Anchor-Pure Reconstruction of Regular Tetration: Riemann–Hilbert Selection, Analytic Base Flow, and Blind Validation
Year: 2026
Type: preprint
Abstract: We develop an anchor-pure method for reconstructing the regular Kneser tetration at a target base d > e^(1/e) from a single known anchor at base e. No tetration, superlogarithm, hub, or response-kernel data at the target base are used in the construction. The key representation decomposes the target tetration into a raw branch obtained by stopped logarithmic peeling and a periodic degree-one correction. We derive the exact base derivative of the raw branch, prove cancellation of the nonperiodic tails in the hub equation, select the base-response field through a Riemann–Hilbert problem, and obtain a closed periodic evolution on a fixed weighted analytic path space. We also develop a finite certification framework based on contraction bounds, segment composition, two-sided fixed-point gluing, and cut-plane continuation. Two independent numerical architectures validate the reconstruction at base 2. A 65-node global base flow reconstructs the regular tetration at base 2 with a blind pointwise discrepancy of 4.0 × 10^−21 on 48 off-grid points and resolves the periodic hub to approximately 30.6 decimal digits. An independently implemented ten-segment re-anchoring march agrees with both the first reconstruction and an independently computed target-base reference to 7.6 × 10^−11. The observed failure and successful subdivision of the final edge segment agree with the predicted Ovsyannikov step-size regime. These experiments establish a reproducible reconstruction method and validate its internal error predictors. The accompanying certification framework is rigorous, while completion of the full interval march remains an open computer-assisted problem.
Author: Justus, Janis
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171835233