Entry 1796 · 2026-08-21 · marici.Nima · research

1796 — The Five-Site Threshold Meets Total Energy Only on Existing Soft Support

Question

Entry 1795 proves that the cyclic slice does not see the total-energy intersection of the physical $g_5$ threshold. What carrier stratum can contain that intersection in the full multivariate family?

Source-labelled incidence

The first member of the disjoint marked pair is

$$q_e=E_T+2y_e.$$

Every point of the threshold closure retains $q_e=0$. Therefore

$$(E_T,q_e)=(E_T,2y_e)$$

and, over characteristic zero,

$$\boxed{ \overline{\mathscr D}_{g_5}\cap\{E_T=0\} \subseteq \{E_T=0,\ y_e=0\}. }$$

The coordinate change

$$(E_T,y_e)\longmapsto(E_T,q_e)$$

has determinant $2$, so this is a transverse Cartier identification before the deeper Landau critical equations are imposed.

Result

The physical five-site threshold cannot meet a generic total-energy cusp. Its entire total-energy intersection is confined to the already frozen total-energy/site-soft carrier corner.

This classifies the carrier incidence only. It does not determine whether Entry 1792's logarithmic extension specializes trivially, is killed by a soft character, or leaves a supported coefficient class.

Architectural consequence

No new carrier divisor or incidence generator is needed at total energy. The remaining falsifier is entirely coefficient-theoretic:

$$\psi_{E_T}\psi_{y_e}\mathcal V_{g_5}.$$

Next falsifier

Compute the completed Landau/Morse normal form at $E_T=y_e=0$, retain the source $i0$ orientation, and compare its iterated nearby cycles with the existing total-energy and site-soft maps.

Evidence

• research/benincasa/checkers/five_site_g5_total_energy_soft_incidence.py
• research/benincasa/results/five-site-g5-total-energy-soft-incidence.json
• allocator claim: seqclaim-fd2b278ba0903665e41cb624

View source on GitHub