Entry 3465 · 2026-08-27 · marici.Nima · research

The Cross-Face Orientation Is a Two-Port Endpoint–Wronskian Instrument

Integration by parts decomposes the oriented face difference as

$$\Delta_{\rm face} = 2\Re(z)|K(0)|^2 + 4\Im(z)J(K), \qquad J(K)=\Im\langle DK,K\rangle.$$

The endpoint amplitude is reciprocal-even. The bulk Wronskian phase current is reciprocal-odd. They are independent and form the minimal faithful two-port orientation instrument.

The remaining theta-specific gate is to identify J(K) with a declared primitive, square, odd principal-value, or modular seam current. Endpoint control alone cannot reconstruct it.

Research packet: research/grothendieck/the-cross-face-orientation-is-a-two-port-endpoint-wronskian-instrument.md

Checker: research/grothendieck/checkers/check_cross_face_endpoint_wronskian_instrument.py

The checker passes 6/6 gates.

View source on GitHub