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
r
m
urn:hailstone:astronomy:structural_equation[75beb8e014c0]
1
structural_equation
10
arxiv.astro-ph.CO.2509.19842v2.eq_1421
σ_{\rm DM}/m=0.,0.01,0.05,0.1,0.2
arxiv_extracted
["M", "D", "m", "r"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.19842v2
cross_domain_amplification
t
A
urn:hailstone:astronomy:structural_equation[a5ad7699065a]
1
structural_equation
10
arxiv.astro-ph.CO.2509.19751v1.eq_1422
\text{R.A.} = 0^\circ
arxiv_extracted
["e", "t", "A", "R", "x"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.19751v1
cross_domain_amplification
t
e
urn:hailstone:astronomy:structural_equation[4549cc56c3c1]
1
structural_equation
10
arxiv.astro-ph.CO.2509.19751v1.eq_1423
\text{Dec} = -27.0^\circ
arxiv_extracted
["t", "D", "e", "x"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.19751v1
cross_domain_amplification
N
r
urn:hailstone:astronomy:structural_equation[402ab27a215c]
1
structural_equation
10
arxiv.astro-ph.CO.2509.17124v4.eq_1424
N_{\mathrm{eff}} = 3.044
arxiv_extracted
["a", "t", "m", "h", "r", "N"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.17124v4
cross_domain_amplification
r
M
urn:hailstone:astronomy:structural_equation[cdcebcd0259c]
1
structural_equation
10
arxiv.astro-ph.CO.2509.16317v1.eq_1425
η(r= 1.0 \, \text{Mpc}) = 0.93^{+0.48}_{-0.40}
arxiv_extracted
["e", "t", "M", "r", "x"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.16317v1
cross_domain_amplification
D_M
t
urn:hailstone:astronomy:structural_equation[de613a4c4bf2]
1
structural_equation
10
arxiv.astro-ph.CO.2509.15308v1.eq_1426
D_M/D_H(z_\mathrm{eff})=4.525\pm0.071
arxiv_extracted
["z", "a", "t", "m", "D_M", "D_H"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.15308v1
cross_domain_amplification
z
r
urn:hailstone:astronomy:structural_equation[e5b9f27dab0e]
1
structural_equation
10
arxiv.astro-ph.CO.2509.15308v1.eq_1427
z_\mathrm{eff}=2.33
arxiv_extracted
["z", "a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.15308v1
cross_domain_amplification
D_H
h
urn:hailstone:astronomy:structural_equation[d58106d1bb9e]
1
structural_equation
10
arxiv.astro-ph.CO.2509.15308v1.eq_1428
D_H(z_\mathrm{eff})/r_d=8.646\pm0.077
arxiv_extracted
["z", "a", "t", "m", "h", "D_H"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.15308v1
cross_domain_amplification
D_M
h
urn:hailstone:astronomy:structural_equation[b85a754a432f]
1
structural_equation
10
arxiv.astro-ph.CO.2509.15308v1.eq_1429
D_M(z_\mathrm{eff})/r_d=38.90\pm0.38
arxiv_extracted
["z", "a", "t", "m", "h", "D_M"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.15308v1
cross_domain_amplification
f
h
urn:hailstone:astronomy:structural_equation[cf0630212300]
1
structural_equation
10
arxiv.astro-ph.CO.2509.15308v1.eq_1430
fσ_8(z_\mathrm{eff}) = 0.37\; ^{+0.055}_{-0.065} \,(\mathrm{stat})\, \pm 0.033 \,(\mathrm{sys})
arxiv_extracted
["f", "z", "a", "t", "m", "h"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.15308v1
cross_domain_amplification
r
m
urn:hailstone:astronomy:structural_equation[ffbc522e75b1]
1
structural_equation
10
arxiv.astro-ph.CO.2509.15012v2.eq_1431
Ω_{\rm m} = 0.192^{+0.305}_{-0.131}
arxiv_extracted
["m", "r"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.15012v2
cross_domain_amplification
E
m
urn:hailstone:astronomy:structural_equation[8d4ce66db78f]
1
structural_equation
10
arxiv.astro-ph.CO.2509.12422v1.eq_1432
δE/E = -0.006\pm0.008
arxiv_extracted
["p", "E", "m"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.12422v1
cross_domain_amplification
d
p
urn:hailstone:astronomy:structural_equation[6cea15269a1c]
1
structural_equation
10
arxiv.astro-ph.CO.2509.12422v1.eq_1433
δ\dot{m_π}/m_π=-(6\pm9)\times10^{-11}\text{ yr}^{-1}
arxiv_extracted
["m_\u03c0", "t", "o", "p", "d", "m_\u03c0}"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.12422v1
cross_domain_amplification
d
a
urn:hailstone:astronomy:structural_equation[19ae515bacfc]
1
structural_equation
10
arxiv.astro-ph.CO.2509.12422v1.eq_1434
\dot{Q}_{0,max} = (3\pm 4)\times10^7 \text{ GeV/yr}
arxiv_extracted
["Q", "a", "t", "m", "o", "d"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.12422v1
cross_domain_amplification
d
Q
urn:hailstone:astronomy:structural_equation[e294168f4396]
1
structural_equation
10
arxiv.astro-ph.CO.2509.12422v1.eq_1435
\dot{Q}_0 =0
arxiv_extracted
["t", "d", "Q", "o"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.12422v1
cross_domain_amplification
r
m
urn:hailstone:astronomy:structural_equation[82511775b004]
1
structural_equation
10
arxiv.astro-ph.CO.2509.12319v2.eq_1436
Ω_{\rm m} = 0.3
arxiv_extracted
["m", "r"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.12319v2
cross_domain_amplification
t_{1b
a
urn:hailstone:astronomy:structural_equation[a22e73f1504d]
1
structural_equation
10
arxiv.astro-ph.CO.2509.12301v1.eq_1437
Δt_{1b,1a}=-39.8_{-3.3}^{+3.9}
arxiv_extracted
["t_{1b", "a"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.12301v1
cross_domain_amplification
m
m
urn:hailstone:astronomy:structural_equation[0691f7e782d5]
1
structural_equation
10
arxiv.astro-ph.CO.2509.12035v2.eq_1438
β_{\mathrm{R_1}} = 3.51 \pm 0.16
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.12035v2
cross_domain_amplification
m
m
urn:hailstone:astronomy:structural_equation[6373948d5b9a]
1
structural_equation
10
arxiv.astro-ph.CO.2509.12035v2.eq_1439
β_{\mathrm{R_3}} = 2.12 \pm 0.16
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.12035v2
cross_domain_amplification
M_{500}
t
urn:hailstone:astronomy:structural_equation[5877c3f6c3f8]
1
structural_equation
10
arxiv.astro-ph.CO.2509.10455v1.eq_1440
M_{500}=10^{13-14}M_\odot
arxiv_extracted
["t", "M", "o", "M_{500}", "d"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.10455v1
cross_domain_amplification
w_0
w_a
urn:hailstone:astronomy:structural_equation[48949ee39c47]
1
structural_equation
10
arxiv.astro-ph.CO.2509.09562v1.eq_1441
w_0=-0.72 \pm 0.21, \, w_a=-0.91^{+0.78}_{-0.64}
arxiv_extracted
["m", "p", "w_0", "w_a"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.09562v1
cross_domain_amplification
c
t
urn:hailstone:astronomy:structural_equation[f02d0aba2f81]
1
structural_equation
10
arxiv.astro-ph.CO.2509.09211v2.eq_1442
c^{3}/G=\text{constant}
arxiv_extracted
["e", "t", "G", "c", "x"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.09211v2
cross_domain_amplification
B
s
urn:hailstone:astronomy:structural_equation[c577a4341061]
1
structural_equation
10
arxiv.astro-ph.CO.2509.08896v2.eq_1443
B_{\rm host}^{\rm local} = 5.44^{+1.13}_{-0.87}μ{\rm G}
arxiv_extracted
["B", "m", "h", "o", "r", "s"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.08896v2
cross_domain_amplification
f
s
urn:hailstone:astronomy:structural_equation[6191e1f188ad]
1
structural_equation
10
arxiv.astro-ph.CO.2509.08896v2.eq_1444
f_{\rm gas} = 0.45^{+0.21}_{-0.19}
arxiv_extracted
["f", "g", "a", "m", "r", "s"]
arxiv
arxiv
arxiv:astro-ph.CO:2509.08896v2
cross_domain_amplification
v
s
urn:hailstone:chemistry_physics:structural_equation[92ad0753f3b8]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.13066v1.eq_1445
\varepsilon = 0
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.13066v1
cross_domain_amplification
v
s
urn:hailstone:chemistry_physics:structural_equation[c82e742e677f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.13066v1.eq_1446
\varepsilon = Ω/2
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.13066v1
cross_domain_amplification
a
m
urn:hailstone:chemistry_physics:structural_equation[7390d588a2f6]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.12246v1.eq_1447
Δa/g = κ\, Δ(q/m)
arxiv_extracted
["g", "m", "q", "a"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.12246v1
cross_domain_amplification
p_c
d
urn:hailstone:chemistry_physics:structural_equation[68c37df6ca91]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.10795v1.eq_1448
p_c \log p_c / d^2 = 1 / 2
arxiv_extracted
["g", "p_c", "o", "d", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.10795v1
cross_domain_amplification
v
s
urn:hailstone:chemistry_physics:structural_equation[58240eff8aa4]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.10395v1.eq_1449
\varepsilon^{\rm BO}=Θ(k_c d/n)
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.10395v1
cross_domain_amplification
S
y
urn:hailstone:chemistry_physics:structural_equation[7e40eb195efb]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.10326v2.eq_1450
S(\infty)/N = (1/N) \ln \binom{N^2}{N}
arxiv_extracted
["f", "t", "y", "S", "i", "n"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.10326v2
cross_domain_amplification
r
m
urn:hailstone:chemistry_physics:structural_equation[593cd2ae4600]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.10326v2.eq_1451
γ_{\rm MC} = 1.946 \pm 0.003
arxiv_extracted
["M", "m", "p", "r", "C"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.10326v2
cross_domain_amplification
w
i
urn:hailstone:chemistry_physics:structural_equation[dd064a490e83]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.09453v1.eq_1452
\widetildeχ = \text{d}\langle m \rangle /\text{d}J
arxiv_extracted
["e", "w", "t", "i", "d"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.09453v1
cross_domain_amplification
S_{BG}
m
urn:hailstone:chemistry_physics:structural_equation[7fc3a633ac9a]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1453
S_{BG}(p)=k\sum^{W}_{i=1}p_{i}\ln 1/p_{i}
arxiv_extracted
["m", "u", "p", "s", "k", "S_{BG}"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
s
p_{i}
urn:hailstone:chemistry_physics:structural_equation[ec598b3dcbb7]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1454
\sum^{W}_{i=1}p_{i}=1
arxiv_extracted
["W", "m", "p_{i}", "i", "u", "s"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
s
p_{i}
urn:hailstone:chemistry_physics:structural_equation[eb7e6a741516]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1455
\sum^{W}_{i=1}p_{i}\,e_{i}=U
arxiv_extracted
["W", "m", "p_{i}", "i", "u", "s"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
S_{q}
m
urn:hailstone:chemistry_physics:structural_equation[79d2a13ed8ae]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1456
S_{q}(p)=k\,(\sum^{W}_{i=1}p_{i}^{q}-1)/(1-q)
arxiv_extracted
["m", "S_{q}", "p", "u", "s", "k"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
s
p_{i}
urn:hailstone:chemistry_physics:structural_equation[284771745770]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1457
\sum^{W}_{i=1} p_{i}^{q^{\prime}}e_{i} / \sum^{W}_{i=1}p_{i}^{q^{\prime}}=U
arxiv_extracted
["W", "m", "p_{i}", "i", "u", "s"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
q
e
urn:hailstone:chemistry_physics:structural_equation[39b1cbc3bc31]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1458
q^{\prime}=1
arxiv_extracted
["e", "q", "m", "i", "p", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
q
e
urn:hailstone:chemistry_physics:structural_equation[46892530ddc7]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1459
q^{\prime}=q
arxiv_extracted
["e", "q", "m", "i", "p", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
q
e
urn:hailstone:chemistry_physics:structural_equation[0f41f95c76f5]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1460
q^{\prime}=2-q
arxiv_extracted
["e", "q", "m", "i", "p", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
T_{q
m
urn:hailstone:chemistry_physics:structural_equation[56c515835fb5]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1461
1/T_{q,q^{\prime}}=\partial S_{q} / \partial U
arxiv_extracted
["q", "m", "i", "p", "r", "T_{q"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
F_{q
m
urn:hailstone:chemistry_physics:structural_equation[d8a31ae86666]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1462
F_{q,q^{\prime}}=U-T_{q,q^{\prime}}S_{q}
arxiv_extracted
["q", "m", "i", "F_{q", "p", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
q
e
urn:hailstone:chemistry_physics:structural_equation[39b1cbc3bc31]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.08860v1.eq_1463
q^{\prime}=1
arxiv_extracted
["e", "q", "m", "i", "p", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.08860v1
cross_domain_amplification
P
m
urn:hailstone:chemistry_physics:structural_equation[5eaa289b56e0]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.05431v1.eq_1464
P(R,T)\sim \exp\big[-(k_F R)^{d+1}Φ_d(u=2R\,T/k_F)\big],
arxiv_extracted
["m", "P", "i", "R", "s", "T"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.05431v1
cross_domain_amplification
S
b
urn:hailstone:chemistry_physics:structural_equation[ea390f51af9e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2605.05366v1.eq_1465
S^2/\mathbb{Z}_2 = \mathbb{RP}^2
arxiv_extracted
["a", "t", "m", "h", "S", "b"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2605.05366v1
cross_domain_amplification
T
r
urn:hailstone:chemistry_physics:structural_equation[d66164a0abf0]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.27746v1.eq_1466
T_\mathrm{N} = 14
arxiv_extracted
["a", "t", "m", "h", "r", "T"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.27746v1
cross_domain_amplification
c_{3
c
urn:hailstone:chemistry_physics:structural_equation[f9ab6e22a708]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.27226v1.eq_1467
c_{3,0} =c_{2,1} = c
arxiv_extracted
["c_{3", "c", "c_{2"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.27226v1
cross_domain_amplification
r
r
urn:hailstone:chemistry_physics:structural_equation[839c238168e6]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.25351v1.eq_1468
β_{\rm fo}=T_{\rm fo}^{-1}
arxiv_extracted
["f", "m", "o", "r", "T"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.25351v1
cross_domain_amplification
d
f
urn:hailstone:chemistry_physics:structural_equation[b2ce695f5521]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.24458v1.eq_1469
\dotΣ = σ_0 f
arxiv_extracted
["t", "f", "d", "o"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.24458v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[d17d22711dc2]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.24458v1.eq_1470
Σ_{\mathrm{life}} = σ_0 \Nstar
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.24458v1
cross_domain_amplification
s
a
urn:hailstone:chemistry_physics:structural_equation[edd27a030a4c]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.24458v1.eq_1471
\sigstar \propto M^{3/4+1/4-1}=M^0
arxiv_extracted
["g", "a", "t", "i", "s"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.24458v1
cross_domain_amplification
D
r
urn:hailstone:chemistry_physics:structural_equation[12dfa278179d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.23752v1.eq_1472
ΔD_\mathrm{KL} = (3/2)[R_0 - \ln R_0 - 1] = (3/2) d_\mathrm{IS}(T_\mathrm{eff}, T_\mathrm{core})
arxiv_extracted
["D", "a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.23752v1
cross_domain_amplification
r
l
urn:hailstone:chemistry_physics:structural_equation[4e8b5897f70f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.22521v2.eq_1473
{\rm TEN} = 2 \ln 2
arxiv_extracted
["T", "m", "r", "E", "l", "N"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.22521v2
cross_domain_amplification
r
l
urn:hailstone:chemistry_physics:structural_equation[d7f09d1a8233]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.22521v2.eq_1474
{\rm TEN} = \ln 2
arxiv_extracted
["T", "m", "r", "E", "l", "N"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.22521v2
cross_domain_amplification
q
f
urn:hailstone:chemistry_physics:structural_equation[bfe1d82e71ee]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.22448v1.eq_1475
Γ(q\to\infty) = βK(1-ξ)
arxiv_extracted
["f", "q", "t", "i", "o", "n"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.22448v1
cross_domain_amplification
q
t
urn:hailstone:chemistry_physics:structural_equation[5bb87a760e90]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.22448v1.eq_1476
q > q_c = κ_0/\sqrt{ξ-1}
arxiv_extracted
["q", "q_c", "t", "r", "s"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.22448v1
cross_domain_amplification
d
l
urn:hailstone:chemistry_physics:structural_equation[a9e976cdeb36]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.21341v1.eq_1477
d_{\rm hull}=1.333\,29(14)=4/3
arxiv_extracted
["m", "h", "u", "r", "d", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.21341v1
cross_domain_amplification
p_c
m
urn:hailstone:chemistry_physics:structural_equation[614d0fd4b92b]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.21165v1.eq_1478
p_c^s = 0.822725 \pm 0.000044
arxiv_extracted
["s", "p", "m", "p_c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.21165v1
cross_domain_amplification
p_c
m
urn:hailstone:chemistry_physics:structural_equation[a4a8c05b3c79]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.21165v1.eq_1479
p_c^b = 0.798161 \pm 0.000044
arxiv_extracted
["p", "b", "m", "p_c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.21165v1
cross_domain_amplification
K_c
K
urn:hailstone:chemistry_physics:structural_equation[69091302cffa]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.16288v1.eq_1480
K_c=K_\#=3π/4
arxiv_extracted
["K", "K_c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.16288v1
cross_domain_amplification
W_β
s
urn:hailstone:chemistry_physics:structural_equation[5278d30f9db7]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.16288v1.eq_1481
W_β(θ)=(e^{β\cos(2πθ)}-1)/β
arxiv_extracted
["e", "o", "W_\u03b2", "s", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.16288v1
cross_domain_amplification
K_c
K
urn:hailstone:chemistry_physics:structural_equation[3efd465a7541]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.16288v1.eq_1482
K_c(β) = K_\#(β)
arxiv_extracted
["K", "K_c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.16288v1
cross_domain_amplification
W_{R}
R
urn:hailstone:chemistry_physics:structural_equation[7808b72f3640]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.16288v1.eq_1483
W_{R}(θ) = (R-2π|θ|)_{+}^2
arxiv_extracted
["R", "W_{R}"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.16288v1
cross_domain_amplification
t
F
urn:hailstone:chemistry_physics:structural_equation[cb6ed25ecc26]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.15420v1.eq_1484
\tilde{F}(Δ)=\sin(\frac{πd}{2}) \log Z_{S^d}
arxiv_extracted
["e", "F", "t", "i", "d", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.15420v1
cross_domain_amplification
d
e
urn:hailstone:chemistry_physics:structural_equation[b45c7859b7d2]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.15420v1.eq_1485
d\tilde{F}/dΔ|_{Δ=Δ_\mathrm{local}}=0
arxiv_extracted
["e", "t", "i", "d", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.15420v1
cross_domain_amplification
r
c
urn:hailstone:chemistry_physics:structural_equation[a878b221e4df]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.13885v2.eq_1486
γ_{\rm c}=2
arxiv_extracted
["c", "m", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.13885v2
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[cbdd82f78e51]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.12340v1.eq_1487
λ_{\mathrm{cut}}^{*} = ε
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.12340v1
cross_domain_amplification
m_{eff}
x
urn:hailstone:chemistry_physics:structural_equation[76461d5e9638]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.11173v1.eq_1488
m_{eff}(x) = m_{eff}|x|^α
arxiv_extracted
["m_{eff}", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.11173v1
cross_domain_amplification
V_{ext}
c
urn:hailstone:chemistry_physics:structural_equation[6f408127fb03]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.11173v1.eq_1489
V_{ext}(x)=\frac{1}{2}m_{eff}ω^2 |x|^{α+2}
arxiv_extracted
["f", "a", "r", "c", "V_{ext}", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.11173v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[4736b3054e9e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.06486v1.eq_1490
\mathcal{R}=L_y/L_x
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.06486v1
cross_domain_amplification
c
e
urn:hailstone:chemistry_physics:structural_equation[48386b782e27]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.06324v1.eq_1491
c_{\text{eff}} = 0.522(1)
arxiv_extracted
["t", "c", "e", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.06324v1
cross_domain_amplification
H_n
n_{i
urn:hailstone:chemistry_physics:structural_equation[c267e344ce44]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.06122v1.eq_1492
H_n(h,σ)=\sum^n_{i=1}h_i(σ_i-m)
arxiv_extracted
["m", "h", "u", "n_{i", "s", "H_n"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.06122v1
cross_domain_amplification
d
l
urn:hailstone:chemistry_physics:structural_equation[e6ec1e787748]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.05772v1.eq_1493
d_{\rm hull} = 1.663(4)
arxiv_extracted
["m", "h", "u", "r", "d", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.05772v1
cross_domain_amplification
d
n
urn:hailstone:chemistry_physics:structural_equation[ff3a19661509]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.05772v1.eq_1494
d_{\rm min} = 1.080(10)
arxiv_extracted
["m", "i", "r", "n", "d"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.05772v1
cross_domain_amplification
d_1
d_2
urn:hailstone:chemistry_physics:structural_equation[3e9302787d5b]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.04922v1.eq_1495
(d_1, d_2) = (1, 0)
arxiv_extracted
["d_2", "d_1"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.04922v1
cross_domain_amplification
d_1
d_2
urn:hailstone:chemistry_physics:structural_equation[36e398e38074]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.04922v1.eq_1496
(d_1, d_2) = (0, 2)
arxiv_extracted
["d_2", "d_1"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.04922v1
cross_domain_amplification
S
S
urn:hailstone:chemistry_physics:structural_equation[f955d1b01526]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.04346v1.eq_1497
|S^z| = S
arxiv_extracted
["z", "S"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.04346v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[574ca8addcef]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.03977v1.eq_1498
\mathcal{O} = χ_{a_1}χ_{a_2}\ldots χ_{a_n}
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.03977v1
cross_domain_amplification
l
r
urn:hailstone:chemistry_physics:structural_equation[04b3d563e81d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.03770v1.eq_1499
χ\left(M\right)=0
arxiv_extracted
["e", "f", "t", "M", "r", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.03770v1
cross_domain_amplification
h
x
urn:hailstone:chemistry_physics:structural_equation[966d4c8ae5cd]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.03711v1.eq_1500
h(x,t)=(3t^2x+x^3)/6t
arxiv_extracted
["t", "h", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.03711v1
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[374da6080573]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.02907v1.eq_1501
\langle ΔN^2(t) \rangle = \langle (N(t) - N(0))^2 \rangle
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.02907v1
cross_domain_amplification
L
G
urn:hailstone:chemistry_physics:structural_equation[454f135e4f36]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.01484v1.eq_1502
Δ(L,T) = A L^{d+η} G_-(L|t/T_c|)
arxiv_extracted
["G", "d", "A", "L", "T"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.01484v1
cross_domain_amplification
c_{5
P
urn:hailstone:chemistry_physics:structural_equation[344429009cc3]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.00870v1.eq_1503
c_{5\text{-Potts}} = 1.1375 \pm 0.0211 i
arxiv_extracted
["e", "c_{5", "t", "P", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.00870v1
cross_domain_amplification
l
a
urn:hailstone:chemistry_physics:structural_equation[b897efce3323]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2604.00115v1.eq_1504
\left(\partial S/\partial H\right)_T = \left(\partial M/\partial T\right)_H
arxiv_extracted
["e", "f", "a", "t", "p", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2604.00115v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[ef8e34effc3e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.29035v1.eq_1505
χ^2/\mathrm{dof}=0.50
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.29035v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[d3e208066318]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.28853v1.eq_1506
\mathcal{N}=4
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.28853v1
cross_domain_amplification
K
r
urn:hailstone:chemistry_physics:structural_equation[e68de4eaffc9]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.28632v1.eq_1507
K_{\mathrm{sech}}=1/(2 π\cosh[(x-y)/2])
arxiv_extracted
["a", "t", "m", "h", "r", "K"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.28632v1
cross_domain_amplification
d
d_c
urn:hailstone:chemistry_physics:structural_equation[f6d7b396bbe5]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.27992v1.eq_1508
d<d_c=4
arxiv_extracted
["d", "d_c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.27992v1
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[3a2b26dd39ba]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.27930v1.eq_1509
\langle Z_0^r Z_R^{\dagger r}\rangle^*=\langle Z_0^r Z_{L-R}^{\dagger r}\rangle
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.27930v1
cross_domain_amplification
m
x
urn:hailstone:chemistry_physics:structural_equation[46ceb3cbe7aa]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.27826v2.eq_1510
ρ_{\max}=0.2771
arxiv_extracted
["m", "a", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.27826v2
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[593e30f3bc6b]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.27322v1.eq_1511
\langle\bar{q}_\text{out}/\bar{q}_\text{in} \rangle = 1.03
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.27322v1
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[69aeca0a7d01]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.27322v1.eq_1512
\langle\barβ_\text{out}/\barβ_\text{in} \rangle = 1.18
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.27322v1
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[c8a1fa8523f0]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.26897v1.eq_1513
\langle Q_3\rangle=0
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.26897v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[91705a8e69b5]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.24746v1.eq_1514
Δ\mathrm{AIC}=16.8
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.24746v1
cross_domain_amplification
J
c
urn:hailstone:chemistry_physics:structural_equation[c65a95590289]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.22736v1.eq_1515
J_{\text{c}}=2.584(8)
arxiv_extracted
["e", "t", "J", "c", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.22736v1
cross_domain_amplification
d
q
urn:hailstone:chemistry_physics:structural_equation[56cc3614af99]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.21391v2.eq_1516
dy/dx = y^q
arxiv_extracted
["q", "d", "y", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.21391v2
cross_domain_amplification
T_c
p_c
urn:hailstone:chemistry_physics:structural_equation[ec5dc9995f16]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.21303v1.eq_1517
T_c(p_c)=0
arxiv_extracted
["p_c", "T_c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.21303v1
cross_domain_amplification
r
M
urn:hailstone:chemistry_physics:structural_equation[d1bfb74abc3d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.21303v1.eq_1518
φ_{\rm RSIM}=1
arxiv_extracted
["M", "m", "S", "r", "R", "I"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.21303v1
cross_domain_amplification
h
a
urn:hailstone:chemistry_physics:structural_equation[dae3b4656d45]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.22347v2.eq_1519
[\hat{S}, \hat{R}] = i\mathcal{D}
arxiv_extracted
["t", "S", "h", "a"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.22347v2
cross_domain_amplification
D
O
urn:hailstone:chemistry_physics:structural_equation[f70259feaaba]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.20917v2.eq_1520
\Dloc(λ)=Cλ^4+O(λ^6)
arxiv_extracted
["D", "O", "o", "c", "l", "C"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.20917v2
cross_domain_amplification