s stringlengths 1 39 | o stringclasses 996
values | p stringlengths 7 77 | confidence float64 0.4 1 | predicate_class stringclasses 2
values | community int64 0 14 ⌀ | equation_name stringlengths 14 73 ⌀ | equation_latex stringlengths 5 217 ⌀ | equation_sympy stringclasses 617
values | equation_form stringclasses 472
values | variables stringlengths 2 85 ⌀ | domain stringclasses 119
values | scm_name stringclasses 165
values | source stringlengths 9 50 ⌀ | extraction_method stringclasses 8
values |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a_1} | r | urn:hailstone:math:structural_equation[6adf452b00c4] | 1 | structural_equation | 4 | arxiv.math.AG.2603.07802v1.eq_121 | Δ_{a_1}=D+\operatorname{ad}_{a_1} | arxiv_extracted | ["e", "D", "a_1}", "o", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2603.07802v1 | cross_domain_amplification | |
X | n | urn:hailstone:math:structural_equation[4a6400ceaf2d] | 1 | structural_equation | 4 | arxiv.math.AG.2603.07062v1.eq_122 | \#X(q)=q^n | arxiv_extracted | ["X", "n", "q"] | arxiv | arxiv | arxiv:math.AG:2603.07062v1 | cross_domain_amplification | |
h | q | urn:hailstone:math:structural_equation[2f6f28ee826e] | 1 | structural_equation | 4 | arxiv.math.AG.2603.07062v1.eq_123 | h^{p,q}=0 | arxiv_extracted | ["p", "q", "h"] | arxiv | arxiv | arxiv:math.AG:2603.07062v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[79022a3b594f] | 1 | structural_equation | 4 | arxiv.math.AG.2603.06844v2.eq_124 | \mathcal I=\{I^n\} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2603.06844v2 | cross_domain_amplification | |
H | E | urn:hailstone:math:structural_equation[120a0e20a925] | 1 | structural_equation | 4 | arxiv.math.AG.2603.03636v1.eq_125 | H^{2}(Γ(E))=0 | arxiv_extracted | ["E", "H"] | arxiv | arxiv | arxiv:math.AG:2603.03636v1 | cross_domain_amplification | |
p_g | K | urn:hailstone:math:structural_equation[7fa644839949] | 1 | structural_equation | 4 | arxiv.math.AG.2603.03132v1.eq_126 | p_g=K^2=1 | arxiv_extracted | ["K", "p_g"] | arxiv | arxiv | arxiv:math.AG:2603.03132v1 | cross_domain_amplification | |
p_g | K_S | urn:hailstone:math:structural_equation[ee52ddcca28a] | 1 | structural_equation | 4 | arxiv.math.AG.2603.03132v1.eq_127 | p_g (S) =K_S^2=1 | arxiv_extracted | ["K_S", "S", "p_g"] | arxiv | arxiv | arxiv:math.AG:2603.03132v1 | cross_domain_amplification | |
m | b | urn:hailstone:math:structural_equation[3d530df3a8ea] | 1 | structural_equation | 4 | arxiv.math.AG.2603.02606v1.eq_128 | \mathbb{V} = R^{2} g_{*} \mathbb{Z} | arxiv_extracted | ["a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2603.02606v1 | cross_domain_amplification | |
s | n | urn:hailstone:math:structural_equation[f032a1410976] | 1 | structural_equation | 4 | arxiv.math.AG.2602.24213v1.eq_129 | Σ_0\,=\, Σ\setminus P | arxiv_extracted | ["e", "t", "m", "i", "s", "n"] | arxiv | arxiv | arxiv:math.AG:2602.24213v1 | cross_domain_amplification | |
m | r | urn:hailstone:math:structural_equation[5789d1f809ce] | 1 | structural_equation | 4 | arxiv.math.AG.2602.21431v2.eq_130 | \mathfrak{g}=T_e G | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2602.21431v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6729771ae87e] | 1 | structural_equation | 4 | arxiv.math.AG.2602.20279v1.eq_131 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.20279v1 | cross_domain_amplification | |
d | t | urn:hailstone:math:structural_equation[5df21301c289] | 1 | structural_equation | 4 | arxiv.math.AG.2602.20027v2.eq_132 | \dim\mathbb{T}=\operatorname{codim}_X Z | arxiv_extracted | ["a", "t", "m", "i", "d"] | arxiv | arxiv | arxiv:math.AG:2602.20027v2 | cross_domain_amplification | |
W | o | urn:hailstone:math:structural_equation[5c89dda57872] | 1 | structural_equation | 4 | arxiv.math.AG.2602.19781v1.eq_133 | . We also give special attention to the case g = 2 in order to extend the work of Aubry and Iezzi on N q (0, | arxiv_extracted | ["e", "a", "W", "o", "s", "l"] | arxiv | arxiv | arxiv:math.AG:2602.19781v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[02ab9cd07c46] | 1 | structural_equation | 4 | arxiv.math.AG.2602.19508v1.eq_134 | \mathcal{H} = \mathcal{H}(W,S) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.19508v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[514b097d24e5] | 1 | structural_equation | 4 | arxiv.math.AG.2602.15717v1.eq_135 | \mathcal{X}: y^p+cy=x^m | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.15717v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[1267ed559504] | 1 | structural_equation | 4 | arxiv.math.AG.2602.15717v1.eq_136 | \mathcal{Y}:y^p+cy=x^n | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.15717v1 | cross_domain_amplification | |
U | e | urn:hailstone:math:structural_equation[77798a443293] | 1 | structural_equation | 4 | arxiv.math.AG.2602.13881v1.eq_137 | U \subseteq S = Spec(\mathcal{O}_K) | arxiv_extracted | ["e", "u", "s", "U", "b"] | arxiv | arxiv | arxiv:math.AG:2602.13881v1 | cross_domain_amplification | |
H | h | urn:hailstone:math:structural_equation[58bdd918be78] | 1 | structural_equation | 4 | arxiv.math.AG.2602.13881v1.eq_138 | H^j(\mathcal{X}_t,\mathcal{O}_{\mathcal{X}_t}) = H^j(\mathcal{Y}_t,\mathcal{O}_{\mathcal{Y}_t}), | arxiv_extracted | ["a", "t", "m", "H", "j", "h"] | arxiv | arxiv | arxiv:math.AG:2602.13881v1 | cross_domain_amplification | |
g | q | urn:hailstone:math:structural_equation[5057982906a0] | 1 | structural_equation | 4 | arxiv.math.AG.2602.11867v1.eq_139 | \gcd(p,q)=1 | arxiv_extracted | ["g", "q", "p", "c", "d"] | arxiv | arxiv | arxiv:math.AG:2602.11867v1 | cross_domain_amplification | |
d | o | urn:hailstone:math:structural_equation[899e7478564a] | 1 | structural_equation | 4 | arxiv.math.AG.2602.08805v1.eq_140 | \dot{g}=\log(\hat{g}) | arxiv_extracted | ["g", "t", "o", "d", "l"] | arxiv | arxiv | arxiv:math.AG:2602.08805v1 | cross_domain_amplification | |
p_g | q | urn:hailstone:math:structural_equation[5971b8c935cf] | 1 | structural_equation | 4 | arxiv.math.AG.2602.07302v1.eq_141 | p_g=q=1 | arxiv_extracted | ["q", "p_g"] | arxiv | arxiv | arxiv:math.AG:2602.07302v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[7ec3a56b28d4] | 1 | structural_equation | 4 | arxiv.math.AG.2602.05314v2.eq_142 | \mathcal M=\mathcal O_X | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.05314v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6729771ae87e] | 1 | structural_equation | 4 | arxiv.math.AG.2602.04946v1.eq_143 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.04946v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6729771ae87e] | 1 | structural_equation | 4 | arxiv.math.AG.2602.04946v1.eq_144 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.04946v1 | cross_domain_amplification | |
s | r | urn:hailstone:math:structural_equation[4b4f68e6c61e] | 1 | structural_equation | 4 | arxiv.math.AG.2602.03500v1.eq_145 | \sum_{i=0}^{m}N(r, 1_{0}\oslash f_{i}) | arxiv_extracted | ["m_{i", "m", "u", "r", "s", "N"] | arxiv | arxiv | arxiv:math.AG:2602.03500v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[5a543d24c60a] | 1 | structural_equation | 4 | arxiv.math.AG.2602.02935v1.eq_146 | \mathcal{C}_2(\mathfrak{sp}_{2n})=\{ (x,y) \in \mathfrak{sp}_{2n} \times \mathfrak{sp}_{2n} \mid [x,y]=0\} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.02935v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[119b8a9ba503] | 1 | structural_equation | 4 | arxiv.math.AG.2602.02935v1.eq_147 | \mathcal{C}_2^{\text{nil}}(\mathfrak{sp}_{2n})=\{ (x,y) \in \mathfrak{sp}_{2n} \times \mathfrak{sp}_{2n} \mid x,y \text{ nilpotent, } [x,y]=0\} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2602.02935v1 | cross_domain_amplification | |
W | x | urn:hailstone:math:structural_equation[126328fe5a7f] | 1 | structural_equation | 4 | arxiv.math.AG.2602.01484v1.eq_148 | W(x) = O(x^{3/5}) | arxiv_extracted | ["W", "O", "x"] | arxiv | arxiv | arxiv:math.AG:2602.01484v1 | cross_domain_amplification | |
K | K | urn:hailstone:math:structural_equation[d51b02b052cf] | 1 | structural_equation | 4 | arxiv.math.AG.2602.01398v1.eq_149 | [K(P):K]=2 | arxiv_extracted | ["K", "P"] | arxiv | arxiv | arxiv:math.AG:2602.01398v1 | cross_domain_amplification | |
E_1 | x | urn:hailstone:math:structural_equation[8047c25f16c8] | 1 | structural_equation | 4 | arxiv.math.AG.2602.01398v1.eq_150 | E_1:\,y^2= x^3 + 4x | arxiv_extracted | ["E_1", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2602.01398v1 | cross_domain_amplification | |
E_2 | x | urn:hailstone:math:structural_equation[3d4821fa99a5] | 1 | structural_equation | 4 | arxiv.math.AG.2602.01398v1.eq_151 | E_2:\,y^2= x^3 - 4x | arxiv_extracted | ["E_2", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2602.01398v1 | cross_domain_amplification | |
F_4 | n | urn:hailstone:math:structural_equation[769e7d66b14d] | 1 | structural_equation | 4 | arxiv.math.AG.2602.01398v1.eq_152 | F_4\colon X^4+Y^4=Z^4 | arxiv_extracted | ["F_4", "o", "n", "c", "l"] | arxiv | arxiv | arxiv:math.AG:2602.01398v1 | cross_domain_amplification | |
G | b | urn:hailstone:math:structural_equation[c987dfe73b12] | 1 | structural_equation | 4 | arxiv.math.AG.2602.00274v1.eq_153 | G_\mathbb{R} = SU(p,q) | arxiv_extracted | ["a", "t", "m", "G", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2602.00274v1 | cross_domain_amplification | |
G | b | urn:hailstone:math:structural_equation[6428a6f6f075] | 1 | structural_equation | 4 | arxiv.math.AG.2602.00274v1.eq_154 | G_{\mathbb{R}} = SO^*(4m+2) | arxiv_extracted | ["a", "t", "m", "G", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2602.00274v1 | cross_domain_amplification | |
r | X | urn:hailstone:math:structural_equation[763f0fc9c274] | 1 | structural_equation | 4 | arxiv.math.AG.2601.22072v1.eq_155 | {\rm lct}(X,Z)=1 | arxiv_extracted | ["t", "m", "X", "r", "c", "l"] | arxiv | arxiv | arxiv:math.AG:2601.22072v1 | cross_domain_amplification | |
r | Y | urn:hailstone:math:structural_equation[5e50f41ff9a9] | 1 | structural_equation | 4 | arxiv.math.AG.2601.22072v1.eq_156 | {\rm lct}(Y,W)=r | arxiv_extracted | ["t", "m", "r", "Y", "c", "l"] | arxiv | arxiv | arxiv:math.AG:2601.22072v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[3dcc12c957b3] | 1 | structural_equation | 4 | arxiv.math.AG.2601.20804v1.eq_157 | [\mathrm{Gr}(d-1,\infty)]\cdot \sum_{i=0}^{r-1}\mathbb L^{di} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2601.20804v1 | cross_domain_amplification | |
m | b | urn:hailstone:math:structural_equation[160fb22451bb] | 1 | structural_equation | 4 | arxiv.math.AG.2601.20593v1.eq_158 | π_0^{\mathbb{A}^1}(X)(F)=\mathcal{S}^2(X)(F) | arxiv_extracted | ["a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2601.20593v1 | cross_domain_amplification | |
e | p | urn:hailstone:math:structural_equation[d95d61eb8662] | 1 | structural_equation | 4 | arxiv.math.AG.2603.00011v3.eq_159 | , equipped with a faithful action of a finite group G, and let Y = X // G denote the categorical quotient with projection | arxiv_extracted | ["e", "q", "i", "p", "u"] | arxiv | arxiv | arxiv:math.AG:2603.00011v3 | cross_domain_amplification | |
q | p_g | urn:hailstone:math:structural_equation[88c2e9fb6a21] | 1 | structural_equation | 4 | arxiv.math.AG.2601.18389v1.eq_160 | q=p_g=0 | arxiv_extracted | ["q", "p_g"] | arxiv | arxiv | arxiv:math.AG:2601.18389v1 | cross_domain_amplification | |
A | t | urn:hailstone:math:structural_equation[b8581ccd10e5] | 1 | structural_equation | 4 | arxiv.math.AG.2601.18389v1.eq_161 | |Aut_\mathbb{Q}(S)| =192 | arxiv_extracted | ["a", "t", "m", "u", "A"] | arxiv | arxiv | arxiv:math.AG:2601.18389v1 | cross_domain_amplification | |
i | f | urn:hailstone:math:structural_equation[e9eabb73c43f] | 1 | structural_equation | 4 | arxiv.math.AG.2601.16271v1.eq_162 | in the form \[ U = D(I-S)(I+S)^{-1}, \] where | arxiv_extracted | ["e", "f", "t", "h", "i", "n"] | arxiv | arxiv | arxiv:math.AG:2601.16271v1 | cross_domain_amplification | |
c | N | urn:hailstone:math:structural_equation[1428fe386494] | 1 | structural_equation | 4 | arxiv.math.AG.2601.16213v2.eq_163 | {\cal N}=4 | arxiv_extracted | ["N", "c", "l", "a"] | arxiv | arxiv | arxiv:math.AG:2601.16213v2 | cross_domain_amplification | |
c | N | urn:hailstone:math:structural_equation[a4edd40d302d] | 1 | structural_equation | 4 | arxiv.math.AG.2601.16213v2.eq_164 | {\cal N}=1 | arxiv_extracted | ["N", "c", "l", "a"] | arxiv | arxiv | arxiv:math.AG:2601.16213v2 | cross_domain_amplification | |
h | d | urn:hailstone:math:structural_equation[f1f428030850] | 1 | structural_equation | 4 | arxiv.math.AG.2601.15543v5.eq_165 | \hat{h}(P)=d | arxiv_extracted | ["a", "t", "P", "h", "d"] | arxiv | arxiv | arxiv:math.AG:2601.15543v5 | cross_domain_amplification | |
X_n | n | urn:hailstone:math:structural_equation[f868a6136a43] | 1 | structural_equation | 4 | arxiv.math.AG.2601.15271v1.eq_166 | X_n\colon y^2=x^{n}-1 | arxiv_extracted | ["X_n", "o", "n", "c", "l"] | arxiv | arxiv | arxiv:math.AG:2601.15271v1 | cross_domain_amplification | |
H | h | urn:hailstone:math:structural_equation[744d31c14602] | 1 | structural_equation | 4 | arxiv.math.AG.2601.15270v1.eq_167 | H^0(M,\mathcal{O}_M) = R | arxiv_extracted | ["a", "t", "M", "m", "H", "h"] | arxiv | arxiv | arxiv:math.AG:2601.15270v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[f64f601c2cf5] | 1 | structural_equation | 4 | arxiv.math.AG.2601.14709v1.eq_168 | \mathrm{Pic}(X) = \mathbb{Z}\cdot H | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2601.14709v1 | cross_domain_amplification | |
h | r | urn:hailstone:math:structural_equation[cdddbfdba0b4] | 1 | structural_equation | 4 | arxiv.math.AG.2601.13526v1.eq_169 | h_{\mathrm{cat}}(Φ) = \logρ(Φ) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2601.13526v1 | cross_domain_amplification | |
p | m | urn:hailstone:math:structural_equation[91657c7a3595] | 1 | structural_equation | 4 | arxiv.math.AG.2601.13340v1.eq_170 | p\geq n=2m+1 | arxiv_extracted | ["e", "g", "q", "m", "p", "n"] | arxiv | arxiv | arxiv:math.AG:2601.13340v1 | cross_domain_amplification | |
R | h | urn:hailstone:math:structural_equation[f6d357f8d8e3] | 1 | structural_equation | 4 | arxiv.math.AG.2601.13151v5.eq_171 | R^kπ_*{\mathcal O}_{\widetilde{X}}=0 | arxiv_extracted | ["a", "t", "m", "h", "R", "k"] | arxiv | arxiv | arxiv:math.AG:2601.13151v5 | cross_domain_amplification | |
h | m | urn:hailstone:math:structural_equation[fff97e5a4ec2] | 1 | structural_equation | 4 | arxiv.math.AG.2601.13151v5.eq_172 | h^k(X):=\dim H^k(X,{\bf Q}) | arxiv_extracted | ["m", "h", "i", "X", "d", "k"] | arxiv | arxiv | arxiv:math.AG:2601.13151v5 | cross_domain_amplification | |
e | d | urn:hailstone:math:structural_equation[987a5b4c6d56] | 1 | structural_equation | 4 | arxiv.math.AG.2601.12643v1.eq_173 | \ell_0:=[(n+d)/d], \ m_0:=\ell_0 d | arxiv_extracted | ["e", "l_0", "n", "d", "l"] | arxiv | arxiv | arxiv:math.AG:2601.12643v1 | cross_domain_amplification | |
n | l_0 | urn:hailstone:math:structural_equation[6c538e70e3db] | 1 | structural_equation | 4 | arxiv.math.AG.2601.12643v1.eq_174 | n-m_0+\ell_0=0 | arxiv_extracted | ["e", "l_0", "m_0", "n", "l"] | arxiv | arxiv | arxiv:math.AG:2601.12643v1 | cross_domain_amplification | |
m | r | urn:hailstone:math:structural_equation[1daf403bffc3] | 1 | structural_equation | 4 | arxiv.math.AG.2601.11736v2.eq_175 | \mathfrak{g}=\mathfrak{sl}_{n+1} | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2601.11736v2 | cross_domain_amplification | |
G | b | urn:hailstone:math:structural_equation[0ce78486cfb4] | 1 | structural_equation | 4 | arxiv.math.AG.2601.11271v1.eq_176 | G_{\mathbb{Q}_p}=GL_3 | arxiv_extracted | ["a", "t", "m", "G", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2601.11271v1 | cross_domain_amplification | |
T | u | urn:hailstone:math:structural_equation[68b5d0a62bf8] | 1 | structural_equation | 4 | arxiv.math.AG.2601.09991v2.eq_177 | T^2_{0,u}X=T^{2,a}_{0,u}X | arxiv_extracted | ["X", "u", "T", "a"] | arxiv | arxiv | arxiv:math.AG:2601.09991v2 | cross_domain_amplification | |
X | Y | urn:hailstone:math:structural_equation[33e9d4b5b427] | 1 | structural_equation | 4 | arxiv.math.AG.2601.09956v1.eq_178 | XY^q-X^qY-Z^{q+1} = 0 | arxiv_extracted | ["X", "Y", "q"] | arxiv | arxiv | arxiv:math.AG:2601.09956v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[4f0f44984d77] | 1 | structural_equation | 4 | arxiv.math.AG.2601.07662v1.eq_179 | \mathcal{N}=1 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2601.07662v1 | cross_domain_amplification | |
f | b | urn:hailstone:math:structural_equation[658af488931c] | 1 | structural_equation | 4 | arxiv.math.AG.2601.07222v1.eq_180 | f_{*}[\mathbb{P}^{1}]=β | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2601.07222v1 | cross_domain_amplification | |
i | c | urn:hailstone:math:structural_equation[99228a95bed0] | 1 | structural_equation | 4 | arxiv.math.AG.2601.05715v1.eq_181 | (κ^{inc}_{2,μ})^{-1}(0)=\{0\} | arxiv_extracted | ["n", "c", "i"] | arxiv | arxiv | arxiv:math.AG:2601.05715v1 | cross_domain_amplification | |
J_{F | Q | urn:hailstone:math:structural_equation[9d603b1a7656] | 1 | structural_equation | 4 | arxiv.math.AG.2601.05571v1.eq_182 | (J_{F,3}:Q)=0 | arxiv_extracted | ["Q", "J_{F"] | arxiv | arxiv | arxiv:math.AG:2601.05571v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[38f80ff1e65a] | 1 | structural_equation | 4 | arxiv.math.AG.2601.03491v1.eq_183 | \mathrm{ht}^\infty = \mathrm{ht}^{\mathrm{reg}} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2601.03491v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[38f80ff1e65a] | 1 | structural_equation | 4 | arxiv.math.AG.2601.03491v1.eq_184 | \mathrm{ht}^\infty = \mathrm{ht}^{\mathrm{reg}} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2601.03491v1 | cross_domain_amplification | |
t | c | urn:hailstone:math:structural_equation[9f91b6c37cff] | 1 | structural_equation | 4 | arxiv.math.AG.2601.02592v1.eq_185 | t^*[\mathcal{A}_{g_1}\times\dots\times \mathcal{A}_{g_k}] = 0 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2601.02592v1 | cross_domain_amplification | |
X | g | urn:hailstone:math:structural_equation[22a9b03de77a] | 1 | structural_equation | 4 | arxiv.math.AG.2601.02235v1.eq_186 | \Xx(d,g,r):=3g-3+ρ(d,g,r)+\dim\operatorname{Aut}(\mathbb{P}^r) | arxiv_extracted | ["g", "X", "r", "d", "x"] | arxiv | arxiv | arxiv:math.AG:2601.02235v1 | cross_domain_amplification | |
d | g | urn:hailstone:math:structural_equation[289f9ec8ad4e] | 1 | structural_equation | 4 | arxiv.math.AG.2601.02235v1.eq_187 | ρ(d,g,r):=g-(r+1)(g-d+r) | arxiv_extracted | ["g", "d", "r"] | arxiv | arxiv | arxiv:math.AG:2601.02235v1 | cross_domain_amplification | |
d | m | urn:hailstone:math:structural_equation[0ddd4b756e84] | 1 | structural_equation | 4 | arxiv.math.AG.2601.02235v1.eq_188 | \dimμ({\Hh})=\min\{3g-3, 3g-3+ρ(d,g,r)\}, | arxiv_extracted | ["H", "m", "h", "i", "d"] | arxiv | arxiv | arxiv:math.AG:2601.02235v1 | cross_domain_amplification | |
c | a | urn:hailstone:math:structural_equation[fe0932055a1e] | 1 | structural_equation | 4 | arxiv.math.AG.2601.01761v2.eq_189 | char({\mathbb F}_0)=0 | arxiv_extracted | ["a", "m", "h", "r", "c"] | arxiv | arxiv | arxiv:math.AG:2601.01761v2 | cross_domain_amplification | |
d | p | urn:hailstone:math:structural_equation[bcc62626083d] | 1 | structural_equation | 4 | arxiv.math.AG.2601.01761v2.eq_190 | \dim B=p+2 | arxiv_extracted | ["B", "m", "i", "p", "d"] | arxiv | arxiv | arxiv:math.AG:2601.01761v2 | cross_domain_amplification | |
r | p | urn:hailstone:math:structural_equation[1db4a6657467] | 1 | structural_equation | 4 | arxiv.math.AG.2601.01761v2.eq_191 | rank(Q)=p | arxiv_extracted | ["Q", "a", "p", "r", "n", "k"] | arxiv | arxiv | arxiv:math.AG:2601.01761v2 | cross_domain_amplification | |
C | p | urn:hailstone:math:structural_equation[205400cb8048] | 1 | structural_equation | 4 | arxiv.math.AG.2601.01761v2.eq_192 | C(Q)=1+\sum_{i=1}^{p}C^k(Q) =1 | arxiv_extracted | ["Q", "m_{i", "u", "p", "s", "C"] | arxiv | arxiv | arxiv:math.AG:2601.01761v2 | cross_domain_amplification | |
r | r | urn:hailstone:math:structural_equation[050fd3f6d420] | 1 | structural_equation | 4 | arxiv.math.AG.2601.01761v2.eq_193 | rank(P)=r=\dim B-1 | arxiv_extracted | ["a", "P", "r", "n", "k"] | arxiv | arxiv | arxiv:math.AG:2601.01761v2 | cross_domain_amplification | |
C | n | urn:hailstone:math:structural_equation[0d7edac1b9ce] | 1 | structural_equation | 4 | arxiv.math.AG.2601.01761v2.eq_194 | C^r(P)=0 \Longrightarrow P\cong Q\oplus B | arxiv_extracted | ["P", "o", "L", "r", "n", "C"] | arxiv | arxiv | arxiv:math.AG:2601.01761v2 | cross_domain_amplification | |
H | k | urn:hailstone:math:structural_equation[f1826a0d4747] | 1 | structural_equation | 4 | arxiv.math.AG.2601.00390v1.eq_195 | H^{p}(X,Ω^{i}_{X/k})=H^{p+1}(X,Ω^{i}_{X/k})= \cdots =H^{2p-1-i}(X,Ω^{i}_{X/k})=0 | arxiv_extracted | ["H", "i", "X", "p", "k"] | arxiv | arxiv | arxiv:math.AG:2601.00390v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[771f038b4e7f] | 1 | structural_equation | 4 | arxiv.math.AG.2601.00052v1.eq_196 | \mathrm{N}_{K/k}(\mathbf{z})=P(x) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2601.00052v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[d3e208066318] | 1 | structural_equation | 4 | arxiv.math.AG.2601.00039v1.eq_197 | \mathcal{N}=4 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2601.00039v1 | cross_domain_amplification | |
r | X | urn:hailstone:math:structural_equation[4b3ffa0c5ed2] | 1 | structural_equation | 4 | arxiv.math.AG.2512.23522v2.eq_198 | {\rm def}(X):=h^{n+1}(X)-h^{n-1}(X) | arxiv_extracted | ["e", "f", "m", "X", "r", "d"] | arxiv | arxiv | arxiv:math.AG:2512.23522v2 | cross_domain_amplification | |
r | g | urn:hailstone:math:structural_equation[a45b7cd4a933] | 1 | structural_equation | 4 | arxiv.math.AG.2512.23522v2.eq_199 | |{\rm Sing}\,X|=1 | arxiv_extracted | ["g", "m", "S", "i", "r", "n"] | arxiv | arxiv | arxiv:math.AG:2512.23522v2 | cross_domain_amplification | |
r | X | urn:hailstone:math:structural_equation[0874275b5b55] | 1 | structural_equation | 4 | arxiv.math.AG.2512.23446v1.eq_200 | {\rm dim}\,X = 1 | arxiv_extracted | ["m", "i", "X", "r", "d"] | arxiv | arxiv | arxiv:math.AG:2512.23446v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[8d15b56c7884] | 1 | structural_equation | 4 | arxiv.math.AG.2512.22614v2.eq_201 | \mathrm{Br}_1(X):=\ker(\mathrm{Br}(X)\to\mathrm{Br}(\overline{X})) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2512.22614v2 | cross_domain_amplification | |
u_tu_ | u_t | urn:hailstone:math:structural_equation[e71707c790a7] | 1 | structural_equation | 4 | arxiv.math.AG.2512.20819v1.eq_202 | u_tu_{xx}=u_tu_x+u_t - 1 | arxiv_extracted | ["u_t", "x", "u_tu_x", "u_tu_"] | arxiv | arxiv | arxiv:math.AG:2512.20819v1 | cross_domain_amplification | |
d | t | urn:hailstone:math:structural_equation[1026ae86a317] | 1 | structural_equation | 4 | arxiv.math.AG.2512.19284v4.eq_203 | \dim_{\mathbb{C}}X=n | arxiv_extracted | ["a", "t", "m", "i", "d"] | arxiv | arxiv | arxiv:math.AG:2512.19284v4 | cross_domain_amplification | |
m | f | urn:hailstone:math:structural_equation[9e76fc8d68d6] | 1 | structural_equation | 4 | arxiv.math.AG.2512.18817v2.eq_204 | \mathsf{P}_2(Σ_b)=π_1(Σ_b \times Σ_b - Δ) | arxiv_extracted | ["f", "a", "t", "m", "h", "s"] | arxiv | arxiv | arxiv:math.AG:2512.18817v2 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[f64c87730404] | 1 | structural_equation | 4 | arxiv.math.AG.2512.18812v1.eq_205 | \mathrm{nd}(Y)=9 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2512.18812v1 | cross_domain_amplification | |
W | U | urn:hailstone:math:structural_equation[eb6b5c55a7ef] | 1 | structural_equation | 4 | arxiv.math.AG.2512.17481v2.eq_206 | W \cap f(U) = W \cap \overline{f(U)} \neq \varnothing | arxiv_extracted | ["f", "a", "W", "p", "U", "c"] | arxiv | arxiv | arxiv:math.AG:2512.17481v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[1ede4828024d] | 1 | structural_equation | 4 | arxiv.math.AG.2512.16578v1.eq_207 | {\mathcal E}_m: y^2=x^3 +t^{m} +1 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2512.16578v1 | cross_domain_amplification | |
m | c | urn:hailstone:math:structural_equation[a97c93cdbe5d] | 1 | structural_equation | 4 | arxiv.math.AG.2601.03264v1.eq_208 | \mathscr{L}=\mathcal{O}_X(α_1,α_1,\cdots,α_s,α_s) | arxiv_extracted | ["a", "t", "m", "h", "s", "c"] | arxiv | arxiv | arxiv:math.AG:2601.03264v1 | cross_domain_amplification | |
h | f | urn:hailstone:math:structural_equation[21948b7899f1] | 1 | structural_equation | 4 | arxiv.math.AG.2512.15060v1.eq_209 | \hbar = \tfrac{\sqrt{-1}}{k} | arxiv_extracted | ["f", "a", "t", "h", "r", "b"] | arxiv | arxiv | arxiv:math.AG:2512.15060v1 | cross_domain_amplification | |
F_1 | s | urn:hailstone:math:structural_equation[f26d5d95d262] | 1 | structural_equation | 4 | arxiv.math.AG.2512.14888v1.eq_210 | \{F_1=0,\ldots,F_r=0,G\not=0\} | arxiv_extracted | ["t", "o", "F_1", "s", "d", "l"] | arxiv | arxiv | arxiv:math.AG:2512.14888v1 | cross_domain_amplification | |
D | b | urn:hailstone:math:structural_equation[09a92ee90b28] | 1 | structural_equation | 4 | arxiv.math.AG.2512.14575v1.eq_211 | D(\textbf{e})=\langle τ_{e_1} \cdots τ_{e_n} \rangle_g | arxiv_extracted | ["e", "D", "t", "b", "x"] | arxiv | arxiv | arxiv:math.AG:2512.14575v1 | cross_domain_amplification | |
t | f | urn:hailstone:math:structural_equation[b8e7ba2ab43c] | 1 | structural_equation | 4 | arxiv.math.AG.2512.14575v1.eq_212 | \textbf{e}=(e_1, \ldots, e_n) | arxiv_extracted | ["f", "e", "t", "b", "x"] | arxiv | arxiv | arxiv:math.AG:2512.14575v1 | cross_domain_amplification | |
g | L | urn:hailstone:math:structural_equation[16dff4e1fcbe] | 1 | structural_equation | 4 | arxiv.math.AG.2512.14464v3.eq_213 | \gcd(n, °L) = 1 | arxiv_extracted | ["g", "L", "c", "n", "d"] | arxiv | arxiv | arxiv:math.AG:2512.14464v3 | cross_domain_amplification | |
o | t | urn:hailstone:math:structural_equation[5875f81c9fa1] | 1 | structural_equation | 4 | arxiv.math.AG.2512.13850v1.eq_214 | \operatorname{depth} X =n | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2512.13850v1 | cross_domain_amplification | |
T | X | urn:hailstone:math:structural_equation[6c63e0f725da] | 1 | structural_equation | 4 | arxiv.math.AG.2512.13203v1.eq_215 | T^1_X = 0 | arxiv_extracted | ["X", "T"] | arxiv | arxiv | arxiv:math.AG:2512.13203v1 | cross_domain_amplification | |
X | s | urn:hailstone:math:structural_equation[b24bfab544a5] | 1 | structural_equation | 4 | arxiv.math.AG.2512.13203v1.eq_216 | X = \{ f = 0 \} \subset \mathbb{C}^{n+1} | arxiv_extracted | ["f", "X", "u", "s", "b"] | arxiv | arxiv | arxiv:math.AG:2512.13203v1 | cross_domain_amplification | |
S_{g} | S | urn:hailstone:math:structural_equation[a989357322b4] | 1 | structural_equation | 4 | arxiv.math.AG.2512.12126v2.eq_217 | S_{g}=\{(x,y)\in SL(2,C)^2 \ | w(x,y)=g\}. | arxiv_extracted | ["y", "S", "i", "S_{g}", "n", "x"] | arxiv | arxiv | arxiv:math.AG:2512.12126v2 | cross_domain_amplification | |
M | t | urn:hailstone:math:structural_equation[2c20a1d625f3] | 1 | structural_equation | 4 | arxiv.math.AG.2512.12126v2.eq_218 | ML(S_{g})=\mathcal{O}(S_{g}) | arxiv_extracted | ["a", "t", "M", "m", "S_{g}", "L"] | arxiv | arxiv | arxiv:math.AG:2512.12126v2 | cross_domain_amplification | |
m | r | urn:hailstone:math:structural_equation[d845357c8102] | 1 | structural_equation | 4 | arxiv.math.AG.2512.12041v1.eq_219 | \mathfrak{m}=\sum_{i=1}^s m_iw_i | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2512.12041v1 | cross_domain_amplification | |
a | d | urn:hailstone:math:structural_equation[ada7e720a0d1] | 1 | structural_equation | 4 | arxiv.math.AG.2512.11072v3.eq_220 | a^5+b^5=c^5+d^5 | arxiv_extracted | ["b", "c", "d", "a"] | arxiv | arxiv | arxiv:math.AG:2512.11072v3 | cross_domain_amplification |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.