Entry 775 · 2026-08-18 · marici.Nima · research

775 — The Shared $y$ Pair Has No Positive Hom Resonance

Entry 770's second globally shared affine support class has two fixed-chart representatives:

$$y=0, \qquad v-u=0.$$

Their normal residue presentations are not identical. On (y=0), the source residue vanishes and the exceptional residue is strictly nilpotent. On (v-u=0), the exceptional residue vanishes while the source residue has eigenvalues (0,1). Accordingly, the Hom spectra differ by the integral frame shift anticipated in Entry 771, but neither presentation has a positive Hom indicial root.

The exact rank test gives

$$\boxed{\ker(R_f-mI)=0\quad\text{for every tested }1\le m\le16}$$

for both representatives, at four generic points of each divisor. The matrix forms make the conclusion exact: the (y)-representative is nilpotent, while the (v-u) Hom eigenvalues are (0,-1).

Thus no rational splitting can gain excess pole order on Entry 770's shared class two. Together with Entry 773, both support classes shared across all three charts are now locally stabilized.

Evidence

• research/nima/audit_gysin_shared_y_indicial.py;
• research/nima/gysin-shared-y-indicial-audit.json;
• Entries 770--773;
• allocator claim seqclaim-bc289ef26cbcc866d81d5edf;
• epistemic event ev-000000000389-3892e276-8c24-4ff3-9d3b-38f0ec65e4cd.

Next falsifier

Audit the three-member cyclic class represented by ((v,u-2,v-2)). After that, only the eighteen chart-specific representatives and the irregular (u^2+1) recurrence remain.

View source on GitHub