# Numerical provenance for T472

All values are measured estimates. No simulation or bootstrap solver was
rerun here. Uncertainties are the authors' stated errors, not certified
physical enclosures. Derived error boxes ignore unavailable correlations
and are not joint confidence regions. All arithmetic in the generator is
rational, with no float conversion.

## Primary inputs

- Chang et al., JHEP 03 (2025) 136, arXiv:2411.15300v2, Table 2:
  eta = 0.036297612(48), nu = 0.62997097(12). Table 1 gives
  Delta_sigma = 0.518148806(24), Delta_epsilon = 1.41262528(29).
- Reehorst, JHEP 09 (2022) 177, arXiv:2111.12093, Table 1 and (4.1):
  Delta_epsilon_prime = 3.82951(61). Subtracting exactly 3 gives omega.
- Hasenbusch, PRB 100 (2019) 224517, arXiv:1910.05916v2, abstract:
  XY nu = 0.67169(7), eta = 0.03810(8), omega = 0.789(4).
- Hasenbusch, PRB 102 (2020) 024406, arXiv:2005.04448v2, abstract:
  Heisenberg nu = 0.71164(10), eta = 0.03784(5), omega = 0.759(2).
- Clisby and Duenweg, PRE 94 (2016) 052102, arXiv:2001.03138 (uploaded
  in 2020), abstract and Section IV B: SAW nu = 0.58759700(40),
  Delta1 = 0.528(8). The spatial correction exponent is Delta1/nu.
- Clisby, JPA 50 (2017) 264003, arXiv:1701.08415, abstract:
  SAW gamma = 1.15695300(95).
- Ballesteros et al., JPA 32 (1999) 1-13, arXiv:cond-mat/9805125v2,
  Table 5: percolation nu = 0.8765(16)(2), eta = -0.04602(27)(7).
  First errors are statistical, second due to the correction fit. The
  stored radii are their sums, 0.0018 and 0.00034. Section 5 and Table 8
  give omega = 1.62(13). This is one identified study, not a consensus.
  Borinsky et al., PRD 103 (2021) 116024, arXiv:2103.16224, Table 19 and
  Section 6.2 discuss substantial dispersion in percolation omega estimates.

Four leading exponents are derived from (nu,eta) for the spin and
percolation classes. For SAW the independent pair is (nu,gamma); eta,
alpha,beta,delta follow by scaling. The formula for each output is
monotone separately in each input on these boxes, so checking the corners
is sufficient. The attached checks use an independent RG eigenvalue
parameterisation with exact Sage rationals. All source uncertainty digits
are preserved; derived radii are rounded upward to two significant figures,
including any rounding of their centres.

## Independent numerical comparisons

- Ising: Hasenbusch 2010, arXiv:1004.4486, (34), (60), (63), for nu,eta,omega.
- XY: Campostrini et al. 2006, arXiv:cond-mat/0605083, abstract and (33),
  for all seven exponents.
- Heisenberg: Campostrini et al. 2002, arXiv:cond-mat/0110336, abstract,
  for all six leading exponents. The old beta = 0.3689 +/- 0.0003 does
  not overlap the box derived from Hasenbusch's 2020 nu and eta. It is
  a difference between empirical determinations, not an arithmetic identity
  failure. Its physical cause has not been established in this build;
  neither error bar is widened and no universal agreement is claimed.
  The newer independent bootstrap result of Chester et al., PRD 104 (2021)
  105013, arXiv:2011.14647v2, Table 1 and (21)-(22), provides an additional
  comparison: Delta_phi = 0.518936(67), Delta_s = 1.59488(81). We use these
  bounds, rather than the narrower non-rigorous estimates in the abstract.
- SAW: Clisby 2010, arXiv:1002.0494, Table I, for nu and Delta1;
  Kompaniets and Panzer 2017, arXiv:1705.06483, (38)-(39), for eta and gamma.
- Percolation: Xu et al., Frontiers of Physics 9 (2014) 113-119,
  arXiv:1310.5399v2, Section III A: yt = 1.1413(15), yh = 2.52293(10).
  Compare yt = 1/nu and yh = (5-eta)/2 without changing source uncertainties.

Heisenberg and percolation omega are transcribed and checked against their
primary-source text, but have no independent numerical validation here.
The five scaling relations do not constrain omega. Do not interpret the
25 successful scaling checks as validation of these two omega estimates.

## Controls and precision

Before checking estimates, checks.py verifies the exact d=2 Ising exponent
set, rejects a deliberately changed gamma, and rejects disjoint real
intervals. It then requires finite positive widths, a common consistent
point and exact independent corner values for all leading exponent sets.
The interval residual calculation uses 384 bits solely to avoid arithmetic
rounding affecting these low-precision input boxes; it makes no 100-digit
claim about physical exponents.