Glossary
Area derivative. An oriented infinitesimal contour-area insertion. In the ordered holonomy model it inserts curvature with its surrounding transport. Its singular continuum domain must be specified.
Loop operator. The composition . Its product rule is conditional on the regulated continuity assumptions explained in I.4.
Planar factorization. Leading factorization of expectation values of products of normalized single traces in the usual large- expansion. It is not multiplicativity of one trace.
Ordered integral. An integral over ordered contour parameters. Products satisfy shuffle relations. Closedness kills its first level but generally leaves a nonzero antisymmetric second level.
Logarithmic Magnus series. A Lie series for the logarithm of an ordered exponential. It differs from the tensor expansion of the exponential itself.
Pairing basis. Candidate invariant tensors built from Kronecker-delta pairings. The count precedes cyclic and dimension-dependent relations and is not an equation rank.
Inconsistency certificate. An exact witness such as , . It certifies failure of the stated system, not every possible ansatz.
Free-word representation. Operators creating and removing letters in a full Fock basis. Creation operators do not commute, and the vacuum state is not a trace.
Self-dual two-form. A Euclidean four-dimensional two-form satisfying . A nonzero real simple tangent bivector cannot have this property.
Hodge-dual surface proposal. The source’s extended area construction. Its literal tensor formula fails the circle test in III.5, so dependent QCD conclusions remain unresolved.
Harmonic versus conformal. Harmonicity solves a Laplace equation; conformality constrains the induced metric. A Hilbert-transform extension of a fixed ellipse parametrization illustrates the difference.
Goldschmidt branch. A disconnected or pinched spanning-surface candidate whose area is additive in the prescribed pieces. Its selection in a QCD ansatz is additional input.
Majorana Pfaffian. The Gaussian integral of a real antisymmetric fermion quadratic form. Its square is a determinant; its sign requires a convention.
Connected loop sum. A trace logarithm. Exponentiation produces disconnected collections in the partition function.
Approximate identity. A normalized family of kernels converging against test functions to a delta distribution. Localization alone does not fix normalization.
Exact WKB. A claim that a semiclassical quantization procedure receives no spectral corrections in the stated setting. It is conjectured for the source construction, not established by a steep Hessian alone.
In-sample fit. Comparison with data used to tune the parameters. A held-out prediction uses data reserved before fitting, without subsequent retuning.