Each volume is a complete orbit around the same fixed point. You do not need to have read the others to use any one. The series is a circuit, not a staircase. G applied to itself five times is Complete Completeness.
G¹ · Volume I
The Orthogonal Operator Framework
Abstract operator algebra and matrix compression. The operator sequence G = U ∘ F ∘ K ∘ C defined and proved. The foundation of the entire series.
Print: 979-8-9954416-2-5 · $47
G² · Volume II
TOGT: Applications Across Domains
Contact geometry realised. The operator chain C → K → F → U instantiated across physics, biology, linguistics, architecture, and formal computation. The threshold constant g₃₃ = 33 identifies the minimum operator cycles for stable lock in any domain.
Print: 979-8-9954416-4-9 · $47
G³ · Volume III
The Mini-Beast: Biological Instantiations
C1→C2 English for researchers. The operator chain in living systems. The cajueiro principle. Entry point for new readers and advanced language learners.
eBook: 979-8-9954416-6-3 · $19.99
G⁴ · Volume IV
GTCT T1 — The IMPA Edition
Temporal contact theory formalised. Bilingual (EN/PT). Submitted to IMPA. Science and language integrated from day 21 of instruction — CEFR → TO/TOGT.
Included in Complete Series
G⁵ · Volume V + AXLE
The Seed — Complete Completeness
Banach Fixed Point Theorem applied to GTCT. Formal Lean 4 verification (AXLE v6.1). 0 axioms beyond Mathlib4. The series proves itself. The fixed point exists.
Print: 979-8-9954416-4-9 · eBook: 979-8-9954416-5-6
G⁶ · Issue 6 — OPEN
The Return: χ(H*(X⁶)) = 33 ∀n
The sixth application of G to itself — a distinct object from the threshold constant g₃₃. The conjecture states that the Euler characteristic of the sixth-level cohomology equals 33 for all n. This is an open problem in algebraic topology. AXLE v6.1 marks it as one honest sorry. Join the work.
Open conjecture · 2026 · Not the same as g₃₃
