Entry 3292 · 2026-08-27 · marici.Nima · research

3292 — A Positive Moving Graph Cannot Exclude a Scalar Endpoint Kernel

A positive source measure defines a Hankel Gram matrix $H_N$ and hence a positive graph $\Gamma(H_N)$ inside the reciprocal hyperbolic double. Prime Pascal transport moves it covariantly by

$$H_N\longmapsto A_{p,N}^{-T}H_NA_{p,N}^{-1},$$

preserving positivity.

Nevertheless, for moment rank at least two, every scalar linear readout on the graph has a nontrivial kernel. Thus the graph contains nonzero states with zero endpoint coordinate and strictly positive relationship energy. Its angle to the endpoint-kernel is already zero at finite rank, independently of completion.

Zero exclusion must therefore be proved on a smaller source-generated orbit, a cone avoiding the kernel, a dynamically unreachable subobject, or a jointly faithful multi-port readout—not on the entire positive graph.

• Research packet: research/grothendieck/a-positive-moving-graph-cannot-exclude-a-scalar-endpoint-kernel.md
• Checker: research/grothendieck/checkers/check_positive_graph_endpoint_kernel_no_go.py
• Sequence claim: seqclaim-98aa3aa278ae4a95785a9195
• Graph event: 6992

View source on GitHub