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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
c | h | urn:hailstone:math:structural_equation[0ca8e89c1f76] | 1 | structural_equation | 4 | arxiv.math.AG.2512.11072v3.eq_221 | (c+d)-(a+b)=h | arxiv_extracted | ["a", "d", "h", "b", "c"] | arxiv | arxiv | arxiv:math.AG:2512.11072v3 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[04cb1fc82fd0] | 1 | structural_equation | 4 | arxiv.math.AG.2512.11072v3.eq_222 | \mathrm{rank}\,E_h(\mathbb{Q}(S))=1 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2512.11072v3 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[04800add399d] | 1 | structural_equation | 4 | arxiv.math.AG.2512.08494v2.eq_223 | \mathrm{H}^{i}(X)=\mathrm{H}^{i}(X,\mathcal{O}_{X}) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2512.08494v2 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[9ee22752713a] | 1 | structural_equation | 4 | arxiv.math.AG.2512.08062v1.eq_224 | \mathcal{N}= 4 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2512.08062v1 | cross_domain_amplification | |
m | f | urn:hailstone:math:structural_equation[1027d39c2295] | 1 | structural_equation | 4 | arxiv.math.AG.2512.07572v1.eq_225 | \mathbf{d} = (d_1, \ldots , d_s) | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2512.07572v1 | cross_domain_amplification | |
v | v | urn:hailstone:math:structural_equation[a8b32e8cf9a7] | 1 | structural_equation | 4 | arxiv.math.AG.2512.06936v1.eq_226 | \vert q\vert =1 | arxiv_extracted | ["e", "q", "t", "r", "v"] | arxiv | arxiv | arxiv:math.AG:2512.06936v1 | cross_domain_amplification | |
f | x | urn:hailstone:math:structural_equation[8c1589102e38] | 1 | structural_equation | 4 | arxiv.math.AG.2512.06618v1.eq_227 | \f(x) = 0 | arxiv_extracted | ["f", "x"] | arxiv | arxiv | arxiv:math.AG:2512.06618v1 | cross_domain_amplification | |
D | c | urn:hailstone:math:structural_equation[c2a25c4182dd] | 1 | structural_equation | 4 | arxiv.math.AG.2512.05308v1.eq_228 | D(S_+) = \Spec(S) \setminus V(S_+) | arxiv_extracted | ["e", "D", "S", "p", "c"] | arxiv | arxiv | arxiv:math.AG:2512.05308v1 | cross_domain_amplification | |
S | l | urn:hailstone:math:structural_equation[5f7b24e216f8] | 1 | structural_equation | 4 | arxiv.math.AG.2512.05308v1.eq_229 | σ(S) = \overline{\Cone}(d \in D \mid S_d \neq 0) | arxiv_extracted | ["e", "S", "o", "r", "l", "v"] | arxiv | arxiv | arxiv:math.AG:2512.05308v1 | cross_domain_amplification | |
P | S | urn:hailstone:math:structural_equation[3c22540d8f79] | 1 | structural_equation | 4 | arxiv.math.AG.2512.05308v1.eq_230 | \Proj^D(S) = X^{\mathrm{gss}}\sslash \Spec(S_0[D]) | arxiv_extracted | ["D", "j", "P", "o", "S", "r"] | arxiv | arxiv | arxiv:math.AG:2512.05308v1 | cross_domain_amplification | |
d | l | urn:hailstone:math:structural_equation[cd046f6a6b50] | 1 | structural_equation | 4 | arxiv.math.AG.2512.05308v1.eq_231 | d \in D = \Cl(X) | arxiv_extracted | ["D", "i", "n", "d", "l", "C"] | arxiv | arxiv | arxiv:math.AG:2512.05308v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[5f587d7a90a5] | 1 | structural_equation | 4 | arxiv.math.AG.2512.04942v1.eq_232 | \mathrm{ed}(f^s)=\mathrm{dim}(A) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2512.04942v1 | cross_domain_amplification | |
p | a | urn:hailstone:math:structural_equation[966e87d5f38b] | 1 | structural_equation | 4 | arxiv.math.AG.2512.04930v1.eq_233 | \{\partial_i H=(\partial_i η_i\wedgeη_i)H\}_{i\in [1, N]} | arxiv_extracted | ["a", "t", "i", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2512.04930v1 | cross_domain_amplification | |
p | a | urn:hailstone:math:structural_equation[ed91431d8fee] | 1 | structural_equation | 4 | arxiv.math.AG.2512.04930v1.eq_234 | \partial_i =\partial/\partial t_i | arxiv_extracted | ["a", "t", "i", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2512.04930v1 | cross_domain_amplification | |
F | h | urn:hailstone:math:structural_equation[457a92e1c0ac] | 1 | structural_equation | 4 | arxiv.math.AG.2512.04641v1.eq_235 | F^+_v = \mathbb{Q}_{p^2} | arxiv_extracted | ["a", "F", "t", "m", "h", "v"] | arxiv | arxiv | arxiv:math.AG:2512.04641v1 | cross_domain_amplification | |
h | b | urn:hailstone:math:structural_equation[c3b888ec635e] | 1 | structural_equation | 4 | arxiv.math.AG.2512.03488v1.eq_236 | h^0_{\rm Ar}(\bar E):=\log \vert E\cap B_1 \vert | arxiv_extracted | ["m", "h", "A", "r", "b"] | arxiv | arxiv | arxiv:math.AG:2512.03488v1 | cross_domain_amplification | |
h | l | urn:hailstone:math:structural_equation[687503960b67] | 1 | structural_equation | 4 | arxiv.math.AG.2512.03488v1.eq_237 | h^0_θ(\bar{E}):=\log\sum_{v\in E}e^{-π\Vert v\Vert^2} | arxiv_extracted | ["a", "h", "r", "b", "E", "l"] | arxiv | arxiv | arxiv:math.AG:2512.03488v1 | cross_domain_amplification | |
C_{p | p | urn:hailstone:math:structural_equation[ac5dd133ccbf] | 1 | structural_equation | 4 | arxiv.math.AG.2512.03299v1.eq_238 | C_{p^2}: y^2=x^{p^2}-1 | arxiv_extracted | ["p", "C_{p", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2512.03299v1 | cross_domain_amplification | |
C | I | urn:hailstone:math:structural_equation[07b742991223] | 1 | structural_equation | 4 | arxiv.math.AG.2512.03213v1.eq_239 | (C18,p=3,\{2I\}) | arxiv_extracted | ["p", "C", "I"] | arxiv | arxiv | arxiv:math.AG:2512.03213v1 | cross_domain_amplification | |
C | I | urn:hailstone:math:structural_equation[07b742991223] | 1 | structural_equation | 4 | arxiv.math.AG.2512.03213v1.eq_240 | (C18,p=3,\{2I\}) | arxiv_extracted | ["p", "C", "I"] | arxiv | arxiv | arxiv:math.AG:2512.03213v1 | cross_domain_amplification | |
C | t | urn:hailstone:math:structural_equation[1f1a27f399a2] | 1 | structural_equation | 4 | arxiv.math.AG.2512.03213v1.eq_241 | (C18,p=3,\emptyset,d_3 D_3) | arxiv_extracted | ["e", "t", "m", "p", "C"] | arxiv | arxiv | arxiv:math.AG:2512.03213v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[454688eaf71e] | 1 | structural_equation | 4 | arxiv.math.AG.2512.03141v1.eq_242 | \mathcal{V}(x) = \|P(x)\|^2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2512.03141v1 | cross_domain_amplification | |
g | q | urn:hailstone:math:structural_equation[8afdb3c34e08] | 1 | structural_equation | 4 | arxiv.math.AG.2512.11825v1.eq_243 | \gcd(a_i, a_j, q-1)=1 | arxiv_extracted | ["a_i", "g", "q", "c", "a_j", "d"] | arxiv | arxiv | arxiv:math.AG:2512.11825v1 | cross_domain_amplification | |
r | r | urn:hailstone:math:structural_equation[47f30bcfb714] | 1 | structural_equation | 4 | arxiv.math.AG.2512.01254v1.eq_244 | {\rm char} (k) = p>0 | arxiv_extracted | ["a", "m", "h", "r", "c"] | arxiv | arxiv | arxiv:math.AG:2512.01254v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[0ca57c890405] | 1 | structural_equation | 4 | arxiv.math.AG.2512.00201v2.eq_245 | \mathrm{M}_d = \mathrm{Rat}_d/\mathrm{SL}_2 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2512.00201v2 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[df07afe5dfba] | 1 | structural_equation | 4 | arxiv.math.AG.2511.23035v1.eq_246 | m=1, m=2 | arxiv_extracted | ["m"] | arxiv | arxiv | arxiv:math.AG:2511.23035v1 | cross_domain_amplification | |
u_1 | u_2 | urn:hailstone:math:structural_equation[16cd82324286] | 1 | structural_equation | 4 | arxiv.math.AG.2511.21457v1.eq_247 | u_1^*=u_2^* | arxiv_extracted | ["u_1", "u_2"] | arxiv | arxiv | arxiv:math.AG:2511.21457v1 | cross_domain_amplification | |
o | i | urn:hailstone:math:structural_equation[2191631511cb] | 1 | structural_equation | 4 | arxiv.math.AG.2511.21457v1.eq_248 | \overline{x_1}=\overline{x_2} | arxiv_extracted | ["e", "o", "i", "r", "l", "v"] | arxiv | arxiv | arxiv:math.AG:2511.21457v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[e48a7c37a6be] | 1 | structural_equation | 4 | arxiv.math.AG.2511.21457v1.eq_249 | \mathrm{cl}(x_1\cap Z)=\mathrm{cl}(x_2\cap Z) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2511.21457v1 | cross_domain_amplification | |
E | C | urn:hailstone:math:structural_equation[96a8ac8ff06e] | 1 | structural_equation | 4 | arxiv.math.AG.2511.21353v2.eq_250 | \End (L/K)=\CD (L/K)\rtimes G(L/K) | arxiv_extracted | ["d", "E", "L", "n", "K", "C"] | arxiv | arxiv | arxiv:math.AG:2511.21353v2 | cross_domain_amplification | |
s | s | urn:hailstone:math:structural_equation[bb5427285266] | 1 | structural_equation | 4 | arxiv.math.AG.2511.20316v1.eq_251 | \sqrt{2γ(F_n)} = \sqrt{2(n-1)} | arxiv_extracted | ["q", "t", "F_n", "r", "s"] | arxiv | arxiv | arxiv:math.AG:2511.20316v1 | cross_domain_amplification | |
f | b | urn:hailstone:math:structural_equation[2cdeb4cf7587] | 1 | structural_equation | 4 | arxiv.math.AG.2511.18545v3.eq_252 | f^{-1}(\mathbb{R} \mathbb{P}^1) = \mathbb{R} X | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2511.18545v3 | cross_domain_amplification | |
d | d | urn:hailstone:math:structural_equation[5c2f0b413f2c] | 1 | structural_equation | 4 | arxiv.math.AG.2511.18545v3.eq_253 | d(f) = (d_1(f), \ldots, d_r(f)) \in \mathbb{N}^{r} | arxiv_extracted | ["f", "d", "l", "d_1"] | arxiv | arxiv | arxiv:math.AG:2511.18545v3 | cross_domain_amplification | |
x | n | urn:hailstone:math:structural_equation[683ee66a83c9] | 1 | structural_equation | 4 | arxiv.math.AG.2511.17456v2.eq_254 | x^4 + y^4 - w^2 = n | arxiv_extracted | ["n", "w", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2511.17456v2 | cross_domain_amplification | |
t | l | urn:hailstone:math:structural_equation[45ef8ff0d54f] | 1 | structural_equation | 4 | arxiv.math.AG.2511.17365v2.eq_255 | \text{alb}_S:\text{CH}_0(S)^{\text{deg}=0}\rightarrow \text{Alb}_S(k) | arxiv_extracted | ["e", "a", "t", "l", "x"] | arxiv | arxiv | arxiv:math.AG:2511.17365v2 | cross_domain_amplification | |
o | i | urn:hailstone:math:structural_equation[e9fac73a979f] | 1 | structural_equation | 4 | arxiv.math.AG.2511.16562v5.eq_256 | \overline{M}_{1,1}=\mathbb P(4,6) | arxiv_extracted | ["e", "o", "i", "r", "l", "v"] | arxiv | arxiv | arxiv:math.AG:2511.16562v5 | cross_domain_amplification | |
o | i | urn:hailstone:math:structural_equation[9841f49b80ea] | 1 | structural_equation | 4 | arxiv.math.AG.2511.16562v5.eq_257 | \overline{F}^{\rm BB}_{U\oplus E_8} = \mathbb P(4,10,\dotsc, 42) | arxiv_extracted | ["e", "o", "i", "r", "l", "v"] | arxiv | arxiv | arxiv:math.AG:2511.16562v5 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[8f4323addb9e] | 1 | structural_equation | 4 | arxiv.math.AG.2511.15953v3.eq_258 | \mathcal{N} = 2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2511.15953v3 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[8f4323addb9e] | 1 | structural_equation | 4 | arxiv.math.AG.2511.15953v3.eq_259 | \mathcal{N} = 2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2511.15953v3 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[1d39629b9cca] | 1 | structural_equation | 4 | arxiv.math.AG.2511.09887v1.eq_260 | \mathcal E = \mathcal L \oplus \mathcal V | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2511.09887v1 | cross_domain_amplification | |
o | t | urn:hailstone:math:structural_equation[81e24650541d] | 1 | structural_equation | 4 | arxiv.math.AG.2511.09887v1.eq_261 | \operatorname{rank} \mathcal L = 1 | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2511.09887v1 | cross_domain_amplification | |
o | t | urn:hailstone:math:structural_equation[89b15a474cdc] | 1 | structural_equation | 4 | arxiv.math.AG.2511.09887v1.eq_262 | \operatorname{rank} \mathcal V = n | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2511.09887v1 | cross_domain_amplification | |
M | s_{i | urn:hailstone:math:structural_equation[b6ffbcb69674] | 1 | structural_equation | 4 | arxiv.math.AG.2511.09176v1.eq_263 | M=\oplus_{i=1}^rM_i | arxiv_extracted | ["M", "s_{i", "o", "u", "p", "l"] | arxiv | arxiv | arxiv:math.AG:2511.09176v1 | cross_domain_amplification | |
r | e | urn:hailstone:math:structural_equation[a3b1e4a2b52b] | 1 | structural_equation | 4 | arxiv.math.AG.2511.09176v1.eq_264 | {\rm aSpec} A = {\rm Spec} A | arxiv_extracted | ["e", "a", "m", "S", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2511.09176v1 | cross_domain_amplification | |
P | K_2 | urn:hailstone:math:structural_equation[7cc1c6e72bff] | 1 | structural_equation | 4 | arxiv.math.AG.2511.08506v1.eq_265 | P^{-1}(K_1) = Q^{-1}(K_2), | arxiv_extracted | ["K_2", "Q", "P", "K_1"] | arxiv | arxiv | arxiv:math.AG:2511.08506v1 | cross_domain_amplification | |
w | J | urn:hailstone:math:structural_equation[5c202a322f65] | 1 | structural_equation | 4 | arxiv.math.AG.2511.08422v1.eq_266 | whose Jacobians admit complex multiplication (CM). Each curve in these families is defined by \[ v^2 = (u+2)\,\varphi_d(u), \quad d = 2^e \text{ or } d=p \geq 3 \text{ prime}, \] where | arxiv_extracted | ["e", "w", "h", "o", "J", "s"] | arxiv | arxiv | arxiv:math.AG:2511.08422v1 | cross_domain_amplification | |
p | o | urn:hailstone:math:structural_equation[46d5022ceaef] | 1 | structural_equation | 4 | arxiv.math.AG.2511.07900v1.eq_267 | \pts_B(A)=\{\mor_{\cat{Rings}}(A,\enm_{\mathbb Z}(M))\}. | arxiv_extracted | ["t", "m", "o", "p", "s_B", "A"] | arxiv | arxiv | arxiv:math.AG:2511.07900v1 | cross_domain_amplification | |
R | x | urn:hailstone:math:structural_equation[69548f8a9923] | 1 | structural_equation | 4 | arxiv.math.AG.2511.04906v1.eq_268 | R^{i}φ_{*}ω_{W}=0 \ \text{ and }R^{i}π_{*}ω_{X} = 0 | arxiv_extracted | ["e", "W", "t", "i", "R", "x"] | arxiv | arxiv | arxiv:math.AG:2511.04906v1 | cross_domain_amplification | |
o | t | urn:hailstone:math:structural_equation[0b095b411aeb] | 1 | structural_equation | 4 | arxiv.math.AG.2511.03885v1.eq_269 | \operatorname{in}_{M_S} (\mathcal{I}_{3,n}) = \operatorname{in}_{C_S} (\mathcal{I}_{3,n}) | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2511.03885v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6729771ae87e] | 1 | structural_equation | 4 | arxiv.math.AG.2510.27199v1.eq_270 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.27199v1 | cross_domain_amplification | |
R | r | urn:hailstone:math:structural_equation[a4d702523975] | 1 | structural_equation | 4 | arxiv.math.AG.2510.26770v1.eq_271 | R_{\mathrm{bdd}}= R_Δ\cup R_{\Diamond} | arxiv_extracted | ["a", "t", "m", "h", "R", "r"] | arxiv | arxiv | arxiv:math.AG:2510.26770v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[4c86b7c52282] | 1 | structural_equation | 4 | arxiv.math.AG.2510.25708v1.eq_272 | \mathcal{N}=(2,2) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.25708v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[4c86b7c52282] | 1 | structural_equation | 4 | arxiv.math.AG.2510.25708v1.eq_273 | \mathcal{N}=(2,2) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.25708v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[4c86b7c52282] | 1 | structural_equation | 4 | arxiv.math.AG.2510.25708v1.eq_274 | \mathcal{N}=(2,2) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.25708v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[6729771ae87e] | 1 | structural_equation | 4 | arxiv.math.AG.2510.25708v1.eq_275 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.25708v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[4c86b7c52282] | 1 | structural_equation | 4 | arxiv.math.AG.2510.25708v1.eq_276 | \mathcal{N}=(2,2) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.25708v1 | cross_domain_amplification | |
d | i | urn:hailstone:math:structural_equation[8513916f93bf] | 1 | structural_equation | 4 | arxiv.math.AG.2510.25245v2.eq_277 | \dim(U) = \dim(V) | arxiv_extracted | ["U", "d", "m", "i"] | arxiv | arxiv | arxiv:math.AG:2510.25245v2 | cross_domain_amplification | |
v | e | urn:hailstone:math:structural_equation[d86de23a61ec] | 1 | structural_equation | 4 | arxiv.math.AG.2510.24977v1.eq_278 | \varpi = e^{2πi / r} | arxiv_extracted | ["e", "a", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:math.AG:2510.24977v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[fede9fa9417a] | 1 | structural_equation | 4 | arxiv.math.AG.2510.24977v1.eq_279 | \mathcal{X}_{s,n,r} = \mathrm{Spec}\bigl((\mathbb{C}[z_1,\dots,z_n])^G\bigr). | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.24977v1 | cross_domain_amplification | |
h_{1 | h_{2 | urn:hailstone:math:structural_equation[1604d852cdb3] | 1 | structural_equation | 4 | arxiv.math.AG.2510.24603v1.eq_280 | h_{1,2} = h_{1,3} = h_{1,4} = h_{2,3} = 0 | arxiv_extracted | ["h_{2", "h_{1"] | arxiv | arxiv | arxiv:math.AG:2510.24603v1 | cross_domain_amplification | |
b | r | urn:hailstone:math:structural_equation[b3f987bdd452] | 1 | structural_equation | 4 | arxiv.math.AG.2510.22678v3.eq_281 | be a perfectoid field. We describe all quotient fields of the perfectoid Tate algebra\begin{equation*}T_{n,K}^{\text{perfd}}=K\langle X_{1}^{1/p^{\infty}},\dots, X_{n}^{1/p^{\infty}}\rangle\end{equation*}in any number | arxiv_extracted | ["e", "a", "p", "r", "b"] | arxiv | arxiv | arxiv:math.AG:2510.22678v3 | cross_domain_amplification | |
m | b | urn:hailstone:math:structural_equation[464e52d64622] | 1 | structural_equation | 4 | arxiv.math.AG.2510.22408v2.eq_282 | \mathbb{A}_I(X,\mathcal{F})\cap\mathbb{A}_J(X,\mathcal{F})=\mathbb{A}_{I\setminus0}(X,\mathcal{F}) | arxiv_extracted | ["a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2510.22408v2 | cross_domain_amplification | |
I | I | urn:hailstone:math:structural_equation[e77e66939103] | 1 | structural_equation | 4 | arxiv.math.AG.2510.22408v2.eq_283 | I\cap J=I\setminus0 | arxiv_extracted | ["a", "p", "J", "c", "I"] | arxiv | arxiv | arxiv:math.AG:2510.22408v2 | cross_domain_amplification | |
m | f | urn:hailstone:math:structural_equation[02b95d9dbe60] | 1 | structural_equation | 4 | arxiv.math.AG.2510.20648v2.eq_284 | \mathbf{G}=1-1/3^2+1/5^2-1/7^2+\cdots | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:math.AG:2510.20648v2 | cross_domain_amplification | |
P_2 | X | urn:hailstone:math:structural_equation[6bfd365716f1] | 1 | structural_equation | 4 | arxiv.math.AG.2510.19706v1.eq_285 | P_2(X) = 1 | arxiv_extracted | ["X", "P_2"] | arxiv | arxiv | arxiv:math.AG:2510.19706v1 | cross_domain_amplification | |
o | t | urn:hailstone:math:structural_equation[2722d569a4bb] | 1 | structural_equation | 4 | arxiv.math.AG.2510.19553v1.eq_286 | 0 < \operatorname{rank} A(K) = \operatorname{rank} A(L) | arxiv_extracted | ["e", "a", "t", "o", "p", "r"] | arxiv | arxiv | arxiv:math.AG:2510.19553v1 | cross_domain_amplification | |
g | f | urn:hailstone:math:structural_equation[637c0c0ae768] | 1 | structural_equation | 4 | arxiv.math.AG.2510.18506v1.eq_287 | \gcd \left( d, q \right) = 1 | arxiv_extracted | ["e", "f", "g", "c", "d", "l"] | arxiv | arxiv | arxiv:math.AG:2510.18506v1 | cross_domain_amplification | |
p_g | X | urn:hailstone:math:structural_equation[4f98044c8e7a] | 1 | structural_equation | 4 | arxiv.math.AG.2510.17678v1.eq_288 | p_g(X)=1 | arxiv_extracted | ["X", "p_g"] | arxiv | arxiv | arxiv:math.AG:2510.17678v1 | cross_domain_amplification | |
K_X | c | urn:hailstone:math:structural_equation[207b3430fe00] | 1 | structural_equation | 4 | arxiv.math.AG.2510.17678v1.eq_289 | K_X^2=\frac1{143} | arxiv_extracted | ["f", "K_X", "a", "r", "c"] | arxiv | arxiv | arxiv:math.AG:2510.17678v1 | cross_domain_amplification | |
p_g | X | urn:hailstone:math:structural_equation[4f98044c8e7a] | 1 | structural_equation | 4 | arxiv.math.AG.2510.17678v1.eq_290 | p_g(X)=1 | arxiv_extracted | ["X", "p_g"] | arxiv | arxiv | arxiv:math.AG:2510.17678v1 | cross_domain_amplification | |
K_X | c | urn:hailstone:math:structural_equation[6571d82c231b] | 1 | structural_equation | 4 | arxiv.math.AG.2510.17678v1.eq_291 | (K_X+B)^2=v(c) | arxiv_extracted | ["K_X", "c", "v", "B"] | arxiv | arxiv | arxiv:math.AG:2510.17678v1 | cross_domain_amplification | |
c | K_0 | urn:hailstone:math:structural_equation[df4671852122] | 1 | structural_equation | 4 | arxiv.math.AG.2510.16912v2.eq_292 | char(K_0)=0 | arxiv_extracted | ["a", "h", "K_0", "r", "c"] | arxiv | arxiv | arxiv:math.AG:2510.16912v2 | cross_domain_amplification | |
c | K_0 | urn:hailstone:math:structural_equation[df4671852122] | 1 | structural_equation | 4 | arxiv.math.AG.2510.16912v2.eq_293 | char(K_0)=0 | arxiv_extracted | ["a", "h", "K_0", "r", "c"] | arxiv | arxiv | arxiv:math.AG:2510.16912v2 | cross_domain_amplification | |
c | K_0 | urn:hailstone:math:structural_equation[df4671852122] | 1 | structural_equation | 4 | arxiv.math.AG.2510.16912v2.eq_294 | char(K_0)=0 | arxiv_extracted | ["a", "h", "K_0", "r", "c"] | arxiv | arxiv | arxiv:math.AG:2510.16912v2 | cross_domain_amplification | |
w | m | urn:hailstone:math:structural_equation[ccb381a5c22c] | 1 | structural_equation | 4 | arxiv.math.AG.2510.16773v1.eq_295 | °(w_\pm)=(0,1,0),(0,0,1) | arxiv_extracted | ["m", "p", "w"] | arxiv | arxiv | arxiv:math.AG:2510.16773v1 | cross_domain_amplification | |
R | w | urn:hailstone:math:structural_equation[c60c599f489b] | 1 | structural_equation | 4 | arxiv.math.AG.2510.16417v2.eq_296 | R(l^3,m^3,n^3)=(l\wedge m\wedge n)^3 | arxiv_extracted | ["w", "m", "R", "n", "l"] | arxiv | arxiv | arxiv:math.AG:2510.16417v2 | cross_domain_amplification | |
d | A | urn:hailstone:math:structural_equation[42ee75e972db] | 1 | structural_equation | 4 | arxiv.math.AG.2510.15126v2.eq_297 | \dim A = 2 | arxiv_extracted | ["A", "d", "m", "i"] | arxiv | arxiv | arxiv:math.AG:2510.15126v2 | cross_domain_amplification | |
X | D | urn:hailstone:math:structural_equation[48f9b5ad048b] | 1 | structural_equation | 4 | arxiv.math.AG.2510.15085v2.eq_298 | (X',D') = (X,D) | arxiv_extracted | ["X", "D"] | arxiv | arxiv | arxiv:math.AG:2510.15085v2 | cross_domain_amplification | |
v | i | urn:hailstone:math:structural_equation[8694831c90b2] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14754v2.eq_299 | \varphi G_{1} \varphi^{-1}=G_{2} | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:math.AG:2510.14754v2 | cross_domain_amplification | |
v | f | urn:hailstone:math:structural_equation[9e798dee7d51] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14434v1.eq_300 | v(Δ(f))=1 | arxiv_extracted | ["f", "v"] | arxiv | arxiv | arxiv:math.AG:2510.14434v1 | cross_domain_amplification | |
f_{d | c | urn:hailstone:math:structural_equation[232ae5465d07] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14397v1.eq_301 | f_{d,c}(x)=x^d+c | arxiv_extracted | ["f_{d", "c", "d", "x"] | arxiv | arxiv | arxiv:math.AG:2510.14397v1 | cross_domain_amplification | |
w | i | urn:hailstone:math:structural_equation[426ae09dda0c] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14352v1.eq_302 | \widetilde α(X)=\frac{n+1}{d} | arxiv_extracted | ["e", "w", "t", "i", "d"] | arxiv | arxiv | arxiv:math.AG:2510.14352v1 | cross_domain_amplification | |
n | d | urn:hailstone:math:structural_equation[83225ce5d1a9] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14352v1.eq_303 | (n,d)=(2,4),(2,6),(3,3),(4,3),(5,3) | arxiv_extracted | ["n", "d"] | arxiv | arxiv | arxiv:math.AG:2510.14352v1 | cross_domain_amplification | |
w | i | urn:hailstone:math:structural_equation[426ae09dda0c] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14352v1.eq_304 | \widetilde α(X)=\frac{n+1}{d} | arxiv_extracted | ["e", "w", "t", "i", "d"] | arxiv | arxiv | arxiv:math.AG:2510.14352v1 | cross_domain_amplification | |
f | d | urn:hailstone:math:structural_equation[cff360fefd30] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14352v1.eq_305 | \frac{n+1}{d}=m+1\in \mathbb Z | arxiv_extracted | ["f", "a", "d", "r", "n", "c"] | arxiv | arxiv | arxiv:math.AG:2510.14352v1 | cross_domain_amplification | |
x | n | urn:hailstone:math:structural_equation[236d80d577d5] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14010v2.eq_306 | x^n+y^n=z^n | arxiv_extracted | ["n", "z", "y", "x"] | arxiv | arxiv | arxiv:math.AG:2510.14010v2 | cross_domain_amplification | |
p_{n | y | urn:hailstone:math:structural_equation[beb87681e412] | 1 | structural_equation | 4 | arxiv.math.AG.2510.14010v2.eq_307 | p_{n-1}(z^n; x^n, y^n)=0 | arxiv_extracted | ["z", "p_{n", "y", "n", "x"] | arxiv | arxiv | arxiv:math.AG:2510.14010v2 | cross_domain_amplification | |
k | p | urn:hailstone:math:structural_equation[d1c9c33a1daa] | 1 | structural_equation | 4 | arxiv.math.AG.2510.12973v1.eq_308 | [k : k^p] = p | arxiv_extracted | ["p", "k"] | arxiv | arxiv | arxiv:math.AG:2510.12973v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[0d50395a56b4] | 1 | structural_equation | 4 | arxiv.math.AG.2510.12118v1.eq_309 | \mathcal{N} = 4 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.12118v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[78e8a45659fa] | 1 | structural_equation | 4 | arxiv.math.AG.2510.11464v4.eq_310 | \mathcal{Q}_m(n)=\mathbb{F}_q[x_1,\dots,x_n]/(x_1^{q^m},\dots,x_n^{q^m}), | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.11464v4 | cross_domain_amplification | |
w | e | urn:hailstone:math:structural_equation[1ec9b7d929bc] | 1 | structural_equation | 4 | arxiv.math.AG.2510.10430v1.eq_311 | , we have \[ χ_G(X, \mathcal{E}):=\sum_{i=0}^{\dim X}(-1)^i[H^i(X, \mathcal{E})]=\frac{1}{|G|}χ(X,\mathcal{E})[\mathbb{C}[G]] + \sum_ZΓ(\mathcal{E})_Z \] where | arxiv_extracted | ["e", "w", "a", "h", "v"] | arxiv | arxiv | arxiv:math.AG:2510.10430v1 | cross_domain_amplification | |
c_1 | c_2 | urn:hailstone:math:structural_equation[a4885760b67c] | 1 | structural_equation | 4 | arxiv.math.AG.2510.09588v1.eq_312 | c_1^2 = 3c_2 - 72 | arxiv_extracted | ["c_2", "c_1"] | arxiv | arxiv | arxiv:math.AG:2510.09588v1 | cross_domain_amplification | |
w | i | urn:hailstone:math:structural_equation[6b3bfdfdf84f] | 1 | structural_equation | 4 | arxiv.math.AG.2510.09588v1.eq_313 | π_1(\widetilde{X}_n)=1 | arxiv_extracted | ["e", "w", "t", "i", "d"] | arxiv | arxiv | arxiv:math.AG:2510.09588v1 | cross_domain_amplification | |
e | p | urn:hailstone:math:structural_equation[9ac85043c355] | 1 | structural_equation | 4 | arxiv.math.AG.2510.09582v2.eq_314 | \ell = p | arxiv_extracted | ["e", "p", "l"] | arxiv | arxiv | arxiv:math.AG:2510.09582v2 | cross_domain_amplification | |
m | r | urn:hailstone:math:structural_equation[ccec6af3d5ec] | 1 | structural_equation | 4 | arxiv.math.AG.2510.08089v1.eq_315 | \mathfrak{e}(D)=0 | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2510.08089v1 | cross_domain_amplification | |
m | m | urn:hailstone:math:structural_equation[1fe2226bb22a] | 1 | structural_equation | 4 | arxiv.math.AG.2510.07416v2.eq_316 | \mathrm{Cer}(C,e):=[C]^{e} - [-1]_* [C]^e | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:math.AG:2510.07416v2 | cross_domain_amplification | |
A_{c | z | urn:hailstone:math:structural_equation[9255524c4029] | 1 | structural_equation | 4 | arxiv.math.AG.2510.07059v2.eq_317 | A_{c,q}=k[x,y,z]/\big(c(x)z-q(x,y)\big), | arxiv_extracted | ["A_{c", "q", "z", "y", "k", "x"] | arxiv | arxiv | arxiv:math.AG:2510.07059v2 | cross_domain_amplification | |
I | b | urn:hailstone:math:structural_equation[3855806960d8] | 1 | structural_equation | 4 | arxiv.math.AG.2510.05628v1.eq_318 | I_\mathbb{X} = J+K | arxiv_extracted | ["a", "t", "m", "h", "b", "I"] | arxiv | arxiv | arxiv:math.AG:2510.05628v1 | cross_domain_amplification | |
I | b | urn:hailstone:math:structural_equation[38a868364427] | 1 | structural_equation | 4 | arxiv.math.AG.2510.05628v1.eq_319 | I_\mathbb{W} = J + K | arxiv_extracted | ["a", "t", "m", "h", "b", "I"] | arxiv | arxiv | arxiv:math.AG:2510.05628v1 | cross_domain_amplification | |
m | a | urn:hailstone:math:structural_equation[b478aec29a35] | 1 | structural_equation | 4 | arxiv.math.AG.2510.04782v2.eq_320 | \mathcal H = \lim_{m\in\mathbb N}\mathbb Z[q]_{(q^m-1)}^\wedge | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:math.AG:2510.04782v2 | cross_domain_amplification |
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