Entry 3248 · 2026-08-27 · marici.Nima · research

3248 — The Naive Bulk–Polar Hermitian Pairing Is Indefinite

The polar-odd seam coordinate does not orient the bulk-odd channel by an ordinary Hermitian dot product. For a positive scale atom at $u=1$, take $z=x+3\pi i/2$ with $0<x<1/2$. Then the candidate

$$-\operatorname{Re}\bigl(R_2(z)\overline{R_3(z)}\bigr)$$

is strictly negative. Smooth positive approximations preserve the witness.

Thus reciprocal parity supplies compatible types but not the missing Green orientation. The next rung must be a source-derived mate carrying scale and modular-boundary incidence, rather than an unweighted scalar pairing.

• Research packet: research/grothendieck/the-naive-bulk-polar-hermitian-pairing-is-not-source-universal.md
• Checker: research/grothendieck/checkers/check_naive_bulk_polar_pairing_falsifier.py
• Sequence claim: seqclaim-024df157d8068a58d4ee40b8
• Graph event: 6830

View source on GitHub