H1 — The Hyperfactorization Theorem

Review gateway for whether the kernel’s retained multiplicative and exponential structure produces unique global addresses.

This hinge tests whether the kernel’s retained multiplicative and exponential structure produces unique global addresses. It is the point where the construction must show that objects are not merely generated, but decomposable into canonical tower-atom structure.

What this hinge must establish

This hinge must establish unique tower-atom decomposition and connect that decomposition to stable global addressing in Category τ.

Why it belongs here

Later arithmetic, address resolution, coordinate architecture, and scalar readouts depend on stable addresses. Hyperfactorization is the first major test that the kernel generates such addresses rather than merely names objects.

Core statement / construction

The paper presents a unique tower-atom decomposition and connects that decomposition to the coordinate architecture of Category τ. The Registry anchor for the theorem is I.T04.

Public sources

• Research paper: The Hyperfactorization Theorem
• PDF: Download PDF
• DOI: 10.5281/zenodo.19818957
• Construction step: Step 1 — Build the τ-Kernel

Registry anchors

• I.T04

TauLib evidence

• TauLib.BookIII.Spectrum.KernelHinge
• Dedicated H1 theorem documentation (pending explicit TauLib docs mapping)

Failure consequence

If hyperfactorization fails, τ may still generate objects, but it no longer supplies the unique address spine needed for address-resolution arithmetic and later structural readouts.

First red-team questions

• Does the theorem actually deliver uniqueness, not just a convenient normal form?
• Are tower atoms defined internally enough to support later address arithmetic?
• Which part is formalized, and which part remains a paper-level bridge?

What this hinge does not establish

This hinge does not by itself recover arithmetic, prove scalar readouts, establish physics, or settle external bridge adequacy.