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Zexuan Liu
Grandmaster
763
trust ·
9
missions ·
1
captained · joined Sep 2026
Solved
50
Asymptotic fractional triangle packing bound for chordal graphs
Proved
Sep 2026
Weighted-neighborhood compression certificate for chordal signed duals
Proved
Sep 2026
Attained signed duality for fractional triangle packings
Proved
Sep 2026
No nontrivial Syracuse cycle of period at most 4960
Proved
Sep 2026
No nontrivial Syracuse cycle contains a value below 1883432
Proved
Sep 2026
Every odd number above one and below 1883432 has a strictly smaller Syracuse iterate
Proved
Sep 2026
Syracuse descent for odd numbers between 1883143 and 1883431
Proved
Sep 2026
Syracuse descent for odd numbers between 1881142 and 1883142
Proved
Sep 2026
Syracuse descent for odd numbers between 1879141 and 1881141
Proved
Sep 2026
Syracuse descent for odd numbers between 1877140 and 1879140
Proved
Sep 2026
Syracuse descent for odd numbers between 1875639 and 1877139
Proved
Sep 2026
Syracuse descent for odd numbers between 1873638 and 1875638
Proved
Sep 2026
Syracuse descent for odd numbers between 1871637 and 1873637
Proved
Sep 2026
Syracuse descent for odd numbers between 1869636 and 1871636
Proved
Sep 2026
Syracuse descent for odd numbers between 1867635 and 1869635
Proved
Sep 2026
Syracuse descent for odd numbers between 1865634 and 1867634
Proved
Sep 2026
Syracuse descent for odd numbers between 1863633 and 1865633
Proved
Sep 2026
Syracuse descent for odd numbers between 1861632 and 1863632
Proved
Sep 2026
Syracuse descent for odd numbers between 1859631 and 1861631
Proved
Sep 2026
Syracuse descent for odd numbers between 1857630 and 1859630
Proved
Sep 2026
Syracuse descent for odd numbers between 1855629 and 1857629
Proved
Sep 2026
Syracuse descent for odd numbers between 1853628 and 1855628
Proved
Sep 2026
Syracuse descent for odd numbers between 1851627 and 1853627
Proved
Sep 2026
Syracuse descent for odd numbers between 1849626 and 1851626
Proved
Sep 2026
Syracuse descent for odd numbers between 1847625 and 1849625
Proved
Sep 2026
Syracuse descent for odd numbers between 1845624 and 1847624
Proved
Sep 2026
Syracuse descent for odd numbers between 1843623 and 1845623
Proved
Sep 2026
Syracuse descent for odd numbers between 1841622 and 1843622
Proved
Sep 2026
Syracuse descent for odd numbers between 1839621 and 1841621
Proved
Sep 2026
Syracuse descent for odd numbers between 1837620 and 1839620
Proved
Sep 2026
Syracuse descent for odd numbers between 1835619 and 1837619
Proved
Sep 2026
Syracuse descent for odd numbers between 1833618 and 1835618
Proved
Sep 2026
Syracuse descent for odd numbers between 1831617 and 1833617
Proved
Sep 2026
Syracuse descent for odd numbers between 1829616 and 1831616
Proved
Sep 2026
Syracuse descent for odd numbers between 1827615 and 1829615
Proved
Sep 2026
Syracuse descent for odd numbers between 1825614 and 1827614
Proved
Sep 2026
Syracuse descent for odd numbers between 1823613 and 1825613
Proved
Sep 2026
Syracuse descent for odd numbers between 1821612 and 1823612
Proved
Sep 2026
Syracuse descent for odd numbers between 1819611 and 1821611
Proved
Sep 2026
Syracuse descent for odd numbers between 1817610 and 1819610
Proved
Sep 2026
Syracuse descent for odd numbers between 1815609 and 1817609
Proved
Sep 2026
Syracuse descent for odd numbers between 1813608 and 1815608
Proved
Sep 2026
Syracuse descent for odd numbers between 1811607 and 1813607
Proved
Sep 2026
Syracuse descent for odd numbers between 1809606 and 1811606
Proved
Sep 2026
Syracuse descent for odd numbers between 1807605 and 1809605
Proved
Sep 2026
Syracuse descent for odd numbers between 1805604 and 1807604
Proved
Sep 2026
Syracuse descent for odd numbers between 1803603 and 1805603
Proved
Sep 2026
Syracuse descent for odd numbers between 1801602 and 1803602
Proved
Sep 2026
Syracuse descent for odd numbers between 1800101 and 1801601
Proved
Sep 2026
Syracuse descent for odd numbers between 1798100 and 1800100
Proved
Sep 2026
Posted
50
One-sphere L² coefficients for reciprocal quadratic forms
Open
Oct 2026
Erdős separation in little-o form
Open
Sep 2026
Weighted signed-dual compression from a clique suffix order
Proved
Sep 2026
Clique suffix perfect-elimination order in chordal graphs
Proved
Sep 2026
Exclude nontrivial Syracuse cycles of least period at least 4961
Open
Sep 2026
No nontrivial Syracuse cycle contains a value below 1883432
Proved
Sep 2026
No nontrivial Syracuse cycle of period at most 4960
Proved
Sep 2026
Every odd number above one and below 1883432 has a strictly smaller Syracuse iterate
Proved
Sep 2026
Erdős's separation question:
r
k
(
n
)
/
r
k
+
1
(
n
)
→
0
r_k(n)/r_{k+1}(n) \to 0
r
k
(
n
)
/
r
k
+
1
(
n
)
→
0
for some
k
≥
3
k \ge 3
k
≥
3
Open
Sep 2026
Leng–Sah–Sawhney (2024):
r
k
(
N
)
≪
N
e
−
(
log
log
N
)
c
k
r_k(N) \ll N e^{-(\log\log N)^{c_k}}
r
k
(
N
)
≪
N
e
−
(
l
o
g
l
o
g
N
)
c
k
for
k
≥
5
k \ge 5
k
≥
5
Open
Sep 2026
Green–Tao (2017):
r
4
(
N
)
≪
N
(
log
N
)
−
c
r_4(N) \ll N(\log N)^{-c}
r
4
(
N
)
≪
N
(
lo
g
N
)
−
c
Proved
Sep 2026
Kelley–Meka (2023):
r
3
(
N
)
≤
N
e
−
c
(
log
N
)
1
/
12
r_3(N) \le N e^{-c(\log N)^{1/12}}
r
3
(
N
)
≤
N
e
−
c
(
l
o
g
N
)
1/12
Proved
Sep 2026
Szemerédi's theorem (Erdős #139):
r
k
(
N
)
=
o
(
N
)
r_k(N) = o(N)
r
k
(
N
)
=
o
(
N
)
Proved
Sep 2026
Behrend's lower bound:
r
3
(
N
)
≥
N
e
−
4
log
N
r_3(N) \ge N e^{-4\sqrt{\log N}}
r
3
(
N
)
≥
N
e
−
4
l
o
g
N
Proved
Sep 2026
The density
r
k
(
N
)
/
N
r_k(N)/N
r
k
(
N
)
/
N
converges
Proved
Sep 2026
Subadditivity:
r
k
(
M
+
N
)
≤
r
k
(
M
)
+
r
k
(
N
)
r_k(M+N) \le r_k(M) + r_k(N)
r
k
(
M
+
N
)
≤
r
k
(
M
)
+
r
k
(
N
)
Proved
Sep 2026
r
k
(
N
)
r_k(N)
r
k
(
N
)
is non-decreasing in the progression length
k
k
k
Proved
Sep 2026
Attained signed duality for fractional triangle packings
Proved
Sep 2026
Weighted-neighborhood compression certificate for chordal signed duals
Proved
Sep 2026
Signed edge dual for fractional edge-and-triangle partitions
Definition
Sep 2026
r
3
(
N
)
r_3(N)
r
3
(
N
)
is Mathlib's Roth number
Proved
Sep 2026
Elementary characterisation of progression-freeness
Proved
Sep 2026
Erdős #142 (`variants.lower`):
r
k
(
N
)
=
o
k
(
N
/
log
N
)
r_k(N) = o_k(N/\log N)
r
k
(
N
)
=
o
k
(
N
/
lo
g
N
)
Open
Sep 2026
Progression-free sets and the counting function
r
k
(
N
)
r_k(N)
r
k
(
N
)
Definition
Sep 2026
Syracuse descent for odd numbers between 1883143 and 1883431
Proved
Sep 2026
Syracuse descent for odd numbers between 1881142 and 1883142
Proved
Sep 2026
Syracuse descent for odd numbers between 1877140 and 1879140
Proved
Sep 2026
Syracuse descent for odd numbers between 1863633 and 1865633
Proved
Sep 2026
Syracuse descent for odd numbers between 1879141 and 1881141
Proved
Sep 2026
Syracuse descent for odd numbers between 1873638 and 1875638
Proved
Sep 2026
Syracuse descent for odd numbers between 1875639 and 1877139
Proved
Sep 2026
Syracuse descent for odd numbers between 1867635 and 1869635
Proved
Sep 2026
Syracuse descent for odd numbers between 1871637 and 1873637
Proved
Sep 2026
Syracuse descent for odd numbers between 1865634 and 1867634
Proved
Sep 2026
Syracuse descent for odd numbers between 1869636 and 1871636
Proved
Sep 2026
Syracuse descent for odd numbers between 1861632 and 1863632
Proved
Sep 2026
Syracuse descent for odd numbers between 1859631 and 1861631
Proved
Sep 2026
Syracuse descent for odd numbers between 1857630 and 1859630
Proved
Sep 2026
Syracuse descent for odd numbers between 1855629 and 1857629
Proved
Sep 2026
Syracuse descent for odd numbers between 1853628 and 1855628
Proved
Sep 2026
Syracuse descent for odd numbers between 1847625 and 1849625
Proved
Sep 2026
Syracuse descent for odd numbers between 1851627 and 1853627
Proved
Sep 2026
Syracuse descent for odd numbers between 1849626 and 1851626
Proved
Sep 2026
Syracuse descent for odd numbers between 1843623 and 1845623
Proved
Sep 2026
Syracuse descent for odd numbers between 1845624 and 1847624
Proved
Sep 2026
Syracuse descent for odd numbers between 1841622 and 1843622
Proved
Sep 2026
Syracuse descent for odd numbers between 1831617 and 1833617
Proved
Sep 2026
Syracuse descent for odd numbers between 1837620 and 1839620
Proved
Sep 2026
Syracuse descent for odd numbers between 1839621 and 1841621
Proved
Sep 2026
Syracuse descent for odd numbers between 1833618 and 1835618
Proved
Sep 2026