  We classify and characterize all invertible anomalies and all allowed
topological terms related to various Standard Models (SM), Grand Unified
Theories (GUT), and Beyond Standard Model (BSM) physics. By all anomalies, we
mean the inclusion of (1) perturbative/local anomalies captured by perturbative
Feynman diagram loop calculations, classified by $\mathbb{Z}$ free classes, and
(2) non-perturbative/global anomalies, classified by finite group
$\mathbb{Z}_N$ torsion classes. Our work built from [arXiv:1812.11967] fuses
the math tools of Adams spectral sequence, Thom-Madsen-Tillmann spectra, and
Freed-Hopkins theorem. For example, we compute bordism groups $\Omega^{G}_d$
and their invertible topological field theory invariants, which characterize
$d$d topological terms and $(d-1)$d anomalies, protected by the following
symmetry group $G$: $Spin\times \frac{SU(3)\times SU(2)\times
U(1)}{\mathbb{Z}_q}$ for SM with $q=1,2,3,6$; $\frac{Spin \times
Spin(n)}{\mathbb{Z}_2^F}$ or $Spin \times Spin(n)$ for SO(10) or SO(18) GUT as
$n=10, 18$; $Spin \times SU(n)$ for Georgi-Glashow SU(5) GUT as $n=5$;
$\frac{Spin\times \frac{SU(4)\times(SU(2)\times
SU(2))}{\mathbb{Z}_{q'}}}{\mathbb{Z}_2^F}$ for Pati-Salam GUT as $q'=1,2$; and
others. For SM with an extra discrete symmetry, we obtain new anomaly matching
conditions of $\mathbb{Z}_{16}$, $\mathbb{Z}_{4}$, and $\mathbb{Z}_{2}$ classes
in 4d beyond the familiar Witten anomaly. Our approach offers an alternative
view of all anomaly matching conditions built from the lower-energy (B)SM or
GUT, in contrast to high-energy Quantum Gravity or String Theory Landscape v.s.
Swampland program, as bottom-up/top-down complements. Symmetries and anomalies
provide constraints of kinematics, we further suggest constraints of quantum
gauge dynamics, and new predictions of possible extended defects/excitations
plus hidden BSM non-perturbative topological sectors.
