| title | Closed-form spectral data for the K7 metric |
|---|---|
| axis | geometry |
| status | dormant |
| opened | 2026-06-11 |
| updated | 2026-06-11 |
Statement. Do the Laplacian spectral data of the K7 geometry admit exact closed forms, and in which basis?
Why it matters. The prediction chain runs through spectra. Exact spectral data would replace numerical inputs by counts, extending the hard core's reach.
Known constraints. Largely negative so far, and the negatives are part of the map: two block coefficients are confirmed torsion-minimizing rationals (19/6 and 7/6), but the K3-block coefficient 64/77 is demoted to a rational approximation (0.41 percent, basin-dependent across seeds, so no exact spectrum behind it); a naive exponent pattern is falsified at the 1e-12 level by interval certification; exhaustive search over rational and standard transcendental bases finds no closed form at 15-digit precision. These refutations were applied to the program's own candidates (negative heuristic in action).
Next step. The only identified non-exhausted route is genuine theory, not search: a Picard-Fuchs analysis of the period structure. Off the critical path; dormant until prioritized.