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