teal-sea / zeta-labstate of record · compiled 14 Aug 2026 · revision 9ebdea0 · source

Library · hunts/jensen_clock/NOTES.md

Spine candidates and loose ends — jensen_clock

301 words · 30 lines · source

Things that belong to other parts of the tree, recorded here rather than done, because this hunt may not touch zeta/.

  1. Docstring line for zeta/li.py's hyperbolicity scanners. The measured fact: hyperbolicity of J^{d,0} at degree d inspects the function at effective de Bruijn–Newman time |x|/(8d) at image position x, so a scan at degree d is blind to any off-line pair whose flow landing time is below |x₀|/(8d). For the Davenport–Heilbronn height-85.7 pair that threshold is d ≈ 2.08·10⁴; every textbook-scale scan (d ≤ 32 here and in hyperbolicity_scan's pinned ranges) sits five hundred times short of it. A sentence in the docstring would stop a future hunt from reading a green low-degree scan as evidence of anything about off-line zeros. (zeta/ change — needs its own tests, not this hunt's.)
  1. Shift-direction dictionary. This hunt fixed the shift n = 0 and varied the degree. The GORZ shift n → ∞ limit is also a heat limit; a matching dictionary t_eff(n, d) for the shifted family J^{d,n} would say which (d, n) cells of a full scan grid can see a given pair at all — turning the blindness corollary from one axis into the whole table. Same instrument would work (the shifted γ-table is a suffix of the same moment table).
  1. The additive identity as a funnel candidate. t_land(d) + |x₀|/(8d) = t\* held at 0.03–0.06% at two degrees. If someone wants a candidate for the discovery funnel, the sharp form (does the defect vanish as d → ∞, with the d⁻¹-correction coefficient computable from the saddle?) is well-posed and cheap to test further. Not entered here: the N-body null already explains the quantity as configuration geometry, so under this repo's rules it is a closure, not a lead.