The Regime Boundaries of AI-Amplified Research: Task Complementarity, Physical Validation, and the Limits of Semi-Endogenous Growth
Author: Ryan S. Lester · University of Houston, Department of Economics · rslester@cougarnet.uh.edu
Working Paper — April 2026 | Under consideration for BUPA (Best Undergraduate Paper Award)
Two facts organize this paper.
In July 2025, Gemini Deep Think achieved a gold-medal score on the International Mathematical Olympiad. Over the same period, FrontierMath — problems requiring hours to days for expert human mathematicians — moved from 2% to 40% AI success in fourteen months. In formalized mathematics, AI systems now complete the full research cycle: conjecture, proof search, and verification.
In pharmaceutical drug discovery over the same period, AI-assisted lead identification drove Phase I clinical trial success rates from a historical 40–65% to 80–90%. Phase II efficacy rates — where a drug must demonstrate therapeutic effect in human patients — remained approximately 40%, unchanged from historical baselines.
These two facts are not anomalies. They are the predicted consequence of a structural feature that semi-endogenous growth theory has not formalized: research is a two-stage process, and AI scales those stages differently.
This paper derives the regime conditions under which Jones (1995) survives intact, under which it is temporarily exceeded, and under which it is permanently dissolved. The answer: Jones survives as the universal long-run attractor everywhere except where validation can be executed digitally and mechanically verified. AI does not rewrite the Jones equation. It extends how long sectors spend above it — and permanently dissolves the ceiling only where proof assistants make validation costless.
Three formal contributions:
Theorem 1 — Bounded Amplification under Task Complementarity. AI amplification of effective research labor is bounded by a complementarity ceiling d_s/(1−d_s) that depends on the sector's digital task share, not AI capacity. Once AI capacity exceeds this ceiling, additional investment cannot raise effective research labor.
Theorem 2 — Steady-State Bifurcation. Sectors bifurcate based on whether their validation-stage digital task share d_V_s exceeds a time-varying threshold d_V*(t) = Φ(t)/(1+Φ(t)):
- Regime I (d_V_s ≤ d_V*): Validation ceiling binds. BGP growth rate = Jones exactly: λn/(1−φ)
- Regime II (d_V_s > d_V*): AI capital scales validation labor. BGP growth rate strictly exceeds Jones: λ[αg_K + (1−α)n]/(1−φ)
Corollary 2.1 — Regime II Transience. For any sector with finite d_V_s < 1, the threshold eventually crosses d_V_s and the sector returns to the Jones attractor. Regime II is extended — potentially decades — but transient. Under baseline calibration (α=0.3, g_K=0.30, n=0.01), the excess growth above Jones is approximately 8.7 percentage points per year during Regime II.
Lemma 1 — The Mechanical Verification Case. Only at d_V_s = 1 — where validation is fully mechanical, established for formalized mathematics (Lean 4, Coq, Isabelle/HOL) — is Regime II permanent. The Jones constraint never reasserts. T* → ∞.
Proposition 2 — Measurement Wedge. Partially explains the Bloom et al. (2020) finding of declining research productivity: as AI capital grows in Regime I sectors, R&D expenditure rises while validated output stays capped by the validation ceiling, generating a systematic downward bias in expenditure-based productivity measures.
The paper contests the hidden aggregation assumption in Jones (1995): that AI augmentation applies uniformly to all research tasks. It doesn't.
| Stage | Examples | AI Scalability |
|---|---|---|
| Generation | Hypothesis search, compound generation, proof attempts, candidate selection | High — AI raises μᴳ toward ceiling dᴳ/(1−dᴳ) |
| Validation | Clinical trials, lab synthesis, human peer review, physical measurement | Bounded — μᵛ bounded by dᵛ/(1−dᵛ) |
When d_G_s > d_V_s — when generation tasks are more digitally executable than validation tasks — AI raises generation capacity faster than validation throughput. Validated output is bounded by the validation ceiling regardless of how fast generation grows.
The null model (symmetric AI amplification) predicts both Phase I and Phase II success rates rise proportionally. Regime I predicts Phase I rises, Phase II stays flat. The data reject the null model.
| Metric | Historical Baseline | AI Era (post-2020) | Ratio |
|---|---|---|---|
| Phase I success rate | ~52% | ~85% | 1.63× ↑ |
| Phase II efficacy rate | ~35% | ~40% | 1.14× (flat) |
Source: Jayatunga et al. (2024); historical baselines from Paul et al. (2010) and Hay et al. (2014)
Proof verification by Lean/Coq is a decidable mechanical task requiring only digital computation. The complementarity ceiling diverges. T* → ∞.
- IMO: AlphaProof silver (2024) → Gemini Deep Think gold (2025) — ~1.86× per year
- miniF2F: Near-saturation at 99.2%
- FrontierMath: 2% → 40% AI success in 14 months
- Lean benchmark: AI completes 74.2% of proof steps (Leeman et al. 2024)
Parameters: α = 0.3, g_K = 0.30, n = 0.01
| Sector | d_V_s | Amplification Ceiling | T* (conservative) | T* (alternative) |
|---|---|---|---|---|
| Formalized mathematics | 1.00 | ∞ | ∞ | ∞ |
| Software engineering | 0.70 | 2.33 | ~36 years | ~18 years |
| Materials science | 0.30 | 0.43 | ~17 years | Already Regime I |
| Biochemistry | 0.15 | 0.18 | ~7 years | Already Regime I |
| Pharmaceuticals (validation) | 0.10 | 0.11 | ~1 year (boundary) | Already Regime I |
Digital task share proxies (d̂_s) constructed from O*NET v30.0 Work Activity Importance scores using digital (analyzing data, working with computers, processing information) vs. physical (handling objects, inspecting equipment, general physical activities) task weights.
| Occupation | SOC Code | d̂_s | Regime (Theory) |
|---|---|---|---|
| Mathematicians | 15-2021.00 | 0.890 | Permanent Regime II (Lemma 1) |
| Software Developers | 15-1252.00 | 0.881 | Transient Regime II (~36 yrs) |
| Biochemists | 19-1021.00 | 0.744 | Near transition (~7 yrs) |
| Materials Scientists | 19-2032.00 | 0.717 | Approaching transition |
| Chemists | 19-2031.00 | 0.636 | Regime I |
Rank ordering is consistent with the framework across all sensitivity checks. Full methodology in Appendix B of the paper.
| Paper | Contribution to This Work |
|---|---|
| Jones (1995) — JPE | Semi-endogenous growth baseline; the universal long-run attractor this paper characterizes the conditions for exceeding |
| Bloom, Jones, Van Reenen & Webb (2020) — AER | Declining research productivity documentation; Proposition 2 offers a partial AI-era explanation |
| Acemoglu & Restrepo (2018, 2020) — AER/JPE | Task-based automation framework; task complementarity structure of Theorem 1 |
| Romer (1990) — JPE | Endogenous growth baseline |
| Aghion, Jones & Jones (2017) — NBER | AI in growth theory; present paper's distinct contribution is the generation-validation decomposition |
| Gans (2025) — NBER 33907 | AI-driven threshold effects in knowledge; this paper differs by making regime boundaries depend on validation-stage task structure, not AI capability level |
All data and code for the ONET analysis (Section 7, Appendix B) and T calibrations (Table 1) are publicly archived on Harvard Dataverse:
DOI: 10.7910/DVN/FA75PH
Pharmaceutical pipeline data are from Jayatunga et al. (2024) and documented in the replication archive. All formal results are analytic; proofs are in the paper appendices.
regime-boundaries/
├── paper/
│ └── regime_boundaries_v5.pdf
├── data/
│ └── README_dataverse.md # Harvard Dataverse documentation
├── code/
│ ├── onet_task_shares.R # O*NET d̂_s proxy construction (Appendix B)
│ ├── t_star_calibrations.R # T* calibration table (Table 1)
│ └── regime_boundary_figure.py # Figure 2: regime boundary dynamics
└── replication/
└── REPLICATION.md
| Milestone | Status |
|---|---|
| Paper (v5) | ✅ Complete |
| Harvard Dataverse DOI | ✅ Active — 10.7910/DVN/FA75PH |
| SSRN posting | ✅ Live — abstract_id=6649740 |
| BUPA submission | ⏳ Targeting mid-May 2026 |
| Journal submission | 📋 Planned |
@unpublished{lester2026regime,
author = {Lester, Ryan S.},
title = {The Regime Boundaries of AI-Amplified Research: Task Complementarity,
Physical Validation, and the Limits of Semi-Endogenous Growth},
year = {2026},
note = {Working Paper. SSRN 6649740.},
url = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6649740},
doi = {10.7910/DVN/FA75PH}
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Ryan S. Lester · rslester@cougarnet.uh.edu · ORCID · RL Perspectives