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 |
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