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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f | t | urn:hailstone:astronomy:structural_equation[8fd2f86d19a5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.04266v1.eq_1221 | f^{\rm orth}_{\rm NL}=-24\pm 86 | arxiv_extracted | ["f", "t", "m", "o", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.04266v1 | cross_domain_amplification | |
f | c | urn:hailstone:astronomy:structural_equation[7ec6f78c3126] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.04266v1.eq_1222 | f^{\rm loc}_{\rm NL}=-0.0\pm 4.1 | arxiv_extracted | ["f", "m", "o", "r", "c", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.04266v1 | cross_domain_amplification | |
k | r | urn:hailstone:astronomy:structural_equation[1a0b595588b7] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03824v1.eq_1223 | k_\mathrm{min} = 0.0015\,h/\mathrm{Mpc} | arxiv_extracted | ["a", "t", "m", "h", "r", "k"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03824v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[b0e9ea4618a6] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03348v1.eq_1224 | α_{\mathrm{dcdm}}=1 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03348v1 | cross_domain_amplification | |
z | f | urn:hailstone:astronomy:structural_equation[68df02f54938] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03231v2.eq_1225 | z_{\rm eff}=0.07 | arxiv_extracted | ["e", "f", "z", "m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03231v2 | cross_domain_amplification | |
f | f | urn:hailstone:astronomy:structural_equation[3b2854859dab] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03231v2.eq_1226 | fσ_8(z_{\rm eff}=0.07) = 0.450 ^{+0.055}_{-0.055} | arxiv_extracted | ["f", "e", "z", "m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03231v2 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[2ee0b3a7c76e] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03231v2.eq_1227 | Ω_\mathrm{m}=0.301^{+0.011}_{-0.011} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03231v2 | cross_domain_amplification | |
f | m | urn:hailstone:astronomy:structural_equation[e27e7d8cc497] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03230v1.eq_1228 | fσ_8(z = 0.07) = 0.4497 \pm 0.0548 | arxiv_extracted | ["f", "p", "m", "z"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03230v1 | cross_domain_amplification | |
r | L | urn:hailstone:astronomy:structural_equation[1cceeb19a411] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03230v1.eq_1229 | γ_{\rm L} = 0.580^{+0.110}_{-0.110} | arxiv_extracted | ["L", "m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03230v1 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[b61f648e575e] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03229v2.eq_1230 | fσ_8 = 0.483_{-0.043}^{+0.080}(\mathrm{stat}) \pm 0.018(\mathrm{sys}) | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03229v2 | cross_domain_amplification | |
f | h | urn:hailstone:astronomy:structural_equation[b412f50254aa] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03229v2.eq_1231 | fσ_8 (z_{\mathrm{eff}}=0.07) = 0.450\pm0.055 | arxiv_extracted | ["f", "z", "a", "t", "m", "h"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03229v2 | cross_domain_amplification | |
f | m | urn:hailstone:astronomy:structural_equation[61bbe4b562da] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03229v2.eq_1232 | (fσ_8 = 0.449 \pm 0.008) | arxiv_extracted | ["f", "p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03229v2 | cross_domain_amplification | |
f | m | urn:hailstone:astronomy:structural_equation[085aef2de2f6] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03228v1.eq_1233 | fσ_8 = 0.450 \pm 0.055 | arxiv_extracted | ["f", "p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03228v1 | cross_domain_amplification | |
l | e | urn:hailstone:astronomy:structural_equation[08af5c873ea0] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.03038v1.eq_1234 | \langle y\rangle = (1.2\pm 2.0) \times 10^{-6} | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.03038v1 | cross_domain_amplification | |
Z | t | urn:hailstone:astronomy:structural_equation[58d4f389c4d1] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.02109v1.eq_1235 | Z/Z_{\odot} = 1.3 \pm 0.7 | arxiv_extracted | ["t", "d", "Z", "o"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.02109v1 | cross_domain_amplification | |
A | m | urn:hailstone:astronomy:structural_equation[27ba0fadf027] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.02109v1.eq_1236 | A_{\rm{V}} = 0.3 \pm 0.3 | arxiv_extracted | ["V", "m", "p", "A", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.02109v1 | cross_domain_amplification | |
w | a | urn:hailstone:astronomy:structural_equation[d02d8c7adc23] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.02067v1.eq_1237 | {Ω_Λ(\widehat{z})/\widehatΩ_Λ}\,=\,\mathscr{O}(1) | arxiv_extracted | ["e", "w", "a", "h", "i", "d"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.02067v1 | cross_domain_amplification | |
l | e | urn:hailstone:astronomy:structural_equation[68ea66ec598f] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.00518v1.eq_1238 | \langle k_\mathrm{B}T \rangle=2.27\substack{+0.15\\-0.11}\thinspace | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.00518v1 | cross_domain_amplification | |
l | e | urn:hailstone:astronomy:structural_equation[e2f9253a1d73] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.00518v1.eq_1239 | \langle Z\rangle=0.19\substack{+0.05\\-0.03}\thinspace Z_\odot | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.00518v1 | cross_domain_amplification | |
R | S_1 | urn:hailstone:astronomy:structural_equation[42dc155401ea] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.00402v1.eq_1240 | R(j_1,j_2)=S_2/S_1 | arxiv_extracted | ["j_1", "j_2", "S_2", "R", "S_1"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.00402v1 | cross_domain_amplification | |
m | r | urn:hailstone:astronomy:structural_equation[d001c8be1f91] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.00402v1.eq_1241 | m_{\mathrm{FDM}}=10^{-22}\,\mathrm{eV} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.00402v1 | cross_domain_amplification | |
l | c_s | urn:hailstone:astronomy:structural_equation[042035638e01] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.22478v2.eq_1242 | \log_{10} c_s^2 = -3.00^{+2.9}_{-0.99} | arxiv_extracted | ["c_s", "l", "g_{10}", "o"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.22478v2 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[f76067f926be] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.22243v3.eq_1243 | σ(f_{\rm NL}^{\rm loc})=34 | arxiv_extracted | ["f", "m", "L", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.22243v3 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[b6f6089a7eb7] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.22243v3.eq_1244 | σ(f_{\rm NL}^{\rm loc})=20 | arxiv_extracted | ["f", "m", "L", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.22243v3 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[b6f6089a7eb7] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.22243v3.eq_1245 | σ(f_{\rm NL}^{\rm loc})=20 | arxiv_extracted | ["f", "m", "L", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.22243v3 | cross_domain_amplification | |
M | r | urn:hailstone:astronomy:structural_equation[498fb819d2ee] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.21824v1.eq_1246 | M_{\mathrm{200c}}=10^7 | arxiv_extracted | ["a", "t", "M", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.21824v1 | cross_domain_amplification | |
l | e | urn:hailstone:astronomy:structural_equation[a232b2d9b55a] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.21634v2.eq_1247 | \langleσ\rangle=0 | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.21634v2 | cross_domain_amplification | |
k | p | urn:hailstone:astronomy:structural_equation[55b767bf8857] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.21289v1.eq_1248 | k=0.55 h{\rm Mpc}^{-1}, z=16.78 | arxiv_extracted | ["M", "m", "h", "p", "r", "k"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.21289v1 | cross_domain_amplification | |
k | p | urn:hailstone:astronomy:structural_equation[5db4622e1147] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.21289v1.eq_1249 | k=0.70 h{\rm Mpc}^{-1}, z=7.05 | arxiv_extracted | ["M", "m", "h", "p", "r", "k"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.21289v1 | cross_domain_amplification | |
m | a | urn:hailstone:astronomy:structural_equation[0b5f19ec6bc7] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.21134v1.eq_1250 | \mathcal{A}=2.0 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.21134v1 | cross_domain_amplification | |
F | n | urn:hailstone:astronomy:structural_equation[fede23d7a362] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.20557v4.eq_1251 | F(R) = R + αR^n | arxiv_extracted | ["n", "R", "F"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.20557v4 | cross_domain_amplification | |
l | r | urn:hailstone:astronomy:structural_equation[f016cde37845] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.20486v1.eq_1252 | \left(ρ+p\right)=l | arxiv_extracted | ["e", "f", "t", "p", "r", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.20486v1 | cross_domain_amplification | |
n | c | urn:hailstone:astronomy:structural_equation[996f4f7f1ff1] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.19615v1.eq_1253 | \nabla\cdot{B}=0 | arxiv_extracted | ["a", "n", "b", "c", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.19615v1 | cross_domain_amplification | |
Y_{Fe | m | urn:hailstone:astronomy:structural_equation[8a066e984bc5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.19603v1.eq_1254 | Y_{Fe,500} = 2.68\pm0.34 | arxiv_extracted | ["p", "m", "Y_{Fe"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.19603v1 | cross_domain_amplification | |
i | i | urn:hailstone:astronomy:structural_equation[c33d6cea0789] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.19386v1.eq_1255 | φ_i, i=\{1,2,3\} | arxiv_extracted | ["i"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.19386v1 | cross_domain_amplification | |
w_{de} | a | urn:hailstone:astronomy:structural_equation[0010e93d091f] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.18657v1.eq_1256 | w_{de}(a) = w_0 + w_b(1-a)^2 | arxiv_extracted | ["w_{de}", "w_0", "a", "w_b"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.18657v1 | cross_domain_amplification | |
w_{de} | a | urn:hailstone:astronomy:structural_equation[1696be62a013] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.18657v1.eq_1257 | w_{de}(a) = w_0 + w_c(1-a)^3 | arxiv_extracted | ["w_{de}", "w_0", "w_c", "a"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.18657v1 | cross_domain_amplification | |
z | r | urn:hailstone:astronomy:structural_equation[a3d9f1ffd346] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.18478v1.eq_1258 | z_{\mathrm{max}} = 1 | arxiv_extracted | ["z", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.18478v1 | cross_domain_amplification | |
z | r | urn:hailstone:astronomy:structural_equation[ca93c154d28e] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.18478v1.eq_1259 | z_{\mathrm{max}}=1 | arxiv_extracted | ["z", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.18478v1 | cross_domain_amplification | |
S_8 | v | urn:hailstone:astronomy:structural_equation[fa8e1b5610db] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.18134v2.eq_1260 | S_8\equivσ_8\sqrt{Ω_m/0.3}=0.805\pm{0.018} | arxiv_extracted | ["e", "q", "S_8", "i", "u", "v"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.18134v2 | cross_domain_amplification | |
g_{p} | i | urn:hailstone:astronomy:structural_equation[cdba396c162e] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.17998v1.eq_1261 | Δg_{p}/g_{p} = (-4.3\pm2.5)\times10^{-5} | arxiv_extracted | ["g_{p}", "t", "m", "i", "p"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.17998v1 | cross_domain_amplification | |
p | e | urn:hailstone:astronomy:structural_equation[c1ff315fb990] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.17998v1.eq_1262 | Δ(μα^{2})/(μα^{2}) = (2.0\pm1.2)\times10^{-5} | arxiv_extracted | ["e", "t", "m", "i", "p"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.17998v1 | cross_domain_amplification | |
g_{p} | i | urn:hailstone:astronomy:structural_equation[8576445847fd] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.17998v1.eq_1263 | Δ(μα^{2}g_{p}^{0.64})/(μα^{2}g_{p}^{0.64}) = (-4.7\pm1.9)\times10^{-6} | arxiv_extracted | ["g_{p}", "t", "m", "i", "p"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.17998v1 | cross_domain_amplification | |
c | m | urn:hailstone:astronomy:structural_equation[c7a8721c7e07] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.16487v2.eq_1264 | Ω_c h^2 = 0.120\pm 0.001 | arxiv_extracted | ["p", "c", "m", "h"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.16487v2 | cross_domain_amplification | |
Z_{ICM} | e | urn:hailstone:astronomy:structural_equation[fa19048eb5a1] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.16448v1.eq_1265 | Z_{ICM} = -0.08^{+0.07}_{-0.07}\, log\left(\frac{M_*}{M_{gas}}\right) + 0.30^{+0.06}_{-0.06} | arxiv_extracted | ["e", "g", "o", "Z_{ICM}", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.16448v1 | cross_domain_amplification | |
c_s | p | urn:hailstone:astronomy:structural_equation[02927189f8c4] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.00056v3.eq_1266 | c_s^2 = κ/\varepsilon | arxiv_extracted | ["e", "a", "c_s", "p", "r", "v"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.00056v3 | cross_domain_amplification | |
w | z | urn:hailstone:astronomy:structural_equation[04ef6137a051] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2512.00056v3.eq_1267 | w(z) = w_0 + w_a z/(1+z) | arxiv_extracted | ["w", "z", "w_0", "w_a"] | arxiv | arxiv | arxiv:astro-ph.CO:2512.00056v3 | cross_domain_amplification | |
f | T | urn:hailstone:astronomy:structural_equation[240553b94e93] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.16304v2.eq_1268 | f(R,T)=R+αT | arxiv_extracted | ["f", "T", "R"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.16304v2 | cross_domain_amplification | |
n_{0} | m | urn:hailstone:astronomy:structural_equation[637ddc9fcab9] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.15828v1.eq_1269 | μ_{0}n_{0}(α=-0.0002)=-2.2_{-0.7}^{+1.0}\,\,GeV/m^{3} | arxiv_extracted | ["e", "V", "m", "G", "n_{0}"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.15828v1 | cross_domain_amplification | |
V | r | urn:hailstone:astronomy:structural_equation[83ea5a92e1e5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.15815v4.eq_1270 | V(z^i, \bar z^{\bar i})=e^K (|DW|^2 - 3 |W|^2) | arxiv_extracted | ["V", "z", "a", "i", "r", "b"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.15815v4 | cross_domain_amplification | |
Z | i | urn:hailstone:astronomy:structural_equation[256849ed87f8] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.15809v1.eq_1271 | Z_{\rm init}=0.001 | arxiv_extracted | ["Z", "m", "i", "r", "n"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.15809v1 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[83716a98ba37] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.15701v2.eq_1272 | f_{\mathrm{NL}}^{\mathrm{loc}}=-180^{+61}_{-86} | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.15701v2 | cross_domain_amplification | |
f | f | urn:hailstone:astronomy:structural_equation[f97373d1e0d9] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.15127v4.eq_1273 | f^{}_μ= f^{}_τ | arxiv_extracted | ["f"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.15127v4 | cross_domain_amplification | |
N | d | urn:hailstone:astronomy:structural_equation[af2bb7c76e47] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.14572v2.eq_1274 | N_{\rm side}=64 | arxiv_extracted | ["m", "i", "r", "s", "d", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.14572v2 | cross_domain_amplification | |
H_{0} | m | urn:hailstone:astronomy:structural_equation[e6b627803df8] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.14332v2.eq_1275 | H_{0} = 75.27 \pm 1.18 | arxiv_extracted | ["H_{0}", "p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.14332v2 | cross_domain_amplification | |
H_{0} | m | urn:hailstone:astronomy:structural_equation[495f047d334d] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.14332v2.eq_1276 | H_{0} = 71.25 \pm 1.59 | arxiv_extracted | ["H_{0}", "p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.14332v2 | cross_domain_amplification | |
H_{0} | m | urn:hailstone:astronomy:structural_equation[ad3acc69e9d1] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.14332v2.eq_1277 | H_{0} = 73.78 \pm 2.17 | arxiv_extracted | ["H_{0}", "p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.14332v2 | cross_domain_amplification | |
N | w | urn:hailstone:astronomy:structural_equation[cd3961f5dbbf] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.12334v1.eq_1278 | N_{\rm gw}=40 | arxiv_extracted | ["g", "w", "m", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.12334v1 | cross_domain_amplification | |
N | w | urn:hailstone:astronomy:structural_equation[a64b06fd34d5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.12334v1.eq_1279 | N_{\rm gw}=100 | arxiv_extracted | ["g", "w", "m", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.12334v1 | cross_domain_amplification | |
N | w | urn:hailstone:astronomy:structural_equation[cd3961f5dbbf] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.12334v1.eq_1280 | N_{\rm gw}=40 | arxiv_extracted | ["g", "w", "m", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.12334v1 | cross_domain_amplification | |
r | m | urn:hailstone:astronomy:structural_equation[f1c6a857db86] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.12017v3.eq_1281 | Ω_{\rm m}=0.320^{+0.015}_{-0.012} | arxiv_extracted | ["m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.12017v3 | cross_domain_amplification | |
H | s | urn:hailstone:astronomy:structural_equation[ee00c1fa5257] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.11795v1.eq_1282 | H(0.44) = 92.3_{-36.6}^{+29.9}\rm\, km s^{-1} Mpc^{-1} | arxiv_extracted | ["m", "H", "r", "s", "k"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.11795v1 | cross_domain_amplification | |
M_{200} | i | urn:hailstone:astronomy:structural_equation[63c84d232257] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10968v1.eq_1283 | M_{200}^{\rm main}=2.68_{-0.92}^{+1.11}\times 10^{14}\,h_{70}^{-1}M_\odot | arxiv_extracted | ["a", "m", "i", "r", "M_{200}"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10968v1 | cross_domain_amplification | |
M_{200} | b | urn:hailstone:astronomy:structural_equation[d2b9bf962394] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10968v1.eq_1284 | M_{200}^{\rm sub}=0.46_{-0.22}^{+0.38}\times 10^{14}\,h_{70}^{-1}M_\odot | arxiv_extracted | ["m", "u", "r", "M_{200}", "s", "b"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10968v1 | cross_domain_amplification | |
s | m | urn:hailstone:astronomy:structural_equation[819767b98211] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10765v1.eq_1285 | \sigmam = 1 \cmg | arxiv_extracted | ["g", "a", "m", "i", "s"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10765v1 | cross_domain_amplification | |
l | r | urn:hailstone:astronomy:structural_equation[21d0b37ef567] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10631v3.eq_1286 | \ln B = -0.57{\scriptstyle\pm0.26} | arxiv_extracted | ["B", "r", "s", "n", "c", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10631v3 | cross_domain_amplification | |
l | r | urn:hailstone:astronomy:structural_equation[e830a01e7f37] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10631v3.eq_1287 | \ln B = -0.30{\scriptstyle\pm0.19} | arxiv_extracted | ["B", "r", "s", "n", "c", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10631v3 | cross_domain_amplification | |
A | r | urn:hailstone:astronomy:structural_equation[1a30acc8c7f8] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10620v2.eq_1288 | A_\textrm{lens} = 1.045 \pm 0.063 | arxiv_extracted | ["e", "t", "A", "r", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10620v2 | cross_domain_amplification | |
V | n | urn:hailstone:astronomy:structural_equation[fd4d21dc4ca4] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10317v2.eq_1289 | V(φ) = V_{0}e^{-λφ} + V_{1}φ^{n} | arxiv_extracted | ["e", "V", "V_{0}", "V_{1}", "n"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10317v2 | cross_domain_amplification | |
t | e | urn:hailstone:astronomy:structural_equation[f20e039ab827] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10317v2.eq_1290 | χ^2_{\text{red}} = 0.989 | arxiv_extracted | ["t", "r", "e", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10317v2 | cross_domain_amplification | |
t | I | urn:hailstone:astronomy:structural_equation[c74bd5780f2d] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10317v2.eq_1291 | Δ\text{BIC} = 2.178 | arxiv_extracted | ["e", "B", "t", "x", "I"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10317v2 | cross_domain_amplification | |
g | e | urn:hailstone:astronomy:structural_equation[0c7c542cde05] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10288v1.eq_1292 | g^\prime=0.5 | arxiv_extracted | ["e", "g", "m", "i", "p", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10288v1 | cross_domain_amplification | |
t | f | urn:hailstone:astronomy:structural_equation[45e8e0b78c26] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10263v1.eq_1293 | Ω_{\text{eff}} = 0.009^{+0.006}_{-0.007} | arxiv_extracted | ["t", "f", "e", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10263v1 | cross_domain_amplification | |
t | I | urn:hailstone:astronomy:structural_equation[55faff88b839] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10263v1.eq_1294 | Δ\text{AIC} = +2.6 | arxiv_extracted | ["e", "x", "t", "A", "I"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10263v1 | cross_domain_amplification | |
T | c | urn:hailstone:astronomy:structural_equation[bdc3f4a54e32] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.10024v1.eq_1295 | Υ(φ, T) = C_1 \frac{T^3}{M_{\text{Pl}}^2} + C_2 \frac{T^3}{φ^2}. | arxiv_extracted | ["f", "a", "C_1", "r", "c", "T"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.10024v1 | cross_domain_amplification | |
l | s | urn:hailstone:astronomy:structural_equation[93a5b7a284eb] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.08685v4.eq_1296 | \log(M_\ast / M_\odot) = a \log(V_{\rm circ,f} / 150~\mathrm{km\,s^{-1}}) + b | arxiv_extracted | ["g", "a", "M", "o", "s", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.08685v4 | cross_domain_amplification | |
l | s | urn:hailstone:astronomy:structural_equation[40d7fe95a984] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.08685v4.eq_1297 | \log(j_\ast / \mathrm{kpc\,km\,s^{-1}}) = a \log(M_\ast / 10^{10.5} M_\odot) + b | arxiv_extracted | ["g", "a", "j", "o", "s", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.08685v4 | cross_domain_amplification | |
f | a | urn:hailstone:astronomy:structural_equation[1f951acffcdb] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.08685v4.eq_1298 | f_{\rm M}=M_\ast/M_{\rm vir} | arxiv_extracted | ["f", "a", "M", "m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.08685v4 | cross_domain_amplification | |
f | a | urn:hailstone:astronomy:structural_equation[70e98f8f3c92] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.08685v4.eq_1299 | f_{\rm j}=j_\ast/j_{\rm vir} | arxiv_extracted | ["f", "a", "m", "j", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.08685v4 | cross_domain_amplification | |
m | t | urn:hailstone:astronomy:structural_equation[80a7b6cd50c8] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.07765v3.eq_1300 | m=1, m=3, \text{ and } m=4 | arxiv_extracted | ["t", "m", "e", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.07765v3 | cross_domain_amplification | |
r | m | urn:hailstone:astronomy:structural_equation[78a09f5f24e4] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.07517v3.eq_1301 | Ω_{\rm m} = 0.330 \pm 0.015 | arxiv_extracted | ["p", "m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.07517v3 | cross_domain_amplification | |
N | N | urn:hailstone:astronomy:structural_equation[6383603ded44] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.06210v1.eq_1302 | N_{\rm DM}:N_{\rm gas} = Ω_{\rm cdm} / Ω_{\rm b} | arxiv_extracted | ["D", "M", "m", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.06210v1 | cross_domain_amplification | |
l | m | urn:hailstone:astronomy:structural_equation[f7b5aaf96f02] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.04748v2.eq_1303 | \log f_{\rm sub} = -2.44^{+0.61}_{-0.86} | arxiv_extracted | ["f", "g", "m", "o", "r", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.04748v2 | cross_domain_amplification | |
F | n | urn:hailstone:astronomy:structural_equation[fff25b8e6df3] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.04610v2.eq_1304 | F(Φ) = 1+ξΦ^{2}e^{nΦ} | arxiv_extracted | ["e", "n", "F"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.04610v2 | cross_domain_amplification | |
U | b | urn:hailstone:astronomy:structural_equation[645953735960] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.04610v2.eq_1305 | U(Φ) = U_{0}+ae^{bΦ^{2}} | arxiv_extracted | ["e", "a", "U", "b", "U_{0}"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.04610v2 | cross_domain_amplification | |
l | c | urn:hailstone:astronomy:structural_equation[0d5f2d7cdd9c] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.03919v1.eq_1306 | (l, b) = (308.4^\circ \pm 2.4^\circ, 29.0^\circ \pm 1.9^\circ) | arxiv_extracted | ["i", "r", "b", "c", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.03919v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[b397653a191f] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.03288v2.eq_1307 | {Ω_{\mathrm{m},0}=0.272} | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.03288v2 | cross_domain_amplification | |
r | z | urn:hailstone:astronomy:structural_equation[882d95b6e822] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.03262v1.eq_1308 | {\rm z} = 1 | arxiv_extracted | ["m", "r", "z"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.03262v1 | cross_domain_amplification | |
C | e | urn:hailstone:astronomy:structural_equation[8fbbd771b2be] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02375v2.eq_1309 | C_{\ell} = A({1000}/{\ell})^β | arxiv_extracted | ["e", "A", "l", "C"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02375v2 | cross_domain_amplification | |
C | e | urn:hailstone:astronomy:structural_equation[b69014712850] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02375v2.eq_1310 | C_{\ell} = A{ν^{-2α}}{\ell^{-β}} | arxiv_extracted | ["e", "A", "l", "C"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02375v2 | cross_domain_amplification | |
t | s | urn:hailstone:astronomy:structural_equation[ca769dc78aef] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02375v2.eq_1311 | t_\text{syn} = 106\,{\pm}\,1 | arxiv_extracted | ["t", "s", "e", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02375v2 | cross_domain_amplification | |
M_{200c | p | urn:hailstone:astronomy:structural_equation[a1c1c233ffdd] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02323v2.eq_1312 | M_{200c,main} = 2.91 \pm 0.72 \times 10^{14}\ M_\odot | arxiv_extracted | ["a", "m", "M_{200c", "i", "p", "n"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02323v2 | cross_domain_amplification | |
M_{200c | i | urn:hailstone:astronomy:structural_equation[f9658cb22817] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02323v2.eq_1313 | M_{200c,S} = 1.23 \pm 0.52 \times 10^{14}\ M_\odot | arxiv_extracted | ["t", "m", "M_{200c", "S", "i", "p"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02323v2 | cross_domain_amplification | |
z | t | urn:hailstone:astronomy:structural_equation[22d33dbf329f] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02220v1.eq_1314 | z_{\rm wt}=0.464^{+0.235}_{-0.120} | arxiv_extracted | ["w", "z", "t", "m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02220v1 | cross_domain_amplification | |
m | a | urn:hailstone:astronomy:structural_equation[a668cf8e227e] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02155v1.eq_1315 | \mathcal{A}=2.26 \pm 0.56 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02155v1 | cross_domain_amplification | |
m | a | urn:hailstone:astronomy:structural_equation[bec1f1a61e0a] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02155v1.eq_1316 | \mathcal{A}=1.38 \pm 0.92 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02155v1 | cross_domain_amplification | |
m | a | urn:hailstone:astronomy:structural_equation[c5cc010d4321] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.02155v1.eq_1317 | \mathcal{A}=1 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.02155v1 | cross_domain_amplification | |
s | l | urn:hailstone:astronomy:structural_equation[81215d1305bd] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.01967v1.eq_1318 | \sum \tilde{m}_ν=-0.018^{+0.085}_{-0.089}~\text{eV}~(68\% ~\text{C.L.}) | arxiv_extracted | ["t", "m", "i", "u", "s", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.01967v1 | cross_domain_amplification | |
w_0 | d | urn:hailstone:astronomy:structural_equation[1639bb307a56] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.01700v1.eq_1319 | w_0 = w(\tilde H = 1) | arxiv_extracted | ["w", "t", "i", "d", "w_0", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.01700v1 | cross_domain_amplification | |
r | t | urn:hailstone:astronomy:structural_equation[8b3edcbec86f] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2511.01195v1.eq_1320 | μ_{\rm host}=5.03\pm 0.02 | arxiv_extracted | ["t", "m", "h", "o", "r", "s"] | arxiv | arxiv | arxiv:astro-ph.CO:2511.01195v1 | cross_domain_amplification |
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