I created a powerful notation family called "binary bisector notation family". The true goal is to reach the limit of Bashicu matrix system (BMS) or (1,3) in Y sequence. That would be really, really strong!
Version: 26.1.1
[26.1.1] February 19th, 2026: Added the prediction for the LXPSBN
[26.1] February 17th, 2026: Added the "Nested pair sequence bisector notation" to differ from "Simple pair sequence bisector notation" after the Bachmann-Howard ordinal.
[26.1 pre-release] February 8th, 2026: Welcome back! I fixed many errors throughout the site.
[26.1.-0.5] January 30th, 2026: Added the goal to reach the limit of BMS.
[26.1.-1] January 27th, 2026: Now your computer is under maintenance. Updated the version number to reflect the new version numbering format per December 2025 announcement for Minecraft.
[1.03_12w1~] December 3rd, 2025: I decided to diverge parts beyond the Bachmann-Howard ordinal (BHO) level into multiple systems
[1.03_11w1~] November 1st, 2025: Happy Halloween Day's substitution! I decided to create the hierarchal extended three-entry bisector notation.
[1.02b] July 29th, 2025: Create an analysis with BMS (three-entry sequence) under the fake test 1.
[1.02a] June 19th, 2025: Added an analysis page with Bashicu matrix system and Y-sequence (alpha).
[1.02] April 23rd, 2025: Began the formal analysis for the pair sequence bisector notation.
[1.01c] April 9th, 2025: Added "asterisk" (*) multiplication symbol as an alternative to "dot" (.), as well as many other variants.
[1.01b] March 30th, 2025: Added the "extended operator bisector notation", based on Jonathan Bowers' extended operator notation.
[1.01a] March 22nd, 2025: The pair sequence bisector notation definition is already completed.
[1.01] February 2nd, 2025: The pair sequence bisector notation is finally out!
[1.00c] January 19th, 2025: Added the "B-growing hierarchy".
[1.00b] January 14th, 2025: Added my operator names
[1.00a] November 10th, 2024: The N in A{X}N{Q} must be a superscript.
[1.00] November 9th, 2024: Initial site creation.
[1] Primitive bisector notation (PBN) — Limit: ε0 (Small Cantor ordinal) [BMS: (0,0)(1,1)| Y: (1,2,4)]
[2.1] Simple pair sequence bisector notation (SPSBN) — Predicted limit: ψ0(Φ(1, 0)) with respect to the extended Buchholz’s function (Extended Buchholz ordinal) [BMS: (0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)| Y: (1,2,4,8,12,15,19)] [WIP]
[3.1] Hierarchal extended three-entry bisector notation (H3EBN) — ???
[2.2] Nested pair sequence bisector notation (NPSBN) — Defined where the notation differs from {{0, 2}} in SPSBN = {{{0, 2}, 1}} in NPSBN — Limit: ψ0(Ω_ω) with respect to the (extended) Buchholz's function (Buchholz ordinal) [BMS: (0,0,0)(1,1,1) | Y: (1,2,4,8)]
[3.2] Line-extended pair sequence bisector notation (LXPSBN) — Defined using the "|" separator to make the notation far more powerful — Predicted limit: [BMS: (0,0,0,0)(1,1,1,1) | Y: (1,2,4,8,16)]
Old plans:
Three-entry bisector notation (3EBN)
Four-entry bisector notation (4EBN)
Multi-entry linear bisector notation (MLBN)
Dimensional bisector notation (DBN)
Multidimensional bisector notation (MBN)
Hyperdimensional bisector notation (HBN)