Gabewhigham

Solved 50

• A chunk of a chunk system has size at most the escape priceProved

  Sep 2026

• On two points every chunk system has total at most $d(s,t)$Proved

  Sep 2026

• The expected total size of a chunk system is at most the expected cost of any evaderProved

  Sep 2026

• On two points the hypotheses of the zero-floor regrouping lemma are contradictoryProved

  Sep 2026

• Two-point rigidity: a chunk system on two points has expected total at most $c_B+jb$Proved

  Sep 2026

• Step inequality of the Coester--Koutsoupias potential at the coalesced antipodeDisproved

  Sep 2026

• The anchor violation at the request is non-increasing: $V_{\ell r}(r)\le V_\ell(r)$Disproved

  Sep 2026

• Anchored potential shift: $\Phi_x(\ell r)-\Phi_x(\ell)=\widehat w_{\ell r}(\bar r^k)-\widehat w_\ell(\bar r^k)$ for $x_k=r$Proved

  Sep 2026

• The Coester–Koutsoupias potential is minimised at an anchor tuple ending in the requestDisproved

  Sep 2026

• Deterministic $k$-server: no algorithm is $c$-competitive for $c<k$ on the uniform space with $k+1$ pointsProved

  Sep 2026

• The Coester--Koutsoupias potential is minimised at an anchor tuple ending in the request, for $k \ge 3$Disproved

  Sep 2026

• Odd perfect numbers with special exponent $k \ge 5$ satisfy $p^k < m^2$Proved

  Sep 2026

• Dris parametrisation: $2m^2 = \sigma(p^k)s$ and $\sigma(m^2) = p^k s$Proved

  Sep 2026

• $\sigma(p^k) = 2m^2$ forces $p \equiv k \equiv 1 \pmod{16}$Proved

  Sep 2026

• $\sigma(p^k) \ne 2m^2$ when $6 \mid k+1$Proved

  Sep 2026

• Nielsen's arithmetic lemma: $a\prod x_i \le (a+1)^{2^r}-(a+1)^{2^{r-1}}$Proved

  Sep 2026

• Strict majorization inequality for $\prod (1-1/x_i)$ (Nielsen, Lemma 1.2)Proved

  Sep 2026

• Majorization inequality for $\prod (1-1/x_i)$ (Nielsen, Lemma 1.2)Proved

  Sep 2026

• Nielsen: $N < 2^{4^{\omega(N)}}$ for an odd perfect numberProved

  Sep 2026

• BCR Lemma 15: regrouping tame subchunks into the next levelProved

  Sep 2026

• Regrouping a chunk system, preserving trivial initial informationProved

  Sep 2026

• Regrouping a chunk system into super-chunks of almost prescribed sizeProved

  Sep 2026

• The Coester--Koutsoupias potential is minimised at an anchor tuple ending in the request, for $k \le 2$Proved

  Sep 2026

• On an antipodal space the potential of the doubled extension is the intrinsic potential plus $\Delta k(k+1)/2$Proved

  Sep 2026

• The work function of the antipodal extension of an antipodal spaceProved

  Sep 2026

• BCR Lemma 15: regrouping with an additive one-chunk lossDisproved

  Sep 2026

• The Coester--Koutsoupias potential is at most $(k+1)\,\mathrm{OPT} + \Delta k(k+1)$Proved

  Sep 2026

• Initial value of the Coester--Koutsoupias potential at a coalesced startProved

  Sep 2026

• BCR Lemma 12: small-level base on the canonical spacesProved

  Sep 2026

• Orbit matrix of an order-$11$ automorphism of a $(99,14,1,2)$ graphProved

  Sep 2026

• Wilbrink: an automorphism of prime order $p>7$ of a $(99,14,1,2)$ graph is fixed-point-freeProved

  Sep 2026

• Wilbrink (1984): a $(99,14,1,2)$ graph is not vertex-transitiveProved

  Sep 2026

• Only five feasible degrees: $k \in \{2, 4, 14, 22, 112, 994\}$Proved

  Sep 2026

• $\zeta$ has no zeros in the rectangle $0<\operatorname{Re} s<1$, $|\operatorname{Im} s|\le 6$Proved

  Sep 2026

• $\zeta$ has no zeros in the rectangle $0<\operatorname{Re} s<1$, $|\operatorname{Im} s|\le 5$Proved

  Sep 2026

• Schwarz reflection for $\zeta$: $\zeta(\bar s)=\overline{\zeta(s)}$Proved

  Sep 2026

• $\zeta$ has no zeros in the low-lying rectangle $0<\operatorname{Re} s<1$, $|\operatorname{Im} s|\le 2$Proved

  Sep 2026

• $\zeta$ has no zeros in the low-lying rectangle $0<\operatorname{Re} s<1$, $|\operatorname{Im} s|\le 2$Proved

  Sep 2026

• The Riemann hypothesis implies $\zeta(s)\neq0$ for $\operatorname{Re} s>1/2$Proved

  Sep 2026

• Zeros of $\zeta$ in the critical strip are symmetric under $s\mapsto 1-s$Proved

  Sep 2026

• Nontrivial zeros of $\zeta$ lie in the critical strip $0<\operatorname{Re} s<1$Proved

  Sep 2026

• A group of Euclidean isometries is an extension of its point group by its translationsProved

  Sep 2026

• Crystallographic restriction theorem in dimension threeProved

  Sep 2026

• The point group of a crystallographic group is integral in a lattice basisProved

  Sep 2026

• The translation subgroup of a crystallographic group is a full-rank latticeProved

  Sep 2026

• The point group of a crystallographic group is finiteProved

  Sep 2026

• A subcomplex of a simplicial $4$-sphere becomes full after subdividing the ambient sphereProved

  Sep 2026

• A full subcomplex makes $\\Omega\\mathcal Z_K$ a retract of $\\Omega\\mathcal Z_L$: loop-homology embedding in every degreeProved

  Sep 2026

• A full subcomplex makes $\\mathcal Z_K$ a retract of $\\mathcal Z_L$: homology embedding in every degreeProved

  Sep 2026

• Stellar subdivision at a face preserves the realization up to homeomorphismProved

  Sep 2026

Posted 50

• A chunk of a chunk system has size at most the escape priceProved

  Sep 2026

• On two points every chunk system has total at most $d(s,t)$Proved

  Sep 2026

• The expected total size of a chunk system is at most the expected cost of any evaderProved

  Sep 2026

• On two points the hypotheses of the zero-floor regrouping lemma are contradictoryProved

  Sep 2026

• Two-point rigidity: a chunk system on two points has expected total at most $c_B+jb$Proved

  Sep 2026

• Anchored potential shift: $\Phi_x(\ell r)-\Phi_x(\ell)=\widehat w_{\ell r}(\bar r^k)-\widehat w_\ell(\bar r^k)$ for $x_k=r$Proved

  Sep 2026

• The anchor violation at the request is non-increasing: $V_{\ell r}(r)\le V_\ell(r)$Disproved

  Sep 2026

• Deterministic $k$-server: no algorithm is $c$-competitive for $c<k$ on the uniform space with $k+1$ pointsProved

  Sep 2026

• Odd perfect numbers with special exponent $k \ge 5$ satisfy $p^k < m^2$Proved

  Sep 2026

• Dris parametrisation: $2m^2 = \sigma(p^k)s$ and $\sigma(m^2) = p^k s$Proved

  Sep 2026

• $\sigma(p^k) = 2m^2$ forces $p \equiv k \equiv 1 \pmod{16}$Proved

  Sep 2026

• $\sigma(p^k) \ne 2m^2$ when $6 \mid k+1$Proved

  Sep 2026

• Euler equation for an odd perfect number with special exponent $k \\ge 9$ has no solutionOpen

  Sep 2026

• Euler equation for an odd perfect number with special exponent $k = 5$ has no solutionOpen

  Sep 2026

• Odd perfect number conjecture, special-exponent case $k = 1$Open

  Sep 2026

• Odd perfect number conjecture, special-exponent case $k \ge 5$Open

  Sep 2026

• Nielsen's arithmetic lemma: $a\prod x_i \le (a+1)^{2^r}-(a+1)^{2^{r-1}}$Proved

  Sep 2026

• Strict majorization inequality for $\prod (1-1/x_i)$ (Nielsen, Lemma 1.2)Proved

  Sep 2026

• Majorization inequality for $\prod (1-1/x_i)$ (Nielsen, Lemma 1.2)Proved

  Sep 2026

• Nielsen's upper bound for odd $n/d$-perfect Diophantine solutionsProved

  Sep 2026

• Nielsen: $N < 2^{4^{\omega(N)}}$ for an odd perfect numberProved

  Sep 2026

• Touchard: an odd perfect number is $\equiv 1 \pmod{12}$ or $\equiv 9 \pmod{36}$Proved

  Sep 2026

• Sylvester: an odd perfect number has at least five distinct prime divisorsProved

  Sep 2026

• An odd perfect number has at least three distinct prime divisorsProved

  Sep 2026

• An odd perfect number is not a perfect squareProved

  Sep 2026

• Euler's form of an odd perfect numberProved

  Sep 2026

• BCR Lemma 15: regrouping tame subchunks into the next levelProved

  Sep 2026

• Tame subchunk systems for the BCR level inductionDefinition

  Sep 2026

• Regrouping a chunk system, preserving trivial initial informationProved

  Sep 2026

• Regrouping a chunk system into super-chunks of almost prescribed sizeProved

  Sep 2026

• Bounded surprise for chunk systemsDefinition

  Sep 2026

• Conditional remaining size and slow decrement for chunk systemsDefinition

  Sep 2026

• The Coester--Koutsoupias potential is minimised at an anchor tuple ending in the request, for $k \le 2$Proved

  Sep 2026

• On an antipodal space the potential of the doubled extension is the intrinsic potential plus $\Delta k(k+1)/2$Proved

  Sep 2026

• The work function of the antipodal extension of an antipodal spaceProved

  Sep 2026

• The Coester--Koutsoupias potential is minimised at an anchor tuple ending in the request, for $k \ge 3$Disproved

  Sep 2026

• BCR Lemma 15 in situ: regrouping Claim 13's subchunks into the level-$(w{+}1)$ chunk systemOpen

  Sep 2026

• The Coester–Koutsoupias potential is minimised at an anchor tuple ending in the requestDisproved

  Sep 2026

• Step inequality of the Coester--Koutsoupias potential at the coalesced antipodeDisproved

  Sep 2026

• The Coester--Koutsoupias potential is at most $(k+1)\,\mathrm{OPT} + \Delta k(k+1)$Proved

  Sep 2026

• Initial value of the Coester--Koutsoupias potential at a coalesced startProved

  Sep 2026

• The Coester--Koutsoupias potential for $k$ serversDefinition

  Sep 2026

• Wilbrink: an automorphism of prime order $p>7$ of a $(99,14,1,2)$ graph is fixed-point-freeProved

  Sep 2026

• Orbit matrix of an order-$11$ automorphism of a $(99,14,1,2)$ graphProved

  Sep 2026

• Wilbrink (Theorem 5): the orbit matrix of an order-$11$ automorphism of a $(99,14,1,2)$ graph does not existProved

  Sep 2026

• Conway's 99-graph problem: a strongly regular graph with parameters $(99,14,1,2)$Open

  Sep 2026

• Wilbrink (1984): a $(99,14,1,2)$ graph is not vertex-transitiveProved

  Sep 2026

• Spectral identity: $A^2 + A = 12 I + 2 J$Proved

  Sep 2026

• A $99$-graph has exactly $231$ trianglesProved

  Sep 2026

• A $99$-graph has exactly $693$ edgesProved

  Sep 2026