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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
l | l | urn:hailstone:ml_ai:structural_equation[6d6db003f343] | 1 | structural_equation | 0 | arxiv.cs.IT.2508.06940v1.eq_821 | \log \|T_ρf\|_q \leq \mathbb{E}_{S} \log \|\mathbb{E}(f|S)\|_q\;. | arxiv_extracted | ["g", "q", "T_\u03c1f", "o", "l"] | arxiv | arxiv | arxiv:cs.IT:2508.06940v1 | cross_domain_amplification | |
n | I | urn:hailstone:ml_ai:structural_equation[e08346844f66] | 1 | structural_equation | 0 | arxiv.cs.IT.2508.06219v1.eq_822 | [n^I = k^I + r^I,\, k^I] | arxiv_extracted | ["n", "r", "k", "I"] | arxiv | arxiv | arxiv:cs.IT:2508.06219v1 | cross_domain_amplification | |
n | F | urn:hailstone:ml_ai:structural_equation[7bfd5da0bea7] | 1 | structural_equation | 0 | arxiv.cs.IT.2508.06219v1.eq_823 | [n^F = λk^I + r^F,\, k^F = λk^I] | arxiv_extracted | ["F", "r", "n", "k", "I"] | arxiv | arxiv | arxiv:cs.IT:2508.06219v1 | cross_domain_amplification | |
v | s | urn:hailstone:ml_ai:structural_equation[37d088bc4853] | 1 | structural_equation | 0 | arxiv.cs.IT.2508.00183v1.eq_824 | \varepsilon = 0.1 | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cs.IT:2508.00183v1 | cross_domain_amplification | |
m | a | urn:hailstone:ml_ai:structural_equation[e4e685350dda] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.23180v1.eq_825 | \{\mathcal{C}_i\}_{i=1}^{\infty} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:cs.IT:2507.23180v1 | cross_domain_amplification | |
g | q | urn:hailstone:ml_ai:structural_equation[80d971304783] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.23179v2.eq_826 | \gcd(φ(p^s),φ(q^t))=2 | arxiv_extracted | ["g", "q", "p", "c", "s", "d"] | arxiv | arxiv | arxiv:cs.IT:2507.23179v2 | cross_domain_amplification | |
m | m | urn:hailstone:ml_ai:structural_equation[9a411d0fc123] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.23179v2.eq_827 | \mathrm{ord}_{p^s}(l)=φ(p^s)/2 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:cs.IT:2507.23179v2 | cross_domain_amplification | |
G | q | urn:hailstone:ml_ai:structural_equation[fd5237b416b5] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.21623v1.eq_828 | (|G|,q)=1 | arxiv_extracted | ["G", "q"] | arxiv | arxiv | arxiv:cs.IT:2507.21623v1 | cross_domain_amplification | |
X | n | urn:hailstone:ml_ai:structural_equation[6b5e4703b475] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.19338v1.eq_829 | (X,U)=\{(X_t,U_t)\}_{t=1}^n | arxiv_extracted | ["t", "n", "X", "U_t", "X_t", "U"] | arxiv | arxiv | arxiv:cs.IT:2507.19338v1 | cross_domain_amplification | |
m | x | urn:hailstone:ml_ai:structural_equation[4f7ac4e41caa] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.19338v1.eq_830 | \max_x P(X=x) | arxiv_extracted | ["a", "m", "P", "X", "x_x", "x"] | arxiv | arxiv | arxiv:cs.IT:2507.19338v1 | cross_domain_amplification | |
n | t | urn:hailstone:ml_ai:structural_equation[28eba46f9878] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.16694v1.eq_831 | σ\not=1 | arxiv_extracted | ["t", "n", "o"] | arxiv | arxiv | arxiv:cs.IT:2507.16694v1 | cross_domain_amplification | |
A | c | urn:hailstone:ml_ai:structural_equation[8f4f64ab44c4] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.15196v5.eq_832 | A+_GA:=\{x+y\colon (x, y)\in G\} | arxiv_extracted | ["G", "y", "A", "c", "x"] | arxiv | arxiv | arxiv:cs.IT:2507.15196v5 | cross_domain_amplification | |
G | c | urn:hailstone:ml_ai:structural_equation[e5b54b1c06c2] | 1 | structural_equation | 0 | arxiv.cs.IT.2507.15196v5.eq_833 | φ_G(A,A):=\{φ(x, y)\colon (x, y)\in G\} | arxiv_extracted | ["G", "y", "A", "c", "x"] | arxiv | arxiv | arxiv:cs.IT:2507.15196v5 | cross_domain_amplification | |
S_8 | v | urn:hailstone:astronomy:structural_equation[dec2b1a753d3] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.13543v1.eq_834 | S_8 \equiv σ_8 \sqrt{Ω_{\rm m}/0.3} = 0.891^{+0.057}_{-0.084} | arxiv_extracted | ["e", "q", "S_8", "i", "u", "v"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.13543v1 | cross_domain_amplification | |
k_{0} | c | urn:hailstone:astronomy:structural_equation[1a7fe46cf847] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.13016v1.eq_835 | k_{0} = 0.01\,{\rm Mpc}^{-1} | arxiv_extracted | ["M", "m", "p", "r", "k_{0}", "c"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.13016v1 | cross_domain_amplification | |
f | z | urn:hailstone:astronomy:structural_equation[83e8a2821f3b] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.12482v1.eq_836 | \fRz = 10^{-5} | arxiv_extracted | ["f", "R", "z"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.12482v1 | cross_domain_amplification | |
l | m | urn:hailstone:astronomy:structural_equation[67d5363905ed] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.11600v1.eq_837 | \log_{10}(m_φ/{\rm eV})=-19.20^{+0.12}_{-0.11} | arxiv_extracted | ["m", "o", "m_\u03c6", "r", "l", "g_{10}"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.11600v1 | cross_domain_amplification | |
f_b | t | urn:hailstone:astronomy:structural_equation[97029aac1e28] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.11083v2.eq_838 | f_b(10^{13}\,M_\odot, z=0.1)/(Ω_b/Ω_m) = 0.10^{+0.09}_{-0.05} | arxiv_extracted | ["t", "M", "o", "f_b", "d"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.11083v2 | cross_domain_amplification | |
r | r | urn:hailstone:astronomy:structural_equation[387bc86bc3a9] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.08907v1.eq_839 | r_\mathrm{v} = 4.7 \pm 2.1 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.08907v1 | cross_domain_amplification | |
g | s | urn:hailstone:astronomy:structural_equation[802536b79a19] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.06659v1.eq_840 | {g}_{\rm obs}=ν(|{g}_{\rm bar}|){g}_{\rm bar} | arxiv_extracted | ["g", "m", "o", "r", "s", "b"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.06659v1 | cross_domain_amplification | |
t | e | urn:hailstone:astronomy:structural_equation[41f84fe8c7ec] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.05310v1.eq_841 | ω_{\text{re}}=0.33^{+0.14}_{-0.36} | arxiv_extracted | ["t", "r", "e", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.05310v1 | cross_domain_amplification | |
p | i | urn:hailstone:astronomy:structural_equation[0698f3cf17b2] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.05122v1.eq_842 | Ω_{\phi0}=0.685 | arxiv_extracted | ["p", "h", "i"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.05122v1 | cross_domain_amplification | |
R_{1 | m | urn:hailstone:astronomy:structural_equation[dfb44b3f36d2] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.03905v1.eq_843 | R_{1/2}=5.4\pm 2.7 | arxiv_extracted | ["p", "m", "R_{1"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.03905v1 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[c9c0985bf3a2] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.03783v1.eq_844 | f_\mathrm{NL}^\mathrm{local}=43 \pm 23 | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.03783v1 | cross_domain_amplification | |
v | m | urn:hailstone:astronomy:structural_equation[256892a4b0b5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.03004v1.eq_845 | v_{\odot} = 307.26^{+32.00}_{-22.28},\mathrm{km \, s^{-1}} | arxiv_extracted | ["t", "m", "o", "d", "v"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.03004v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[dbde72605e42] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.03004v1.eq_846 | (\mathrm{RA},\mathrm{DEC}) = (156.40^{+4.72}_{-4.71}, -3.38^{+5.54}_{-8.23})^\circ | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.03004v1 | cross_domain_amplification | |
h | m | urn:hailstone:astronomy:structural_equation[51397716e55b] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.02428v1.eq_847 | h^R_0=0.730\pm0.010 | arxiv_extracted | ["p", "m", "R_0", "h"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.02428v1 | cross_domain_amplification | |
h | m | urn:hailstone:astronomy:structural_equation[d1bd52545d26] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.02428v1.eq_848 | h^P_0=0.674\pm 0.005 | arxiv_extracted | ["p", "m", "h", "P_0"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.02428v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[e0088de37d3c] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.01994v1.eq_849 | δ_\mathrm{e,v} = -0.58 \pm 0.30 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.01994v1 | cross_domain_amplification | |
r | m | urn:hailstone:astronomy:structural_equation[ecf3c97dc186] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.01990v1.eq_850 | Ω_{\rm b}h^2=0.02236\pm0.00090 | arxiv_extracted | ["m", "h", "p", "r", "b"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.01990v1 | cross_domain_amplification | |
r | t | urn:hailstone:astronomy:structural_equation[52b4abf62398] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.01990v1.eq_851 | σ_{\rm host}=0.794^{+0.064}_{-0.067} | arxiv_extracted | ["t", "m", "h", "o", "r", "s"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.01990v1 | cross_domain_amplification | |
r | m | urn:hailstone:astronomy:structural_equation[dddd59a6f20c] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.01990v1.eq_852 | Ω_{\rm b}h^2=0.02248\pm0.00018 | arxiv_extracted | ["m", "h", "p", "r", "b"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.01990v1 | cross_domain_amplification | |
r | t | urn:hailstone:astronomy:structural_equation[d99b373b31b2] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.01990v1.eq_853 | σ_{\rm host}=0.711^{+0.024}_{-0.025} | arxiv_extracted | ["t", "m", "h", "o", "r", "s"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.01990v1 | cross_domain_amplification | |
r | P | urn:hailstone:astronomy:structural_equation[a19cdeb4cba5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.01963v1.eq_854 | θ_{\rm AP} = 2 | arxiv_extracted | ["A", "m", "r", "P"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.01963v1 | cross_domain_amplification | |
A | L | urn:hailstone:astronomy:structural_equation[24659f448938] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.01946v1.eq_855 | A_{\rm{L}}=1.0656_{-0.0303}^{+0.0304} | arxiv_extracted | ["L", "m", "A", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.01946v1 | cross_domain_amplification | |
A | L | urn:hailstone:astronomy:structural_equation[4cdbf31cf53d] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.01946v1.eq_856 | A_{\rm{L}}=1.0795_{-0.0289}^{+0.0260} | arxiv_extracted | ["L", "m", "A", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.01946v1 | cross_domain_amplification | |
N | r | urn:hailstone:astronomy:structural_equation[a6f2ade83f14] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00821v1.eq_857 | N_{\rm part} = 1024^3 | arxiv_extracted | ["a", "m", "p", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00821v1 | cross_domain_amplification | |
m | r | urn:hailstone:astronomy:structural_equation[ab189dba2dd8] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00821v1.eq_858 | m_{\rm part} = 2.08\times10^{10}M_\odot | arxiv_extracted | ["p", "m", "r", "a"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00821v1 | cross_domain_amplification | |
e | l | urn:hailstone:astronomy:structural_equation[46bc910f5ae0] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00821v1.eq_859 | \ell = 5000 | arxiv_extracted | ["e", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00821v1 | cross_domain_amplification | |
N | r | urn:hailstone:astronomy:structural_equation[b0ee51f35977] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00821v1.eq_860 | N_{\rm part} = 2048^3 | arxiv_extracted | ["a", "m", "p", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00821v1 | cross_domain_amplification | |
m | r | urn:hailstone:astronomy:structural_equation[e2fbbe4ee408] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00821v1.eq_861 | m_{\rm part} = 2.60\times10^{9}M_\odot | arxiv_extracted | ["p", "m", "r", "a"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00821v1 | cross_domain_amplification | |
r | O | urn:hailstone:astronomy:structural_equation[395f84f02db3] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00450v1.eq_862 | r_{\rm{BAO}}^{\rm{real}} = 132\pm 8\,h^{-1}\,{\rm Mpc} | arxiv_extracted | ["B", "O", "m", "A", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00450v1 | cross_domain_amplification | |
r | O | urn:hailstone:astronomy:structural_equation[7cd401dfa899] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00450v1.eq_863 | r_{\rm{BAO}}^{z} = 139 \pm 7\,h^{-1}\,{\rm Mpc} | arxiv_extracted | ["B", "O", "m", "A", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00450v1 | cross_domain_amplification | |
f | m | urn:hailstone:astronomy:structural_equation[2771b5930be2] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00450v1.eq_864 | fσ_8 = 0.344 \pm 0.105 | arxiv_extracted | ["f", "p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00450v1 | cross_domain_amplification | |
r | m | urn:hailstone:astronomy:structural_equation[7bb399f17a76] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00122v1.eq_865 | _{\rm P}=(1.15^{+0.24}_{-0.21})\times10^{-4} | arxiv_extracted | ["t", "m", "P", "i", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00122v1 | cross_domain_amplification | |
y | t | urn:hailstone:astronomy:structural_equation[5755ea197f3b] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00122v1.eq_866 | y/Z_{\odot}=2.12^{+0.31}_{-0.29} | arxiv_extracted | ["Z", "t", "y", "o", "d"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00122v1 | cross_domain_amplification | |
n | l | urn:hailstone:astronomy:structural_equation[9d3594c3ae8a] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2605.00105v2.eq_867 | n_{\rm gal}=30 | arxiv_extracted | ["g", "a", "m", "r", "n", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2605.00105v2 | cross_domain_amplification | |
a_B | H_0 | urn:hailstone:astronomy:structural_equation[11c45758f7e1] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.28013v1.eq_868 | -5a_B=M_B+5\lg (c/H_0/\mathrm{Mpc})+25 | arxiv_extracted | ["g", "a_B", "M_B", "H_0", "c", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.28013v1 | cross_domain_amplification | |
w | r | urn:hailstone:astronomy:structural_equation[a2a7c6801a9f] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.25373v1.eq_869 | w_\mathrm{de} = w_0 + w_a(1-a) | arxiv_extracted | ["w", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.25373v1 | cross_domain_amplification | |
k | x | urn:hailstone:astronomy:structural_equation[936c51fbc347] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.25171v2.eq_870 | k_{\rm max}=0.20\,h\,\mathrm{Mpc}^{-1} | arxiv_extracted | ["a", "m", "r", "k", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.25171v2 | cross_domain_amplification | |
r | r | urn:hailstone:astronomy:structural_equation[c01e2a21e0f5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.24144v2.eq_871 | Δ^{2}_{\rm UL}(k) = (173.13)^{2}\,{\rm mK^{2}} | arxiv_extracted | ["m", "L", "r", "U", "k"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.24144v2 | cross_domain_amplification | |
r | r | urn:hailstone:astronomy:structural_equation[d62d6e6af96d] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.24144v2.eq_872 | Δ_{\rm UL}^2(k)=(98.67)^{2}\,{\rm mK}^{2} | arxiv_extracted | ["m", "L", "r", "U", "k"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.24144v2 | cross_domain_amplification | |
l | m | urn:hailstone:astronomy:structural_equation[c1b3a403ebb2] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.23631v1.eq_873 | \log_{10}|f_R| = -4.7 \pm 1.2 | arxiv_extracted | ["m", "o", "p", "f_R", "l", "g_{10}"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.23631v1 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[5814ca267c7a] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.22961v1.eq_874 | f_{\mathrm{PBH}}=1 | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.22961v1 | cross_domain_amplification | |
m | r | urn:hailstone:astronomy:structural_equation[6bbca2fab071] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.22961v1.eq_875 | m_{\mathrm{PBH}} = 10^3 M_\odot | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.22961v1 | cross_domain_amplification | |
a | l | urn:hailstone:astronomy:structural_equation[3f58f7c9000d] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.22460v1.eq_876 | , a metallicity of 12+log(O/H) = 7.84 | arxiv_extracted | ["e", "a", "t", "m", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.22460v1 | cross_domain_amplification | |
l | c | urn:hailstone:astronomy:structural_equation[0ae04a13cd98] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.21790v1.eq_877 | \left(b_φ = 2δ_c\left(b_1 - 1\right)\right) | arxiv_extracted | ["e", "f", "t", "b_\u03c6", "c", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.21790v1 | cross_domain_amplification | |
r | h | urn:hailstone:astronomy:structural_equation[3007661fb1de] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.19449v2.eq_878 | Ω_{\rm m}h^2=0.146^{+0.009}_{-0.009} | arxiv_extracted | ["m", "r", "h"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.19449v2 | cross_domain_amplification | |
h | b_2} | urn:hailstone:astronomy:structural_equation[bfc71ecad978] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.18861v1.eq_879 | h(χ) = γe^{b_1χ}χ^{b_2} | arxiv_extracted | ["e", "b_1\u03c7}", "b_2}", "h"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.18861v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[acadb094cb99] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.17682v1.eq_880 | Ω_{m0} = 0.292 \pm 0.008 | arxiv_extracted | ["p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.17682v1 | cross_domain_amplification | |
z | a | urn:hailstone:astronomy:structural_equation[76ce8bd07611] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.17660v1.eq_881 | z_{\rm peak} = 2.600^{+0.114}_{-0.087} | arxiv_extracted | ["e", "z", "a", "m", "p", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.17660v1 | cross_domain_amplification | |
t | m | urn:hailstone:astronomy:structural_equation[ad4d11865342] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.16600v1.eq_882 | 10^5\times\mathrm{D/H} = 2.442\pm0.040 | arxiv_extracted | ["e", "t", "m", "i", "s"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.16600v1 | cross_domain_amplification | |
l | a | urn:hailstone:astronomy:structural_equation[e89a06363d6e] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.15287v1.eq_883 | \log_{10}G_{\mathrm{eff}} = -1.77 | arxiv_extracted | ["a", "m", "G", "o", "l", "g_{10}"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.15287v1 | cross_domain_amplification | |
l | a | urn:hailstone:astronomy:structural_equation[045e17fef74b] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.15287v1.eq_884 | \log_{10}G_{\mathrm{eff}} = -5 | arxiv_extracted | ["a", "m", "G", "o", "l", "g_{10}"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.15287v1 | cross_domain_amplification | |
l | m | urn:hailstone:astronomy:structural_equation[746f17933a49] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.15287v1.eq_885 | \log_{10}G_{\rm eff} = -6 | arxiv_extracted | ["G", "m", "o", "r", "l", "g_{10}"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.15287v1 | cross_domain_amplification | |
r | t | urn:hailstone:astronomy:structural_equation[e95cbe890460] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.14145v1.eq_886 | λ_{\rm int}=1.12^{+0.05}_{-0.06} | arxiv_extracted | ["t", "m", "i", "r", "n"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.14145v1 | cross_domain_amplification | |
r | n | urn:hailstone:astronomy:structural_equation[7175ff99ad68] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.13718v1.eq_887 | τ_{reion} = 0.0581^{+0.0105}_{-0.0096} | arxiv_extracted | ["e", "o", "i", "r", "n"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.13718v1 | cross_domain_amplification | |
g | G | urn:hailstone:astronomy:structural_equation[8702768a16f5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.12910v2.eq_888 | g^{}_\star = G M_h / r_{\texttt{c}}^2 | arxiv_extracted | ["g", "a", "t", "G", "r", "s"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.12910v2 | cross_domain_amplification | |
l | o | urn:hailstone:astronomy:structural_equation[58b7db10665d] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.07440v1.eq_889 | \log(M_{200}/M_{\odot})=12.9^{+0.4}_{-0.3} | arxiv_extracted | ["g", "M", "o", "M_{200}", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.07440v1 | cross_domain_amplification | |
n | B | urn:hailstone:astronomy:structural_equation[06df2b3a306a] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.07327v1.eq_890 | n_{\rm B}=-2.9 | arxiv_extracted | ["n", "m", "r", "B"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.07327v1 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[05c66de726ee] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.05213v1.eq_891 | f^\mathrm{loc}_\mathrm{NL}=2.1_{-8.3}^{+8.8} | arxiv_extracted | ["f", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.05213v1 | cross_domain_amplification | |
T | h | urn:hailstone:astronomy:structural_equation[5365e923c504] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.05078v1.eq_892 | T_{\rm reh}=2 \times 10^{14}\,\mathrm{GeV} | arxiv_extracted | ["e", "m", "h", "r", "T"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.05078v1 | cross_domain_amplification | |
e | l | urn:hailstone:astronomy:structural_equation[e7af203bd6ff] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.04897v1.eq_893 | \ell = 2 | arxiv_extracted | ["e", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.04897v1 | cross_domain_amplification | |
f | r | urn:hailstone:astronomy:structural_equation[4745478cd3cf] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.04867v1.eq_894 | f_{\rm NL}^{\rm loc} = 15.9_{-34.4}^{+34.6} | arxiv_extracted | ["f", "m", "L", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.04867v1 | cross_domain_amplification | |
w_0 | w_a | urn:hailstone:astronomy:structural_equation[be3b5925256a] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.03756v2.eq_895 | w_0+w_a=-1.37^{+0.19}_{-0.17} | arxiv_extracted | ["w_0", "w_a"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.03756v2 | cross_domain_amplification | |
w_0 | w_a | urn:hailstone:astronomy:structural_equation[866475d7a543] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.03756v2.eq_896 | w_0 + w_a =-1.29_{-0.17}^{+0.20} | arxiv_extracted | ["w_0", "w_a"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.03756v2 | cross_domain_amplification | |
H | C | urn:hailstone:astronomy:structural_equation[9f02821b419c] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.03381v2.eq_897 | H_{\text{CTL}} \left( T \right) = f^{-1}_{\text{max}} H_{Λ\text{CDM}}\left( T\right) | arxiv_extracted | ["e", "t", "H", "C", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.03381v2 | cross_domain_amplification | |
t | t | urn:hailstone:astronomy:structural_equation[91ccede5454b] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.03381v2.eq_898 | \texttt{fctl}= 1 | arxiv_extracted | ["t", "e", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.03381v2 | cross_domain_amplification | |
t | t | urn:hailstone:astronomy:structural_equation[95c6369317af] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.03381v2.eq_899 | \texttt{fctl} = 3\left( \text{CCC+TL} \right) | arxiv_extracted | ["t", "e", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.03381v2 | cross_domain_amplification | |
d | m | urn:hailstone:astronomy:structural_equation[ffe0cd558242] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.02433v1.eq_900 | dM/dz = 0.07 \pm 0.07 | arxiv_extracted | ["z", "M", "m", "p", "d"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.02433v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[a1badb179cfc] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.02410v1.eq_901 | α_{\mathrm{int}}^{\mathrm{NE}} = -0.91 \pm 0.06 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.02410v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[0d350d87cf09] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.02410v1.eq_902 | α_{\mathrm{int}}^{\mathrm{SW}} = -0.83 \pm 0.05 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.02410v1 | cross_domain_amplification | |
m | a | urn:hailstone:astronomy:structural_equation[445dfb4857f5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.02410v1.eq_903 | \mathcal{M}_{\mathrm{NE}} = 3.1^{+0.1}_{-0.1} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.02410v1 | cross_domain_amplification | |
m | a | urn:hailstone:astronomy:structural_equation[ccdc4f6e617d] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.02410v1.eq_904 | \mathcal{M}_{\mathrm{SW}} = 3.2^{+0.1}_{-0.1} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.02410v1 | cross_domain_amplification | |
A | P | urn:hailstone:astronomy:structural_equation[b7ec39385b91] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2604.01255v1.eq_905 | A(r) = h_{\rm Plummer}(r) - α | arxiv_extracted | ["m", "P", "h", "A", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2604.01255v1 | cross_domain_amplification | |
R | r | urn:hailstone:astronomy:structural_equation[09b63be073cc] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.28019v1.eq_906 | R_\mathrm{h}=ct | arxiv_extracted | ["a", "t", "m", "h", "R", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.28019v1 | cross_domain_amplification | |
R | r | urn:hailstone:astronomy:structural_equation[09b63be073cc] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.28019v1.eq_907 | R_\mathrm{h}=ct | arxiv_extracted | ["a", "t", "m", "h", "R", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.28019v1 | cross_domain_amplification | |
R | r | urn:hailstone:astronomy:structural_equation[09b63be073cc] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.28019v1.eq_908 | R_\mathrm{h}=ct | arxiv_extracted | ["a", "t", "m", "h", "R", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.28019v1 | cross_domain_amplification | |
R | r | urn:hailstone:astronomy:structural_equation[09b63be073cc] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.28019v1.eq_909 | R_\mathrm{h}=ct | arxiv_extracted | ["a", "t", "m", "h", "R", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.28019v1 | cross_domain_amplification | |
R | r | urn:hailstone:astronomy:structural_equation[09b63be073cc] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.28019v1.eq_910 | R_\mathrm{h}=ct | arxiv_extracted | ["a", "t", "m", "h", "R", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.28019v1 | cross_domain_amplification | |
k | x | urn:hailstone:astronomy:structural_equation[3b224ff1711b] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.27966v2.eq_911 | k_{\rm max} = 0.15\,\, h \, {\rm Mpc}^{-1} | arxiv_extracted | ["a", "m", "r", "k", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.27966v2 | cross_domain_amplification | |
l | t | urn:hailstone:astronomy:structural_equation[b36b3ea1a4aa] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.26869v1.eq_912 | \log σ\, \mathrm{[km \, s^{-1}] = 1.5} | arxiv_extracted | ["g", "a", "t", "m", "o", "l"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.26869v1 | cross_domain_amplification | |
q | a | urn:hailstone:astronomy:structural_equation[5c0c9ad5b169] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.26640v2.eq_913 | q=b/a,s=c/a | arxiv_extracted | ["q", "a", "s", "b", "c"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.26640v2 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[35493782b8ed] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.25851v1.eq_914 | Ω_{m0}=0.296 \pm 0.044 | arxiv_extracted | ["p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.25851v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[918bcd8b77d8] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.25851v1.eq_915 | Ω_{m0}=0.271 \pm 0.016 | arxiv_extracted | ["p", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.25851v1 | cross_domain_amplification | |
f | y | urn:hailstone:astronomy:structural_equation[88f0a8831c47] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.25650v1.eq_916 | f_{\rm sky}=1 | arxiv_extracted | ["f", "m", "y", "r", "s", "k"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.25650v1 | cross_domain_amplification | |
z | r | urn:hailstone:astronomy:structural_equation[a716209a37d6] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.24179v1.eq_917 | z_\mathrm{s} = 0.5 | arxiv_extracted | ["z", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.24179v1 | cross_domain_amplification | |
d_L | z | urn:hailstone:astronomy:structural_equation[3552e3d7c5ad] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.23373v1.eq_918 | d_L(z) = (1+z)^2 D_A(z) | arxiv_extracted | ["D_A", "d_L", "z"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.23373v1 | cross_domain_amplification | |
z | z | urn:hailstone:astronomy:structural_equation[8ead7f4f8686] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.23373v1.eq_919 | η_1(z) = 1 + η_0 z | arxiv_extracted | ["z"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.23373v1 | cross_domain_amplification | |
z | z | urn:hailstone:astronomy:structural_equation[1dfe84a3bbab] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2603.23373v1.eq_920 | η_2(z) = 1 + η_0 z/(1+z) | arxiv_extracted | ["z"] | arxiv | arxiv | arxiv:astro-ph.CO:2603.23373v1 | cross_domain_amplification |
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