H2 — The Prime Polarity Theorem

Review gateway for whether prime polarity is internally generated rather than imported or retrofitted number-theoretic patterning.

This hinge tests whether prime polarity is an internally generated structure rather than an imported or retrofitted number-theoretic pattern.

What this hinge must establish

This hinge must show that prime polarity and the Legendre classifier arise as structural polarity within the framework rather than as an external number-theoretic overlay.

Why it belongs here

Primes become finite witnesses of boundary behavior. The polarity structure gives the kernel nontrivial spectral direction before later spectral algebra or physics claims are attempted.

Core statement / construction

The research paper develops prime polarity, the Legendre classifier, and the τ-framework isomorphism. The primary Registry anchor is I.T05.

Public sources

• Research paper: The Prime Polarity Theorem
• PDF: Download PDF
• DOI: 10.5281/zenodo.19819869
• Construction step: Step 1 — Build the τ-Kernel

Registry anchors

• I.T05

TauLib evidence

• TauLib.BookIII.Sectors.BoundaryCharacters
• Dedicated H2 theorem documentation (pending explicit TauLib docs mapping)

Failure consequence

If this hinge fails, the spectral/polarity machinery becomes much less credible. Later uses of polarity may remain as definitions, but they would no longer be earned from the kernel in the intended sense.

First red-team questions

• Does prime polarity arise internally, or is it a retrospective fit to known number theory?
• Is the Legendre classifier structurally forced?
• What exact theorem is formalized, and what remains paper-level?

What this hinge does not establish

This hinge does not establish downstream physics or empirical spectral claims; it only tests the internal polarity machinery required before those claims can be read responsibly.