s stringlengths 1 39 | o stringclasses 996
values | p stringlengths 7 77 | confidence float64 0.4 1 | predicate_class stringclasses 2
values | community int64 0 14 ⌀ | equation_name stringlengths 14 73 ⌀ | equation_latex stringlengths 5 217 ⌀ | equation_sympy stringclasses 617
values | equation_form stringclasses 472
values | variables stringlengths 2 85 ⌀ | domain stringclasses 119
values | scm_name stringclasses 165
values | source stringlengths 9 50 ⌀ | extraction_method stringclasses 8
values |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
r | m | urn:hailstone:astronomy:structural_equation[75beb8e014c0] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.19842v2.eq_1421 | σ_{\rm DM}/m=0.,0.01,0.05,0.1,0.2 | arxiv_extracted | ["M", "D", "m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.19842v2 | cross_domain_amplification | |
t | A | urn:hailstone:astronomy:structural_equation[a5ad7699065a] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.19751v1.eq_1422 | \text{R.A.} = 0^\circ | arxiv_extracted | ["e", "t", "A", "R", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.19751v1 | cross_domain_amplification | |
t | e | urn:hailstone:astronomy:structural_equation[4549cc56c3c1] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.19751v1.eq_1423 | \text{Dec} = -27.0^\circ | arxiv_extracted | ["t", "D", "e", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.19751v1 | cross_domain_amplification | |
N | r | urn:hailstone:astronomy:structural_equation[402ab27a215c] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.17124v4.eq_1424 | N_{\mathrm{eff}} = 3.044 | arxiv_extracted | ["a", "t", "m", "h", "r", "N"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.17124v4 | cross_domain_amplification | |
r | M | urn:hailstone:astronomy:structural_equation[cdcebcd0259c] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.16317v1.eq_1425 | η(r= 1.0 \, \text{Mpc}) = 0.93^{+0.48}_{-0.40} | arxiv_extracted | ["e", "t", "M", "r", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.16317v1 | cross_domain_amplification | |
D_M | t | urn:hailstone:astronomy:structural_equation[de613a4c4bf2] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.15308v1.eq_1426 | D_M/D_H(z_\mathrm{eff})=4.525\pm0.071 | arxiv_extracted | ["z", "a", "t", "m", "D_M", "D_H"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.15308v1 | cross_domain_amplification | |
z | r | urn:hailstone:astronomy:structural_equation[e5b9f27dab0e] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.15308v1.eq_1427 | z_\mathrm{eff}=2.33 | arxiv_extracted | ["z", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.15308v1 | cross_domain_amplification | |
D_H | h | urn:hailstone:astronomy:structural_equation[d58106d1bb9e] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.15308v1.eq_1428 | D_H(z_\mathrm{eff})/r_d=8.646\pm0.077 | arxiv_extracted | ["z", "a", "t", "m", "h", "D_H"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.15308v1 | cross_domain_amplification | |
D_M | h | urn:hailstone:astronomy:structural_equation[b85a754a432f] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.15308v1.eq_1429 | D_M(z_\mathrm{eff})/r_d=38.90\pm0.38 | arxiv_extracted | ["z", "a", "t", "m", "h", "D_M"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.15308v1 | cross_domain_amplification | |
f | h | urn:hailstone:astronomy:structural_equation[cf0630212300] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.15308v1.eq_1430 | fσ_8(z_\mathrm{eff}) = 0.37\; ^{+0.055}_{-0.065} \,(\mathrm{stat})\, \pm 0.033 \,(\mathrm{sys}) | arxiv_extracted | ["f", "z", "a", "t", "m", "h"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.15308v1 | cross_domain_amplification | |
r | m | urn:hailstone:astronomy:structural_equation[ffbc522e75b1] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.15012v2.eq_1431 | Ω_{\rm m} = 0.192^{+0.305}_{-0.131} | arxiv_extracted | ["m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.15012v2 | cross_domain_amplification | |
E | m | urn:hailstone:astronomy:structural_equation[8d4ce66db78f] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.12422v1.eq_1432 | δE/E = -0.006\pm0.008 | arxiv_extracted | ["p", "E", "m"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.12422v1 | cross_domain_amplification | |
d | p | urn:hailstone:astronomy:structural_equation[6cea15269a1c] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.12422v1.eq_1433 | δ\dot{m_π}/m_π=-(6\pm9)\times10^{-11}\text{ yr}^{-1} | arxiv_extracted | ["m_\u03c0", "t", "o", "p", "d", "m_\u03c0}"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.12422v1 | cross_domain_amplification | |
d | a | urn:hailstone:astronomy:structural_equation[19ae515bacfc] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.12422v1.eq_1434 | \dot{Q}_{0,max} = (3\pm 4)\times10^7 \text{ GeV/yr} | arxiv_extracted | ["Q", "a", "t", "m", "o", "d"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.12422v1 | cross_domain_amplification | |
d | Q | urn:hailstone:astronomy:structural_equation[e294168f4396] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.12422v1.eq_1435 | \dot{Q}_0 =0 | arxiv_extracted | ["t", "d", "Q", "o"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.12422v1 | cross_domain_amplification | |
r | m | urn:hailstone:astronomy:structural_equation[82511775b004] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.12319v2.eq_1436 | Ω_{\rm m} = 0.3 | arxiv_extracted | ["m", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.12319v2 | cross_domain_amplification | |
t_{1b | a | urn:hailstone:astronomy:structural_equation[a22e73f1504d] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.12301v1.eq_1437 | Δt_{1b,1a}=-39.8_{-3.3}^{+3.9} | arxiv_extracted | ["t_{1b", "a"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.12301v1 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[0691f7e782d5] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.12035v2.eq_1438 | β_{\mathrm{R_1}} = 3.51 \pm 0.16 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.12035v2 | cross_domain_amplification | |
m | m | urn:hailstone:astronomy:structural_equation[6373948d5b9a] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.12035v2.eq_1439 | β_{\mathrm{R_3}} = 2.12 \pm 0.16 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.12035v2 | cross_domain_amplification | |
M_{500} | t | urn:hailstone:astronomy:structural_equation[5877c3f6c3f8] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.10455v1.eq_1440 | M_{500}=10^{13-14}M_\odot | arxiv_extracted | ["t", "M", "o", "M_{500}", "d"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.10455v1 | cross_domain_amplification | |
w_0 | w_a | urn:hailstone:astronomy:structural_equation[48949ee39c47] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.09562v1.eq_1441 | w_0=-0.72 \pm 0.21, \, w_a=-0.91^{+0.78}_{-0.64} | arxiv_extracted | ["m", "p", "w_0", "w_a"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.09562v1 | cross_domain_amplification | |
c | t | urn:hailstone:astronomy:structural_equation[f02d0aba2f81] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.09211v2.eq_1442 | c^{3}/G=\text{constant} | arxiv_extracted | ["e", "t", "G", "c", "x"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.09211v2 | cross_domain_amplification | |
B | s | urn:hailstone:astronomy:structural_equation[c577a4341061] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.08896v2.eq_1443 | B_{\rm host}^{\rm local} = 5.44^{+1.13}_{-0.87}μ{\rm G} | arxiv_extracted | ["B", "m", "h", "o", "r", "s"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.08896v2 | cross_domain_amplification | |
f | s | urn:hailstone:astronomy:structural_equation[6191e1f188ad] | 1 | structural_equation | 10 | arxiv.astro-ph.CO.2509.08896v2.eq_1444 | f_{\rm gas} = 0.45^{+0.21}_{-0.19} | arxiv_extracted | ["f", "g", "a", "m", "r", "s"] | arxiv | arxiv | arxiv:astro-ph.CO:2509.08896v2 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[92ad0753f3b8] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.13066v1.eq_1445 | \varepsilon = 0 | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.13066v1 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[c82e742e677f] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.13066v1.eq_1446 | \varepsilon = Ω/2 | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.13066v1 | cross_domain_amplification | |
a | m | urn:hailstone:chemistry_physics:structural_equation[7390d588a2f6] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.12246v1.eq_1447 | Δa/g = κ\, Δ(q/m) | arxiv_extracted | ["g", "m", "q", "a"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.12246v1 | cross_domain_amplification | |
p_c | d | urn:hailstone:chemistry_physics:structural_equation[68c37df6ca91] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.10795v1.eq_1448 | p_c \log p_c / d^2 = 1 / 2 | arxiv_extracted | ["g", "p_c", "o", "d", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.10795v1 | cross_domain_amplification | |
v | s | urn:hailstone:chemistry_physics:structural_equation[58240eff8aa4] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.10395v1.eq_1449 | \varepsilon^{\rm BO}=Θ(k_c d/n) | arxiv_extracted | ["e", "a", "p", "r", "s", "v"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.10395v1 | cross_domain_amplification | |
S | y | urn:hailstone:chemistry_physics:structural_equation[7e40eb195efb] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.10326v2.eq_1450 | S(\infty)/N = (1/N) \ln \binom{N^2}{N} | arxiv_extracted | ["f", "t", "y", "S", "i", "n"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.10326v2 | cross_domain_amplification | |
r | m | urn:hailstone:chemistry_physics:structural_equation[593cd2ae4600] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.10326v2.eq_1451 | γ_{\rm MC} = 1.946 \pm 0.003 | arxiv_extracted | ["M", "m", "p", "r", "C"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.10326v2 | cross_domain_amplification | |
w | i | urn:hailstone:chemistry_physics:structural_equation[dd064a490e83] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.09453v1.eq_1452 | \widetildeχ = \text{d}\langle m \rangle /\text{d}J | arxiv_extracted | ["e", "w", "t", "i", "d"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.09453v1 | cross_domain_amplification | |
S_{BG} | m | urn:hailstone:chemistry_physics:structural_equation[7fc3a633ac9a] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1453 | S_{BG}(p)=k\sum^{W}_{i=1}p_{i}\ln 1/p_{i} | arxiv_extracted | ["m", "u", "p", "s", "k", "S_{BG}"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
s | p_{i} | urn:hailstone:chemistry_physics:structural_equation[ec598b3dcbb7] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1454 | \sum^{W}_{i=1}p_{i}=1 | arxiv_extracted | ["W", "m", "p_{i}", "i", "u", "s"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
s | p_{i} | urn:hailstone:chemistry_physics:structural_equation[eb7e6a741516] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1455 | \sum^{W}_{i=1}p_{i}\,e_{i}=U | arxiv_extracted | ["W", "m", "p_{i}", "i", "u", "s"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
S_{q} | m | urn:hailstone:chemistry_physics:structural_equation[79d2a13ed8ae] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1456 | S_{q}(p)=k\,(\sum^{W}_{i=1}p_{i}^{q}-1)/(1-q) | arxiv_extracted | ["m", "S_{q}", "p", "u", "s", "k"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
s | p_{i} | urn:hailstone:chemistry_physics:structural_equation[284771745770] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1457 | \sum^{W}_{i=1} p_{i}^{q^{\prime}}e_{i} / \sum^{W}_{i=1}p_{i}^{q^{\prime}}=U | arxiv_extracted | ["W", "m", "p_{i}", "i", "u", "s"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
q | e | urn:hailstone:chemistry_physics:structural_equation[39b1cbc3bc31] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1458 | q^{\prime}=1 | arxiv_extracted | ["e", "q", "m", "i", "p", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
q | e | urn:hailstone:chemistry_physics:structural_equation[46892530ddc7] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1459 | q^{\prime}=q | arxiv_extracted | ["e", "q", "m", "i", "p", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
q | e | urn:hailstone:chemistry_physics:structural_equation[0f41f95c76f5] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1460 | q^{\prime}=2-q | arxiv_extracted | ["e", "q", "m", "i", "p", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
T_{q | m | urn:hailstone:chemistry_physics:structural_equation[56c515835fb5] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1461 | 1/T_{q,q^{\prime}}=\partial S_{q} / \partial U | arxiv_extracted | ["q", "m", "i", "p", "r", "T_{q"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
F_{q | m | urn:hailstone:chemistry_physics:structural_equation[d8a31ae86666] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1462 | F_{q,q^{\prime}}=U-T_{q,q^{\prime}}S_{q} | arxiv_extracted | ["q", "m", "i", "F_{q", "p", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
q | e | urn:hailstone:chemistry_physics:structural_equation[39b1cbc3bc31] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.08860v1.eq_1463 | q^{\prime}=1 | arxiv_extracted | ["e", "q", "m", "i", "p", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.08860v1 | cross_domain_amplification | |
P | m | urn:hailstone:chemistry_physics:structural_equation[5eaa289b56e0] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.05431v1.eq_1464 | P(R,T)\sim \exp\big[-(k_F R)^{d+1}Φ_d(u=2R\,T/k_F)\big], | arxiv_extracted | ["m", "P", "i", "R", "s", "T"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.05431v1 | cross_domain_amplification | |
S | b | urn:hailstone:chemistry_physics:structural_equation[ea390f51af9e] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2605.05366v1.eq_1465 | S^2/\mathbb{Z}_2 = \mathbb{RP}^2 | arxiv_extracted | ["a", "t", "m", "h", "S", "b"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2605.05366v1 | cross_domain_amplification | |
T | r | urn:hailstone:chemistry_physics:structural_equation[d66164a0abf0] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.27746v1.eq_1466 | T_\mathrm{N} = 14 | arxiv_extracted | ["a", "t", "m", "h", "r", "T"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.27746v1 | cross_domain_amplification | |
c_{3 | c | urn:hailstone:chemistry_physics:structural_equation[f9ab6e22a708] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.27226v1.eq_1467 | c_{3,0} =c_{2,1} = c | arxiv_extracted | ["c_{3", "c", "c_{2"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.27226v1 | cross_domain_amplification | |
r | r | urn:hailstone:chemistry_physics:structural_equation[839c238168e6] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.25351v1.eq_1468 | β_{\rm fo}=T_{\rm fo}^{-1} | arxiv_extracted | ["f", "m", "o", "r", "T"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.25351v1 | cross_domain_amplification | |
d | f | urn:hailstone:chemistry_physics:structural_equation[b2ce695f5521] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.24458v1.eq_1469 | \dotΣ = σ_0 f | arxiv_extracted | ["t", "f", "d", "o"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.24458v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[d17d22711dc2] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.24458v1.eq_1470 | Σ_{\mathrm{life}} = σ_0 \Nstar | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.24458v1 | cross_domain_amplification | |
s | a | urn:hailstone:chemistry_physics:structural_equation[edd27a030a4c] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.24458v1.eq_1471 | \sigstar \propto M^{3/4+1/4-1}=M^0 | arxiv_extracted | ["g", "a", "t", "i", "s"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.24458v1 | cross_domain_amplification | |
D | r | urn:hailstone:chemistry_physics:structural_equation[12dfa278179d] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.23752v1.eq_1472 | ΔD_\mathrm{KL} = (3/2)[R_0 - \ln R_0 - 1] = (3/2) d_\mathrm{IS}(T_\mathrm{eff}, T_\mathrm{core}) | arxiv_extracted | ["D", "a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.23752v1 | cross_domain_amplification | |
r | l | urn:hailstone:chemistry_physics:structural_equation[4e8b5897f70f] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.22521v2.eq_1473 | {\rm TEN} = 2 \ln 2 | arxiv_extracted | ["T", "m", "r", "E", "l", "N"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.22521v2 | cross_domain_amplification | |
r | l | urn:hailstone:chemistry_physics:structural_equation[d7f09d1a8233] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.22521v2.eq_1474 | {\rm TEN} = \ln 2 | arxiv_extracted | ["T", "m", "r", "E", "l", "N"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.22521v2 | cross_domain_amplification | |
q | f | urn:hailstone:chemistry_physics:structural_equation[bfe1d82e71ee] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.22448v1.eq_1475 | Γ(q\to\infty) = βK(1-ξ) | arxiv_extracted | ["f", "q", "t", "i", "o", "n"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.22448v1 | cross_domain_amplification | |
q | t | urn:hailstone:chemistry_physics:structural_equation[5bb87a760e90] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.22448v1.eq_1476 | q > q_c = κ_0/\sqrt{ξ-1} | arxiv_extracted | ["q", "q_c", "t", "r", "s"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.22448v1 | cross_domain_amplification | |
d | l | urn:hailstone:chemistry_physics:structural_equation[a9e976cdeb36] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.21341v1.eq_1477 | d_{\rm hull}=1.333\,29(14)=4/3 | arxiv_extracted | ["m", "h", "u", "r", "d", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.21341v1 | cross_domain_amplification | |
p_c | m | urn:hailstone:chemistry_physics:structural_equation[614d0fd4b92b] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.21165v1.eq_1478 | p_c^s = 0.822725 \pm 0.000044 | arxiv_extracted | ["s", "p", "m", "p_c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.21165v1 | cross_domain_amplification | |
p_c | m | urn:hailstone:chemistry_physics:structural_equation[a4a8c05b3c79] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.21165v1.eq_1479 | p_c^b = 0.798161 \pm 0.000044 | arxiv_extracted | ["p", "b", "m", "p_c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.21165v1 | cross_domain_amplification | |
K_c | K | urn:hailstone:chemistry_physics:structural_equation[69091302cffa] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.16288v1.eq_1480 | K_c=K_\#=3π/4 | arxiv_extracted | ["K", "K_c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.16288v1 | cross_domain_amplification | |
W_β | s | urn:hailstone:chemistry_physics:structural_equation[5278d30f9db7] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.16288v1.eq_1481 | W_β(θ)=(e^{β\cos(2πθ)}-1)/β | arxiv_extracted | ["e", "o", "W_\u03b2", "s", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.16288v1 | cross_domain_amplification | |
K_c | K | urn:hailstone:chemistry_physics:structural_equation[3efd465a7541] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.16288v1.eq_1482 | K_c(β) = K_\#(β) | arxiv_extracted | ["K", "K_c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.16288v1 | cross_domain_amplification | |
W_{R} | R | urn:hailstone:chemistry_physics:structural_equation[7808b72f3640] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.16288v1.eq_1483 | W_{R}(θ) = (R-2π|θ|)_{+}^2 | arxiv_extracted | ["R", "W_{R}"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.16288v1 | cross_domain_amplification | |
t | F | urn:hailstone:chemistry_physics:structural_equation[cb6ed25ecc26] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.15420v1.eq_1484 | \tilde{F}(Δ)=\sin(\frac{πd}{2}) \log Z_{S^d} | arxiv_extracted | ["e", "F", "t", "i", "d", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.15420v1 | cross_domain_amplification | |
d | e | urn:hailstone:chemistry_physics:structural_equation[b45c7859b7d2] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.15420v1.eq_1485 | d\tilde{F}/dΔ|_{Δ=Δ_\mathrm{local}}=0 | arxiv_extracted | ["e", "t", "i", "d", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.15420v1 | cross_domain_amplification | |
r | c | urn:hailstone:chemistry_physics:structural_equation[a878b221e4df] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.13885v2.eq_1486 | γ_{\rm c}=2 | arxiv_extracted | ["c", "m", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.13885v2 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[cbdd82f78e51] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.12340v1.eq_1487 | λ_{\mathrm{cut}}^{*} = ε | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.12340v1 | cross_domain_amplification | |
m_{eff} | x | urn:hailstone:chemistry_physics:structural_equation[76461d5e9638] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.11173v1.eq_1488 | m_{eff}(x) = m_{eff}|x|^α | arxiv_extracted | ["m_{eff}", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.11173v1 | cross_domain_amplification | |
V_{ext} | c | urn:hailstone:chemistry_physics:structural_equation[6f408127fb03] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.11173v1.eq_1489 | V_{ext}(x)=\frac{1}{2}m_{eff}ω^2 |x|^{α+2} | arxiv_extracted | ["f", "a", "r", "c", "V_{ext}", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.11173v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[4736b3054e9e] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.06486v1.eq_1490 | \mathcal{R}=L_y/L_x | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.06486v1 | cross_domain_amplification | |
c | e | urn:hailstone:chemistry_physics:structural_equation[48386b782e27] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.06324v1.eq_1491 | c_{\text{eff}} = 0.522(1) | arxiv_extracted | ["t", "c", "e", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.06324v1 | cross_domain_amplification | |
H_n | n_{i | urn:hailstone:chemistry_physics:structural_equation[c267e344ce44] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.06122v1.eq_1492 | H_n(h,σ)=\sum^n_{i=1}h_i(σ_i-m) | arxiv_extracted | ["m", "h", "u", "n_{i", "s", "H_n"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.06122v1 | cross_domain_amplification | |
d | l | urn:hailstone:chemistry_physics:structural_equation[e6ec1e787748] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.05772v1.eq_1493 | d_{\rm hull} = 1.663(4) | arxiv_extracted | ["m", "h", "u", "r", "d", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.05772v1 | cross_domain_amplification | |
d | n | urn:hailstone:chemistry_physics:structural_equation[ff3a19661509] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.05772v1.eq_1494 | d_{\rm min} = 1.080(10) | arxiv_extracted | ["m", "i", "r", "n", "d"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.05772v1 | cross_domain_amplification | |
d_1 | d_2 | urn:hailstone:chemistry_physics:structural_equation[3e9302787d5b] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.04922v1.eq_1495 | (d_1, d_2) = (1, 0) | arxiv_extracted | ["d_2", "d_1"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.04922v1 | cross_domain_amplification | |
d_1 | d_2 | urn:hailstone:chemistry_physics:structural_equation[36e398e38074] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.04922v1.eq_1496 | (d_1, d_2) = (0, 2) | arxiv_extracted | ["d_2", "d_1"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.04922v1 | cross_domain_amplification | |
S | S | urn:hailstone:chemistry_physics:structural_equation[f955d1b01526] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.04346v1.eq_1497 | |S^z| = S | arxiv_extracted | ["z", "S"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.04346v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[574ca8addcef] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.03977v1.eq_1498 | \mathcal{O} = χ_{a_1}χ_{a_2}\ldots χ_{a_n} | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.03977v1 | cross_domain_amplification | |
l | r | urn:hailstone:chemistry_physics:structural_equation[04b3d563e81d] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.03770v1.eq_1499 | χ\left(M\right)=0 | arxiv_extracted | ["e", "f", "t", "M", "r", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.03770v1 | cross_domain_amplification | |
h | x | urn:hailstone:chemistry_physics:structural_equation[966d4c8ae5cd] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.03711v1.eq_1500 | h(x,t)=(3t^2x+x^3)/6t | arxiv_extracted | ["t", "h", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.03711v1 | cross_domain_amplification | |
l | e | urn:hailstone:chemistry_physics:structural_equation[374da6080573] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.02907v1.eq_1501 | \langle ΔN^2(t) \rangle = \langle (N(t) - N(0))^2 \rangle | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.02907v1 | cross_domain_amplification | |
L | G | urn:hailstone:chemistry_physics:structural_equation[454f135e4f36] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.01484v1.eq_1502 | Δ(L,T) = A L^{d+η} G_-(L|t/T_c|) | arxiv_extracted | ["G", "d", "A", "L", "T"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.01484v1 | cross_domain_amplification | |
c_{5 | P | urn:hailstone:chemistry_physics:structural_equation[344429009cc3] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.00870v1.eq_1503 | c_{5\text{-Potts}} = 1.1375 \pm 0.0211 i | arxiv_extracted | ["e", "c_{5", "t", "P", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.00870v1 | cross_domain_amplification | |
l | a | urn:hailstone:chemistry_physics:structural_equation[b897efce3323] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2604.00115v1.eq_1504 | \left(\partial S/\partial H\right)_T = \left(\partial M/\partial T\right)_H | arxiv_extracted | ["e", "f", "a", "t", "p", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2604.00115v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[ef8e34effc3e] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.29035v1.eq_1505 | χ^2/\mathrm{dof}=0.50 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.29035v1 | cross_domain_amplification | |
m | a | urn:hailstone:chemistry_physics:structural_equation[d3e208066318] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.28853v1.eq_1506 | \mathcal{N}=4 | arxiv_extracted | ["a", "t", "m", "h", "c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.28853v1 | cross_domain_amplification | |
K | r | urn:hailstone:chemistry_physics:structural_equation[e68de4eaffc9] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.28632v1.eq_1507 | K_{\mathrm{sech}}=1/(2 π\cosh[(x-y)/2]) | arxiv_extracted | ["a", "t", "m", "h", "r", "K"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.28632v1 | cross_domain_amplification | |
d | d_c | urn:hailstone:chemistry_physics:structural_equation[f6d7b396bbe5] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.27992v1.eq_1508 | d<d_c=4 | arxiv_extracted | ["d", "d_c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.27992v1 | cross_domain_amplification | |
l | e | urn:hailstone:chemistry_physics:structural_equation[3a2b26dd39ba] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.27930v1.eq_1509 | \langle Z_0^r Z_R^{\dagger r}\rangle^*=\langle Z_0^r Z_{L-R}^{\dagger r}\rangle | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.27930v1 | cross_domain_amplification | |
m | x | urn:hailstone:chemistry_physics:structural_equation[46ceb3cbe7aa] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.27826v2.eq_1510 | ρ_{\max}=0.2771 | arxiv_extracted | ["m", "a", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.27826v2 | cross_domain_amplification | |
l | e | urn:hailstone:chemistry_physics:structural_equation[593e30f3bc6b] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.27322v1.eq_1511 | \langle\bar{q}_\text{out}/\bar{q}_\text{in} \rangle = 1.03 | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.27322v1 | cross_domain_amplification | |
l | e | urn:hailstone:chemistry_physics:structural_equation[69aeca0a7d01] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.27322v1.eq_1512 | \langle\barβ_\text{out}/\barβ_\text{in} \rangle = 1.18 | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.27322v1 | cross_domain_amplification | |
l | e | urn:hailstone:chemistry_physics:structural_equation[c8a1fa8523f0] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.26897v1.eq_1513 | \langle Q_3\rangle=0 | arxiv_extracted | ["e", "g", "a", "n", "l"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.26897v1 | cross_domain_amplification | |
m | m | urn:hailstone:chemistry_physics:structural_equation[91705a8e69b5] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.24746v1.eq_1514 | Δ\mathrm{AIC}=16.8 | arxiv_extracted | ["a", "t", "m", "h", "r"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.24746v1 | cross_domain_amplification | |
J | c | urn:hailstone:chemistry_physics:structural_equation[c65a95590289] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.22736v1.eq_1515 | J_{\text{c}}=2.584(8) | arxiv_extracted | ["e", "t", "J", "c", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.22736v1 | cross_domain_amplification | |
d | q | urn:hailstone:chemistry_physics:structural_equation[56cc3614af99] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.21391v2.eq_1516 | dy/dx = y^q | arxiv_extracted | ["q", "d", "y", "x"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.21391v2 | cross_domain_amplification | |
T_c | p_c | urn:hailstone:chemistry_physics:structural_equation[ec5dc9995f16] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.21303v1.eq_1517 | T_c(p_c)=0 | arxiv_extracted | ["p_c", "T_c"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.21303v1 | cross_domain_amplification | |
r | M | urn:hailstone:chemistry_physics:structural_equation[d1bfb74abc3d] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.21303v1.eq_1518 | φ_{\rm RSIM}=1 | arxiv_extracted | ["M", "m", "S", "r", "R", "I"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.21303v1 | cross_domain_amplification | |
h | a | urn:hailstone:chemistry_physics:structural_equation[dae3b4656d45] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.22347v2.eq_1519 | [\hat{S}, \hat{R}] = i\mathcal{D} | arxiv_extracted | ["t", "S", "h", "a"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.22347v2 | cross_domain_amplification | |
D | O | urn:hailstone:chemistry_physics:structural_equation[f70259feaaba] | 1 | structural_equation | 2 | arxiv.cond-mat.stat-mech.2603.20917v2.eq_1520 | \Dloc(λ)=Cλ^4+O(λ^6) | arxiv_extracted | ["D", "O", "o", "c", "l", "C"] | arxiv | arxiv | arxiv:cond-mat.stat-mech:2603.20917v2 | cross_domain_amplification |
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