Candidate databases: PubChem, COCONUT, LOTUS, NPAtlas, SuperNatural, NPASS, ChEMBL — sizes, overlaps, licences, and the pool-size arithmetic

TL;DR. The "natural-product universe" is far smaller than its headline numbers: COCONUT's October-2026 CSV has 738,794 rows but only 479,690 unique InChIKey14 connectivities; LOTUS (151,885 InChIKey14) is 99.8 % inside COCONUT; the largest published deduplicated union of 29 NP sources (THEOBROMA, June 2026) is 1,133,004 full InChIKeys = 486,215 InChIKey14 families. PubChem is 124.7 M compounds (live count, 2026-10-07), i.e. ~260x larger, but adds almost no probability mass for this test set, and every published pool-size experiment (MetFrag 2010→2016, CSI:FingerID 2015, Kaggle 2026 write-ups) shows rank degrading roughly linearly with candidate count. A ±10 ppm neutral-mass window in InChIKey14-deduplicated COCONUT yields a median 36 (mean 87, p90 204) candidates per molecule — small enough that re-ranking is tractable; in PubChem the same window is ~10^4.

1. Sizes, versions, dates (what is actually counted)

Notes. (i) COCONUT 2.0's "695,133" is a canonical-SMILES count with stereo; THEOBROMA attributes 920,039 full-InChIKey entries to the same COCONUT release ("exceed the 695,133 … by 224,906 compounds, reflecting the resolution of stereoisomer, protonation, and isotopologue variants"). At the metric's granularity (InChIKey14) COCONUT is ~480 k, matching the "480k natural products from COCONUT" in the Laudicina Kaggle write-up. (ii) PubChem compound count growth: 119 M (Sep 2024) → 124.7 M (Oct 2026), +2.4 %/yr.

2. Overlaps

Union at InChIKey14 level (Q3). The only published all-NP-database deduplication is THEOBROMA: 1,133,004 full InChIKeys collapsing to 486,215 connectivity families. Combined with the computed 479,690 for COCONUT alone, the practical answer is: the open NP universe at the CASMI metric's resolution is ≈0.49 M, not 1–3 M. Numbers in the 1–3 M range (THEOBROMA 1.13 M, Wang 1.03 M, COCONUT 2.0's 1.02 M curated rows) are stereo/protonation-expanded. The 2–3x gap between "entries" and IK14 is the single most important bookkeeping fact for pool construction.

3. Downloads and licences

Kaggle's own rules on external-data licensing could not be re-verified in this session (web-search budget exhausted); treat NC-licensed sources as "do not upload", which costs nothing because they are subsumed by COCONUT.

4. Neutral-mass windowing in COCONUT (computed, InChIKey14-deduplicated, Oct 2026)

A ±10 ppm window is ±3.0 mDa at 300 Da, ±5.0 mDa at 500 Da, ±8.0 mDa at 800 Da. Counting at the literal masses 300.000/500.000/800.000 Da is meaningless (3 / 0 / 0 hits) because real molecules sit on mass-defect ridges; the useful statistic is per-molecule: for each COCONUT structure, how many other COCONUT IK14s fall within ±10 ppm of its own exact mass.

Cross-check with Kaggle write-ups: nghianguyen7171 reports a 712,199-structure train+COCONUT pool (not IK14-deduplicated) giving "approximately 107 candidates per molecule" at ±10 ppm (30 ppm fallback) with 70.8 % of in-window candidates sharing the true formula; a stereo-expanded pool and test masses concentrated in the 300–500 Da band (where my median is 49–64) explain the gap to my 36. Formula knowledge removes only ~30 % of the window in this regime — mass is already nearly as selective as formula for NP-sized molecules.

Published candidates-per-query statistics for comparison: MetFrag2010 averaged 338 candidates/compound in Feb-2006 PubChem (median rank 8) and 2,508 in 2009 PubChem (median rank 31.5), 102-compound Hill dataset; CASMI 2016 candidate lists came from ChemSpider at ±5 ppm (208 challenges). MassSpecGym mass-based candidate sets are capped at 256 and the random baseline's Hit@1 of 0.37 % ≈ 1/270 shows the cap is almost always hit, i.e. the "mass-based" track is effectively 256 random PubChem isobars; its formula-based random Hit@1 of 3.06 % implies ~33 effective isomers. Scaling MetFrag's 2009 figure by PubChem growth (~25 M → 125 M CIDs) gives ~10^4 candidates per ±10 ppm window in today's PubChem, versus 36 in IK14-COCONUT: a ~300x ratio.

5. Evidence that larger pools hurt (Q7)

6. "One-step analogs" and NP-like PubChem subsets (Q6)

• No maintained "COCONUT analogs" enumerated library exists in the sources opened. The closest public objects: (a) 67,064,204 LSTM-generated NP-like SMILES (Tay et al., Sci Data 2023; trained on 325,535 COCONUT structures; NP-score KL divergence to COCONUT 0.064 nats; 59.3 M carry NPClassifier pathway labels) — a distribution-matched decoy/analog pool, 165x the known NP space; (b) THEOBROMA ships Morgan/MACCS fingerprints and FAISS index for 1.13 M; (c) ChEMBL's natural_product flag + np_likeness_score (ChEMBL 32 blog: ChEMBL median ≈ −1 vs ChEBI NPs median 1.47).
• NP-likeness thresholding of PubChem: Ertl's 2008 score (range −5…5; NP training set 130 k) was applied to PubChem only for scaffold mining; no published "PubChem with NP-likeness > 0" subset size was found. Note COCONUT itself has 28.5 % of structures at NP-likeness ≤ 0, so a threshold of 0 would discard a quarter of the reference NP set — any threshold must be calibrated on enveda-np-examples, not assumed.
• Practical analog route for the challenge: enumerate single-step transforms (O-methyl/demethyl, ±H2, ±O, glycosylation/deglycosylation, acetylation) of the top-k COCONUT hits, i.e. a query-conditioned analog pool of ~10^2–10^3 per spectrum, not a global one. nghianguyen7171's "Class-3 enumeration" (v7) changed LB by 0.000 — enumeration without a ranker that can score novel structures buys nothing.

Forced analogy: search-and-rescue probability map (Koopman)

Statement. Koopman's search theory: the ocean is partitioned into cells i with prior probability p_i that the target is there; a detection function b(z) = 1 − e^{−w z} gives the probability of finding it with effort z. The optimal plan allocates the next unit of effort to the cell with the largest marginal return p_i·w·e^{−w z_i}, so effort goes where posterior density per cell is highest, and a huge low-density region is searched only after the dense region's marginal value has decayed to the same level. Mapping: cell = candidate structure; prior p_i = P(hidden molecule is this structure) before seeing the spectrum, determined by which database(s) it is in; effort = the 25 submission slots; detection = the ranker's ability to recognise the truth.

Arithmetic. Let c_S be the probability that the true molecule is in source set S and n_S the number of S-candidates inside the ±10 ppm window.

• COCONUT: back-solved recall@25 ≈ 0.55 at LB 0.417 and nghianguyen7171's "Class 3 ≈ 39 % not retrievable" put c_COCONUT ≈ 0.55–0.61; n ≈ 36–107. Prior density per candidate ρ ≈ 0.6/50 ≈ 1.2 × 10^-2.
• PubChem-only (not in any NP DB): Laudicina: "the hidden-test answers are mostly not PubChem-only"; an upper bound c ≈ 0.05–0.10; n ≈ 10^4. ρ ≈ 0.08/10^4 ≈ 8 × 10^-6.
• Density ratio ≈ 1,500–2,000x. Under Koopman, a PubChem-only candidate deserves a slot only when the spectrum's likelihood ratio in its favour exceeds ~10^3; with 25 slots and a ranker whose per-decoy "false-outrank" probability is q, the expected rank of the truth is ≈ 1 + q·n. MetFrag2010's own numbers give q ≈ 7/338 ≈ 0.02, which predicts rank ≈ 53 at n = 2,508 (observed 31.5 — right order, sub-linear because decoys are not exchangeable). For a modern fingerprint ranker take q ≈ 0.002: COCONUT window → E[rank] ≈ 1.1 (MRR|in-pool ≈ 0.7–0.9); PubChem window → E[rank] ≈ 21, i.e. straddling the MRR@25 cliff. Expected MRR: COCONUT-only ≈ 0.6 × 0.75 ≈ 0.45 ceiling; merged ≈ (0.6+0.08) × 1/21 ≈ 0.03 if PubChem decoys are allowed to flood the window. That is the Laudicina result (0.112 → 0.079, with 68 % of top-1 slots captured by PubChem-only decoys) reproduced in sign and magnitude: the coverage gain (+0.08 at most) cannot pay for a ~200x dilution of the prior.

Testable rule. Score each candidate as s' = s_ranker(spectrum, cand) + λ·log π(cand), with π(cand) ∝ c_S / n_S for the finest source set S the candidate belongs to; operationally, log π ≈ log(coverage of its database) − log(its database's window count) + μ·log(1 + k) where k is the number of independent NP databases attesting the structure (THEOBROMA's attestation table gives k directly; mean 1.34). Predictions: (1) λ > 0 is optimal and PubChem-only candidates enter the top-25 only with a log-likelihood margin of ≈ 7 nats; (2) μ > 0 on known-structure validation (enveda-np-examples, 99.6 % in COCONUT) but μ ≈ 0 or < 0 on the hidden test's never-published novel compounds — so fit μ on the three-mask validation protocol, not on random train hold-outs. (3) gnshx's result (PubChem top-50 injected only when library confidence < 0.7 fails, LB 0.384 → 0.420) is exactly a Koopman second-phase allocation: search the sparse map only after the dense one is exhausted.

Does it hold? Partially. Holds: the allocation logic and the density arithmetic. Breaks in three places: (a) ~40 % of targets are in no cell (Class 3), where Koopman has no answer — the map must be extended (analog enumeration / de novo), not searched harder; (b) detection across cells is not independent: near-isomers share fingerprints, so q is correlated and the effective number of decoys is smaller than n (which is why rank grows sub-linearly with pool size); (c) effort is 25 discrete, all-or-nothing slots, not a continuous budget, so the correct objective is top-25 set selection, closer to Stone's discrete-cell variant than Koopman's continuous one.

Gotchas / what could fool us

1. Entry counts are not structure counts. COCONUT 695,133 (paper) / 738,794 rows (Oct 2026) / 920,039 (THEOBROMA attribution) all collapse to 479,690 InChIKey14. Submitting stereo variants wastes slots: three stereoisomers of one connectivity occupy three of 25 guesses for one chance.
2. Tautomer mismatch. The metric canonicalises tautomers with RDKit 2026.03.3 before taking InChIKey14. COCONUT's stored InChIKeys are not tautomer-canonical; keto/enol and lactam/lactim pairs can map to different IK14s. Re-canonicalise every candidate with the exact RDKit version, then dedupe — otherwise the correct structure can be in the pool under an InChIKey14 that does not match the hidden key.
3. Window counts at round masses are noise (3 hits at 300.000 Da, 0 at 500/800). Report per-molecule distributions; expect median 20–64 depending on mass band, with a fat tail (max 1,761 isobars).
4. Formula artefacts. C6H5N3O has 1,761 distinct IK14s in COCONUT, chemically impossible for that formula — a curation bug (likely mis-assigned formula on a block of entries). Triglyceride formulas C50–C57H*O6 contribute 645–731 isomers each and dominate the 800–1000 Da band (mean 158 candidates). Formula-based filters inherit these errors; compute formula from the SMILES, not from the CSV column.
5. COCONUT is not all natural. 28.5 % of its structures have NP-likeness ≤ 0 (ZINC NP, SuperNatural II derivatives, UNPD synthetics). "Candidate is in COCONUT ⇒ natural product" is false; the prior should be learned per-source, not binary.
6. Revoked entries. The dev statistics page lists 38,771 revoked molecules (5 %); the lite CSV may include them.
7. Licence drift. COCONUT's download page says CC0, its Zenodo deposit and THEOBROMA say CC BY 4.0; NPAtlas moved to CC BY-NC at 2024_09; SuperNatural 3.0 and NPASS are CC BY-NC; ChEMBL is CC BY-SA 3.0 (share-alike propagates). 19.9 % of THEOBROMA rows are NC. None of the NC sources adds structures beyond COCONUT at IK14 level, so the clean move is to not ship them.
8. LOTUS adds 254 structures to COCONUT. Its value is organism/taxon metadata (37,476 organisms, 91,421 references), not pool coverage. Its headline "290 k structures" counts stereo variants; IK14 is 151,885.
9. Circular sources. ChEMBL's NP flag is defined by COCONUT matching; NPAtlas, NPASS, KNApSAcK, SuperNatural II, CMAUP are COCONUT inputs. Counting "number of databases containing X" overstates independence unless provenance is traced (THEOBROMA's attestation table does this).
10. Pool composition changes ranker behaviour. With PubChem merged, 68 % of top-1 picks were PubChem-only (Laudicina) — a sign the ranker's scores are not calibrated across sources (synthetic-like decoys with "clean" fingerprints score high). Any ensemble trained on a COCONUT pool will mis-calibrate when the pool changes.
11. Benchmark priors do not transfer. MassSpecGym's candidate order (PubChem default = popularity) alone yields 49.98 % Hit@1; CASMI 2026's hidden set is "none previously published", so popularity priors may invert. Validate μ (membership weight) on the enveda-np-examples three-mask protocol, which is the only split reported to predict LB ordering (shiferaxa, nghianguyen7171).
12. MassSpecGym "mass-based" ≠ a ±10 ppm window. Its sets are capped at 256 random isobars (random Hit@1 0.37 % ≈ 1/270); hit rates there say nothing about 10^4-candidate PubChem windows.
13. PubChem growth. 2.4 %/yr compound growth is slow, but the FTP dumps (CID-SMILES 1.49 GB gz) are from 2026-09-27; CID-Mass.gz (1.39 GB) gives monoisotopic mass directly and avoids RDKit mass computation on 125 M SMILES.

Implications for the challenge

1. Build the base pool as COCONUT Oct-2026 ∪ train structures, deduplicated at InChIKey14 after RDKit-2026.03.3 tautomer canonicalisation (expect ≈ 480 k + ≈ 275 k train minus overlap). Compute neutral mass from the canonical SMILES, not the CSV columns.
2. Retrieve at ±10 ppm on neutral mass (±5 mDa at 500 Da); expect median ~36–60 candidates, p90 ~200; cap nothing below 25.
3. Do not merge PubChem wholesale. If used at all, apply it as a second phase (Koopman) gated by a confidence threshold on the COCONUT-phase top-1, injecting at most ~50 candidates with a log-prior penalty of ≈ −7 nats; measure on the three-mask enveda-np-examples split.
4. Add a source-prior term λ·log(c_S/n_S) + μ·log(1+k) and sweep λ, μ; expect λ > 0 robustly and μ unstable between known-structure validation and novel hidden test.
5. Skip NPAtlas/SuperNatural/NPASS/KNApSAcK files entirely: zero IK14 gain over COCONUT, NC/All-rights licences. Use THEOBROMA only for its provenance/attestation column and precomputed fingerprints if its NC rows are dropped.
6. Treat formula selectivity as weak: 70.8 % of in-window candidates already share the true formula, so formula prediction buys ≤ 30 % pool reduction; spend effort on the ranker and on Class-3 coverage instead.
7. For the ~40 % of hidden molecules outside every database, generate query-conditioned analog sets (single-step transforms of top-k COCONUT hits, or Tay et al.'s 67 M NP-like library filtered by the mass window) and score them with the same ranker; measure whether MRR@25 on masked-out validation molecules moves — nghianguyen7171's enumeration gave +0.000, so expect this to need a ranker that generalises, not just a bigger map.
8. Fix the C6H5N3O-class formula artefacts and drop revoked rows before computing any per-formula statistic.

Open questions

• How many hidden-test molecules are in COCONUT at IK14 after tautomer canonicalisation? The 0.55–0.61 estimates are back-solved from leaderboard scores; a direct measurement on enveda-np-examples (99.6 % in COCONUT) with the exact RDKit pipeline would nail c_S.
• What is the IK14-level PubChem window count distribution for NP-mass molecules today? (Needs CID-Mass.gz + CID-InChI-Key.gz, ~9 GB; not run here.)
• Does the THEOBROMA attestation count k predict membership in the hidden test (novel NPs) positively or negatively?
• Kaggle's current external-data licence rules for NC datasets (not verified this session).
• NPAtlas 2025 release: npatlas.org still lists v2024_09 as latest; whether a 2025/2026 file exists was not determinable.

Sources

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• COCONUT Oct-2026 CSV-lite: https://coconut.s3.uni-jena.de/prod/downloads/2026-10/coconut_csv_lite-10-2026.zip (analysed in this work; scripts in session scratchpad coconut_stats.py, overlap.py)
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