks and achiral input reduces to the ordinary backbone.Under the stated conditions, proper-motion invariance, unit-order invariance, and atom-permutation equivariance hold after canonical alignment.Source: §4.3 · p. 5
4.4 Parity-Compatible ECD Readout
- The ECD readout assigns Number and Position to the even stream and Symbol to an odd score conditioned on the even stream, producing complementary Symbol logits under inversion.All three ECD metrics use one encoder and checkpoint.Source: §4.4 · p. 5
4.5 Training and Complexity
- Direct evaluation costs O(L|S|N^2d), with stereogenic-unit count as the asymptotic penalty; on ACMP, units average 1.07 per molecule.With the field disabled, the same backbone runs 2.36× faster; evaluating both ECD signs doubles encoder arithmetic without changing asymptotic order.Source: §4.5 · p. 6
5 Experiments
The experiments compare GSF-χ with geometric, stereochemistry-aware, and ECD/attention baselines on central and axial chirality tasks. GSF-χ leads every central-ECD output and achieves strong axial Rotation and Symbol accuracy.
5.1 Experimental Setup
- The central tasks use ChIRo partitions for 466,683 R/S conformers and 34,560 Ranking pairs, plus 20,662 CMCDS molecules for ECD.Axial experiments use 1,192 ACMP molecules, split 952/120/120 for training, validation, and test; controlled studies retrain ECDFormer, ChiDeK, and GSF-χ on identical data and budgets.Source: §5.1 · p. 6
5.2 Overall Performance
- GSF-χ reaches 99.9% R/S and 72.9% Ranking accuracy and leads every central-ECD output, raising Symbol accuracy from 50.3% to 53.8%.ECD outputs come from one jointly trained checkpoint; the primary split keeps enantiomer partners together.Source: §5.2 · p. 7
- GSF-χ reaches 77.8% Rotation and 74.5% Symbol accuracy and leads or ties all four axial outputs.Its largest margins are on Rotation and Symbol, whose targets change under handedness reversal.Source: §5.2 · p. 7
6 Ablation Studies
The ablations indicate that global interaction support, rather than correction size alone, underlies key gains, while C2 projection enforces mirror consistency with supervision-dependent accuracy trade-offs. Additional tests examine automatic unit extraction, conformational shifts, and representations during axial rotation.
6.1 Why Does the Global Field Work?
- Restricting the global field degrades Ranking and joint-ECD metrics, while removing signed input returns axial Rotation and Symbol to chance with even targets largely unchanged.The same axial ablations find that local injection and pooled-token alternatives remove most Rotation and Symbol gains.Source: §6 · p. 7, §6.1 · p. 8
- C2 projection lowers raw Symbol accuracy by about 5% but guarantees exact enantiomer-pair complements; it becomes predictive when mirror supervision is scarce.With complete pairs, the unconstrained head remains more accurate; projection is a structural guarantee rather than a universal regularizer.Source: §6.1 · p. 8, §6 · p. 8
6.2 Support Interventions and Structural Evidence
- At equal correction budgets, random-global and distance-matched support improve Rotation over query-anchor support by 11.11% and 10.28%.Equal counts isolate placement from support size, and the ordering is specific to Rotation.Source: §6.2 · p. 8
- All 85 operator and readout tests pass, and coordinate reflection yields machine-precision field residuals and zero output-parity residuals across 1,192 ACMP molecules.The audit includes stereogenic-unit extraction and canonical gauge construction.Source: §6.2 · pp. 8–9
6.3 Beyond Curated Units and Conformations
- With frozen checkpoints, automatic unit extraction costs about 6% of Rotation and 9% of Symbol accuracy while leaving parity-even targets unchanged.The automatic setting still exceeds ChiDeK with curated annotations; the passage locates the limitation in upstream detection rather than the operator.Source: §6.3 · p. 9
- On 283 physical mirror pairs from 59 held-out molecules, GSF-χ remains strongest under conformational shift, with its margins over ChiDeK widening to +15.4 and +10.7 points.The reported ACMP margins are +12.6 and +7.9 points.Source: §6.3 · p. 9
- The projected Symbol head complements all 283 physical mirror pairs with zero variance across three runs, whereas the unprojected Rotation head flips on most pairs.The heads share one representation and checkpoint and differ only by projection.Source: §6.3 · p. 9
6.4 Representations under Axial Rotation
- During axial rotation, the even context stays essentially fixed while the odd trajectory varies with torsion, separating the nine +χ from the nine −χ conformers.Figure 5 shows the z− UMAP trajectory and polar cosine similarities for z− and z+ relative to the 0° conformer.Source: §6.4 · p. 10, Figure 5 · p. 10
7 Conclusion
GSF-χ distinguishes enantiomers while preserving relabeling and proper-rotation invariance. Its even stereochemical field distributes handedness-signed interactions, and its parity-split readout enforces exact mirror symmetry for ECD outputs.
7 Conclusion
- GSF-χ distinguishes enantiomers with the same atoms, bonds, and pairwise distances while preserving relabeling and proper-rotation invariance.It attributes gains to global signed interactions rather than model size or edge count.Source: §7 · p. 10
A Full GSF-χ Parameterization
- The pipeline stacks field-modulated Chiral-RoPE blocks with ordinary transformer updates, then routes pooled states to task heads or parity-projected ECD decoding.The ECD readout predicts peak counts, positions, and signs.Source: Figure 6 · p. 13
A.1 Stereochemical Units and Even Inputs
- Each stereogenic unit supplies parity-even atom–unit relations and a descriptor, with central and axial units represented using different geometric and graph features.The inputs also include unit type, anchors, handedness, and annotation confidence.Source: §A.1 · p. 13
A.2 Field Network and Initialization
- The chemistry-informed phase initialization uses branch and side terms plus graph distance, while excluding handedness.Graph distance propagates initialization beyond the first shell.Source: §A.2 · p. 14
A.3 Conditioned Rotations and Pair Gates
- Chiral-RoPE applies unit-conditioned rotations to selected latent query–key blocks, and pair gates modulate their bilinear compatibility correction.The correction is distinct from a conventional additive attention bias; frequencies are learned from logarithmic initializations.Source: §A.3 · p. 14
A.4 Heads, Objectives, and Regularization
- Task heads use pooled graph representations, while ECD heads separate even Number and Position outputs from odd Symbol scores.Ranking combines an MSE term with a pairwise margin loss; whole-unit dropout uses the same mask in both mirror forwards.Source: §A.4 · p. 15
A.5 Task-Specific Training Configurations
Task-specific configurations vary sharing, dropout, and ECD decoding choices. Direct evaluation scales with the number of layers, stereogenic units, atom pairs, and model width.
A.5 Task-Specific Training Configurations
- The best central Ranking configuration shares the unit encoder, latent axes, and frequencies across 12 layers, but keeps phase fields, attention projections, and feed-forward blocks layer-specific.It has 28,895,233 trainable parameters; central ECD uses parity-split readout, while axial ECD uses ordinal Number.Source: §A.5 · p. 15
A.6 Implementation Cost and Scope
- Direct evaluation costs O(L|S|N^2d) time and stores O(B|S||Hχ|N^2M) rotary intermediates.Eq. 15 is applied only to selected heads, and units, heads, blocks, and atom pairs are vectorized.Source: §A.6 · p. 16
B Proofs of the Structural Guarantees
The proofs establish symmetry guarantees for GSF-χ under explicit input, canonicalization, and shared-mask assumptions. They distinguish signed operator behavior from exact output parity and delimit what those guarantees establish.
B.1 Assumptions and Notation; B.2 Operational Canonicalization and Reflection Audit
- The guarantees assume reflection-even input tensors, relabeling-equivariant shared maps, canonical axial roles, and shared weights and stochastic masks for paired ECD forwards.The coordinate-reflection audit verifies the released ACMP preprocessing path, but not arbitrary conformer generators or uncertain stereochemical annotations.Source: §B.1 · p. 16, §B.2 · p. 17
B.3 Why Parity-Sensitive Information Is Necessary
- A reflection-blind encoder cannot deterministically predict a nonzero mirror-odd target on both members of an enantiomeric pair.The result requires some parity-sensitive information, not specifically GSF-χ's handedness input.Source: §B.3 · p. 17
B.4 Inverse Response to Handedness and Pair Direction; B.5 Exact Even–Odd Decomposition of a Rotary Block
- Handedness inversion and pair reversal invert complete rotary blocks, while each block’s logit correction decomposes into exact even and odd parts.The odd component is first-order in the signed phase difference, while the even term begins at second order; this decomposition is conditional on the current query and key states.Source: §B.4 · p. 18, §B.5 · p. 18
B.6 Gauge, Endpoint, and Unit-Order Independence
- Unit contributions combine as scalar logit terms, making their aggregation invariant to unit order without multiplying non-commuting rotations.Endpoint-order independence depends separately on canonical endpoint roles.Source: §B.6 · p. 18
B.7 Interaction-Support Hierarchy
- Global interaction support contains anchor-incident and query-anchor support, with strict containment when non-anchor queries and non-anchor pairs are present.The global model leaves remote–remote paths available to continuous gates rather than hard-coding them to zero.Source: §B.7 · p. 19
B.8 Proper Rigid Motions, Relabeling, and Achiral Reduction
- The encoder is invariant to proper rigid motions, equivariant to atom relabeling, and reduces exactly to its ordinary graph-attention backbone when no valid stereogenic unit exists.Masked pooling removes the remaining atom axis to produce a permutation-invariant molecular representation.Source: §B.8 · p. 19
B.9 Reflection-Group Projection and Exact ECD Output Parity; B.10 Combined Structural Statement
- The C2-projected ECD readout makes Number and Position mirror-even and exchanges Symbol logits under reflection.The guarantee applies to the declared outputs, not to the physical meaning of arbitrary hidden channels or predictive accuracy.Source: §B.10 · p. 20
C.1 Dataset Audit
The primary central-ECD comparison uses a pair-preserving split and controlled retraining. The dataset audit also flags a smaller usable public archive, while the mechanism-results passage describes its controlled ablation setup.
C.1 Dataset Audit; C.2 Controlled Central-ECD Retraining
- The central-ECD analysis uses fewer usable public spectra than the published processed benchmark, and reports the exact molecule counts rather than imputing missing examples or mixing splits.The controlled retraining compares methods under the same preprocessing, budget, and three-run setting.Source: §C.1 · p. 20, §C.2 · p. 21
C.2 Controlled Central-ECD Retraining
- GSF-χ leads all three central-ECD outputs on the primary pair-preserving split, which has zero train–test pair overlap.Across run statistics, Welch tests report p < 0.01 for Position and Symbol against both baselines and Number against ECDFormer; Number against ChiDeK gives p = 0.034.Source: §C.2 · p. 21, Table 6 · p. 21
D.1 Full Central-Chirality Mechanism Results
- The mechanism trends are presented with bar values, with each variant changing one component while architecture, training budget, three-run set, and checkpoint rule remain fixed.All central rows use one joint-ECD checkpoint for Number, Position, and Symbol.Source: §D.1 · p. 21
D.2 Axial Ablation Setup
The axial ablation isolates metric-dependent effects of support and internal modules. The accompanying evaluations test robustness to annotation corruption, subtype variation, restricted support, inference cost, test-set uncertainty, and automatic unit detection.
D.2 Axial Ablation Setup
- Restricting stereogenic-anchor queries lowers Rotation from 77.78% to 69.17%, a decrease of 8.61%.All nine rows instantiate 154,440 parameters; removing the learned pair gate lowers Symbol by 8.07%, while removing unit-conditioned axes lowers Rotation by 2.50% and Symbol by 0.63%.Source: Table 8 · p. 22, §D.2 · p. 22
E.1 Annotation Corruption
- At 10% pair-level annotation corruption, official Symbol decreases by 0.64% while Number and Position remain unchanged.Mirror residuals remain exactly zero, so incorrect annotations can hurt accuracy without breaking the output law.Source: §E.1 · pp. 22–23
E.4 Head Allocation and Capacity
- Making every head chiral reduces Symbol by 8.28%, while a 64-times larger model worsens Number and Symbol despite slightly improving Position.The larger d=256, L=8 model loses 5.31% Symbol accuracy.Source: §E.4 · p. 23, Table 11 · p. 24
E.5 Efficiency and Scope of the Evaluation; E.6 End-to-End Cost of the C2 Projection
- At batch size 32, the signed-field model processes 6,370 molecules/s versus 15,033 for the reflection-even control, with 754 versus 173 MiB peak memory.The C2 projection adds 1.93× peak allocation at batch size 32; central ECD uses a reproducible public subset, and the implementation assumes a supplied stereogenic-unit set.Source: §E.5 · p. 24, §E.6 · p. 24
E.3 Distance-Resolved Field Reach
- Keeping only anchor-query corrections lowers Symbol by 5.31%, while keeping all anchor-incident corrections lowers it by 5.73%.Aggregate Number and Position metrics are unchanged across the masks; comparable correction magnitudes at graph distances 0 through 4+ indicate reliance on remote–remote corrections.Source: §E.3 · p. 23, Table 13 · p. 25
E.7 Pair-Level Uncertainty for Parity-Odd Targets
- Paired bootstrap intervals exclude zero for GSF-χ advantages on parity-odd Rotation and ECD Symbol; Rotation tests give p=0.0154 and p=0.0251.The analysis jointly resamples complete enantiomer pairs, keeping each pair's two configurations together.Source: §E.7 · p. 25
E.2 Axial Subtypes and Number of Units
- Only biaryls have 30 test pairs and 81.44% real-peak Symbol accuracy; every other subtype has at most nine pairs.The perfect multi-unit row contains only two pairs, and molecular-size bins are confounded with subtype.Source: §E.2 · p. 23, Table 14 · p. 26, Table 15 · p. 26
E.8 Automatic Stereogenic-Unit Detection
- With automatically extracted units, Rotation is 68.61 ± 3.76% and Symbol 62.00 ± 3.51%, falling 5.56 and 9.34 points versus curated units.The extractor recovers 92.66% of curated units while proposing roughly twice as many candidates; detection precision is 42.57%, so this is not an annotation-free pipeline.Source: §E.8 · pp. 25–26
E.9 Conformer Robustness on RotA
Conformer evaluation tests whether predictions remain stable across alternative conformations of held-out molecules, while further controls examine support placement and missing mirror supervision. The results report RotA performance, exact projected mirror consistency, and supervision-dependent gains.
E.9 Conformer Robustness on RotA
- On RotA, GSF-χ reaches 73.1% Rotation and 72.8% Symbol, with margins over matched ChiDeK widening to +15.4 and +10.7 points.Across 283 mirror pairs, projected Symbol complements exactly; coordinate reflection preserves parity-even inputs and reverses supplied pseudoscalars. ECDFormer returns identical mirror outputs, forcing Rotation to chance.Source: §E.9 · pp. 26–27
E.10 Training-Time Support-Budget Controls
- At the identical 6.5% budget, random-global and distance-matched global support improve Rotation by 11.11% and 10.28%, respectively.Full support adds another 8.61–9.44%; Symbol does not share this ordering, and hard top-k selection collapses near chance at all three budgets.Source: §E.10 · pp. 27–28
E.11 Low-Data Mirror Generalization
- Projection improves withheld-mirror Symbol accuracy by 13.20% and enforces exact pair complement; its gain shrinks from 8.49% at 25% to 4.78% at 50%, reversing with complete supervision.One-side supervision withholds the mirror from both optimization and checkpoint selection.Source: §E.11 · p. 28
F Comparison and Analysis Procedures
The section reports matched axial retraining and continuous-rotation construction, then presents selected paired ECD examples and operator diagnostics. These include both a high-loss failure and cases where mirror consistency does not ensure accurate predictions.
F Comparison and Analysis Procedures
- Matched comparisons use the same molecules, splits, budgets, and evaluators, with prespecified run sets and hyperparameters.Table 1 reports best benchmark settings; its ECDFormer and ChiDeK ECD columns are matched retrainings.Source: F Comparison and Analysis Procedures · p. 28
F.2 Continuous Axial-Rotation Construction
- Each ACMP rotation series contains 18 conformers, sampled every 20° from 0° to 340°, with nine conformers of each configuration.The selected axial-bond component is rotated, then each conformer passes through ordinary unit extraction, role canonicalization, feature building, and one locked encoder.Source: §F.2 · p. 29
G Case-Study Selection and Additional Examples
- GSF-χ preserves the paired law on ACMP pair 601, predicts both Symbols correctly, and places peaks at (3, 10), one bin from the reference.Both configurations have Number 2 and Positions (3, 11); ECDFormer repeats a three-peak prediction, while ChiDeK predicts inconsistent counts and signs across the pair.Source: G Case-Study Selection and Additional… · p. 29
- The paired-example selection rule chooses cases where GSF-χ predicts Number and Symbol exactly, obeys the pair law, and misses Position by at most one bin.It then maximizes ChiDeK’s combined Number and Symbol errors; the rule affects illustrations, not model selection or aggregate metrics.Source: G Case-Study Selection and Additional… · p. 29
- Figure 9 shows inversion preserving the parity-even field and gates while negating every signed latent angle, including in a two-unit molecule.The residuals verify operator inversion to numerical precision; atom-pair indices are not physical rotation angles.Source: G Case-Study Selection and Additional… · p. 29, Figure 9 · p. 31
F.1 Controlled Axial Retraining
- p=4.9 × 10^-4 for Rotation and p=5.8 × 10^-4 for Symbol; Position is tied at reported precision in the matched ACMP retraining.The comparison retrains ECDFormer and ChiDeK on the same 1,192 ACMP molecules, pair-preserving split, evaluator, and 25-epoch budget.Source: §F.1 · p. 28, Table 24 · p. 31
G.1 Additional Paired ECD Predictions
- Pair 27 matches the released complementary Symbols but predicts two rather than four peaks; pair 368 preserves Number and Position across reflection but shifts its second Position from 9 to 11.The two-unit example predicts both complementary Symbols without imposing an order over stereogenic units.Source: Figure 12 · p. 33, Figure 13 · p. 34
- Pair 261 obeys the exact mirror law despite inaccurate Positions and two of three Symbols; GSF-χ classifies 2/6 real-peak Symbols in this largest paired Symbol-NLL failure.Query-anchor also classifies 2/6, while no-chirality classifies 3/6; the experiment does not identify a chemical explanation.Source: G Case-Study Selection and Additional… · p. 30, Figure 14 · p. 34