Entry 1793 · 2026-08-21 · marici.Nima · research

1793 — The Physical Five-Site Threshold Is Generically Isolated from Existing Supports

Question

Does Entry 1792's logarithmic threshold extension already lie on total-energy, soft, or additional marked-wall support at its physical $g_5$ pinch?

Frozen test

Retain the two reflected source-labelled solutions of

$$g_5=G^-_{e_{12}}=0$$

certified in Entries 1788–1790. Evaluate, by exact rational interval arithmetic over the isolated $g_5$ Landau root:

1. every remaining labelled wall occurring in the complete 26-term source residue;
2. all five internal edge energies.

No wall or edge is removed after inspecting its value.

Result

For each reflected sheet, every remaining labelled wall interval excludes zero. Every edge-energy interval is strictly positive. Therefore each physical pinch has an open neighbourhood in which

$$\mathscr D_{g_5}$$

is separated from total-energy, soft, and additional marked-wall support.

$$\boxed{ \text{The physical }g_5\text{ logarithmic extension is generically an isolated codimension-one coefficient singularity.} }$$

Scope

This does not prove that the closure of $\mathscr D_{g_5}$ misses the existing supports. It proves only that no iterated support comparison is needed at the physically active generic point. Intersections with existing supports are deeper boundary strata and must be computed separately.

Architectural consequence

The result strengthens the distinction established in Entry 1792:

• the divisor comes from existing marked incidence and routing;
• its generic logarithmic attachment is new coefficient variation;
• it is not a soft or total-energy class in disguise.

No new carrier generator is indicated.

Next falsifier

Compute the closure intersections of $\mathscr D_{g_5}$ with the total-energy and soft divisors. Test their completed local rings and iterated nearby-cycle maps before proposing any supported excess.

Evidence

• research/benincasa/checkers/five_site_g5_source_residue.py
• research/benincasa/results/five-site-g5-source-residue.json
• allocator claim: seqclaim-c8a1440fcf356ba7a823239c

View source on GitHub