E-013 — xi-prime certificate constants from D1 diagonal law (Remark 7.1 reproduced to 5e-6)
08-18-2026 · 3 rows · script
research/numerics/scripts/E-013-xiprime-R-constants.py
Metadata
R-functional with xi' diagonal law D1 (pair kernel x - 4x^2 + ...) reproduces Remark 7.1 constants; D1(x) <= x quantifies tight-pair suppression
Validation checks
| V1_flat_matches_085838 |
PASS |
| V2_quartic_matches_086864 |
PASS |
| V3_perfect_square_node_mechanism |
PASS |
| V4_xi_kernel_sanity_4_3 |
PASS |
Key values
| R_xiprime_flat | 1.14161504167725 |
| cert_flat_computed | 0.858384958322751 |
| cert_flat_paper | 0.85838 |
| R_xiprime_quartic | 1.13135848298565 |
| cert_quartic_computed | 0.868641517014353 |
| cert_quartic_paper | 0.86864 |
| R_xi_flat_sanity | 1.33333242971717 |
| node_ratio_D1(0.5)/0.5 | 0.0892003 |
| relative_suppression_at_node | 0.9108 |
| pair_integral_xi_flat | 0.333332429717 |
| pair_integral_xiprime_flat | 0.141615041677 |
Parameters
Caveats
- paper decimals are certified lower bounds (truncated); computed values sit slightly above, as expected
- R-formula per E-001; D1 per Zeta23/XiPrime/Certificate/D1.lean
Data preview (3 rows total)