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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
m | f | urn:hailstone:chemistry_physics:structural_equation[1d7b28a0e744] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.23704v1.eq_1621 | \mathbf{q}=0 | arxiv_extracted | ["f", "a", "t", "m", "h", "b"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.23704v1 | cross_domain_amplification | |
J_{z | r | urn:hailstone:chemistry_physics:structural_equation[8c48b25b603f] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.23704v1.eq_1622 | J_{z\pm} = 1/\sqrt{2} | arxiv_extracted | ["q", "m", "p", "J_{z", "r", "s"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.23704v1 | cross_domain_amplification | |
J_{z | r | urn:hailstone:chemistry_physics:structural_equation[8c48b25b603f] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.23704v1.eq_1623 | J_{z\pm} = 1/\sqrt{2} | arxiv_extracted | ["q", "m", "p", "J_{z", "r", "s"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.23704v1 | cross_domain_amplification | |
t | z | urn:hailstone:chemistry_physics:structural_equation[f5f938400962] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.21336v1.eq_1624 | Ψ_\text{pzc} = Ψ_\text{eq}[1 - \hat{Z}(0)/R_F] | arxiv_extracted | ["e", "z", "t", "p", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.21336v1 | cross_domain_amplification | |
x_1 | s | urn:hailstone:chemistry_physics:structural_equation[1832d3fdc182] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.21269v2.eq_1625 | x_1^s=1/4x_2^s | arxiv_extracted | ["s", "x_1", "x_2"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.21269v2 | cross_domain_amplification | |
c | N | urn:hailstone:chemistry_physics:structural_equation[ddb1fa5fbdba] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.20758v2.eq_1626 | {\cal N}=2 | arxiv_extracted | ["N", "c", "l", "a"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.20758v2 | cross_domain_amplification | |
f | g_{YM} | urn:hailstone:chemistry_physics:structural_equation[e97833b65e38] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.20758v2.eq_1627 | \frac{1}{g_{YM}^2}=0 | arxiv_extracted | ["f", "a", "g_{YM}", "r", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.20758v2 | cross_domain_amplification | |
R | D | urn:hailstone:chemistry_physics:structural_equation[9d3088405160] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.20758v2.eq_1628 | θ_{RDM}= θ_{4D}-π | arxiv_extracted | ["M", "D", "R"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.20758v2 | cross_domain_amplification | |
l | i | urn:hailstone:chemistry_physics:structural_equation[0c593f2d36ee] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.20003v2.eq_1629 | \lim_{t\to\infty} C_α(t,t)=T_B/Ω^2 | arxiv_extracted | ["t", "m_{t", "o", "i", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.20003v2 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[60329d0bd4d6] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.19459v2.eq_1630 | \varphi = 0 | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.19459v2 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[db785559101c] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.19459v2.eq_1631 | \varphi = π/2 | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.19459v2 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[d42c86318f41] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.21803v2.eq_1632 | \varepsilon=(P_c-P)/P_c | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.21803v2 | cross_domain_amplification | |
v | i | urn:hailstone:chemistry_physics:structural_equation[65e8784bdc04] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.17637v2.eq_1633 | Δ_\varphi=(d-2+η)/2 | arxiv_extracted | ["a", "h", "i", "p", "r", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.17637v2 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[f606c3ef4b33] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.17637v2.eq_1634 | Δ_\varepsilon=d-1/ν | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.17637v2 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[c9f23b77a646] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.12614v1.eq_1635 | \mathcal R_0 = 1 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.12614v1 | cross_domain_amplification | |
x_{t | t | urn:hailstone:chemistry_physics:structural_equation[ff24333f6c3e] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.11763v1.eq_1636 | x_{t+1}=A_t x_t+η_t | arxiv_extracted | ["t", "A_t", "x_t", "x_{t"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.11763v1 | cross_domain_amplification | |
s_i | t | urn:hailstone:chemistry_physics:structural_equation[f4b0804372bb] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.10723v1.eq_1637 | s_i(t)=1 | arxiv_extracted | ["t", "s_i"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.10723v1 | cross_domain_amplification | |
s_i | t | urn:hailstone:chemistry_physics:structural_equation[4d542c98fd6e] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.10723v1.eq_1638 | s_i(t)=-1 | arxiv_extracted | ["t", "s_i"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.10723v1 | cross_domain_amplification | |
s_i | t | urn:hailstone:chemistry_physics:structural_equation[70bb57ad86d8] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.10723v1.eq_1639 | s_i(t)=0 | arxiv_extracted | ["t", "s_i"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.10723v1 | cross_domain_amplification | |
x_{i} | t | urn:hailstone:chemistry_physics:structural_equation[77b48d93599d] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.10723v1.eq_1640 | x_{i}(t)=x_{i-1}(t) | arxiv_extracted | ["t", "x_{i", "x_{i}"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.10723v1 | cross_domain_amplification | |
D | c | urn:hailstone:chemistry_physics:structural_equation[7df72c75a195] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.10723v1.eq_1641 | D(t)={\frac{\sum_{i=1}^N \vert s_i(t)+s_{i-1}(t)\vert} {2N}} | arxiv_extracted | ["f", "D", "a", "t", "r", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.10723v1 | cross_domain_amplification | |
d | x | urn:hailstone:chemistry_physics:structural_equation[4e9db44285d7] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.10435v1.eq_1642 | γ\dot{x} = -U'(x) + ξ | arxiv_extracted | ["t", "o", "U", "d", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.10435v1 | cross_domain_amplification | |
l | e | urn:hailstone:chemistry_physics:structural_equation[52bb7d7d646a] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.10435v1.eq_1643 | \langle \exp(βU)\rangle = \lim_{L\rightarrow \infty} L^{-1} \int_0^L \exp(βU(x))dx | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.10435v1 | cross_domain_amplification | |
p | L | urn:hailstone:chemistry_physics:structural_equation[e1465c028ce4] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.10435v1.eq_1644 | τ(\pm L) = 0 | arxiv_extracted | ["p", "m", "L"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.10435v1 | cross_domain_amplification | |
E_{GS} | N_m | urn:hailstone:chemistry_physics:structural_equation[7c5d4974db2b] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.09482v2.eq_1645 | E_{GS}(N_m)/N_m = E_{0} + E_1 /N_m + E_{3/2}/N_m^{3/2}+ ... | arxiv_extracted | ["E_{GS}", "N_m", "E_{0}", "E_1"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.09482v2 | cross_domain_amplification | |
v | d | urn:hailstone:chemistry_physics:structural_equation[e2276b826375] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.07571v1.eq_1646 | Δ(\vec{x}, t, d{t}) = \frac{\partial f}{ \partial t} d{t} | arxiv_extracted | ["e", "t", "d", "c", "v", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.07571v1 | cross_domain_amplification | |
D | K | urn:hailstone:chemistry_physics:structural_equation[0b232e22a3f6] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.07571v1.eq_1647 | D_{\text{KL}}(f + Δ|| f) = A^2 d{t}^2 | arxiv_extracted | ["e", "D", "t", "K", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.07571v1 | cross_domain_amplification | |
f | a | urn:hailstone:chemistry_physics:structural_equation[38e43c2454fb] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.07571v1.eq_1648 | \frac{\partial f}{ \partial t} = - κf (\ln{f} - \int f \ln{f} d{\vec{x}}) | arxiv_extracted | ["f", "a", "p", "r", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.07571v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[6729771ae87e] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2510.07383v1.eq_1649 | \mathcal{N}=2 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2510.07383v1 | cross_domain_amplification | |
J_2 | J_1 | urn:hailstone:chemistry_physics:structural_equation[108d93ae3e53] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.21512v1.eq_1650 | J_2/J_1 = -1/4 | arxiv_extracted | ["J_2", "J_1"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.21512v1 | cross_domain_amplification | |
c | k | urn:hailstone:chemistry_physics:structural_equation[8bb877f6c9e2] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.19617v1.eq_1651 | c(k, l) = c(l, k) | arxiv_extracted | ["c", "l", "k"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.19617v1 | cross_domain_amplification | |
N | r | urn:hailstone:chemistry_physics:structural_equation[4faf22b1b90c] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.18966v1.eq_1652 | N_\mathrm{f} = 4 | arxiv_extracted | ["a", "t", "m", "h", "r", "N"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.18966v1 | cross_domain_amplification | |
s | t | urn:hailstone:chemistry_physics:structural_equation[02cb36578057] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.14175v1.eq_1653 | \sqrt{s^*}=27(11)\text{ keV} | arxiv_extracted | ["s", "t", "q", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.14175v1 | cross_domain_amplification | |
w | i | urn:hailstone:chemistry_physics:structural_equation[4ff0ed60a687] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.13222v2.eq_1654 | with finitely many critical points, and consider the solution of the stochastic differential equation \[ d\boldsymbol{x}_ε(t)=-\nabla U(\boldsymbol{x}_ε(t))\,dt \,+\,\sqrt{2ε}\, d\boldsymbol{w}_{t}\,, \] where | arxiv_extracted | ["f", "w", "t", "h", "i"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.13222v2 | cross_domain_amplification | |
J_2 | J_1 | urn:hailstone:chemistry_physics:structural_equation[1e31ae8a501d] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.11437v1.eq_1655 | J_2/|J_1| = 0.20, 0.22, 0.23, 0.24, 0.3, 0.5, 0.8, | arxiv_extracted | ["J_2", "J_1"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.11437v1 | cross_domain_amplification | |
J_2 | J_1 | urn:hailstone:chemistry_physics:structural_equation[8112bc2ee427] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.11437v1.eq_1656 | J_2/|J_1| = 0.20, 0.22, 0.23, | arxiv_extracted | ["J_2", "J_1"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.11437v1 | cross_domain_amplification | |
J_2 | J_1 | urn:hailstone:chemistry_physics:structural_equation[d9ae6bcb188e] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.11437v1.eq_1657 | J_2/|J_1| = 0.5, 0.8 | arxiv_extracted | ["J_2", "J_1"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.11437v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[a74ab9f70fb9] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.09640v1.eq_1658 | \mathrm{Var}(W)=\frac{1}{2}\sum_r r\,(a_r^2+b_r^2) | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.09640v1 | cross_domain_amplification | |
N | r | urn:hailstone:chemistry_physics:structural_equation[80bf0a916b6c] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.06528v1.eq_1659 | N_\textrm{core}=4 | arxiv_extracted | ["e", "t", "r", "N", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.06528v1 | cross_domain_amplification | |
c | J_4 | urn:hailstone:chemistry_physics:structural_equation[c0b1ba678bf8] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.05715v2.eq_1660 | β_2 {\cal P} η_c =-J_4 ησ | arxiv_extracted | ["J_4", "a", "P", "c", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.05715v2 | cross_domain_amplification | |
c_{1} | e | urn:hailstone:chemistry_physics:structural_equation[e184a473d7aa] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.04391v2.eq_1661 | (c_{1},c_{2})=(1/e,0) | arxiv_extracted | ["e", "c_{2}", "c_{1}"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.04391v2 | cross_domain_amplification | |
S_{2} | l | urn:hailstone:chemistry_physics:structural_equation[8ee6e4351231] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.02044v2.eq_1662 | S_{2}(\ell) = α\ell - γ | arxiv_extracted | ["e", "l", "S_{2}"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.02044v2 | cross_domain_amplification | |
t | c | urn:hailstone:chemistry_physics:structural_equation[20581106a8bc] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.01036v1.eq_1663 | η_{\text{c}} = 0.0 | arxiv_extracted | ["t", "c", "e", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.01036v1 | cross_domain_amplification | |
t | b | urn:hailstone:chemistry_physics:structural_equation[2e66bdff49af] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.01036v1.eq_1664 | η_{\text{b}} = 1.0 | arxiv_extracted | ["t", "b", "e", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.01036v1 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[e30ef28853f8] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.00610v3.eq_1665 | \varepsilon = 0, 1 | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.00610v3 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[ee9e0fd9bc48] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.00610v3.eq_1666 | \varepsilon = 1 | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.00610v3 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[fdd3e680af27] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.00610v3.eq_1667 | \varepsilon=1 | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.00610v3 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[e0621adffa9a] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.00610v3.eq_1668 | \varepsilon=0 | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.00610v3 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[ee2456d0db5f] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.00467v1.eq_1669 | \mathcal{A}=M_{N \times N}(\mathbb{R}) | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.00467v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[f8467d995584] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2509.00467v1.eq_1670 | \mathcal{A}= \mathbb{R}^{N} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2509.00467v1 | cross_domain_amplification | |
T | e | urn:hailstone:chemistry_physics:structural_equation[027da9b4c057] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.17548v1.eq_1671 | T^{\text{eq}}(E)=\arg\min_T\{E/T-F(T)/T\} | arxiv_extracted | ["t", "T", "e", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.17548v1 | cross_domain_amplification | |
E | e | urn:hailstone:chemistry_physics:structural_equation[91c0d7e31adc] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.17548v1.eq_1672 | E^{\text{eq}}(T)=\arg\min_E\{E-TS(E)\} | arxiv_extracted | ["t", "E", "e", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.17548v1 | cross_domain_amplification | |
J_{xy} | x | urn:hailstone:chemistry_physics:structural_equation[e60ee1a2b1a9] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.15666v1.eq_1673 | J_{xy}=J(|x-y|)= J/|x-y|^α | arxiv_extracted | ["J_{xy}", "y", "J", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.15666v1 | cross_domain_amplification | |
D | e | urn:hailstone:chemistry_physics:structural_equation[b5654091d074] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.14862v1.eq_1674 | D_{\text{eff}}=v_0^2 τ/[2(1+ ω^2 τ^2)] | arxiv_extracted | ["t", "D", "e", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.14862v1 | cross_domain_amplification | |
F | c | urn:hailstone:chemistry_physics:structural_equation[8bfe2025f2e1] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.14862v1.eq_1675 | F_{\text{ch}}(z)=\text{sech}(πz) | arxiv_extracted | ["e", "F", "t", "c", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.14862v1 | cross_domain_amplification | |
G | c | urn:hailstone:chemistry_physics:structural_equation[ad6a98413c8e] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.14862v1.eq_1676 | G_{\text{ch}}(z)=\mathcal {N}/[e^{αz} + e^{-βz}] | arxiv_extracted | ["e", "t", "G", "c", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.14862v1 | cross_domain_amplification | |
G | c | urn:hailstone:chemistry_physics:structural_equation[a6a7ee721f2f] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.14862v1.eq_1677 | G_{\text{ch}}(z)=(α/π)\,\mathrm{sech}(αz) | arxiv_extracted | ["e", "t", "G", "c", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.14862v1 | cross_domain_amplification | |
S_δ | m_{i | urn:hailstone:chemistry_physics:structural_equation[32c5b96b2896] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1678 | S_δ(\{p_{i}\}) = k\sum_{i=1}^W p_i \Bigl(\ln \frac{1}{p_i} \Bigr)^δ\;(δ>0,\,S_1=S_{BG}) | arxiv_extracted | ["m_{i", "p_{i}", "u", "S_\u03b4", "s", "k"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
S_{BG} | W | urn:hailstone:chemistry_physics:structural_equation[6f9dcb998222] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1679 | S_{BG}=k\sum_{i=1}^W p_i \ln \frac{1}{p_i} | arxiv_extracted | ["W", "m_{i", "u", "s", "k", "S_{BG}"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
S_{δ | n | urn:hailstone:chemistry_physics:structural_equation[7ce8aa68e6a7] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1680 | S_{δ=1/γ}(\{1/W(N)\})=k[\ln W(N)]^{\frac{1}γ} \propto N | arxiv_extracted | ["k", "W", "S_{\u03b4", "n", "l", "N"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
S_q | m_{i | urn:hailstone:chemistry_physics:structural_equation[feeea3716c8c] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1681 | S_q(\{p_{i}\})=k\sum_{i=1}^W p_i \ln_q \frac{1}{p_i} \;(q\in \mathbb{R},\;S_1=S_{BG}) | arxiv_extracted | ["m_{i", "p_{i}", "u", "s", "S_q", "k"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
l | a | urn:hailstone:chemistry_physics:structural_equation[9f3715086dd5] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1682 | \ln_q z =\frac{z^{1-q}-1}{1-q}\; (z\geq0,\;q\in\mathbb{R},\;\ln_1 z=\ln z) | arxiv_extracted | ["f", "z", "a", "n_q", "r", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
l | i | urn:hailstone:chemistry_physics:structural_equation[805cfad03295] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1683 | \ln_q (x\otimes_q y) =\ln_q x + \ln_q y,\, x,y\geq1,\,q\leq 1 | arxiv_extracted | ["t", "n_q", "o", "i", "l", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
x | e | urn:hailstone:chemistry_physics:structural_equation[9729f6119ba1] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1684 | x\otimes_q y=[x^{1-q}+y^{1-q}-1]^{\frac{1}{1-q}}_{+}\;(x\otimes_1 y=xy) | arxiv_extracted | ["e", "t", "m", "i", "o", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
S_{q | m_{i | urn:hailstone:chemistry_physics:structural_equation[cba46c50969f] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1685 | S_{q,δ}(\{p_{i}\})=k\sum_{i=1}^W p_i \Bigl(\ln_q \frac{1}{p_i} \Bigr)^δ\;(q\in\mathbb{R},δ>0) | arxiv_extracted | ["m_{i", "p_{i}", "u", "S_{q", "s", "k"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
S_{q | S_q | urn:hailstone:chemistry_physics:structural_equation[391d743b2ccc] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1686 | S_{q,1}=S_q | arxiv_extracted | ["S_{q", "S_q"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
S_{1 | S_δ | urn:hailstone:chemistry_physics:structural_equation[d4b2d3c2faef] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1687 | S_{1,δ}=S_δ | arxiv_extracted | ["S_{1", "S_\u03b4"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
S_{1 | S_{BG} | urn:hailstone:chemistry_physics:structural_equation[da25532d4686] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.13324v2.eq_1688 | S_{1,1}=S_{BG} | arxiv_extracted | ["S_{1", "S_{BG}"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.13324v2 | cross_domain_amplification | |
d | S | urn:hailstone:chemistry_physics:structural_equation[c450a00e7a90] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.10502v2.eq_1689 | d_{\rm DFS} = 1 + g/8 | arxiv_extracted | ["D", "F", "m", "S", "r", "d"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.10502v2 | cross_domain_amplification | |
p | a | urn:hailstone:chemistry_physics:structural_equation[7a5e722bef03] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.09879v2.eq_1690 | \partial_t ρ+\partial_x j[ρ]=0 | arxiv_extracted | ["a", "t", "i", "p", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.09879v2 | cross_domain_amplification | |
T | T | urn:hailstone:chemistry_physics:structural_equation[24e5a4ffedd7] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.05956v2.eq_1691 | {ρ_T} = \frac{1}{T}\int_0^T {δ( {r(t) - 1} )} dt | arxiv_extracted | ["f", "a", "T", "r", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.05956v2 | cross_domain_amplification | |
P | e | urn:hailstone:chemistry_physics:structural_equation[4a4833fd3c81] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.05956v2.eq_1692 | P(ρ_T= ρ) \sim e^{-T I(ρ)} | arxiv_extracted | ["e", "m", "P", "i", "s", "T"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.05956v2 | cross_domain_amplification | |
c | d | urn:hailstone:chemistry_physics:structural_equation[34c003e75cce] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2508.05956v2.eq_1693 | ρ_c^{(d)}=d(d-4)/(2d-4) | arxiv_extracted | ["c", "d"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2508.05956v2 | cross_domain_amplification | |
r | s | urn:hailstone:chemistry_physics:structural_equation[1ed62f41d37b] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2507.23507v1.eq_1694 | r\lesssim L(t)=(Dt)^{1/2}, | arxiv_extracted | ["e", "s", "l", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2507.23507v1 | cross_domain_amplification | |
b | r | urn:hailstone:economics:structural_equation[d2fdaa3fb160] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2605.04690v1.eq_1695 | \barρ = 0.0073 | arxiv_extracted | ["b", "r", "a"] | arxiv | arxiv | arxiv:q-fin.MF:2605.04690v1 | cross_domain_amplification | |
d | t | urn:hailstone:economics:structural_equation[6fafb47fdfc2] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2604.10492v2.eq_1696 | dF(i) := (\mathcal{E} \circ F)(i)(1) | arxiv_extracted | ["a", "F", "t", "m", "i", "d"] | arxiv | arxiv | arxiv:q-fin.MF:2604.10492v2 | cross_domain_amplification | |
F | F | urn:hailstone:economics:structural_equation[324d80382e21] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2604.09986v1.eq_1697 | F(β^*)=O(F(0)^{1/3}) | arxiv_extracted | ["O", "F"] | arxiv | arxiv | arxiv:q-fin.MF:2604.09986v1 | cross_domain_amplification | |
a | e | urn:hailstone:economics:structural_equation[3a3c9a1e2a9a] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2603.27940v1.eq_1698 | and the weak transport functional \[ V_S^C(μ,ν) := \inf_{π\inΠ_S(μ,ν)} \int_\mathbb{R} C(x,π_x)\,μ(d x), \] for some appropriate cost function | arxiv_extracted | ["e", "a", "t", "h", "n", "d"] | arxiv | arxiv | arxiv:q-fin.MF:2603.27940v1 | cross_domain_amplification | |
m | a | urn:hailstone:economics:structural_equation[16e566a4369d] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2603.04880v1.eq_1699 | \mathcal{C}:=([0,T]\times\mathbb{R}^d)\setminus\mathcal{D} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:q-fin.MF:2603.04880v1 | cross_domain_amplification | |
a | m | urn:hailstone:economics:structural_equation[0c14403f3618] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2602.08527v1.eq_1700 | θ_α^\ast = V^{-1}(μ-r\mathbf{1})+α\,V^{-1}\operatorname{diag}(V)\mathbf{1} | arxiv_extracted | ["V", "a", "t", "m", "r", "s"] | arxiv | arxiv | arxiv:q-fin.MF:2602.08527v1 | cross_domain_amplification | |
a | r | urn:hailstone:economics:structural_equation[1d31fd317fd1] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2602.08527v1.eq_1701 | θ_α^\ast=(μ-r)/σ^{2}+α | arxiv_extracted | ["s", "t", "r", "a"] | arxiv | arxiv | arxiv:q-fin.MF:2602.08527v1 | cross_domain_amplification | |
k | o | urn:hailstone:economics:structural_equation[3b5a9de4ed62] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2602.00784v2.eq_1702 | \{k/n:k=1,\ldots,n\} | arxiv_extracted | ["k", "o", "n", "d", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2602.00784v2 | cross_domain_amplification | |
s | s | urn:hailstone:economics:structural_equation[80d778592422] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2601.10812v1.eq_1703 | ψ(s) = s | arxiv_extracted | ["s"] | arxiv | arxiv | arxiv:q-fin.MF:2601.10812v1 | cross_domain_amplification | |
P | i | urn:hailstone:economics:structural_equation[4426b2a88d83] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2601.06507v1.eq_1704 | P^{(m)}_j(r,λ)=\bigl(1-λ/λ_{\max,j}\bigr)^m r | arxiv_extracted | ["j", "m", "P", "i", "r", "b"] | arxiv | arxiv | arxiv:q-fin.MF:2601.06507v1 | cross_domain_amplification | |
t | h | urn:hailstone:economics:structural_equation[1697d2f871e4] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2601.01269v1.eq_1705 | σ_{\text{th}}^{*} = \sqrt{π/2} \approx 125.3\% | arxiv_extracted | ["t", "h", "e", "x"] | arxiv | arxiv | arxiv:q-fin.MF:2601.01269v1 | cross_domain_amplification | |
N | i | urn:hailstone:economics:structural_equation[448cab3b149e] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2601.01189v1.eq_1706 | N^{-1} \sum_{j=1}^{N} θ_{ij} \int_{0}^{t} φ(t-s)\,dZ_s^{j,N} | arxiv_extracted | ["m_{j", "i", "u", "s", "N"] | arxiv | arxiv | arxiv:q-fin.MF:2601.01189v1 | cross_domain_amplification | |
b | K | urn:hailstone:economics:structural_equation[15c7c2d800f9] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2512.17791v1.eq_1707 | b(T^{-})=K | arxiv_extracted | ["K", "b", "T"] | arxiv | arxiv | arxiv:q-fin.MF:2512.17791v1 | cross_domain_amplification | |
v | e | urn:hailstone:economics:structural_equation[9be41f0787e1] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2512.11765v1.eq_1708 | \vartheta_0=(n-1)/2 | arxiv_extracted | ["e", "a", "t", "h", "r", "v"] | arxiv | arxiv | arxiv:q-fin.MF:2512.11765v1 | cross_domain_amplification | |
v | e | urn:hailstone:economics:structural_equation[3ad32f3968ed] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2512.11765v1.eq_1709 | \vartheta_T=1/2 | arxiv_extracted | ["e", "a", "t", "h", "r", "v"] | arxiv | arxiv | arxiv:q-fin.MF:2512.11765v1 | cross_domain_amplification | |
v | e | urn:hailstone:economics:structural_equation[549972f92118] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2512.11765v1.eq_1710 | \vartheta_0=\vartheta_T=1/2 | arxiv_extracted | ["e", "a", "t", "h", "r", "v"] | arxiv | arxiv | arxiv:q-fin.MF:2512.11765v1 | cross_domain_amplification | |
v | e | urn:hailstone:economics:structural_equation[9be41f0787e1] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2512.11765v1.eq_1711 | \vartheta_0=(n-1)/2 | arxiv_extracted | ["e", "a", "t", "h", "r", "v"] | arxiv | arxiv | arxiv:q-fin.MF:2512.11765v1 | cross_domain_amplification | |
v | e | urn:hailstone:economics:structural_equation[3ad32f3968ed] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2512.11765v1.eq_1712 | \vartheta_T=1/2 | arxiv_extracted | ["e", "a", "t", "h", "r", "v"] | arxiv | arxiv | arxiv:q-fin.MF:2512.11765v1 | cross_domain_amplification | |
W | i | urn:hailstone:economics:structural_equation[0eff499558ed] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2503.13328v2.eq_1713 | . We are interested in finding \[ \sup_{\mathcal M} \sup_τ \mathbb{E}^{\mathcal M} \left[ a(X) I_{ \{ τ= 1 \} } + b(Y) I_{ \{ τ= 2 \} } \right] \] where the first supremum is taken over consistent models | arxiv_extracted | ["e", "a", "W", "i", "r"] | arxiv | arxiv | arxiv:q-fin.MF:2503.13328v2 | cross_domain_amplification | |
Z | n | urn:hailstone:economics:structural_equation[b8d8e01ba6a0] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2503.13328v2.eq_1714 | Z=(z,Z_1,Z_2)=(\int_{\mathbb R} x μ(dx) = \int_{\mathbb R} y ν(dy), X, Y) | arxiv_extracted | ["Z", "z", "Z_2", "Z_1", "i", "n"] | arxiv | arxiv | arxiv:q-fin.MF:2503.13328v2 | cross_domain_amplification | |
p | l | urn:hailstone:economics:structural_equation[c3b454667f56] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2502.08613v8.eq_1715 | p=-\frac{1}α\log\mathbb{E}\exp[-αP] \notag | arxiv_extracted | ["f", "a", "p", "r", "c", "l"] | arxiv | arxiv | arxiv:q-fin.MF:2502.08613v8 | cross_domain_amplification | |
L | t | urn:hailstone:economics:structural_equation[5407243b19fa] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2412.19020v2.eq_1716 | L(x, {\partial_x}) := v^2(x,t) (\partial_x^2 -\partial_x) | arxiv_extracted | ["a", "t", "p", "r", "L", "x"] | arxiv | arxiv | arxiv:q-fin.MF:2412.19020v2 | cross_domain_amplification | |
x | t | urn:hailstone:economics:structural_equation[5ed88c98971f] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2412.10592v2.eq_1717 | x(t):=x_{N(t)}. | arxiv_extracted | ["t", "x_{N", "x"] | arxiv | arxiv | arxiv:q-fin.MF:2412.10592v2 | cross_domain_amplification | |
I_{t} | t_{0} | urn:hailstone:economics:structural_equation[00df27fdad58] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2410.15824v2.eq_1718 | I_{t}^{(a,b)}:=\int_{0}^{t}b(Y_{s})e^{-\int_{s}^{t}a(Y_{r})dr}ds, \quad t\ge 0 | arxiv_extracted | ["a", "t_{0}", "i", "I_{t}", "n", "b"] | arxiv | arxiv | arxiv:q-fin.MF:2410.15824v2 | cross_domain_amplification | |
E_πa | s | urn:hailstone:economics:structural_equation[0deebe83676d] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2410.15824v2.eq_1719 | E_πa(\cdot):=\sum_{j\in S}π_{j}a(j) | arxiv_extracted | ["t", "E_\u03c0a", "d", "o", "s", "c"] | arxiv | arxiv | arxiv:q-fin.MF:2410.15824v2 | cross_domain_amplification | |
I | b | urn:hailstone:economics:structural_equation[a8947d977ba1] | 1 | structural_equation | 5 | arxiv.q-fin.MF.2410.15824v2.eq_1720 | I^{(a,b)}_{}:=(I^{(a,b)}_{t}:t\ge 0). | arxiv_extracted | ["b", "a", "I"] | arxiv | arxiv | arxiv:q-fin.MF:2410.15824v2 | cross_domain_amplification |
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