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_{ij}
L_{ji}
urn:hailstone:chemistry_physics:structural_equation[cd914c7922c3]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.20773v1.eq_1521
L_{ij}=L_{ji}
arxiv_extracted
["L_{ij}", "L_{ji}"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.20773v1
cross_domain_amplification
c
C_p
urn:hailstone:chemistry_physics:structural_equation[db15de12055d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.20773v1.eq_1522
Γ_c=λ_p/λ_v=C_v/C_p
arxiv_extracted
["C_v", "p", "C_p", "c", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.20773v1
cross_domain_amplification
m
S
urn:hailstone:chemistry_physics:structural_equation[24000cac93c9]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.20773v1.eq_1523
Γ_m=λ_s/λ_t=κ_T/κ_S
arxiv_extracted
["t", "m", "S", "s", "T"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.20773v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[5f87f30332c2]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.20423v4.eq_1524
\mathrm{d}g_{ij} = \mathcal{D}_{ij}[g]\,\mathrm{d}τ+ \ell_P\,\mathrm{d}W_{ij}
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.20423v4
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[9474c4071f4d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.19887v1.eq_1525
\mathrm{d}ΔT/\mathrm{d}t = -[γ_0 + \mathcal{M}Q(t)][ΔT - \mathcal{I}Q(t)]
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.19887v1
cross_domain_amplification
c
v_{eff}
urn:hailstone:chemistry_physics:structural_equation[c6795134a71f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.20330v2.eq_1526
λ_{c}(δ)=2\sqrt{v_{eff}w}
arxiv_extracted
["v_{eff}", "q", "t", "r", "s", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.20330v2
cross_domain_amplification
v_{vff}
v
urn:hailstone:chemistry_physics:structural_equation[a9fb6001720e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.20330v2.eq_1527
v_{vff}=\sqrt{v^{2}-δ^{2}}
arxiv_extracted
["q", "v_{vff}", "t", "r", "s", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.20330v2
cross_domain_amplification
a
D
urn:hailstone:chemistry_physics:structural_equation[b04bed5626bd]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.17509v1.eq_1528
(a,d,q)(n)=2\,(A,D,Q)(n)-n
arxiv_extracted
["D", "q", "a", "A", "n", "d"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.17509v1
cross_domain_amplification
m
i
urn:hailstone:chemistry_physics:structural_equation[5846a30c956f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.15290v1.eq_1529
|ψ|_{\max}=A\,|\tildeψ|_{\max}
arxiv_extracted
["a", "t", "m", "i", "A", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.15290v1
cross_domain_amplification
l
n
urn:hailstone:chemistry_physics:structural_equation[0ff490683fe2]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.14154v2.eq_1530
2\ln 2/(3\ln(4/3)) = 1.606
arxiv_extracted
["n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.14154v2
cross_domain_amplification
m
x
urn:hailstone:chemistry_physics:structural_equation[91570862dd1d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.14072v1.eq_1531
_{\max}=2.7
arxiv_extracted
["m", "a", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.14072v1
cross_domain_amplification
n
m
urn:hailstone:chemistry_physics:structural_equation[c01d22c8495e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.13896v1.eq_1532
\nabla^2\mathcal{R}(i) = κ\,σ_{\rm prev}(i)
arxiv_extracted
["a", "m", "n", "b", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.13896v1
cross_domain_amplification
h
a
urn:hailstone:chemistry_physics:structural_equation[a9518cbf4c2f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.12148v1.eq_1533
\hat C = \hat P_T + \hat H
arxiv_extracted
["t", "C", "h", "a"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.12148v1
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[9882596ee1d4]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.10683v2.eq_1534
\langle \mathbf{b} \rangle = \mathbf{0}
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.10683v2
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[5c2c870e8895]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.10683v2.eq_1535
\langle \mathbf{b} \rangle = \mathbf{B}_0
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.10683v2
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[dddf35b9ee0c]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.08991v1.eq_1536
β_m(α) = \min(α, m)
arxiv_extracted
["n", "m", "i"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.08991v1
cross_domain_amplification
e
L
urn:hailstone:chemistry_physics:structural_equation[98de2e523239]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.08666v1.eq_1537
α=α(\ell=L)
arxiv_extracted
["e", "L", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.08666v1
cross_domain_amplification
W
l
urn:hailstone:chemistry_physics:structural_equation[626a9e7a0e85]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.06111v1.eq_1538
W_{\ell}=1
arxiv_extracted
["W", "l", "e"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.06111v1
cross_domain_amplification
n
n
urn:hailstone:chemistry_physics:structural_equation[d8e05f2ea606]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.06111v1.eq_1539
ω_n^{\ast}= Q_0/(2n \hbar)
arxiv_extracted
["a", "t", "Q_0", "s", "n"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.06111v1
cross_domain_amplification
W
d
urn:hailstone:chemistry_physics:structural_equation[1a2c6d6dbe78]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.06111v1.eq_1540
W_{\ell} =\{\cdots 1,1,-1,1,1,-1 \cdots \}
arxiv_extracted
["e", "W", "d", "c", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.06111v1
cross_domain_amplification
N_c
m
urn:hailstone:chemistry_physics:structural_equation[9cfe293e2177]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2603.05374v1.eq_1541
N_c l^2 = 6.850923 \pm 0.00014
arxiv_extracted
["N_c", "p", "m", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2603.05374v1
cross_domain_amplification
N
i
urn:hailstone:chemistry_physics:structural_equation[f31fd6c7040d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.21003v1.eq_1542
β_N(ε)=\partial_εS_N
arxiv_extracted
["a", "t", "i", "p", "r", "N"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.21003v1
cross_domain_amplification
N
i
urn:hailstone:chemistry_physics:structural_equation[254feb924e74]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.21003v1.eq_1543
γ_N(ε)=\partial^2_εS_N
arxiv_extracted
["a", "t", "i", "p", "r", "N"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.21003v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[49c8f2921169]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.16390v1.eq_1544
\mathcal{E}_* = E_{\rm loop}/(k_B T_m) \approx 25.1
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.16390v1
cross_domain_amplification
m
t
urn:hailstone:chemistry_physics:structural_equation[7c636b5c3e15]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.16331v1.eq_1545
\mathtt{q}=3
arxiv_extracted
["t", "h", "m", "a"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.16331v1
cross_domain_amplification
m
t
urn:hailstone:chemistry_physics:structural_equation[440e70662069]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.16331v1.eq_1546
\mathtt{q}=4
arxiv_extracted
["t", "h", "m", "a"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.16331v1
cross_domain_amplification
q
l
urn:hailstone:chemistry_physics:structural_equation[8fb4e46c584e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.15098v1.eq_1547
q^\ell=1
arxiv_extracted
["e", "l", "q"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.15098v1
cross_domain_amplification
T
m
urn:hailstone:chemistry_physics:structural_equation[1c701996d97e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.14928v4.eq_1548
\Tc/J = 4.511 \pm 0.005
arxiv_extracted
["m", "p", "c", "J", "T"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.14928v4
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[c754e9ba557d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.13782v2.eq_1549
\mathrm{Sym}^N(M) = M^{\otimes N}/S_N
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.13782v2
cross_domain_amplification
C_{1}
r
urn:hailstone:chemistry_physics:structural_equation[eac9689407ab]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.13664v2.eq_1550
C_{1}=17 \ln 10 /(3 \sqrt{42}-19) \approx 16.7
arxiv_extracted
["C_{1}", "q", "r", "s", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.13664v2
cross_domain_amplification
v
s
urn:hailstone:chemistry_physics:structural_equation[78d0934b3c1d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.11369v1.eq_1551
\varepsilon = 4-d
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.11369v1
cross_domain_amplification
v_{n1}
x
urn:hailstone:chemistry_physics:structural_equation[3af70c6d5f41]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.10421v2.eq_1552
v_{n1}=λC_{n1} f(x), v_{n2}(x)=-λ\,C_{n2}m_{n}^{-2}ω_{n}^{-2}f(x)
arxiv_extracted
["f", "v_{n1}", "C_{n1}", "v_{n2}", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.10421v2
cross_domain_amplification
V
b
urn:hailstone:chemistry_physics:structural_equation[2180d9c7f326]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.08436v1.eq_1553
V(\mathbf r)=μr^{2}/2
arxiv_extracted
["V", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.08436v1
cross_domain_amplification
m
e
urn:hailstone:chemistry_physics:structural_equation[1fc8eb8facc0]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.05212v1.eq_1554
m_{\rm coex} = m(T;L)
arxiv_extracted
["e", "m", "o", "r", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.05212v1
cross_domain_amplification
t
w
urn:hailstone:chemistry_physics:structural_equation[9e70faf653f1]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2602.03790v2.eq_1555
t_{\text{w}}=τ
arxiv_extracted
["t", "w", "e", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2602.03790v2
cross_domain_amplification
q_c
F
urn:hailstone:chemistry_physics:structural_equation[150a982904d4]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.22840v1.eq_1556
q_c^{MF} = 4
arxiv_extracted
["q_c", "M", "F"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.22840v1
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[cab3df120d87]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.22247v3.eq_1557
\langle hν\rangle = π^4 E_c/[30\,ζ(3)] \approx 2.701\,E_c
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.22247v3
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[659b119f4380]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.22247v3.eq_1558
\mathcal{S} = \ln W
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.22247v3
cross_domain_amplification
J_3
J_1
urn:hailstone:chemistry_physics:structural_equation[d7a52ff987e9]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.19648v1.eq_1559
J_3/J_1 = -1
arxiv_extracted
["J_3", "J_1"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.19648v1
cross_domain_amplification
m
t
urn:hailstone:chemistry_physics:structural_equation[653ad5457598]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.19567v2.eq_1560
m^{\ast} = 2
arxiv_extracted
["s", "t", "m", "a"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.19567v2
cross_domain_amplification
m
t
urn:hailstone:chemistry_physics:structural_equation[5177fa02a47c]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.19567v2.eq_1561
m^{\ast} = 3
arxiv_extracted
["s", "t", "m", "a"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.19567v2
cross_domain_amplification
E
r
urn:hailstone:chemistry_physics:structural_equation[f521ab3a883f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.18869v1.eq_1562
E_{\mathrm{av}} = \langle ψ| H | ψ\rangle
arxiv_extracted
["a", "t", "m", "h", "r", "E"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.18869v1
cross_domain_amplification
p
a
urn:hailstone:chemistry_physics:structural_equation[970fa0eb7513]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.18561v1.eq_1563
\partial_tψ(x,t)-\frac{1}{2}\partial^2_{x^2} ψ(x,t)=g\, S(x,t)^2\, ψ(x,t)
arxiv_extracted
["a", "t", "i", "p", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.18561v1
cross_domain_amplification
b
r
urn:hailstone:chemistry_physics:structural_equation[84a27c05bcf5]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.18822v1.eq_1564
b^{(α)}_{qe}(t)=\frac14[E_α(-λ^αt^α)]^2\sin^2(ωt)
arxiv_extracted
["e", "f", "q", "t", "r", "b"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.18822v1
cross_domain_amplification
u_{B}
e
urn:hailstone:chemistry_physics:structural_equation[177ca0c92c86]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.16181v1.eq_1565
u_{B}^{\text{eff}} = u + σ_y^2/2 > u_{A}^{\text{eff}}
arxiv_extracted
["t", "x", "e", "u_{B}"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.16181v1
cross_domain_amplification
b_{qe}
c
urn:hailstone:chemistry_physics:structural_equation[f99ba99dc4e8]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.12435v1.eq_1566
b_{qe}(t)=\frac{1}{4}e^{-λt}\sin^2(ωt)
arxiv_extracted
["f", "b_{qe}", "a", "t", "r", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.12435v1
cross_domain_amplification
c
L
urn:hailstone:chemistry_physics:structural_equation[98e89c487075]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.12309v1.eq_1567
{\cal N}=uL^3
arxiv_extracted
["a", "u", "L", "c", "l", "N"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.12309v1
cross_domain_amplification
q
l
urn:hailstone:chemistry_physics:structural_equation[2b68ec8ca27c]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.09009v2.eq_1568
q_{\parallel}=0
arxiv_extracted
["q", "a", "p", "r", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.09009v2
cross_domain_amplification
v_B
b
urn:hailstone:chemistry_physics:structural_equation[777c1475f59f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.08021v1.eq_1569
v_B(\mathbf{x})=\mathbf{t}(\mathbf{x})^{\!\top}\mathbf{D}\,\mathbf{n}(\mathbf{x})
arxiv_extracted
["a", "t", "v_B", "m", "h", "b"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.08021v1
cross_domain_amplification
t
m
urn:hailstone:chemistry_physics:structural_equation[3e7bd78483d9]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.06010v1.eq_1570
t_{\text{mix}} = \exp [Ω(L)]
arxiv_extracted
["t", "m", "e", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.06010v1
cross_domain_amplification
T
r
urn:hailstone:chemistry_physics:structural_equation[f668a62b7379]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.02681v2.eq_1571
T_{\mathrm{BKT}}=0.8928(2)
arxiv_extracted
["a", "t", "m", "h", "r", "T"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.02681v2
cross_domain_amplification
t
h
urn:hailstone:chemistry_physics:structural_equation[1697d2f871e4]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.01269v1.eq_1572
σ_{\text{th}}^{*} = \sqrt{π/2} \approx 125.3\%
arxiv_extracted
["t", "h", "e", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.01269v1
cross_domain_amplification
n
p
urn:hailstone:chemistry_physics:structural_equation[46f6d707caa9]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2601.02417v1.eq_1573
\nabla^2 p = 0
arxiv_extracted
["a", "p", "n", "b", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2601.02417v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[4f0f44984d77]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.25054v1.eq_1574
\mathcal{N}=1
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.25054v1
cross_domain_amplification
t
o
urn:hailstone:chemistry_physics:structural_equation[2fb6a851d691]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.24397v1.eq_1575
κ_4/κ^2_2 = (9/5)τ_{\text{hop}}/T
arxiv_extracted
["e", "t", "h", "o", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.24397v1
cross_domain_amplification
c
m
urn:hailstone:chemistry_physics:structural_equation[01be5ed7873b]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.23195v1.eq_1576
α_c(κ)=\frac{2}{π\,\mathbb E[(κ-Z)_+^2]}
arxiv_extracted
["f", "a", "m", "r", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.23195v1
cross_domain_amplification
x
x
urn:hailstone:chemistry_physics:structural_equation[b8dc0e38940d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.23195v1.eq_1577
(x)_+=\max\{x,0\}
arxiv_extracted
["m", "a", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.23195v1
cross_domain_amplification
n
n
urn:hailstone:chemistry_physics:structural_equation[17dbb88c7cfa]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.22276v1.eq_1578
φ_{n+1}=F(φ_{n})
arxiv_extracted
["n", "F"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.22276v1
cross_domain_amplification
s
t
urn:hailstone:chemistry_physics:structural_equation[9f1d5ff2c350]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.18307v1.eq_1579
s_{\text{tri,kag}} = s_{\text{dim,hex}} = \frac{1}{2 π} \int_0^{ 2 π/3} \log( 2 + 2 \cos k) dk \approx 0.323065947\ldots
arxiv_extracted
["s", "t", "e", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.18307v1
cross_domain_amplification
f
r
urn:hailstone:chemistry_physics:structural_equation[5d9f23e3cdc3]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.16536v1.eq_1580
f_\mathrm{c}=\lim_{\hatλ\to0}\hatλ/\hatμ_\mathrm{c}^2(\hatλ)
arxiv_extracted
["f", "a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.16536v1
cross_domain_amplification
f
r
urn:hailstone:chemistry_physics:structural_equation[f29aa7c29dc0]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.16536v1.eq_1581
f_\mathrm{c}=11.1097(20)_\mathrm{stat}(09)_\mathrm{sys}=11.1097(22)_\mathrm{tot}
arxiv_extracted
["f", "a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.16536v1
cross_domain_amplification
J
y
urn:hailstone:chemistry_physics:structural_equation[376191b5f039]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.12124v1.eq_1582
J(x,y)=o(|x-y|^{-2})
arxiv_extracted
["o", "y", "J", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.12124v1
cross_domain_amplification
S
r
urn:hailstone:chemistry_physics:structural_equation[1a1da26758b4]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.11965v1.eq_1583
S_{\mathrm{imp}}(T \to 0) = \ln[2\cos(π/(n+2))]
arxiv_extracted
["a", "t", "m", "h", "S", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.11965v1
cross_domain_amplification
S
r
urn:hailstone:chemistry_physics:structural_equation[8959b94e4ad1]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.11965v1.eq_1584
S_{\mathrm{imp}}(T \to 0) = \ln 2
arxiv_extracted
["a", "t", "m", "h", "S", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.11965v1
cross_domain_amplification
v
i
urn:hailstone:chemistry_physics:structural_equation[1ef4262093bd]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.10389v1.eq_1585
\varphi=N^+/N
arxiv_extracted
["a", "h", "i", "p", "r", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.10389v1
cross_domain_amplification
d
t
urn:hailstone:chemistry_physics:structural_equation[503f1a7a7dd9]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.07659v1.eq_1586
ds^{2} = C_{\mathrm{vac}}/I(x,x+ε)
arxiv_extracted
["a", "t", "m", "s", "d", "C"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.07659v1
cross_domain_amplification
X
l
urn:hailstone:chemistry_physics:structural_equation[d5b887ca0789]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.07659v1.eq_1587
X_{\text{loc}}=2
arxiv_extracted
["e", "t", "X", "l", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.07659v1
cross_domain_amplification
g_{ij}
j
urn:hailstone:chemistry_physics:structural_equation[d14b86f013a4]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.07659v1.eq_1588
g_{ij} = V^{2/D}γ_{ij}
arxiv_extracted
["V", "D", "j", "i", "g_{ij}"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.07659v1
cross_domain_amplification
X
l
urn:hailstone:chemistry_physics:structural_equation[d5b887ca0789]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.07659v1.eq_1589
X_{\text{loc}}=2
arxiv_extracted
["e", "t", "X", "l", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.07659v1
cross_domain_amplification
S_{q
u
urn:hailstone:chemistry_physics:structural_equation[806c4fe95d7b]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.00894v1.eq_1590
S_{q,s}(p)=k_{s}\sum^{W}_{i\geq1}p_{i}\ln_{q}1/p_{i}
arxiv_extracted
["p", "S_{q", "u", "s", "k_{s}"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.00894v1
cross_domain_amplification
k_{s}
a
urn:hailstone:chemistry_physics:structural_equation[b7245c10145f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.00894v1.eq_1591
k_{s}=k^{q}(e_{\max}/(W^σ-1))^{1-q}
arxiv_extracted
["e", "q", "a", "m", "k_{s}", "k"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.00894v1
cross_domain_amplification
p
a
urn:hailstone:chemistry_physics:structural_equation[612a38cc579b]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.00894v1.eq_1592
\partial S_{q,s}/\partial U=1/\vert T\vert^{q}_{\pm}
arxiv_extracted
["a", "t", "i", "p", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.00894v1
cross_domain_amplification
p
a
urn:hailstone:chemistry_physics:structural_equation[fe24ab9b3c98]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2512.00894v1.eq_1593
\partial S_{BG}/\partial U=1/T
arxiv_extracted
["a", "t", "i", "p", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2512.00894v1
cross_domain_amplification
d
m
urn:hailstone:chemistry_physics:structural_equation[2ceffae1b3bc]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.21004v1.eq_1594
(d,m)=(3,1)
arxiv_extracted
["d", "m"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.21004v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[24ee74ef1d7e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.20907v1.eq_1595
\mathcal H_{xt}=L^2(\mathcal M_{xt})
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.20907v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[1ff40f3961f2]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.20907v1.eq_1596
\mathcal H_{\text{total}} = \mathcal H_{xt} \oplus \mathcal H_{kE}
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.20907v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[e792b551a724]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.20907v1.eq_1597
\mathcal H_{kE}=L^2(\mathcal M_{kE})
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.20907v1
cross_domain_amplification
m
b
urn:hailstone:chemistry_physics:structural_equation[c5cea30e77ef]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.18510v1.eq_1598
\mathbb{H}^2 = {(x,y)}|y>0
arxiv_extracted
["a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.18510v1
cross_domain_amplification
J_2
J_1
urn:hailstone:chemistry_physics:structural_equation[d8092a1ea55e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.14081v1.eq_1599
J_2/J_1 = 0.1, 0.5
arxiv_extracted
["J_2", "J_1"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.14081v1
cross_domain_amplification
J_2
J_1
urn:hailstone:chemistry_physics:structural_equation[d8092a1ea55e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.14081v1.eq_1600
J_2/J_1 = 0.1, 0.5
arxiv_extracted
["J_2", "J_1"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.14081v1
cross_domain_amplification
I
t
urn:hailstone:chemistry_physics:structural_equation[ebfe30c51037]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.12247v1.eq_1601
I \propto \sum_{i=1}^N \vec{r}_i^{\,2}
arxiv_extracted
["t", "o", "p", "r", "I"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.12247v1
cross_domain_amplification
V
r
urn:hailstone:chemistry_physics:structural_equation[ebb939c9889d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.12247v1.eq_1602
V(r) = (1/2)\, m\, ω^2 r^2
arxiv_extracted
["V", "m", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.12247v1
cross_domain_amplification
v
v_0
urn:hailstone:chemistry_physics:structural_equation[b5ae95bfde60]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.10405v2.eq_1603
v=v_0=-1
arxiv_extracted
["v_0", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.10405v2
cross_domain_amplification
p
l
urn:hailstone:chemistry_physics:structural_equation[3c065b59cd15]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.10405v2.eq_1604
(p,\ell)=(2,2)
arxiv_extracted
["e", "p", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.10405v2
cross_domain_amplification
R
B
urn:hailstone:chemistry_physics:structural_equation[a6ad845e75fe]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.10393v2.eq_1605
R_\text{BB}=R_\text{FK}
arxiv_extracted
["e", "B", "t", "R", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.10393v2
cross_domain_amplification
h_n
n
urn:hailstone:chemistry_physics:structural_equation[8688da769687]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.09280v1.eq_1606
h_n(k) = n h(k/n)
arxiv_extracted
["k", "n", "h_n", "h"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.09280v1
cross_domain_amplification
S
S_k
urn:hailstone:chemistry_physics:structural_equation[0e5f0e533d28]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.09280v1.eq_1607
\{S\geq h_n\} = \{S_k\geq h_n(k)\;\forall k\in\{0,\dots,n\}\}
arxiv_extracted
["e", "g", "q", "S_k", "S", "h_n"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.09280v1
cross_domain_amplification
P
h_n
urn:hailstone:chemistry_physics:structural_equation[99195056d91d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.09280v1.eq_1608
P(S\geq h_n \,|\, S_0=0,\, S_n=\lceil h_n(n) \rceil) = e^{n\int_0^1 I(h'(s)) \,ds + o(n)}
arxiv_extracted
["e", "g", "q", "S", "P", "h_n"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.09280v1
cross_domain_amplification
P
o
urn:hailstone:chemistry_physics:structural_equation[ecad8b4d46d2]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.09280v1.eq_1609
P^h_n = P(\cdot \,|\, S\geq h_n, S_0=0, S_n=\lceil h_n(n) \rceil)
arxiv_extracted
["d", "P", "o", "h_n", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.09280v1
cross_domain_amplification
m
b
urn:hailstone:chemistry_physics:structural_equation[50cb1348f322]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.09280v1.eq_1610
\mathbb{P}_n^h (S_k \geq h_n(k) + t n^{1/3} ) = e^{-Θ(t^{3/2})}
arxiv_extracted
["a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.09280v1
cross_domain_amplification
E_n
r
urn:hailstone:chemistry_physics:structural_equation[1db251e6f36a]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.09280v1.eq_1611
E_n^h((S_k-h_n(k))^r) = Θ(n^{r/3})
arxiv_extracted
["E_n", "S_k", "h", "h_n", "r", "k"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.09280v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[e81124639e6c]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.09280v1.eq_1612
\mathrm{Var}_{P_n^h}(S_k) = Θ(n^{2/3})
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.09280v1
cross_domain_amplification
m
r
urn:hailstone:chemistry_physics:structural_equation[8d0a3de308de]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.06975v1.eq_1613
\mathfrak{P}_{F,A}:=\sup_{ρ\in \mathcal{P}(T)}\{ F(\int A(x)ρ(\mathrm{d}x))+h(ρ)\} .
arxiv_extracted
["f", "a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.06975v1
cross_domain_amplification
v
i
urn:hailstone:chemistry_physics:structural_equation[af05b468d10f]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.06975v1.eq_1614
\varphi _{n}(x)=n^{-1}(\varphi (x)+\varphi (T(x))+\cdots +\varphi (T^{n-1}(x)))
arxiv_extracted
["a", "h", "i", "p", "r", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.06975v1
cross_domain_amplification
x
y
urn:hailstone:chemistry_physics:structural_equation[93784b2fb0ce]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.08635v1.eq_1615
σ_{xy}=1/2
arxiv_extracted
["y", "x"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.08635v1
cross_domain_amplification
h
r
urn:hailstone:chemistry_physics:structural_equation[b82489155614]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.04597v1.eq_1616
β\hbar ω=16
arxiv_extracted
["b", "r", "h", "a"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.04597v1
cross_domain_amplification
L
r
urn:hailstone:chemistry_physics:structural_equation[6af1b457d94d]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.03843v3.eq_1617
λ_L^{\rm forward} = λ_L^{\rm backward}
arxiv_extracted
["f", "m", "o", "L", "r"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.03843v3
cross_domain_amplification
v
s
urn:hailstone:chemistry_physics:structural_equation[fcfa833108d0]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2511.01971v1.eq_1618
\varepsilon=4-d
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2511.01971v1
cross_domain_amplification
l
e
urn:hailstone:chemistry_physics:structural_equation[39fa5400985e]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2510.25747v4.eq_1619
\langle ξ_x \rangle / \langle ξ_y \rangle = -T_y/T_x
arxiv_extracted
["e", "g", "a", "n", "l"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2510.25747v4
cross_domain_amplification
n
c
urn:hailstone:chemistry_physics:structural_equation[d0fd0ec4dab9]
1
structural_equation
2
arxiv.cond-mat.stat-mech.2510.24091v5.eq_1620
κ_{n+1}=κ_n(1+\frac{κ_n}{2^{n}}α)
arxiv_extracted
["f", "a", "r", "n", "c"]
arxiv
arxiv
arxiv:cond-mat.stat-mech:2510.24091v5
cross_domain_amplification