◆ The Frontier · 18 open problems
Grand Hard Problems
The grand hard problems an AI Scientist could one day crack — registered as framing pages: the governing equation and what "solved" would mean. Not yet benchmarked or verified — unlike PWM's mature, reproduced computational-imaging benchmarks. Help define them and earn PWM. Life sciences & longevity lead.
Life Sciences & Aging
— reverse aging · longevity · cancer · regeneration · 5Restore a youthful epigenome with partial reprogramming — turn biological age down without losing cell identity.
dA/dt = k_dmg − k_rep · u(t); Age_bio = Clock(M_methylation)
Bend the Gompertz mortality curve — slow the rate of aging itself, extending healthspan, not just lifespan.
μ(t) = A + B·e^{G·t}; dG/dθ = −Σ_i w_i·intervention_i
Treat the tumor as an evolving population — schedule therapy to keep it controllable forever instead of selecting for resistance.
dx_s/dt = r_s x_s(1−N/K) − d·u(t)·x_s; dx_r/dt = r_r x_r(1−N/K)
Steer wounded tissue toward regeneration instead of scar — control the morphogen / ECM dynamics that decide fibrosis vs repair.
∂u/∂t = D_u∇²u + f(u,v); ∂[ECM]/∂t = k_p·TGFβ − k_d·[ECM]
Predict and reverse age-driven protein aggregation — the proteostasis collapse behind Alzheimer's and Parkinson's.
dM/dt = 2 k_+ m(t) P(t); dP/dt = k_n m^{nc} + k_2 m^{n2} M − k_clear·P
Quantum Technology
— fault tolerance · repeaters · control · compilation · 4Cross the fault-tolerance threshold — decode the surface code fast enough that adding qubits drives the logical error rate down, not up.
p_L ≈ A·(p/p_th)^{(d+1)/2}; Λ = p_L(d) / p_L(d+2)
Build a quantum internet — distribute entanglement over continental distances by beating fibre loss with repeaters and memories.
R_direct ∝ η = e^{−L/L_att}; R_repeater ∝ (η^{1/n})·p_swap^{n−1}·f(τ_mem)
Hit the gate fidelities fault tolerance needs — shape control pulses that beat decoherence and crosstalk on real hardware.
U(T) = T exp(−i ∫₀ᵀ H[u(t)] dt); F = |Tr(U_target† U)|² / d²
Make quantum programs runnable — compile and route circuits to hardware with the fewest two-qubit gates so the result survives noise.
minimize N₂(routing, synthesis) s.t. coupling graph; P_success ≈ (1−ε₂)^{N₂}
Nanotechnology
— atomically precise manufacturing · DNA self-assembly · nanomedicine · 4Build matter atom by atom — place reactive groups with positional control to assemble structures no bulk chemistry can reach.
rate ∝ exp(−ΔE‡/k_BT); yield = P(correct site | σ_position, E(r))
Program matter to fold itself — design DNA sequences that self-assemble into a target nanostructure at high yield.
ΔG = Σ ΔG_NN; yield = Z_target / Z_total over the folding landscape
Deliver drugs only where they're needed — design nanoparticles that navigate the body and accumulate in target tissue, sparing the rest.
∂C/∂t = ∇·(D∇C) − v·∇C − k_clear·C + k_on·R·C; uptake = ∫_target C dV
Compute with single molecules — predict and design the quantum conductance of a molecule wired between two electrodes.
G = (2e²/h)·T(E_F); T(E) = Tr[Γ_L G^r Γ_R G^a] (NEGF)
Physics & Cosmology
— quantum gravity · dark matter · dark energy · superconductivity · 5Reconstruct the geometry of spacetime from quantum entanglement — test whether gravity is emergent (Ryu–Takayanagi).
S(A) = Area(γ_A) / 4 G_N (Ryu–Takayanagi)
Pin down the dark-matter halo from how galaxies rotate — distinguish particle dark matter from modified gravity.
v(r) = √(G·M(r)/r); ρ_NFW(r) = ρ_s / [(r/r_s)(1+r/r_s)²]
Measure whether dark energy is a constant or evolving — reconstruct the equation of state w(z) from the expansion history.
H(z)² = H₀²[Ω_m(1+z)³ + Ω_DE·e^{3∫(1+w)/(1+z)dz}]
Show that black holes preserve information — recover the unitary Page curve of Hawking radiation via the island formula.
S_rad = min ext_I [ Area(∂I)/4G_N + S_bulk(R∪I) ] (island formula)
Design a material that superconducts at room temperature — predict Tc from electron–phonon coupling and invert for high-Tc structures.
Tc = (ω_log/1.2)·exp(−1.04(1+λ) / (λ − μ*(1+0.62λ))) (Allen–Dynes)
These are open problems, not finished benchmarks. Propose a sharper governing equation, a digital twin, or the first real benchmark for one — and earn PWM.
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