| Boundary realization of the seam | statement | proposition 2.2 | arxiv |
| Conservative sheet operator | statement | theorem 6.1 | arxiv |
| Equivariant chart decoration | statement | lemma 7.1 | arxiv |
| 4JZ4Y62QXA | statement | theorem picture | arxiv |
| Admissible sheet enrichment | definition | definition 5.4 | arxiv |
| Mellin integral of a Bessel mode | statement | lemma 10.1 | arxiv |
| A common reflection coordinate | statement | corollary 11.5 | arxiv |
| The $3+4$ incidence correspondence | statement | theorem 16.2 | arxiv |
| Equivariant averaging commutes with Mellin transformation | statement | proposition 11.6 | arxiv |
| Three-seed with specified gluing | definition | definition 2.6 | arxiv |
| Metric triangular cycles | statement | corollary 2.5 | arxiv |
| Hyperbolic Poisson transform | statement | theorem 9.1 | arxiv |
| Lattice reciprocity | statement | proposition 11.2 | arxiv |
| Invariant evolution and energy conservation | statement | corollary 6.2 | arxiv |
| Fourier--Bessel cusp modes | statement | theorem 8.1 | arxiv |
| A product tower | statement | corollary 12.4 | arxiv |
| Marked-coordinate symmetry reduction | statement | proposition 13.3 | arxiv |
| Mellin-compatible transition | definition | definition 14.1 | arxiv |
| Foliated incidence datum | definition | definition 2.1 | arxiv |
| Rank-one holonomy parameters | statement | proposition 16.1 | arxiv |
| Normalized lattice pair | definition | definition 11.1 | arxiv |
| Invariant seam reduction | statement | theorem 3.2 | arxiv |
| Eight triangular channels | statement | proposition 2.4 | arxiv |
| Closed seam energy | statement | lemma 3.1 | arxiv |
| Boundary transfer | definition | definition 7.3 | arxiv |
| Local solutions and their seam defect | statement | proposition 6.6 | arxiv |
| Two ends and the choice of core metric | statement | lemma 5.3 | arxiv |
| Reciprocal-logarithmic integral | statement | lemma 7.2 | arxiv |
| Split rank-two Mellin compatibility | statement | theorem 12.3 | arxiv |
| Full-level Maass functional equation | statement | theorem 10.2 | arxiv |
| Admissible reciprocal theta pair | definition | definition 11.3 | arxiv |
| The Fourier exchange law | statement | lemma 12.1 | arxiv |
| Harmonic extension with seam matching | statement | theorem 6.4 | arxiv |
| Enriched bonding datum | definition | definition 13.1 | arxiv |
| Quotient descent criterion | statement | lemma 13.2 | arxiv |
| Criterion for a multiplicative color action | statement | proposition 16.3 | arxiv |
| Equivariant transfer by averaging | statement | proposition 7.4 | arxiv |
| Completed zeta from the invariant seam | statement | theorem 4.3 | arxiv |
| Descent to a meromorphic line-bundle section | statement | lemma 14.4 | arxiv |
| Doubled inverse-limit base | definition | definition 13.4 | arxiv |
| Geometric duality of the doubled base | statement | theorem 13.5 | arxiv |
| The triangular period and its harmonics | statement | proposition 3.6 | arxiv |
| Eight scalar channels and Reynolds projection | statement | proposition 4.5 | arxiv |
| A self-adjoint determinant criterion | statement | proposition 15.3 | arxiv |
| Reciprocity of the seam theta state | statement | theorem 4.2 | arxiv |
| Mellin reflection for a reciprocal pair | statement | theorem 11.4 | arxiv |
| An action--angle sheet | statement | proposition 5.1 | arxiv |
| Gaussian Fourier transform and Poisson summation | statement | lemma 4.1 | arxiv |
| The trace equation on a geodesic plane | statement | lemma 9.2 | arxiv |
| Normalized collar extension | statement | proposition 8.2 | arxiv |
| A compatible Gaussian lift | statement | proposition 12.2 | arxiv |
| Heat trace and normalization | statement | corollary 3.5 | arxiv |
| Duality and assembly | statement | theorem 14.2 | arxiv |
| Coercivity on the compact core | statement | lemma 6.3 | arxiv |
| A nonempty reference family | example | example 14.5 | arxiv |
| Dirichlet-to-Neumann matching | statement | proposition 6.7 | arxiv |
| Reflection of divisors | statement | proposition 15.1 | arxiv |
