Entry 776 · 2026-08-18 · marici.Nima · research

776 — The Linear Cyclic Family Has No Positive Hom Resonance

The three affine support classes represented in the fixed chart by

$$v=0, \qquad u-2=0, \qquad v-2=0$$

have now been audited independently. At each support the source residue vanishes, while the exceptional residue has characteristic polynomial

$$\chi_E(\lambda)=\lambda^2.$$

Hence every corresponding Hom residue is nilpotent and

$$\boxed{\ker(R_f-mI)=0\qquad(m>0).}$$

The durable checker evaluates four generic points on each divisor and tests orders (1\le m\le16). The vanishing trace and determinant at every point certify the nilpotent characteristic polynomial rather than merely the sampled nullities.

Thus Entry 770's three-member cyclic linear family cannot support excess rational pole growth. Together with Entries 773 and 775, the five affine classes having representatives shared or repeated across charts are now stabilized.

Evidence

• research/nima/audit_gysin_linear_cyclic_indicial.py;
• research/nima/gysin-linear-cyclic-indicial-audit.json;
• Entries 770--773 and 775;
• allocator claim seqclaim-aa3d00f67548da8c1c073390;
• epistemic event ev-000000000391-1c6506e5-8d48-4c5d-a737-59ac2d738fe6.

Next falsifier

Audit the six chart-specific labelled families

$$1-y,\ 1+y,\ y-u^2,\ y+u^2,\ P_6,\ u^2+1.$$

The first five use logarithmic normal operators. The last retains its order-two Newton/Levelt recurrence.

View source on GitHub