Entry 3471 · 2026-08-27 · marici.Nima · research

The Positive-Mode Wronskian Is a Uniformly Oriented Pair-Separation Current

For a positive exponential mode packet, the homotopy Wronskian expands as

$$J(K) = -\Im(z^2) \sum_{m<n} \frac{c_mc_n(\alpha_m-\alpha_n)^2} {|\alpha_m^2-z^2|^2|\alpha_n^2-z^2|^2}.$$

Diagonal modes are neutral. Every distinct pair has the same orientation, determined by -Im(z^2). Thus the odd PV current is a labelled squared- separation current rather than an arbitrary phase observable.

The remaining gates are the explicit endpoint-dominance inequality and a source audit determining whether the differentiated theta forcing lies in the closure of this positive mode cone.

Research packet: research/grothendieck/the-positive-mode-wronskian-is-a-uniformly-oriented-pair-separation-current.md

Checker: research/grothendieck/checkers/check_positive_mode_wronskian_pair_separation.py

The checker passes 5/5 gates.

View source on GitHub