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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
X | m | urn:hailstone:math:structural_equation[7f134c85b01d] | 1 | structural_equation | 4 | arxiv.math.AG.2510.04515v1.eq_321 | X^{*}=X\setminus D | arxiv_extracted | ["e", "t", "m", "X", "s"] | arxiv | arxiv | arxiv:math.AG:2510.04515v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6ff6298cce15] | 1 | structural_equation | 4 | arxiv.math.AG.2510.03193v1.eq_322 | \mathcal B_X:=\mathrm{coker}(\mathcal O_X\to F_* \mathcal O_X) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.03193v1 | cross_domain_amplification | |
s | n | urn:hailstone:math:structural_equation[77f835f93080] | 1 | structural_equation | 4 | arxiv.math.AG.2510.03193v1.eq_323 | \sum d_i = n | arxiv_extracted | ["d_i", "m", "u", "s", "n"] | arxiv | arxiv | arxiv:math.AG:2510.03193v1 | cross_domain_amplification | |
o | i | urn:hailstone:math:structural_equation[21552f2ddb7a] | 1 | structural_equation | 4 | arxiv.math.AG.2510.00250v2.eq_324 | \overline{X_w} = Y_w \times \mathbb C^d | arxiv_extracted | ["e", "o", "i", "r", "l", "v"] | arxiv | arxiv | arxiv:math.AG:2510.00250v2 | cross_domain_amplification | |
o | i | urn:hailstone:math:structural_equation[ded0fbd0dfdc] | 1 | structural_equation | 4 | arxiv.math.AG.2510.00131v2.eq_325 | \overline{X_{w}} = Y_{w} \times \mathbb{C}^{k} | arxiv_extracted | ["e", "o", "i", "r", "l", "v"] | arxiv | arxiv | arxiv:math.AG:2510.00131v2 | cross_domain_amplification | |
F_m | T | urn:hailstone:math:structural_equation[73bb3bc68464] | 1 | structural_equation | 4 | arxiv.math.AG.2509.23521v2.eq_326 | F_m = F_m(G,T) | arxiv_extracted | ["F_m", "T", "G"] | arxiv | arxiv | arxiv:math.AG:2509.23521v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[4f0f44984d77] | 1 | structural_equation | 4 | arxiv.math.AG.2509.23042v1.eq_327 | \mathcal{N}=1 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2509.23042v1 | cross_domain_amplification | |
C_{m | u | urn:hailstone:math:structural_equation[b522cc0e6650] | 1 | structural_equation | 4 | arxiv.math.AG.2509.20872v1.eq_328 | C_{m,n}(q,t) = \sum_λf_λ(q,t) s_λ(x) | arxiv_extracted | ["q", "C_{m", "t", "u", "s", "n"] | arxiv | arxiv | arxiv:math.AG:2509.20872v1 | cross_domain_amplification | |
C | s | urn:hailstone:math:structural_equation[d715ad858347] | 1 | structural_equation | 4 | arxiv.math.AG.2509.20872v1.eq_329 | C^f_{m,n}(q,t) = \sum_λf_λ(q,t) K_{λf} | arxiv_extracted | ["f_{m", "q", "t", "s", "n", "C"] | arxiv | arxiv | arxiv:math.AG:2509.20872v1 | cross_domain_amplification | |
H | h | urn:hailstone:math:structural_equation[1e57c257c5e1] | 1 | structural_equation | 4 | arxiv.math.AG.2509.17939v2.eq_330 | H^1(S, \mathbb{F}_2)=0 | arxiv_extracted | ["a", "t", "m", "H", "S", "h"] | arxiv | arxiv | arxiv:math.AG:2509.17939v2 | cross_domain_amplification | |
K_X | R_Δ | urn:hailstone:math:structural_equation[a91d812b2458] | 1 | structural_equation | 4 | arxiv.math.AG.2509.17927v1.eq_331 | K_X+Δ=f^*(K_X+Δ)+R_Δ | arxiv_extracted | ["f", "K_X", "R_\u0394"] | arxiv | arxiv | arxiv:math.AG:2509.17927v1 | cross_domain_amplification | |
f | P | urn:hailstone:math:structural_equation[a90a94e25473] | 1 | structural_equation | 4 | arxiv.math.AG.2509.17927v1.eq_332 | f^{-s}(P)=P | arxiv_extracted | ["f", "s", "P"] | arxiv | arxiv | arxiv:math.AG:2509.17927v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[cea5318250fd] | 1 | structural_equation | 4 | arxiv.math.AG.2509.25212v5.eq_333 | \mathrm{Spec}_{\!Φ}(R)=\{P\in\mathrm{Spec}(R):Φ^{\!*}(P)=P\}, | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2509.25212v5 | cross_domain_amplification | |
A | J | urn:hailstone:math:structural_equation[230e88d4a4c7] | 1 | structural_equation | 4 | arxiv.math.AG.2509.25212v5.eq_334 | Φ^{\!*}(A)=A+J | arxiv_extracted | ["A", "J"] | arxiv | arxiv | arxiv:math.AG:2509.25212v5 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[5d598bd4d703] | 1 | structural_equation | 4 | arxiv.math.AG.2509.25212v5.eq_335 | \mathrm{rad}_{\!Φ}(I)=\sqrt{Φ^{\!*}(I)} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2509.25212v5 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[4ed58e210228] | 1 | structural_equation | 4 | arxiv.math.AG.2509.25212v5.eq_336 | \mathrm{rad}_{\!Φ}(I)=\mathrm I(V(I)) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2509.25212v5 | cross_domain_amplification | |
g | x | urn:hailstone:math:structural_equation[d4c108d2d1dc] | 1 | structural_equation | 4 | arxiv.math.AG.2509.15438v1.eq_337 | g(t_{0} \ast x) = g(x)+c(t_{0}) h(x) | arxiv_extracted | ["g", "a", "t", "t_{0}", "s", "x"] | arxiv | arxiv | arxiv:math.AG:2509.15438v1 | cross_domain_amplification | |
s | t | urn:hailstone:math:structural_equation[78aa904bb73b] | 1 | structural_equation | 4 | arxiv.math.AG.2509.15348v1.eq_338 | {\sf M}:=(\mathcal{E},r) | arxiv_extracted | ["f", "a", "t", "M", "m", "s"] | arxiv | arxiv | arxiv:math.AG:2509.15348v1 | cross_domain_amplification | |
d | b | urn:hailstone:math:structural_equation[51ecc8680ccb] | 1 | structural_equation | 4 | arxiv.math.AG.2509.14871v1.eq_339 | d(\mathbb F_q):= \lfloor2\sqrt{q}\rfloor^2-4q | arxiv_extracted | ["a", "t", "m", "h", "b", "d"] | arxiv | arxiv | arxiv:math.AG:2509.14871v1 | cross_domain_amplification | |
w | i | urn:hailstone:math:structural_equation[0da8809e5708] | 1 | structural_equation | 4 | arxiv.math.AG.2509.13473v4.eq_340 | \widetilde{\mathcal{N}}=T^*G/B | arxiv_extracted | ["e", "w", "t", "i", "d"] | arxiv | arxiv | arxiv:math.AG:2509.13473v4 | cross_domain_amplification | |
H | e | urn:hailstone:math:structural_equation[21f12fe86e84] | 1 | structural_equation | 4 | arxiv.math.AG.2509.13473v4.eq_341 | H^i(\widetilde{\mathcal{N}_θ},\mathcal{O}_{\widetilde{\mathcal{N}_θ}}(λ))=0 | arxiv_extracted | ["e", "w", "H", "i", "d"] | arxiv | arxiv | arxiv:math.AG:2509.13473v4 | cross_domain_amplification | |
e | r | urn:hailstone:math:structural_equation[3dd6cdefb75e] | 1 | structural_equation | 4 | arxiv.math.AG.2509.11280v1.eq_342 | \ell(μ)=r | arxiv_extracted | ["e", "l", "r"] | arxiv | arxiv | arxiv:math.AG:2509.11280v1 | cross_domain_amplification | |
H | h | urn:hailstone:math:structural_equation[88c27f6bdda5] | 1 | structural_equation | 4 | arxiv.math.AG.2509.11227v3.eq_343 | H^1(Y, \mathcal{O}_Y(kE)) = 0 | arxiv_extracted | ["a", "t", "m", "H", "h", "Y"] | arxiv | arxiv | arxiv:math.AG:2509.11227v3 | cross_domain_amplification | |
m | b | urn:hailstone:math:structural_equation[cb228af6155f] | 1 | structural_equation | 4 | arxiv.math.AG.2509.07720v1.eq_344 | \mathbb E=\int_{\mathbb X\in \mathrm{Mod}(\mathbb X)}\mathbb X\otimes \mathbb{X}' | arxiv_extracted | ["a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2509.07720v1 | cross_domain_amplification | |
K_X | D | urn:hailstone:math:structural_equation[8e01cc3e0fdc] | 1 | structural_equation | 4 | arxiv.math.AG.2509.07508v1.eq_345 | K_X+D=0 | arxiv_extracted | ["K_X", "D"] | arxiv | arxiv | arxiv:math.AG:2509.07508v1 | cross_domain_amplification | |
R | a | urn:hailstone:math:structural_equation[36bace91211a] | 1 | structural_equation | 4 | arxiv.math.AG.2509.06352v1.eq_346 | R^d , d = 1, 2, . . . be an open bounded smooth domain, and | arxiv_extracted | ["e", "a", "R", "b", "d"] | arxiv | arxiv | arxiv:math.AG:2509.06352v1 | cross_domain_amplification | |
a | s | urn:hailstone:math:structural_equation[81a44b170803] | 1 | structural_equation | 4 | arxiv.math.AG.2509.06352v1.eq_347 | are designated as x = (x ' , y) | arxiv_extracted | ["e", "a", "r", "s", "d"] | arxiv | arxiv | arxiv:math.AG:2509.06352v1 | cross_domain_amplification | |
D | H_0 | urn:hailstone:math:structural_equation[52869d044141] | 1 | structural_equation | 4 | arxiv.math.AG.2509.06352v1.eq_348 | D(A) = \{v\in H_0^1(Ω); \tilde{c}\nabla v \in H^1(Ω)\}. | arxiv_extracted | ["D", "i", "A", "H_0", "n", "v"] | arxiv | arxiv | arxiv:math.AG:2509.06352v1 | cross_domain_amplification | |
t | c | urn:hailstone:math:structural_equation[ee2bcc9ccd98] | 1 | structural_equation | 4 | arxiv.math.AG.2509.06352v1.eq_349 | \tilde{c}(x) = \tilde{c}(x ' , y) = c(y). | arxiv_extracted | ["e", "t", "i", "c", "d", "l"] | arxiv | arxiv | arxiv:math.AG:2509.06352v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[ce19e1c6b541] | 1 | structural_equation | 4 | arxiv.math.AG.2509.04978v1.eq_350 | \mathcal{G}=\mathrm{Spec}(A) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2509.04978v1 | cross_domain_amplification | |
v | i_K | urn:hailstone:math:structural_equation[e0b67057e518] | 1 | structural_equation | 4 | arxiv.math.AG.2509.04978v1.eq_351 | \varphi_K: G_0(A^D)\rightarrow G_0(A^D_K)=G_0(K[G]) | arxiv_extracted | ["a", "h", "p", "r", "i_K", "v"] | arxiv | arxiv | arxiv:math.AG:2509.04978v1 | cross_domain_amplification | |
m | r | urn:hailstone:math:structural_equation[71855e06bfe8] | 1 | structural_equation | 4 | arxiv.math.AG.2509.01386v1.eq_352 | \mathfrak{a}^x:=\mathfrak{a}^{G_x}\le \mathfrak{a} | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2509.01386v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[233c48b53783] | 1 | structural_equation | 4 | arxiv.math.AG.2508.21717v1.eq_353 | \mathcal{H}=\mathrm{Hilb}^{l}(\mathbb{A}^3) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2508.21717v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[91680623bc1e] | 1 | structural_equation | 4 | arxiv.math.AG.2508.20838v2.eq_354 | \mathcal{RH}_2[4]^{hyp} = \mathcal{RH}_2[4] | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2508.20838v2 | cross_domain_amplification | |
V_{P_j} | q | urn:hailstone:math:structural_equation[5bddc3f48e07] | 1 | structural_equation | 4 | arxiv.math.AG.2508.20480v1.eq_355 | \{V_{P_j}\}_{j=1}^{q} | arxiv_extracted | ["V_{P_j}", "j", "q"] | arxiv | arxiv | arxiv:math.AG:2508.20480v1 | cross_domain_amplification | |
q | e | urn:hailstone:math:structural_equation[5a593cdd731f] | 1 | structural_equation | 4 | arxiv.math.AG.2508.20480v1.eq_356 | \|\,\,\, (q-M-1-λ)T_f(r) \leq \sum_{j=M+2}^q \tfrac{1}{d_j}N(r,1_{\mathbb{T}} \oslash P_j \circ f) + o(T_f(r)), | arxiv_extracted | ["e", "q", "M", "r", "T_f", "l"] | arxiv | arxiv | arxiv:math.AG:2508.20480v1 | cross_domain_amplification | |
A | I | urn:hailstone:math:structural_equation[45c34fef0e44] | 1 | structural_equation | 4 | arxiv.math.AG.2508.20199v2.eq_357 | [A,B] = λI | arxiv_extracted | ["I", "A", "B"] | arxiv | arxiv | arxiv:math.AG:2508.20199v2 | cross_domain_amplification | |
A | I | urn:hailstone:math:structural_equation[93740ab1e0a6] | 1 | structural_equation | 4 | arxiv.math.AG.2508.20199v2.eq_358 | [A,B]=λI | arxiv_extracted | ["I", "A", "B"] | arxiv | arxiv | arxiv:math.AG:2508.20199v2 | cross_domain_amplification | |
X | M_n | urn:hailstone:math:structural_equation[7ffbfb2b6d0f] | 1 | structural_equation | 4 | arxiv.math.AG.2508.20199v2.eq_359 | X = \{ (A,B) \in M_n(k) \times M_n(k) \mid A,B \text{ nilpotent}, [A,B]=λI, λ\in k \} | arxiv_extracted | ["B", "i", "X", "A", "M_n", "n"] | arxiv | arxiv | arxiv:math.AG:2508.20199v2 | cross_domain_amplification | |
d | e | urn:hailstone:math:structural_equation[a28aa240f90c] | 1 | structural_equation | 4 | arxiv.math.AG.2508.18191v1.eq_360 | denote the number of solutions to the generalized Markoff-Hurwitz-type equation \[(a_1X_1^m+\cdots + a_nX_n^m+a)^k=bX_1\cdots X_n \] over the finite field | arxiv_extracted | ["e", "t", "o", "n", "d"] | arxiv | arxiv | arxiv:math.AG:2508.18191v1 | cross_domain_amplification | |
W | S | urn:hailstone:math:structural_equation[db195777e5f4] | 1 | structural_equation | 4 | arxiv.math.AG.2508.18165v1.eq_361 | W =\left\{ S \in \mathrm{Sym}^2 (\mathrm{Sym}^2\, V^*)\oplus \mathrm{Sym}^2 \left(Λ^2 V^*\right) : τS = S \right\} \subset \mathrm{Sym}^2(V^*\otimes V^*) | arxiv_extracted | ["f", "e", "W", "t", "S", "l"] | arxiv | arxiv | arxiv:math.AG:2508.18165v1 | cross_domain_amplification | |
m | f | urn:hailstone:math:structural_equation[0b89072ca184] | 1 | structural_equation | 4 | arxiv.math.AG.2508.17485v1.eq_362 | \mathsf{CM} := (\mathbb{C},+,\cdot,0,1,CM) | arxiv_extracted | ["f", "a", "t", "m", "h", "s"] | arxiv | arxiv | arxiv:math.AG:2508.17485v1 | cross_domain_amplification | |
m | b | urn:hailstone:math:structural_equation[f1b509d15ca8] | 1 | structural_equation | 4 | arxiv.math.AG.2508.15065v2.eq_363 | \mathbb{L} = [\mathbb{A}^1_{K}] | arxiv_extracted | ["a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2508.15065v2 | cross_domain_amplification | |
t | X | urn:hailstone:math:structural_equation[1110beff1cdc] | 1 | structural_equation | 4 | arxiv.math.AG.2508.14876v1.eq_364 | π_1^{ét}(X) = 1 | arxiv_extracted | ["t", "X"] | arxiv | arxiv | arxiv:math.AG:2508.14876v1 | cross_domain_amplification | |
p_g | K | urn:hailstone:math:structural_equation[cbd067ef5e77] | 1 | structural_equation | 4 | arxiv.math.AG.2508.13594v1.eq_365 | p_g=q=0, K^2=9 | arxiv_extracted | ["K", "q", "p_g"] | arxiv | arxiv | arxiv:math.AG:2508.13594v1 | cross_domain_amplification | |
p_g | q | urn:hailstone:math:structural_equation[b3520a0afeba] | 1 | structural_equation | 4 | arxiv.math.AG.2508.13594v1.eq_366 | p_g=q=0 | arxiv_extracted | ["q", "p_g"] | arxiv | arxiv | arxiv:math.AG:2508.13594v1 | cross_domain_amplification | |
E_p | p | urn:hailstone:math:structural_equation[4ae8aa15d282] | 1 | structural_equation | 4 | arxiv.math.AG.2508.12340v1.eq_367 | E_p:y^2=x(x-2)(x-p) | arxiv_extracted | ["E_p", "p", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2508.12340v1 | cross_domain_amplification | |
q | c_1 | urn:hailstone:math:structural_equation[22654d5b1d29] | 1 | structural_equation | 4 | arxiv.math.AG.2508.12339v1.eq_368 | q=0,p_g=0,c_1^2=9 | arxiv_extracted | ["c_1", "q", "p_g"] | arxiv | arxiv | arxiv:math.AG:2508.12339v1 | cross_domain_amplification | |
J | A | urn:hailstone:math:structural_equation[aed91bac2a3b] | 1 | structural_equation | 4 | arxiv.math.AG.2508.12113v1.eq_369 | J_\cA = J_\cA^{top} | arxiv_extracted | ["c", "A", "J"] | arxiv | arxiv | arxiv:math.AG:2508.12113v1 | cross_domain_amplification | |
w | e | urn:hailstone:math:structural_equation[2519aa5bc711] | 1 | structural_equation | 4 | arxiv.math.AG.2508.11268v1.eq_370 | with \begin{equation*}\lVert\varpi^{1/p^{n}}\rVert=\lVert\varpi\rVert^{1/p^{n}}\end{equation*}for all | arxiv_extracted | ["e", "w", "t", "h", "i", "b"] | arxiv | arxiv | arxiv:math.AG:2508.11268v1 | cross_domain_amplification | |
C | C | urn:hailstone:math:structural_equation[e738d79eb3f3] | 1 | structural_equation | 4 | arxiv.math.AG.2508.08753v5.eq_371 | \Char(R)=\Char(k) | arxiv_extracted | ["a", "h", "R", "r", "C"] | arxiv | arxiv | arxiv:math.AG:2508.08753v5 | cross_domain_amplification | |
g | d | urn:hailstone:math:structural_equation[96e6aac1d0cd] | 1 | structural_equation | 4 | arxiv.math.AG.2508.07060v1.eq_372 | g^{e}=g_1^{e_1} \cdots g_s^{e_s} | arxiv_extracted | ["e", "g", "g_1", "d", "e_1}", "c"] | arxiv | arxiv | arxiv:math.AG:2508.07060v1 | cross_domain_amplification | |
M | c | urn:hailstone:math:structural_equation[e78f3f7aa409] | 1 | structural_equation | 4 | arxiv.math.AG.2508.07060v1.eq_373 | M_{\mathcal N}=T_{\mathcal N}=Pos(K) | arxiv_extracted | ["a", "t", "M", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2508.07060v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[3c8d889d6546] | 1 | structural_equation | 4 | arxiv.math.AG.2508.06865v2.eq_374 | \mathcal{N}=(0,1) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2508.06865v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[3c8d889d6546] | 1 | structural_equation | 4 | arxiv.math.AG.2508.06865v2.eq_375 | \mathcal{N}=(0,1) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2508.06865v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[0b5611cec051] | 1 | structural_equation | 4 | arxiv.math.AG.2508.06865v2.eq_376 | \mathcal{N}=(0,2) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2508.06865v2 | cross_domain_amplification | |
W | r | urn:hailstone:math:structural_equation[1501738bf265] | 1 | structural_equation | 4 | arxiv.math.AG.2508.05329v1.eq_377 | W_{\mathrm{rat}} (K) = Γ(\mathrm{spec}\, K , (\underline{\mathbb{Z}}\mathcal{O})^{\sharp}) | arxiv_extracted | ["a", "W", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2508.05329v1 | cross_domain_amplification | |
u | X | urn:hailstone:math:structural_equation[5a07aefc8758] | 1 | structural_equation | 4 | arxiv.math.AG.2508.03892v1.eq_378 | \uprho(X/Z)=1 | arxiv_extracted | ["h", "o", "X", "p", "u", "r"] | arxiv | arxiv | arxiv:math.AG:2508.03892v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[d3e208066318] | 1 | structural_equation | 4 | arxiv.math.AG.2508.02891v2.eq_379 | \mathcal{N}=4 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2508.02891v2 | cross_domain_amplification | |
m | b | urn:hailstone:math:structural_equation[bd16e640f6f8] | 1 | structural_equation | 4 | arxiv.math.AG.2508.01374v2.eq_380 | \mathbb{E} := E^3/\langle E, E, E\rangle^Y | arxiv_extracted | ["a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2508.01374v2 | cross_domain_amplification | |
t | H | urn:hailstone:math:structural_equation[618cbdad14f1] | 1 | structural_equation | 4 | arxiv.math.AG.2507.20076v1.eq_381 | \text{CH}_0(X)^{\text{deg}=0}\to Alb_X(k) | arxiv_extracted | ["e", "t", "H", "C", "x"] | arxiv | arxiv | arxiv:math.AG:2507.20076v1 | cross_domain_amplification | |
d | d | urn:hailstone:math:structural_equation[233db286c5fd] | 1 | structural_equation | 4 | arxiv.math.AG.2507.19163v2.eq_382 | \dim V=2d | arxiv_extracted | ["V", "d", "m", "i"] | arxiv | arxiv | arxiv:math.AG:2507.19163v2 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[84b29901129e] | 1 | structural_equation | 4 | arxiv.math.AG.2507.18613v1.eq_383 | \mathrm{gcd}(r,d)=1 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2507.18613v1 | cross_domain_amplification | |
a | c | urn:hailstone:math:structural_equation[2f3f52f04c17] | 1 | structural_equation | 4 | arxiv.math.AG.2507.17967v3.eq_384 | a^2 + 28b^3 = 27 c^7 | arxiv_extracted | ["b", "c", "a"] | arxiv | arxiv | arxiv:math.AG:2507.17967v3 | cross_domain_amplification | |
E | x | urn:hailstone:math:structural_equation[2dd8d78f31cc] | 1 | structural_equation | 4 | arxiv.math.AG.2507.16785v1.eq_385 | E: y^2 = x^3 - x | arxiv_extracted | ["E", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2507.16785v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[db58a239640e] | 1 | structural_equation | 4 | arxiv.math.AG.2507.16785v1.eq_386 | \mathcal{X} = \mathbb{P}^1 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2507.16785v1 | cross_domain_amplification | |
h_X | t | urn:hailstone:math:structural_equation[505e455f8aec] | 1 | structural_equation | 4 | arxiv.math.AG.2507.16547v1.eq_387 | h_X(t):= h^0(\mathcal{I}_X(t)) | arxiv_extracted | ["a", "t", "m", "h", "h_X"] | arxiv | arxiv | arxiv:math.AG:2507.16547v1 | cross_domain_amplification | |
r | i | urn:hailstone:math:structural_equation[110896ccf618] | 1 | structural_equation | 4 | arxiv.math.AG.2507.15785v2.eq_388 | {\rm Split}_{\rm rad}(I_A)=3 | arxiv_extracted | ["m", "S", "i", "p", "r", "l"] | arxiv | arxiv | arxiv:math.AG:2507.15785v2 | cross_domain_amplification | |
C_4 | p | urn:hailstone:math:structural_equation[800093db393c] | 1 | structural_equation | 4 | arxiv.math.AG.2507.14950v2.eq_389 | C_4(X,p)=C_3(X,p) | arxiv_extracted | ["X", "p", "C_4", "C_3"] | arxiv | arxiv | arxiv:math.AG:2507.14950v2 | cross_domain_amplification | |
m | r | urn:hailstone:math:structural_equation[df3401326abe] | 1 | structural_equation | 4 | arxiv.math.AG.2507.12954v1.eq_390 | \mathfrak{T}(T)=Λ_{\mathbb R}/Λ | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2507.12954v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6729771ae87e] | 1 | structural_equation | 4 | arxiv.math.AG.2507.12510v2.eq_391 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2507.12510v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6729771ae87e] | 1 | structural_equation | 4 | arxiv.math.AG.2507.12510v2.eq_392 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2507.12510v2 | cross_domain_amplification | |
u | n | urn:hailstone:math:structural_equation[baad34552025] | 1 | structural_equation | 4 | arxiv.math.AG.2507.11717v1.eq_393 | u^W(M)=W_{-1}\underline{Hom}(M,M) | arxiv_extracted | ["W", "n", "u", "M"] | arxiv | arxiv | arxiv:math.AG:2507.11717v1 | cross_domain_amplification | |
f_1 | s | urn:hailstone:math:structural_equation[17792f3062ce] | 1 | structural_equation | 4 | arxiv.math.AG.2507.11514v2.eq_394 | f_1=\ldots=f_s = 0 | arxiv_extracted | ["t", "f_1", "o", "s", "d", "l"] | arxiv | arxiv | arxiv:math.AG:2507.11514v2 | cross_domain_amplification | |
f | h | urn:hailstone:math:structural_equation[bc98159034aa] | 1 | structural_equation | 4 | arxiv.math.AG.2507.11304v1.eq_395 | f : S = \mathbb{P} (\mathcal{O}_Y \oplus \mathcal{O}_Y (E)) \to Y | arxiv_extracted | ["f", "a", "t", "m", "S", "h"] | arxiv | arxiv | arxiv:math.AG:2507.11304v1 | cross_domain_amplification | |
v | i | urn:hailstone:math:structural_equation[be3e0d4a85c5] | 1 | structural_equation | 4 | arxiv.math.AG.2507.11304v1.eq_396 | \varphi = f_{|_X} : X \to Y | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:math.AG:2507.11304v1 | cross_domain_amplification | |
d | h | urn:hailstone:math:structural_equation[362260425d9b] | 1 | structural_equation | 4 | arxiv.math.AG.2507.11207v1.eq_397 | d(n,k)={{n+2}\choose {2}}-{{n+2-k}\choose {2}}. | arxiv_extracted | ["h", "c", "n", "d", "k"] | arxiv | arxiv | arxiv:math.AG:2507.11207v1 | cross_domain_amplification | |
d | n | urn:hailstone:math:structural_equation[d770033ba8ec] | 1 | structural_equation | 4 | arxiv.math.AG.2507.11207v1.eq_398 | d(n,1)=n+1 | arxiv_extracted | ["n", "d"] | arxiv | arxiv | arxiv:math.AG:2507.11207v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[1857f299659c] | 1 | structural_equation | 4 | arxiv.math.AG.2507.09392v2.eq_399 | \mathrm{char} \ k = p | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2507.09392v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6729771ae87e] | 1 | structural_equation | 4 | arxiv.math.AG.2507.07971v1.eq_400 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2507.07971v1 | cross_domain_amplification | |
f | x | urn:hailstone:math:structural_equation[0a1d5716e302] | 1 | structural_equation | 4 | arxiv.math.AG.2507.06865v1.eq_401 | f(x) = x^{2g+1} + c_1 x^{2g} + \dots + c_{2g+1} \in k[x] | arxiv_extracted | ["f", "g", "c_1", "x"] | arxiv | arxiv | arxiv:math.AG:2507.06865v1 | cross_domain_amplification | |
C | x | urn:hailstone:math:structural_equation[b01f99371ac1] | 1 | structural_equation | 4 | arxiv.math.AG.2507.06865v1.eq_402 | C : y^2 = f(x) | arxiv_extracted | ["f", "y", "C", "x"] | arxiv | arxiv | arxiv:math.AG:2507.06865v1 | cross_domain_amplification | |
t | h | urn:hailstone:math:structural_equation[a8945bc741ca] | 1 | structural_equation | 4 | arxiv.math.AG.2507.06754v1.eq_403 | \text{char}(\mathbb{F}_q) = 3,2 | arxiv_extracted | ["e", "t", "h", "c", "x"] | arxiv | arxiv | arxiv:math.AG:2507.06754v1 | cross_domain_amplification | |
E | e | urn:hailstone:math:structural_equation[1cd95d8ecd02] | 1 | structural_equation | 4 | arxiv.math.AG.2507.05690v1.eq_404 | χ(E\otimes F)= 0 | arxiv_extracted | ["e", "t", "m", "i", "o", "E"] | arxiv | arxiv | arxiv:math.AG:2507.05690v1 | cross_domain_amplification | |
H | i | urn:hailstone:math:structural_equation[0586a4697eb0] | 1 | structural_equation | 4 | arxiv.math.AG.2507.05690v1.eq_405 | H^0(X, E\otimes F) = 0 = H^1(X, E\otimes F) | arxiv_extracted | ["t", "H", "o", "X", "i", "E"] | arxiv | arxiv | arxiv:math.AG:2507.05690v1 | cross_domain_amplification | |
W | v | urn:hailstone:math:structural_equation[30a0d7717b07] | 1 | structural_equation | 4 | arxiv.math.AG.2507.05027v1.eq_406 | . We prove that \begin{align} \lim_{n \to \infty} \frac{h_{Y}(f^{n}(x))}{h_{H}(f^{n}(x)) } = 0, \end{align} where | arxiv_extracted | ["e", "W", "o", "p", "r", "v"] | arxiv | arxiv | arxiv:math.AG:2507.05027v1 | cross_domain_amplification | |
l | i | urn:hailstone:math:structural_equation[fe1ad3a0d0de] | 1 | structural_equation | 4 | arxiv.math.AG.2507.05027v1.eq_407 | \lim_{n \to \infty} \frac{h_{Y}(f^{n}(x))}{h_{H}(f^{n}(x)) } = 0, | arxiv_extracted | ["m_{n", "t", "o", "i", "l"] | arxiv | arxiv | arxiv:math.AG:2507.05027v1 | cross_domain_amplification | |
x | y | urn:hailstone:math:structural_equation[9c77d3b9c3d4] | 1 | structural_equation | 4 | arxiv.math.AG.2507.03128v1.eq_408 | x^4 + y^4 + z^4 + t(x^2y^2 + x^2z^2 + y^2z^2)=0 \, \mbox{ where } t \in \bar{\mathbb{C}} | arxiv_extracted | ["t", "z", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2507.03128v1 | cross_domain_amplification | |
x | p | urn:hailstone:math:structural_equation[d68acad0bccf] | 1 | structural_equation | 4 | arxiv.math.AG.2507.03128v1.eq_409 | x^{2p}+y^{2p}+z^{2p}+t(x^p y^p +x^p z^p +y^p z^p)=0\mbox{ where } t \in \bar{\mathbb{C}}. | arxiv_extracted | ["p", "z", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2507.03128v1 | cross_domain_amplification | |
X | X | urn:hailstone:math:structural_equation[26302ab99b91] | 1 | structural_equation | 4 | arxiv.math.AG.2507.01797v1.eq_410 | χ(X, ω_X) = 0 | arxiv_extracted | ["X"] | arxiv | arxiv | arxiv:math.AG:2507.01797v1 | cross_domain_amplification | |
p_g | K | urn:hailstone:math:structural_equation[7b388f52e117] | 1 | structural_equation | 4 | arxiv.math.AG.2507.01405v1.eq_411 | p_g=0, K^2=7 | arxiv_extracted | ["K", "p_g"] | arxiv | arxiv | arxiv:math.AG:2507.01405v1 | cross_domain_amplification | |
p_g | S | urn:hailstone:math:structural_equation[3f2d41272e3e] | 1 | structural_equation | 4 | arxiv.math.AG.2507.01405v1.eq_412 | p_g(S)=0 | arxiv_extracted | ["S", "p_g"] | arxiv | arxiv | arxiv:math.AG:2507.01405v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[14979c8b9d71] | 1 | structural_equation | 4 | arxiv.math.AG.2506.21995v1.eq_413 | \mathrm{Sb}(\mathcal{T}) := \mathrm{Stab}(\mathcal{T})/\sim | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2506.21995v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[38aa0000d847] | 1 | structural_equation | 4 | arxiv.math.AG.2506.21995v1.eq_414 | \mathcal{T} = \mathrm{D}^b(X) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2506.21995v1 | cross_domain_amplification | |
R | Y | urn:hailstone:math:structural_equation[74f09e8b4a8b] | 1 | structural_equation | 4 | arxiv.math.AG.2506.21381v1.eq_415 | R^1π_*ω_Y=0 | arxiv_extracted | ["Y", "R"] | arxiv | arxiv | arxiv:math.AG:2506.21381v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[e2f9db74a74a] | 1 | structural_equation | 4 | arxiv.math.AG.2506.21381v1.eq_416 | \mathrm{dim}(X)=3 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2506.21381v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[cb6d0fe6fb81] | 1 | structural_equation | 4 | arxiv.math.AG.2506.20565v2.eq_417 | \mathcal{P}:=\{P_1,\ldots,P_s\} \subset \R[X_1,\ldots,X_n] | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2506.20565v2 | cross_domain_amplification | |
E_{A | o | urn:hailstone:math:structural_equation[f3db712fafc9] | 1 | structural_equation | 4 | arxiv.math.AG.2506.18874v1.eq_418 | E_{A,B} \colon y^2 = x^3 + Ax + B | arxiv_extracted | ["B", "o", "E_{A", "c", "l"] | arxiv | arxiv | arxiv:math.AG:2506.18874v1 | cross_domain_amplification | |
H_{α | x | urn:hailstone:math:structural_equation[b5865667b603] | 1 | structural_equation | 4 | arxiv.math.AG.2506.18874v1.eq_419 | H_{α, β}(E_{A,B}) := \max\{ α|A|^3, βB^2 \} | arxiv_extracted | ["H_{\u03b1", "a", "B", "m", "E_{A", "x"] | arxiv | arxiv | arxiv:math.AG:2506.18874v1 | cross_domain_amplification | |
b_2 | l | urn:hailstone:math:structural_equation[25fca6f6f2ad] | 1 | structural_equation | 4 | arxiv.math.AG.2506.18388v1.eq_420 | b_2(X_{w,P})=b_{2\ell(w)-2}(X_{w,P}) | arxiv_extracted | ["e", "X_{w", "b_2", "b_{2", "P", "l"] | arxiv | arxiv | arxiv:math.AG:2506.18388v1 | cross_domain_amplification |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.