H5 — τ-Holomorphy on the Boundary Algebra

Review gateway for whether the boundary algebra supports a genuine transformation grammar rather than a relabeled notation.

This hinge tests whether the boundary algebra supports a genuine transformation grammar. The question is not only whether split-complex notation can be written down, but whether the framework earns a holomorphic machinery that controls admissible transformations.

What this hinge must establish

This hinge must show that τ-holomorphy gives an admissible boundary-transformer grammar over the boundary algebra.

Why it belongs here

The hinge belongs to Step 1 because holomorphy is part of the kernel becoming generative. It supplies the grammar through which boundary data can later determine interior structure.

Core statement / construction

The research paper develops τ-holomorphy through omega-germ transformers, wave-equation Cauchy-Riemann structure, and the earned categorical machine used by later hinges.

Public sources

• Research paper: τ-Holomorphy on the Boundary Algebra
• PDF: Download PDF
• DOI: 10.5281/zenodo.19818852
• Construction step: Step 1 — Build the τ-Kernel

Registry anchors

• I.D42
• I.D43
• I.D47

TauLib evidence

• TauLib.BookI.Holomorphy.DHolomorphic
• TauLib.BookI.Holomorphy.TauHolomorphic
• TauLib.BookI.Holomorphy.IdentityTheorem

Failure consequence

If τ-holomorphy fails, the later boundary-to-interior program loses its analytic grammar. The kernel may still have a boundary algebra, but it would not yet have the transformation discipline needed for later construction.

First red-team questions

• Is τ-holomorphy a real transformation grammar or a relabeling of known split-complex analysis?
• Are the Cauchy-Riemann-style conditions earned in the boundary algebra?
• Which transformation claims are formalized?

What this hinge does not establish

This hinge does not by itself prove the Central Theorem, empirical readouts, or ontic closure.