H4 — The Split-Complex Boundary Algebra D

Review gateway for whether the boundary algebra used by the framework is canonically forced rather than chosen for convenience.

This hinge tests whether the boundary algebra used by the framework is canonically forced rather than chosen for convenience.

One inspection point is the split-complex unit relation:

What this hinge must establish

This hinge must show that the split-complex boundary algebra is forced by the construction and supplies the four-atom generator dictionary needed by later boundary and truth machinery.

Why it belongs here

The boundary algebra belongs to Step 1 because it is part of what the kernel becomes at infinity. It records the infinity-facing structure exposed by orbit and polarity machinery.

Core statement / construction

The research paper develops a countable profinite construction, a canonical uniqueness argument, and a four-atom generator dictionary.

Public sources

• Research paper: The Split-Complex Boundary Algebra D
• PDF: Download PDF
• DOI: 10.5281/zenodo.19818743
• Construction step: Step 1 — Build the τ-Kernel

Registry anchors

• I.T10
• I.D20

TauLib evidence

• TauLib.BookI.Boundary.SplitComplex
• TauLib.BookI.Boundary.Ring

Failure consequence

If the split-complex boundary algebra is not forced, then τ-holomorphy, four-valued internal logic, and downstream scalar readouts become less structurally grounded.

First red-team questions

• Is the split-complex algebra forced rather than selected because it is useful?
• Does the four-atom dictionary follow from the construction?
• Where does the formalization stop and the paper-level uniqueness argument begin?

What this hinge does not establish

This hinge does not establish holomorphy, physics, measurement, or scalar readouts by itself; it supplies the boundary algebra these later steps inspect.