Computational analysis of Hecke algebras at singular 3-adic fibers, with focus on the level-163 Heegner node. 51 datasets with notes, spectra, and certificates.
| Dataset | Description |
|---|---|
| Hecke Trace Gram Matrix at Level 163 | Exact 7×7 integer Gram matrix G(d,d') = Tr(T_d T_d' | S_2(Γ_0(163))), eigenvalues, distance matrix, centered operator, and Hecke eigenvalues for E = 163a1. |
| Byte-Level Compression Benchmark | PPM-C variants vs gzip, bzip2, xz, and neural compressors on enwik8. Full 20-experiment ablation table. Scaling behavior. Lean-verified roundtrip. |
| 49-Language Reference Table | 49-language harmonic fraction reference table from the cross-linguistic atlas. |
| Harmonic Cycle Catalogues | Harmonic cycle catalogues (980 entries, 49 languages). |
| Dataset | Description | Files |
|---|---|---|
| Eigenvalue Spectrum | Hecke eigenvalue spectrum on the frozen distance-max background | json gallery dos levels spacing wallbands |
| Wide Interior Spectrum | Wide interior Hecke spectrum on the frozen 32^3 background | json dos levels spacing |
| Finite Spectral Law | Finite spectral law for the full 13-mode Hecke operator | json plot |
| Spherical Spectrum | Hecke spherical spectrum construction | — |
| Resolvent | Exact characteristic polynomial and resolvent of the 7x7 Hecke kernel | json curve traces |
| Dataset | Description | Files |
|---|---|---|
| Singular 3-adic Factor | The singular 3-adic Hecke factor at level 163 | json |
| Arithmetic Module | The arithmetic module on the singular local ring | json |
| Branch Model | Branch model of the singular 3-adic Hecke factor | json |
| Conductor | Conductor of the singular 3-adic Hecke factor | json |
| Exact Presentation | Exact presentation of the singular local Hecke order | json |
| Explicit Normal Form | Explicit normal form of the singular local Hecke order | json |
| Lattice Identification | Exact lattice identification of the singular Hecke order | json |
| Index-3 Overorder | The index-3 overorder above the singular local Hecke factor | json |
| State Machine | Local state-machine form of the singular Hecke module | json |
| Dataset | Description | Files |
|---|---|---|
| Jacobson Filtration | Exact Jacobson filtration of the singular Hecke order | json |
| Regular Module Filtration | Jacobson filtration of the singular regular module | json |
| Associated Graded | Associated graded structure of the singular Hecke order | json |
| Residue Structure | Exact residue-module structure of the singular Hecke node | json |
| Residue Ext Table | Residue Ext table and block decomposition | json |
| Dataset | Description | Files |
|---|---|---|
| Homological Structure | Homological structure of the pair node | json |
| Singularity Category | Singularity category of the Hecke node | json |
| Stable Ext Algebra | Stable Ext algebra of the Hecke node | json |
| Path Normal Forms | Path normal forms in the stable Ext algebra | json |
| Triangulated Invariants | Triangulated invariants of the Hecke node | json |
| Matrix Factorizations | Matrix factorizations and Ext for the Hecke node | json |
| Ideal Classification | Exact ideal classification in the pair factor | json |
| Ideal Layers | Ideal layers in the pair factor | json |
| Module Classification | CM / torsion-free module classification for the pair factor | json |
| Endomorphism Order | Matrix order of the CM generator algebra | json |
| Dataset | Description | Files |
|---|---|---|
| Auslander Skeleton | Auslander skeleton of the pair node | json |
| Auslander Center | Center of the Auslander algebra | json |
| Auslander Residue | Residue Auslander algebra of the pair node | json |
| Dataset | Description | Files |
|---|---|---|
| Regge Bridge | Hecke-Regge bridge at level 163 | json spectrum |
| Broad Scan | Broad Hecke-Regge bridge scan across prime levels | json plot |
| Spectral Map | Hecke-Regge spectral map | json plot |
| Family Trend | Regge-Hecke family trend across class-number-1 levels | json |
| Regge Curvature | Hecke Regge curvature on the 7-node Heegner graph | — |
| Dataset | Description | Files |
|---|---|---|
| Singular Characters | Singular Q_3 characters of the Hecke algebra at level 163 | json |
| Singular Ideal Classification | Ideal classification in the full singular order | json |
| Height / L-function | Height / L-function decomposition for K(163,163) | json |
| Syndrome Lift | 3-adic lift of the syndrome algebra at level 163 | json |
| Kernel Transformer | Hecke kernel transformer at level 163 | json |
| Dataset | Description | Files |
|---|---|---|
| 3-adic Thickening | 3-adic thickening of the level-163 Hecke fiber | json |
| 3-adic Selector Scan | 3-adic discriminant vs. singular quotient scan | json |
| Q3 Signature Scan | 3-adic local T_2 signatures in the comparison family | json |
| Atkin-Lehner Law Scan | Atkin-Lehner coordinate law scan | json |
| Coordinate Law Family | Full coordinate laws of Heegner operators on canonical mod-3 levels | json |
| Candidate Invariants | Candidate invariants probe for qdim=3 levels | json |
| Dataset | Description | Files |
|---|---|---|
| Node Geometry | Canonical geometry of the singular Hecke node | json |
| Interaction Certificate | Interaction-system certificate for the level-163 Hecke node | json |
| Level-163 Stabilizer | Stabilizer extraction from Hecke syndrome geometry | json |
| Dataset | Description | Files |
|---|---|---|
| Prime Node Census (N ≤ 500) | Singular 3-adic Hecke nodes at prime levels up to 500 | json |
| Prime Node Census (N ≤ 1000) | Singular 3-adic Hecke nodes at prime levels up to 1000 | json |
