Data & Environment · Frontier STEM problems

Research-grade STEM problems with determinate answers.

Expert-authored, closed-ended problems spanning graduate-level material through research-frontier questions. Each item is independently verified and evaluated against current reasoning models before release.

Filtered against frontier models Exact-match gradeable
Pipeline

From a research question to a gradable item.

Each item is authored by a domain expert, filtered against frontier models, and verified by a second expert before it enters the set.

01Frontier source

A specific result from current literature in the author's discipline.

domain expert
02Authoring

The result becomes a closed-ended question; the machinery it depends on is stated in the prompt.

domain expert
03Solver filter

The strongest available reasoning models attempt every item before release.

frontier models
solved reliably → removed
04Blind review

A second expert confirms the unique answer without seeing the author's derivation.

independent expert
Difficulty

Three bands.

Each item is authored to one band. Sets are composed to a specified mix of subject and band. Every band passes the same solver filter—items current models solve reliably are removed; Band C sets the bar higher still and requires an outright incorrect answer.

Band CFrontier
Band BExpert
Band AGraduate
difficulty  ·  width ∝ share of items
A

Graduate level. Authored or verified by experts at or above the caliber of those behind Humanity's Last Exam; problems at graduate level.

B

Expert level. Long, difficult tasks drawn from domain experts' professional workflows; close to the research frontier.

C

Frontier level. Retained only if the strongest reasoning models available at authoring time answer incorrectly. Re-filtered as stronger models are released.

Mathematics Physics & quantum Biology & medicine Chemistry CS & AI
Examples

What an item looks like.

Four items from Bands A and B, shown in full. Answers are withheld; each resolves to a single value or statement a blind second expert can verify.

Band A · GraduateChemistry · zeolite catalysis exact-match

Given: A commercial HY zeolite (faujasite Y, $\mathrm{Si/Al}=15$) is desilicated in aqueous $\mathrm{NaOH}$ at increasing severity to give HY-parent and HY-strong. After washing to $\mathrm{pH}=8$, drying, and calcining in dry air at $550\,{}^{\circ}\mathrm{C}$:

  • XRD / $\mathrm{N_2}$ physisorption: HY-parent is crystalline; HY-strong is essentially amorphous and has much larger external and mesopore surface area.
  • $\mathrm{NH_3}$ temperature-programmed desorption (same saturation at $120\,{}^{\circ}\mathrm{C}$ and same He purge): HY-parent shows peaks at $200\,{}^{\circ}\mathrm{C}$ and $350\,{}^{\circ}\mathrm{C}$. HY-strong loses the $350\,{}^{\circ}\mathrm{C}$ peak and gains a dominant new peak at $500\,{}^{\circ}\mathrm{C}$.
  • $^{27}\mathrm{Al}$ magic-angle spinning NMR: HY-parent shows signals near $60\,\mathrm{ppm}$ (tetrahedral Al) and $0\,\mathrm{ppm}$ (octahedral Al). HY-strong shows no detectable $0\,\mathrm{ppm}$ signal; the $60\,\mathrm{ppm}$ signal persists but is strongly broadened. Any octahedral Al fraction above 5% would be detectable.
  • Hydrothermal catalysis (water-rich, $170\,{}^{\circ}\mathrm{C}$, 6 h): only HY-strong gives high selectivity to levulinic acid from the biomass-derived substrate D-xylose at comparable conversion.
  • Mechanistic constraint: levulinic acid forms via (i) dehydration of D-xylose to furfural, (ii) acid-assisted net transfer-hydrogenation of furfural to furfuryl alcohol in $\mathrm{H_2O}$, (iii) hydrolytic ring-opening to levulinic acid.

In-situ IR spectroscopy at $170\,{}^{\circ}\mathrm{C}$ in $\mathrm{H_2O}$-saturated He after He pretreatment at $350\,{}^{\circ}\mathrm{C}$. Two bulky bases that cannot enter intact faujasite micropores are dosed separately:

  • Probe A: 2,6-di-tert-butylpyridine. Brønsted protonation gives a $\sim 1640\,\mathrm{cm^{-1}}$ band; it is purge-labile if weakly stabilized.
  • Probe B: 2,6-diphenylpyridine. A purge-persistent $\sim 1600\,\mathrm{cm^{-1}}$ band at constant $T$ indicates a stable pyridine-to-Lewis-acid adduct.
  • OH rule: negligible change at $3610\,\mathrm{cm^{-1}}$ means bridging OH groups were not significantly consumed.

Observed on HY-strong:

  • After A: $3610\,\mathrm{cm^{-1}}$ decreases only slightly; a weak $1638\,\mathrm{cm^{-1}}$ band appears and largely vanishes on He purge at $170\,{}^{\circ}\mathrm{C}$.
  • After B: $3610\,\mathrm{cm^{-1}}$ is essentially unchanged; a strong $1605\,\mathrm{cm^{-1}}$ band appears and persists on He purge at $170\,{}^{\circ}\mathrm{C}$.

Task: Identify the predominant structural identity of the new $500\,{}^{\circ}\mathrm{C}$ acid sites in HY-strong that are external or mesopore-accessible and implicated in levulinic acid selectivity. Provide one chemically specific site description.

answer withheld · blind-reviewed 1 / 4
Band A · GraduatePhysics · quantum mechanics closed-ended derivation

Consider the one-dimensional motion of an uncharged spin-$\frac{1}{2}$ particle with magnetic moment $\mu = -\frac{2\mu_0}{\hbar}\,s$. The particle is confined in an infinite square well extending from $x = -L$ to $x = L$. In region I $(x < 0)$ there is a uniform magnetic field $B = B_0\,e_z$ along the $z$ direction, and in region II $(x > 0)$ there is a uniform magnetic field $B = B_0\,e_x$ of the same magnitude pointing in the $x$ direction; $e_x$, $e_z$ are the unit vectors along $x$ and $z$.

  1. In the weak-field limit $B_0 \ll \frac{1}{2m\mu_0}\left(\frac{\hbar}{L}\right)^2$, use perturbation theory to find the energy and wave function (spin and spatial) of the ground state.
  2. For arbitrary $B_0$, find the general expression for the energy eigenfunction $\psi_{\mathrm{I}}$ in region I satisfying the left boundary condition, spatial and spin, and likewise $\psi_{\mathrm{II}}$ in region II satisfying the right boundary condition.
  3. Find the equation determining the energy eigenvalue $E$.
answer withheld · blind-reviewed 2 / 4
Band B · ExpertPhysics · scattering theory exact-match

Radial two-channel scattering is described by a matrix Schrödinger equation whose potential $V(r)$ is a real symmetric matrix function, taken short-ranged and allowed a centrifugal term. The Jost matrix is the transposed $r\to0$ limit of the matrix solution carrying plane-wave asymptotics at infinity; allowing for a centrifugal singularity $V(r\to0)\to r^{-2}\nu(\nu-1)$ at the origin it reads $F(E)=\lim_{r\to0} f^{t}(r,E)\,r^{\nu}/(2\nu-1)!!$ with $f(r\to\infty)\to\exp(i\sqrt{E}\,r)$. The scattering matrix $S(E)$ is the matrix coefficient in the solution $\psi(r,E)$ that vanishes at the origin and carries an outgoing plane wave at infinity, $\psi(r\to\infty,E)\to \exp(il\pi/2-i\sqrt{E}\,r)-\exp(-il\pi/2+i\sqrt{E}\,r)\,S(E)$, with $V(r\to\infty)\to r^{-2}l(l-1)$. Call a matrix nontrivially coupled when no constant similarity transformation brings it to diagonal form.

Which of the following are true? List the numbers of all correct statements.

  1. A nontrivially coupled $S(E)$ implies a nontrivially coupled $V(r)$.
  2. A diagonal $S(E)$ implies a diagonal $V(r)$.
  3. A nontrivially coupled $V(r)$ implies a nontrivially coupled $F(E)$.
  4. A nontrivially coupled $F(E)$ implies a nontrivially coupled $S(E)$.
  5. Nontrivially coupled potentials $V(r)$ with diagonal Jost matrices $F(E)$ exist.
answer withheld · blind-reviewed 3 / 4
Band B · ExpertCondensed matter · topological order exact-match

A bosonic integer quantum Hall state at filling $\nu=2$ is characterised by the K-matrix $\sigma_x=\begin{pmatrix}0&1\\1&0\end{pmatrix}$. Suppose instead that the bosons forming this state are themselves Cooper pairs of composite fermions, each composite fermion having two flux quanta bound to it.

Write down the K-matrix of the fractional state that results.

answer withheld · blind-reviewed 4 / 4
What you get

Item, answer, and the reasoning behind both.

Graded records

Each item ships with its unique answer, the expert derivation, subject and difficulty labels, and the solver runs that qualified it for its band.

Aimed coverage

Specify subjects and difficulty bands; the set is authored to that mix.

Re-filtered on release

When a stronger model is released, the set is re-run against it and items that no longer fail are flagged.

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