KLDM: Lifting Crystal-Coordinate Diffusion from the Torus to Euclidean Velocity Space

0. Link verification table

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1. Search, deduplication, and random selection

1.1 Deduplication

Checked ml-report-index.md. The AI4Science core work in the past 14 days was Elucidating the Design Space of Multimodal Protein Language Models on 2026-08-16, concerning supervised geometry of discrete protein sequence–structure tokens. This issue excludes protein multimodal tokenization and DPLM2.1. KLDM studies toroidal fractional coordinates, kinetic diffusion, and material-stability validation, with different objects and technical foundations.

1.2 Candidate pool (20 papers) and random draw

Candidates came from ICML 2025 PMLR accepted papers, checked against arXiv, OpenReview, repositories, and full texts. All fall within today's AI4Science/interdisciplinary scope and were published within 24 months.

1. Raptor: training-free embeddings for 3D medical volumes
2. BounDr.E: one-class boundary learning for drug similarity
3. Expert-level Graph-of-Thought medical reasoning
4. A variational perspective on generative protein-fitness optimization
5. DiffMS: mass-spectrum-conditioned molecular diffusion
6. Conformer generation with SO(3)-averaged Flow Matching and Reflow
7. LDMol: latent diffusion for text-to-molecule generation
8. All-atom protein-complex design
9. Hierarchical graph tokenization for molecule–language alignment
10. OmniArch: a foundation model for scientific computing
11. Accelerating PDE-constrained optimization with neural-operator derivatives
12. KLDM: kinetic Langevin diffusion for crystalline materials
13. CLIMB: large-scale multimodal clinical foundation data
14. Synthetic data for difficult medical examples
15. Predicting mutation effects on protein binding from folding energies
16. Scalable nonequivariant 3D molecular generation through rotational alignment
17. Extracting biological concepts from microscopy foundation models using dictionary learning
18. MF-LAL: drug generation through multifidelity latent active learning
19. WyckoffDiff: generative diffusion for crystal symmetry
20. MedRAX: a medical reasoning agent for chest X-rays

Running shuf -i 1-20 -n 1 returned 12. KLDM has a 30-page conference paper, official code, results on four public datasets, three/six-run statistics, and multiple ablations. Materials were sufficient, zero redraws.

2. In-depth analysis of the core paper

2.1 Motivation: periodic coordinates are not ordinary 3D vectors

A crystal unit cell is (x=(f,l,a)): (f\in[0,1)^{3\times K}) contains fractional coordinates for (K) atoms, (l) the lattice, and (a) element types. Coordinates 0 and 1 represent the same point, making the space a high-dimensional torus (\mathbb T^{3K}), not a bounded Euclidean cube. Gaussian noise in (\mathbb R^{3K}) followed by clipping incorrectly treats 0.99 and 0.01 as distant; wrapped-normal/Riemannian diffusion instead complicates forward kernels, scores, and integration. Pages 1–3 identify this as crystal generation's hardest continuous modality.

Existing methods recognize symmetry: CDVAE encodes periodic boundaries; DiffCSP uses periodic-(E(3))-equivariant networks and wrapped-normal fractional-coordinate diffusion; EquiCSP adds lattice-permutation/periodic-translation equivariance; FlowMM avoids score prediction through Riemannian flow matching. All still define generation directly on the position manifold. KLDM asks: Can motion remain correct on the torus while the learning target moves to a fixed Euclidean space?

This matters practically. MP-20 contains 45,231 crystals with at most 20 atoms; MPTS-52 contains 40,476 with at most 52 (Appendix Table 6, p.25). Toroidal dimension reaches 156 as atom counts grow, amplifying boundary and global-translation redundancy. On difficult MPTS-52 @1, KLDM raises FlowMM's 17.54 match rate to 23.93, an absolute gain of +6.39 pp and relative +36.43%(Table 1, p.7), showing changed diffusion state spaces can substantially improve structural prediction.

2.2 Narrative: lift, constrain, then collapse initial velocities to zero

The argument has four turning points.

First, treat each toroidal coordinate as an (SO(2)) rotation: positions remain on the correct manifold, while added velocities (v) lie in its Lie algebra, a fixed Euclidean space for tori. Second, noise enters only velocities, with positions moving naturally through them; training predicts Gaussian-velocity scores rather than coordinate scores involving periodic sums. Third, global periodic translations preserve crystals, so subtract the center-of-mass/Riemannian mean from predicted velocities to force zero net translation. Fourth, setting initial velocities to a zero point mass makes conditional velocity distributions analytical, simplifying scores from learning both means/scales to predicting clean-coordinate-related terms alone. Figure 1 and Appendix Table 3 show this simplification is a major gain source, not decoration.

The tradeoff is expanded state: sampling integrates positions and velocities, adding friction (\gamma), terminal time (T), and predictor–corrector steps. PC often improves @1 but not always @20. MPTS-52 KLDM-(x_0) falls from EM's 37.77 to PC's 37.10 (Table 1), showing extra correction does not guarantee better candidate coverage.

2.3 Dissecting the methodology and mechanisms

2.3.1 Formal definition

Map fractional coordinates to (\hat f\in SO(2)^{3K}), adding Lie-algebra velocity (\hat v) at each position. The forward kinetic Langevin SDE is:

[ d\hat f_t=\hat f_t\hat v_t,dt,\qquad d\hat v_t=-\gamma\hat v_t,dt+\sqrt{2\gamma},dw_t^{\mathfrak g}. \tag{12, main text p.4} ]

The first equation is noiseless transport; the second is an Ornstein–Uhlenbeck velocity process. The reverse process retains position dynamics but adds conditional scores to velocity drift:

[ d\hat f_t=-\hat f_t\hat v_t,dt, \quad d\hat v_t={\gamma\hat v_t+2\gamma\nabla_{\hat v_t} \log p_t(\hat v_t\mid\hat f_t)},dt+\sqrt{2\gamma},d\bar w_t^{\mathfrak g}. \tag{13, main text p.4} ]

Velocity denoising score matching is combined with lattice and element-modality losses:

[ \mathcal L=\lambda_v\mathcal L_v+\lambda_l\mathcal L_l+ \lambda_a\mathcal L_a,\qquad \lambda_v=\lambda_l=1. ]

Element types use continuous one-hot (C), analog bits (C-AB), or discrete absorbing diffusion (D), with respective (\lambda_a) values 20, 1, and 0.33 (Appendix E, pp.24–25). Zero initial velocity (v_0=0) eliminates some conditional-Gaussian mean terms, yielding Equation (19)'s simplified parameterization, easier to learn than Equation (18)'s direct form.

2.3.2 Workflow diagram

Crystal x0=(fractional coordinates f0, lattice l0, elements a0)
       │
       ├─ f0: T^(3K) ≅ SO(2)^(3K) ── add Euclidean velocities v0=0
       │                                  │
       │                         Kinetic forward SDE
       │                     Positions follow velocity; noise enters velocity only
       │                                  │
       │                     Network predicts velocity scores
       │                                  │
       │              Subtract mean → enforce zero-net velocity
       │                                  │
       │                Reverse with EM or Predictor–Corrector
       │
       ├─ l0: ordinary Euclidean diffusion ──────────┤
       └─ a0: C / C-AB / D element diffusion ────────┤
                                                  ↓
                                  Candidate crystals → structural matching / MatterSim

2.3.3 Key mechanisms and engineering details

2.4 Experimental design, benchmarks, and metrics

Data comes from Appendix Table 6 (PDF p.25). CSP predicts structure from composition: Match Rate (MR, higher is better) measures structural matches; RMSE (lower is better) is computed only on matches. @1 uses one sample, @20 uses 20 candidates per composition. DNG generates composition and structure jointly: RMSD measures displacement after MatterSim relaxation, lower energy above hull indicates stability, stable is the fraction below a threshold, and SUN intersects stable, unique, and novel.

2.5 Main results: complete CSP matrix

Values are transcribed from Table 1 (PDF p.7). “—” means unreported, never invented. KLDM reports means±standard errors over 3 sampling runs; baseline values come from their papers.

@1: single-candidate structure prediction

The strongest evidence appears on difficult datasets rather than PEROV-5: KLDM-x₀ PC versus FlowMM on MPTS-52 MR gains +6.39 pp / +36.43%; versus EquiCSP, +9.08 pp / +61.14%. Yet EquiCSP still has the best RMSE at 0.1169, versus KLDM-x₀ PC's 0.1276, a difference of 9.15%. KLDM matches more samples but does not minimize coordinate errors among matched cases.

@20: multicandidate coverage

@20 reveals parameterization–sampler interactions: the strongest single-sample x₀-PC is not best for coverage. On MPTS-52, ε-PC scores 39.81 versus x₀-PC's 37.10, lower by 2.71 pp / 6.81%. Simplified scores cannot be assumed better under every budget; they mainly improve @1 and post-match RMSE, while candidate diversity may decline.

2.6 DNG: stability rises while SUN falls

Table 2 (PDF p.8) evaluates 10,000 samples per KLDM variant with MatterSim relaxation over three sampling runs. Starred baselines train on reoptimized, filtered MP-20, while KLDM uses raw unfiltered MP-20; this is not a matched-data comparison.

KLDM-D versus MatterGen raises stable from 47.05 to 59.21, +12.16 pp / +25.84% and reduces above-hull energy from 0.201 to 0.155, a 22.89% decrease; RMSD, however, rises 0.147→0.283, a 92.52% deterioration, and SUN drops 25.76→18.52, -7.24 pp / -28.11%. The central scientific conclusion is not that KLDM generates the best materials, but that: Discrete element diffusion substantially improves surrogate-potential stability rates without simultaneously solving novelty, uniqueness, or geometric relaxation distance.

2.7 Multilevel ablations, sensitivity, and phase transitions

Appendix Table 3 (PDF p.21) directly compares direct and simplified scores:

Under PC, simplified versus direct gives MP-20 MR +2.08 pp / +3.29%, RMSE a 23.01% decrease; MPTS-52 MR +5.61 pp / +35.39%, RMSE a 19.63% decrease. Simplified parameterization yields larger MR gains on harder datasets, supporting reduced score-learning burden over more complex networks.

Figure 1 (p.9) uses 6 training seeds, comparing initial-velocity variances (0,0.1,0.5,1), zero-net velocity, and two score forms. Curves show means±standard errors without exact point values, so this report does not guess numbers. Cautiously supported conclusions: zero velocities clearly beat positive variance, simplified beats direct, and zero-net projection adds only marginal gains. A transition signal appears between (\mathrm{Var}(v_0)=0) and any positive variance. Without a denser ([0,0.1]) sweep, a steep continuous decline cannot be distinguished from a genuine theoretical discontinuity.

The paper also Not reported systematic sensitivity curves for (\gamma), (T), PC corrector counts, network width, and sampling steps, and lacks accuracy–NFE or wall-clock Pareto frontiers. Parameterization sensitivity is established; robustness to dynamics hyperparameters is not.

2.8 Statistical significance

Most KLDM CSP/DNG main results use 3 sampling seeds with means±standard errors, while Figure 1 uses 6 training seeds—better than single-point reporting. On MPTS-52 @1, x₀-PC 23.93±0.2 versus ε-PC 21.46±0.2 differs by 2.47pp, roughly 12 times either standard error. But raw samples, CIs, and paired tests are absent; single-point baselines prevent fair significance comparisons. Ten thousand DNG samples and three runs do not imply independent identically distributed material candidates; tiny standard errors cannot replace chemical validation.

2.9 Genuine contributions, reusable designs, and transfer potential

KLDM's contribution is a general design principle rather than another crystal diffusion model: When data lies on a Lie group/torus and scores are difficult to learn, retain group-valued position dynamics but move randomness and learning into a fixed Lie-algebra velocity space. This transfers beyond a specific EGNN: protein/RNA torsion angles, periodic molecular dynamics, robot joint angles, and phase data are toroidal. TDM establishes the idea for broader Lie groups; KLDM adds periodic crystal translation, lattices, and discrete-element multimodal coupling.

Reusable modules include zero-velocity-derived simplified scores, zero-net projection of network outputs, separately chosen diffusion processes for continuous structures and discrete types, reporting @1 and @20 to distinguish precision from coverage, and reporting stable alongside SUN to expose stable-but-repeated/non-novel outputs. The last evaluation habit is especially valuable scientifically.

3. Limitations and additional critique

3.1 Author-stated limitations

1. No final DFT validation. The conclusion (p.9) explicitly identifies DFT validation as a natural next step. Table 2 depends on MatterSim machine-learned potentials; stability is therefore surrogate-model stability.
2. Dynamics and architecture remain improvable. The conclusion proposes alternative velocity noising, score architectures better matched to periodicity, and modality-specific schedules, showing (\gamma=1,T=2) and the current EGNN are not final choices.
3. Incomplete symmetry coverage. Appendix I.4 (PDF p.29) acknowledges absent lattice-permutation invariance; space-group/Wyckoff information, property-conditioned generation, and MOFs are also future work.

3.2 Independent critique (evidence → inference)

1. [Experimental design] Unmatched training data. MatterGen/DiffCSP baselines use reoptimized, filtered MP-20, while KLDM uses raw unfiltered MP-20 (Table 2 note). The stable-rate gain 59.21 versus 47.05 (+12.16pp) mixes in dataset-version effects and cannot all be attributed to kinetic lifting.
2. [Metric validity] Stability and discoverability diverge. KLDM-D has the highest stable rate at 59.21%, but SUN is only 18.52%, 7.24pp below MatterGen. Many extra stable samples fail uniqueness/novelty; stable rate is not sufficient as a discovery-yield proxy.
3. [Failing subtask] Much worse relaxation distance. KLDM-D RMSD of 0.283 Å is nearly 1.93× MatterGen's 0.147 Å, implying initial structures farther from potential-energy minima. This can raise relaxation costs and weakens claims of high-quality direct generation.
4. [Argument gap] No compute-matched efficiency comparison. The PC code example uses 1,000 steps, while the paper reports only a single 24GB GPU, without GPU-hours, NFE, throughput, or MatterSim relaxation costs. Whether +6.39pp MPTS-52 MR justifies auxiliary velocity/corrector costs is unknown.
5. [Metric validity] RMSE is conditional. RMSE is evaluated only on successful matches. EquiCSP MPTS-52 has RMSE 0.1169/MR 14.85, while KLDM-x₀ PC has 0.1276/23.93, so their evaluation subsets differ. The 9.15% gap cannot directly establish EquiCSP is more accurate on identical samples.
6. [Hyperparameter reproducibility] The transition is not located. Figure 1 scans initial variances 0, 0.1, 0.5, and 1, without dense (10^{-4})–(10^{-1}) values. Zero velocity is supported as special, but why is not quantitatively tied to mixing time or score variance.
7. [Missing key competitor] Symmetry-aware generation is not compared directly. Same-conference WyckoffDiff explicitly generates Wyckoff/space-group information, while KLDM has no space-group conditioning or matched-data/budget comparison in Tables 1/2. The relative importance of momentum lifting and explicit symmetry priors remains unclear.
8. [Reproducibility] Public code but limited checkpoints/environment evidence. The accessible repository includes training/evaluation entry points and MP-20 data, but no formal release or pretrained weights were found. Only RTX 3090/A5000 is specified, without drivers, full runtimes, or seed lists, requiring reproduction from scratch.

4. Related-work retrospective: how the problem evolves

4.1 CDVAE — 2022, ICLR

What it solved. CDVAE moves periodic crystal generation beyond general graph VAEs through physically informed diffusion decoders: coordinates denoise along low-energy-like directions, element types update with local bonding, and periodic boundaries plus permutation/translation/rotation invariance are handled explicitly. Its Perov-5/Carbon-24/MP-20 data and evaluation become shared baselines in Table 1.

Remaining gap. VAE latents handle lattices/compositions, while coordinate denoising does not prioritize fractional-coordinate torus geometry. Encoding adds a reconstruction/generation bottleneck. CDVAE's MPTS-52 @1 MR of 5.34 in KLDM Table 1 indicates inadequate coverage for larger atom counts.

KLDM's response and design inheritance. KLDM inherits multimodal decomposition and datasets/metrics, replacing VAE-based coordinate generation with direct modeling in expanded ((f,v)) space. Periodicity moves from network invariance to defining the stochastic process itself.

4.2 DiffCSP — 2023, NeurIPS

What it solved. DiffCSP jointly generates lattices and positions in fractional rather than Cartesian coordinates, using periodic-(E(3))-equivariant denoisers for crystal symmetries. It directly supplies KLDM's network structure and CSP protocol.

Remaining gap. It applies wrapped-normal/Riemannian diffusion directly on toroidal coordinates, learning position scores while global-translation redundancy remains entangled with score parameterization. MPTS-52 MR of 12.19 @1 and 34.02 @20 (KLDM Table 1) shows large cells remain difficult.

KLDM's response and design inheritance. KLDM retains fractional coordinates and EGNNs but moves scores from positions to Euclidean velocities and removes global translation modes with zero-net velocity. Choosing the correct representation space evolves into choosing the correct diffusion-process space.

4.3 EquiCSP — 2024, ICML

What it solved. EquiCSP identifies incomplete lattice-permutation/periodic-translation equivariance and designs noising algorithms preserving them throughout. Forward noise mechanisms must match network symmetry, not rely only on endpoint augmentation.

Remaining gap. Equivariant noising still acts directly on the coordinate manifold, and correct constraints do not guarantee coverage: MPTS-52 @1 MR is 14.85 despite best RMSE 0.1169.

KLDM's response and design inheritance. KLDM preserves translation symmetry throughout training/inference through mean-projected velocities, but does not inherit lattice-permutation invariance, explicitly acknowledged in Appendix I.4. The methods are complementary, not simple substitutes.

4.4 FlowMM — 2024, ICML

What it solved. FlowMM formulates crystal generation as Riemannian flow matching with flexible base distributions, includes quantum-chemical validation, and claims approximately one-third the integration steps of prior open methods for stable-material discovery. It shifts attention from fixed diffusion schedules to simpler continuous transport.

Remaining gap. Flow matching still constructs vector fields on crystal product manifolds; MPTS-52 @1 MR of 17.54 shows simpler paths do not fully solve large-cell coverage. Integration efficiency is its strength, but KLDM lacks equal-NFE comparisons.

KLDM's response and design inheritance. KLDM simplifies diffusion scores through kinetic lifting instead of flow matching: expanding state versus simplifying paths. It improves MPTS-52 MR over FlowMM without comparing speed, leaving the overall tradeoff unresolved.

4.5 TDM — 2025, ICLR

What it solved. TDM trivializes momentum, mapping position-dependent tangent velocities on Lie groups into a fixed Lie algebra, with manifold-preserving integrators. Validated on protein/RNA torsions, tori, (SO(N),U(N)), it is KLDM's closest technical source.

Remaining gap. General Lie-group TDM lacks crystals' multiatom global-translation redundancy, continuous lattices, discrete elements, and CSP/DNG evaluation pipeline.

KLDM's response and design inheritance. KLDM specializes auxiliary momentum into per-atom periodic velocities, adds zero-net projection, and jointly models lattices with three element-diffusion choices. The critical inheritance is not copying the SDE, but finding that (v_0=0) yields simpler, empirically stronger scores for crystals.

5. Technical evolution

2022 CDVAE [periodic boundaries + diffusion decoder + shared data/metrics]
       │
       ├── 2023 DiffCSP [fractional coordinates + joint equivariant diffusion]
       │          │
       │          ├── 2024 EquiCSP [lattice-permutation/periodic-translation equivariance]
       │          │
       │          └── 2024 FlowMM [score diffusion → Riemannian flow]
       │
2024→2025 TDM [Lie-group positions + fixed Lie-algebra momentum + manifold-preserving integration]
       │
       └──────────────────────────────┐
                                      ↓
2025 KLDM [crystal torus positions + Euclidean velocities + zero-net projection
           + lattice diffusion + continuous/discrete element diffusion + CSP/DNG]

The progression is from networks recognizing periodicity, to entire stochastic processes respecting it, to auxiliary variables changing learning geometry. DiffCSP's fractional coordinates remove unit-cell choices from Cartesian coordinates; EquiCSP requires equivariant forward noise; FlowMM then simplifies transport, while TDM/KLDM expand state. Evaluation shifts from validity/coverage toward MatterSim/DFT stability and SUN, but KLDM's stable–SUN divergence shows metrics remain unsettled.

6. Open challenges and actionable opportunities

6.1 Theory

1. Locate the zero-velocity transition. With fixed networks/training budgets, compare (\mathrm{Var}(v_0)\in{0,10^{-5},10^{-4},10^{-3},10^{-2},10^{-1}}), reporting score variance, mixing time, MR, and RMSE. Test whether zero's advantage comes from analytical parameterization or degenerate dynamics.
2. Sample complexity of expanded states versus direct manifold scores. On synthetic (\mathbb T^d) with (d=6,30,60,156), compare KLDM and wrapped-normal scores under equal parameter counts/function evaluations, deriving error bounds and measuring scaling slopes.
3. Complete symmetry projections. Combine zero-net velocity with EquiCSP lattice-permutation equivariance in four ablations: neither, velocity projection only, lattice permutation only, and both, directly addressing Appendix I.4.

6.2 Engineering and Applications

1. Equal-budget KLDM versus FlowMM. On identical MP-20/MPTS-52 splits and EGNNs, match NFE, GPU-hours, and peak memory; plot MR–time and SUN–time Pareto curves. This is the missing decisive test of kinetic lifting versus flow matching.
2. Calibrate MatterSim against DFT. Randomly select at least 500 MatterSim-stable samples per method for DFT relaxation; report precision, energy-ranking Spearman correlation, and false-stable rates. Otherwise 59.21% remains an internal surrogate-model figure.
3. Samplers and coverage. Compare EM, PC, and different corrector counts at @1/@5/@10/@20/@50, reporting pairwise structural diversity to test whether x₀-PC's @20 decline reflects mode contraction.
4. Reproducible experiment packages. Release fixed containers, hashes for all four datasets, three/six-seed checkpoints, and logs. Validate public-checkpoint inference and training from scratch separately, reducing the risk of available code that cannot reproduce Table 1.

6.3 Emerging Directions

1. Explicit space-group conditioning. Under matched MP data and MatterSim/DFT pipelines, compare KLDM, WyckoffDiff, and KLDM+Wyckoff conditioning, stratifying validity/stable/SUN across 230 space groups to test complementarity of momentum and symbolic symmetry priors.
2. Property-conditioned generation. Add band-gap, bulk-modulus, or magnetism conditions; compare classifier-free and reward guidance through condition-hit-rate/DFT-error/SUN Pareto surfaces rather than single property averages.
3. Larger periodic systems and defects. Extend beyond 52 atoms to MOFs, surfaces, and vacancy/doped supercells. Compare memory, NFE, and structural validity within atom-count bins to test whether benefits continue growing with toroidal dimension.

7. Other recent work worth watching

1. WyckoffDiff(ICML 2025): Explicit Wyckoff positions/crystal symmetry make this the most direct competitor for space-group priors absent from KLDM.
2. Efficient Molecular Conformer Generation with SO(3)-Averaged Flow Matching and Reflow(ICML 2025): Group averaging and reflow target equivariance and shorter paths, contrasting with KLDM's state expansion.
3. Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment(ICML 2025): Challenges the assumption that strong 3D generation requires equivariance throughout; worth testing at matched parameters/throughput.
4. DiffMS(ICML 2025): Maps mass-spectrum conditions into molecular generation, emphasizing experimental-observation constraints over unconditional priors.
5. MF-LAL(ICML 2025): Multifidelity active learning brings expensive experimental/simulation feedback into drug latent-space search, informing DFT-in-the-loop crystal generation.
6. OmniArch(ICML 2025): A unified architecture for scientific computing, relevant to the boundary between generality and specialized geometric priors.
7. Towards scientific discovery with dictionary learning(ICML 2025): Extracts interpretable biological concepts from microscopy foundation models, linking representations, mechanisms, and automated discovery.

8. Conclusion

KLDM shows that material-generation geometry need not be solved only with more complex equivariant networks: moving diffusion noise into Euclidean velocities can substantially ease score learning. MPTS-52 single-candidate MR rises from FlowMM's 17.54 to 23.93, the strongest geometric evidence. Discrete element diffusion raises MatterSim stable to 59.21%, but SUN is 7.24pp below MatterGen and RMSD nearly 1.93× higher. Alongside differing training-data versions and missing DFT, greater surrogate stability does not yet mean discovering more synthesizable novel materials.

Verification and transparency

• All table values are transcribed from conference-paper Tables 1–6 or calculated directly from them; derived percentages use two decimal places.
• OpenReview triggered browser verification during automated access. URLs came from PMLR Related Material or explicit paper/code links; inaccessible review content was not used as evidence.
• No KLDM pretrained weights, separate project page, or video were found; Figure 1 values were not guessed from pixels.
• Full KLDM training and DFT relaxation could not be run here; reproducibility judgments rely on visible paper/repository evidence.
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• The deduplication index was updated after this output.