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Bohr radius for the bidisc

59a
Upper bound, last-listed row
| $0.302825279492$ | [P2026] | Set $U=(1+z)(1-w)$, $V=1+zw$, $P=LU+iTV$, $Q=LV+iTU$, and $f=(SQ-P)/(SQ+P)$, with $L=2500000000$, $T=3067398171$, and $S=10^{15}$. Two independent exact computations of the 841 coefficients with $0\le j,k\le N=28$ give a finite majorant greater than $1+10^{-26}$ at $r=302825279492/10^{12}$. [Proof package v1.0.0, DOI: 10.5281/zenodo.22341928](https://doi.org/10.5281/zenodo.22341928); archived `bidisc-bohr-certificate-v1.0.0.zip` SHA-256: `afc77b42cdd9de9b82e3d4c6a973dc32bf82b2c19960df58507b9a5cf333928b`. [P2026-ub-K2-0-302825279492] |
exact pinned row| $0.302825279492$ | <a href="#P2026">[P2026]</a> | Set $U=(1+z)(1-w)$, $V=1+zw$, $P=LU+iTV$, $Q=LV+iTU$, and $f=(SQ-P)/(SQ+P)$, with $L=2500000000$, $T=3067398171$, and $S=10^{15}$. Two independent exact computations of the 841 coefficients with $0\le j,k\le N=28$ give a finite majorant greater than $1+10^{-26}$ at $r=302825279492/10^{12}$. [Proof package v1.0.0, DOI: 10.5281/zenodo.22341928](https://doi.org/10.5281/zenodo.22341928); archived `bidisc-bohr-certificate-v1.0.0.zip` SHA-256: `afc77b42cdd9de9b82e3d4c6a973dc32bf82b2c19960df58507b9a5cf333928b`. <a href="#P2026-ub-K2-0-302825279492">[P2026-ub-K2-0-302825279492]</a> |
value changed 2026-09-26
Lower bound, last-listed row
| $0.3006$ | [Kne2025] | Lower bound for the bidisc: $K_2\ge 0.3006$. [Kne2025-lb-K2-0-3006] |
exact pinned row| $0.3006$ | <a href="#Kne2025">[Kne2025]</a> | Lower bound for the bidisc: $K_2\ge 0.3006$. <a href="#Kne2025-lb-K2-0-3006">[Kne2025-lb-K2-0-3006]</a> |
tracked since 2026-07-24 — no movement seen yet
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Cite this rowBounds Ledger — Bohr radius for the bidisc (59a) upper bound: $0.302825279492$ (value changed 2026-09-26) lower bound: $0.3006$ (tracked since 2026-07-24 — no movement seen yet) Mirrored from teorth/optimizationproblems@2c1968c. These are the last-listed rows of that constant's bounds table — a listing position, not a statement that this bound is the strongest or most recent. A snapshot at that sha, not a live read. https://u00dxk2.github.io/bounds-ledger/c/59a.html