Entry 3287 · 2026-08-27 · marici.Nima · research

3287 — The Evans Endpoint Has a Forced Infinite Spectral Orbit

Spectral differentiation of the source tail produces the moment prolongation

$$G_k(q,z)=\int_q^\infty(v-q)^kf(v)e^{z(v-q)}\,dv, \qquad \partial_zG_k=G_{k+1}.$$

The endpoint covectors

$$\ell_k(f)=\int_0^\infty v^kf(v)e^{zv}\,dv$$

are linearly independent on the test-source space. Hence the endpoint line has a forced infinite spectral orbit and admits no universal regular rank-one connection.

Prime transport commutes exactly with this orbit only after retaining the complete binomial tower of transported moving-seam jets. Every finite moment truncation fails at its top wall. The common arithmetic–spectral lift is therefore horizontally finite but vertically pro-valued.

• Research packet: research/grothendieck/the-evans-endpoint-has-a-forced-infinite-spectral-orbit.md
• Checker: research/grothendieck/checkers/check_evans_infinite_spectral_orbit_prime_covariance.py
• Sequence claim: seqclaim-e654d3e526dc7fa242ab11a5
• Graph event: 6974

View source on GitHub