Formal status changed: Erdős Problem 44: Extending Sidon Sets
The formal record now marks Erdős Problem 44: Extending Sidon Sets as mixed, previously open.
Breaking
The newest dated claims, announcements and changes the register holds, the latest first. Each claim shows how far its evidence has come, from a bare claim to a rebuild by someone independent of its authors, and every announcement's first-hour kit is listed below.
Refreshed .
Seen in the last week
What qed.bot's monitors have picked up from lab announcements, arXiv, Formal Conjectures and the other sources on the status page. None of it is graded until the register has read the source itself.
Reading what the monitors have seen…
30 Sep 2026
Formal status changed: Erdős Problem 80
The formal record now marks Erdős Problem 80 as mixed, previously open.
Formal status changed: Erdős Problem 331
The formal record now marks Erdős Problem 331 as solved, previously mixed.
Formal status changed: Erdős Problem 1084
The formal record now marks Erdős Problem 1084 as solved, previously mixed.
Formal status changed: Erdős Problem 1099
The formal record now marks Erdős Problem 1099 as solved, previously mixed.
Formal status changed: Erdős Problem 1106
The formal record now marks Erdős Problem 1106 as mixed, previously open.
Record superseded: Bounded gaps between primes
AxiomProver: Proved a bound of 212, building on Stadlmann's work, with a Lean certificate of the deduction. Autonomy A1, evidence V2.
New record: Bounded gaps between primes
GPT-6 Astra: Proved that infinitely many pairs of consecutive primes are at most 186 apart. Autonomy A3, evidence V2.
Record superseded: Bounded gaps between primes
Claude, ChatGPT and Codex: Proved that infinitely many pairs of consecutive primes are at most 236 apart, improving Stadlmann's 240. Autonomy A1, evidence V2.
29 Sep 2026
Fidelity regraded: Erdős Problem 789
The fidelity grade for Erdős Problem 789 moved from F0 to F2.
Fidelity regraded: Particular values of the Riemann zeta function
The fidelity grade for Particular values of the Riemann zeta function moved from F0 to F2.
Fidelity regraded: Green's Open Problem 25
The fidelity grade for Green's Open Problem 25 moved from F0 to F2.
Machine-checked: Erdős Problem 67
Erdős Problem 67 is now machine-checked, by Palomar.
Fidelity regraded: Erdős Problem 67
The fidelity grade for Erdős Problem 67 moved from F0 to F2.
Palomar registration: Erdős Problem 67
Palomar registered a rebuild of Erdős Problem 67, attached here as a check.
28 Sep 2026
Formal status changed: Erdős Problem 3
The formal record now marks Erdős Problem 3 as mixed, previously open.
Formal status changed: Erdős Problem 19
The formal record now marks Erdős Problem 19 as mixed, previously unclassified.
Formal status changed: Erdős Problem 30
The formal record now marks Erdős Problem 30 as mixed, previously open.
Formal status changed: Erdős Problem 78
The formal record now marks Erdős Problem 78 as mixed, previously unclassified.
Formal status changed: Erdős Problem 102
The formal record now marks Erdős Problem 102 as mixed, previously unclassified.
Formal status changed: Erdős Problem 103
The formal record now marks Erdős Problem 103 as open, previously unclassified.
Formal status changed: Erdős Problem 148
The formal record now marks Erdős Problem 148 as mixed, previously unclassified.
Fidelity regraded: Erdős Problem 261
The fidelity grade for Erdős Problem 261 moved from F0 to F2.
Fidelity regraded: Erdős Problem 302
The fidelity grade for Erdős Problem 302 moved from F0 to F2.
Formal status changed: Erdős Problem 482
The formal record now marks Erdős Problem 482 as solved, previously unclassified.
Fidelity regraded: Erdős Problem 482
The fidelity grade for Erdős Problem 482 moved from F0 to F2.
Formal status changed: Erdős Problem 522
The formal record now marks Erdős Problem 522 as solved, previously mixed.
Fidelity regraded: Erdős Problem 522
The fidelity grade for Erdős Problem 522 moved from F0 to F2.
Fidelity regraded: Erdős 809
The fidelity grade for Erdős 809 moved from F0 to F2.
Formal status changed: Erdős Problem 995
The formal record now marks Erdős Problem 995 as mixed, previously unclassified.
Fidelity regraded: Erdős Problem 1054
The fidelity grade for Erdős Problem 1054 moved from F0 to F2.
Fidelity regraded: Erdős 1219
The fidelity grade for Erdős 1219 moved from F0 to F2.
Formal status changed: Green's Open Problem 47
The formal record now marks Green's Open Problem 47 as mixed, previously open.
Fidelity regraded: Green's Open Problem 47
The fidelity grade for Green's Open Problem 47 moved from F0 to F2.
Fidelity regraded: Conjectures in Complexity Theory
The fidelity grade for Conjectures in Complexity Theory moved from F0 to F2.
Fidelity regraded: Pentanacci π sequence
The fidelity grade for Pentanacci π sequence moved from F2 to F0.
Formal status changed: a(n) = 3a(n−1) + a(n−2) − 3a(n−3)
The formal record now marks a(n) = 3a(n−1) + a(n−2) − 3a(n−3) as solved, previously open.
Fidelity regraded: a(n) = 3a(n−1) + a(n−2) − 3a(n−3)
The fidelity grade for a(n) = 3a(n−1) + a(n−2) − 3a(n−3) moved from F0 to F2.
Formal status changed: Smallest power with base>1 and exponent n without digit 0
The formal record now marks Smallest power with base>1 and exponent n without digit 0 as mixed, previously open.
Formal status changed: Group structure via subgroup counts
The formal record now marks Group structure via subgroup counts as solved, previously mixed.
Fidelity regraded: Group structure via subgroup counts
The fidelity grade for Group structure via subgroup counts moved from F0 to F2.
27 Sep 2026
Fidelity regraded: Erdős 1220
The fidelity grade for Erdős 1220 moved from F0 to F2.
Full resolution claimed: Finite-time blowup for the incompressible porous media equation with smooth forcing
Claude, GPT-5.6 Sol and GPT-6 Astra: Finite-time blowup for the incompressible porous media equation on the two-dimensional torus with a force smooth in space and time, extending Córdoba and Martínez-Zoroa's result with a spatially smooth force. Autonomy A1, evidence V1.
Full resolution claimed: Finite-time blowup for the 3D incompressible Euler equations with smooth forcing
Claude, GPT-5.6 Sol and GPT-6 Astra: A finite-time singularity for the incompressible Euler equations on ℝ³ with a force smooth in space and time up to and including the blowup time. Autonomy A1, evidence V1.
Full resolution claimed: Finite-time blowup for the inviscid Boussinesq equations with smooth forcing
Claude, GPT-5.6 Sol and GPT-6 Astra: Finite-time blowup for the inviscid Boussinesq system on ℝ² with smooth forcing in both equations: the temperature stays bounded while its gradient and the vorticity blow up. Autonomy A1, evidence V1.
21 Sep 2026
Advisory Group on Mathematics and Artificial Intelligence
0 of 100 results identified, 0 written up, 0 checkable. First-hour kit
D0
9 Sep 2026
Existence and Smoothness of the Navier–Stokes Equation
Formalised the Navier–Stokes and Euler results in Lean, checked with Comparator against the Formal Conjectures statements of alternatives (C) and (D).
Evidence: artifact published·stage 3 of 4
full
A1
V2
F3
8 Sep 2026
On the Navier–Stokes Millennium Prize Problem
2 of 2 results identified, 2 written up, 2 checkable. First-hour kit
D3
Existence and Smoothness of the Navier–Stokes Equation
Finite-time blowup for the 3D incompressible Navier–Stokes equations with smooth forcing, on Euclidean space and on the torus: Fefferman's alternatives (C) and (D), a negative answer to the Millennium problem. Unforced Euler blowup is proved alongside.
Evidence: artifact published·stage 3 of 4
full
A2
V2
F3
7 Sep 2026
Finite-time blowup with smooth forcing for porous media, Boussinesq and Euler
4 of 4 results identified, 3 written up, 0 checkable. First-hour kit
D1
Finite-time blowup for the incompressible porous media equation with smooth forcing
Finite-time blowup for the incompressible porous media equation on the two-dimensional torus with a force smooth in space and time, extending Córdoba and Martínez-Zoroa's result with a spatially smooth force.
Evidence: written up·stage 2 of 4
full
A1
V1
F0
Finite-time blowup for the 3D incompressible Euler equations with smooth forcing
A finite-time singularity for the incompressible Euler equations on ℝ³ with a force smooth in space and time up to and including the blowup time.
Evidence: written up·stage 2 of 4
full
A1
V1
F0
Finite-time blowup for the inviscid Boussinesq equations with smooth forcing
Finite-time blowup for the inviscid Boussinesq system on ℝ² with smooth forcing in both equations: the temperature stays bounded while its gradient and the vorticity blow up.
Evidence: written up·stage 2 of 4
full
A1
V1
F0
4 Sep 2026
Formalizing Fermat's Last Theorem
1 of 1 results identified, 1 written up, 1 checkable. First-hour kit
D3
Fermat's Last Theorem
A complete Lean 4 proof of Fermat's Last Theorem on the standard axioms, deriving Mathlib's own statement, with the classical inputs proved in the strength the argument needs rather than assumed.
Evidence: artifact published·stage 3 of 4
full
A1
V2
F2
3 Sep 2026
Bounded gaps between primes
Proved a bound of 212, building on Stadlmann's work, with a Lean certificate of the deduction.
Evidence: artifact published·stage 3 of 4
superseded
A1
V2
F2
Bounded gaps between primes
Proved that infinitely many pairs of consecutive primes are at most 186 apart.
Evidence: artifact published·stage 3 of 4
record
A3
V2
F2
1 Sep 2026
Bounded gaps between primes
Proved that infinitely many pairs of consecutive primes are at most 236 apart, improving Stadlmann's 240.
Evidence: artifact published·stage 3 of 4
superseded
A1
V2
F2
23 Aug 2026
Largest known rank of an elliptic curve over the rationals
An elliptic curve over the rationals of rank at least 31, verified by ICARM's leaderboard.
Evidence: artifact published·stage 3 of 4
record
A1
V2
F0
20 Aug 2026
Largest known rank of an elliptic curve over the rationals
An elliptic curve over the rationals of rank at least 30, the first above Elkies and Klagsbrun's 29.
Evidence: artifact published·stage 3 of 4
superseded
A1
V2
F0
First-hour kits
6One for every announcement the register holds, the latest first: what was claimed, how much of it can be inspected, and whether anyone independent has checked it.
D0
D3
D1
D3
D3
D3
Follow by feed
Every statement, record and system has its own Atom feed, linked from its page. The whole register, and each collection, can be followed here.
By collection · 25
- Algorithms
- AlphaEvolve problems
- Analytic number theory
- Books
- Discrete geometry
- Erdős
- Extremal combinatorics
- Fluid dynamics
- Green's open problems
- Hilbert
- Kourovka notebook
- Litt's problems
- MathOverflow
- Mathlib
- Millennium
- Number theory
- OEIS
- Open quantum problems
- Optimization constants
- Other
- Papers
- Subsets
- Wikipedia
- Written on the Wall II
- arXiv