Citation breakout prediction

For every academic-paper row with a populated citation trajectory we fit the Wang-Song-Barabási log-normal model — the academic gold-standard for paper-level impact (~0.75 Spearman vs observed 10-year counts in Wang, Song & Barabási, Science 342:127-132, 2013). Three views on the catalog: papers most likely to break out (still-growing fastest), papers that look hyped today but won't last (saturation phase below cohort median), and the sleeping beauties — slow-burn impact with low immediacy but long tail.

96 Pre-growth 41%

74 Growth 32%

28 Saturation 12%

35 Underfit data 15%

39 rows fit from real citation trajectories · 159 rows fit from synthesised series · median R² (trajectory only) = 0.99 · field constant m = 42 (catalog median citations per paper).

Panel 1 — Top-15 predicted breakouts

Growth-phase papers (latest cumulative cites < 50 % of predicted asymptote) ranked by the ratio of predicted asymptote to current cites. The watchlist: these papers still have the most citation runway left. Restricted to rows with real bucketed trajectories (not synthesised fallbacks).

#	Paper	Section	Obs	c_∞	CI	Run-up	Break P	R²
1	S³ T4	Recent method papers — theorized, no distinct product	5	20k	5.8k–37k	3968×	100%	0.96
2	Toolformer T3	Recent method papers — theorized, no distinct product	30	2.0k	602–6.7k	67.8×	92%	0.95
3	Recurrent Memory Transformer (RMT) T3	Recent method papers — theorized, no distinct product	13	835	311–2.1k	64.3×	59%	0.97
4	EWC (Elastic Weight Consolidation) T3	Recent method papers — theorized, no distinct product	9	456	262–775	50.7×	19%	0.99
5	Generative Agents T3	Recent method papers — theorized, no distinct product	31	687	268–1.2k	22.2×	9%	0.99
6	ITER-RETGEN T3	Retrieval-as-memory hybrids	4	59	36–90	14.8×	0%	0.99
7	Retroformer T4	Recent method papers — theorized, no distinct product	4	59	36–90	14.8×	0%	0.99
8	YaRN T3	Recent method papers — theorized, no distinct product	12	105	73–147	8.77×	0%	0.92
9	Reflexion T3	Recent method papers — theorized, no distinct product	23	57	34–86	2.47×	0%	0.97
10	LoRA T3	Training infrastructure	15	34	22–49	2.29×	0%	0.96
11	Self-RAG T4	Retrieval-as-memory hybrids	17	35	22–44	2.03×	0%	0.99

Panel 2 — Underperformers (saturation below cohort median)

Saturation-phase papers whose predicted asymptote is below the median for their 2-year publication cohort. Read as "hyped but won't last" — citation-count-as-quality-proxy is over-rating these relative to the model's long-run estimate. Real-trajectory fits only.

#	Paper	Section	Year	Obs	c_∞	R²
1	Neural Episodic Control T3	Recent method papers — theorized, no distinct product	2024	5	7	1.00
2	AriGraph T3	Recent method papers — theorized, no distinct product	2024	7	8	0.99
3	ReadAgent T4	Recent method papers — theorized, no distinct product	2024	8	8	1.00
4	Agent Workflow Memory T3	Recent method papers — theorized, no distinct product	2024	10	10	0.99
5	ExpeL T3	Recent method papers — theorized, no distinct product	2024	11	11	0.99
6	RAPTOR T3	Retrieval-as-memory hybrids	2024	15	16	0.98
7	RULER T3	Memory benchmarks & evaluation	2024	16	16	0.99
8	InfiniteBench (∞Bench) T3	Memory benchmarks & evaluation	2024	16	16	1.00
9	LongMemEval T3	Memory benchmarks & evaluation	2024	26	24	0.98
10	MemGPT v2 / agent-tools T3	Recent method papers — theorized, no distinct product	2024	31	31	1.00
11	LoCoMo T3	Memory benchmarks & evaluation	2024	38	38	0.99
12	DreamerV3 T3	Recent method papers — theorized, no distinct product	2023	5	5	1.00
13	LongLoRA T3	Recent method papers — theorized, no distinct product	2023	8	9	0.99
14	Self-Refine T3	Recent method papers — theorized, no distinct product	2023	11	10	0.99
15	FLARE T3	Retrieval-as-memory hybrids	2023	10	12	1.00

Panel 3 — Sleeping beauties

Papers with small λ but large σ + late μ. Citation accumulation profile is slow-burn rather than front-loaded — typical of papers that are cited years after publication when adjacent fields mature. WSB 2013 introduced the concept; we report the catalog's top candidates.

#	Paper	Section	λ	μ	σ	Obs	c_∞	R²
1	ITER-RETGEN T3	Retrieval-as-memory hybrids	0.88	4.90	3.00	4	59	0.99
2	Retroformer T4	Recent method papers — theorized, no distinct product	0.88	4.90	3.00	4	59	0.99
3	EWC (Elastic Weight Consolidation) T3	Recent method papers — theorized, no distinct product	2.47	4.60	1.97	9	456	0.99
4	Recurrent Memory Transformer (RMT) T3	Recent method papers — theorized, no distinct product	3.04	4.30	2.35	13	835	0.97
5	DPO T3	Training infrastructure	0.27	0.70	0.60	11	13	0.98
6	S³ T4	Recent method papers — theorized, no distinct product	6.16	4.30	1.52	5	20k	0.96
7	HyDE T3	Retrieval-as-memory hybrids	0.32	0.70	0.66	11	16	1.00
8	Toolformer T3	Recent method papers — theorized, no distinct product	3.90	4.00	2.46	30	2.0k	0.95
9	YaRN T3	Recent method papers — theorized, no distinct product	1.25	2.50	1.73	12	105	0.92
10	Voyager T3	Recent method papers — theorized, no distinct product	0.50	1.00	0.76	16	27	0.93

Methodology — Wang-Song-Barabási log-normal citation model

For each academic-paper row with a populated citation trajectory we fit the log-normal cumulative-citation formula introduced in Wang, Song & Barabási, "Quantifying long-term scientific impact," Science 342:127-132 (2013):

c(t) = m · (exp(λ · Φ((log(t) − μ) / σ)) − 1)

m: Field-constant — we use the catalog-wide median citations-per-paper (42 for this run). Wang-Song-Barabási use m ≈ 30 for the PNAS corpus; we substitute the actual catalog median to keep the scale honest. Same constant applies to every row; long-run impact differences are driven by λ.
λ (immediacy): Overall "ultimate impact" parameter. As t → ∞, c(t) → m·(exp(λ) − 1) is the asymptote. We constrain λ ∈ [0.1, 7] so the asymptote stays within a sensible extrapolation envelope on our 2-8 yr trajectories.
μ (peak time): Log-time of the citation peak — μ = ln(T_peak). Low μ means citations accumulate early; high μ means a slow-burn sleeping-beauty profile.
σ (longevity): Peak width on the log-time axis. Small σ + late μ = slow, sustained accumulation (the sleeping-beauty signature). Large σ = diffuse accumulation across many years.
10-year prediction: "10y prediction" in the WSB framework means the count at t = 10 years from publication — not 10 years from today. Computed as c(10) from the fitted curve.
Fit method: Coarse 3-d grid search over (λ, μ, σ) — 12 × 11 × 10 points — followed by three local refinement passes around the best grid point. Deterministic; no randomness. ~1700 grid evaluations per fit; ~1 ms each on V8.
Bootstrap CI: 90 % confidence band on the asymptote derived from 100 bootstrap resamples of the observed (year, count) pairs. RNG is seeded from each record's id so reruns produce identical CIs.
Signal sources: Priority: (1) real bucketed trajectory — yearly cumulative inbound-citation counts from the S2 reference cache, T3-prep-2 / issue #51 (requires ≥3 distinct years); (2) synthesised fallback — 4-anchor monotone ramp from (total cites, cites/yr, publication year) for paper rows with ≥1 year of life but a short trajectory. Synthesised fits are flagged with a "synth" badge and are excluded from the breakout / sleeping-beauty leaderboards — the fitted parameters are only suggestive on a 4-point monotone ramp. Implementation in web/src/lib/analyses/citation-prediction.ts.

R² distribution across trajectory fits

39 rows fit from real bucketed trajectories. The median R² of 0.99 is well above the 0.85 acceptance bar; the histogram below shows the distribution.

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