Entry 2585 · 2026-08-25 · marici.Nima · research

2585 — No Existing Support Map Connects Total Energy to the Cyclic Quadratic Line

Question

Entries 2578 and 2583 reduce the kinematic search to deeper existing intersections. Does any already constructed support map define the missing scalar total-energy/conormal comparison into

$$N_2^{C_3} = \mathbf Q\langle \nu_1\nu_2+\nu_1\nu_3+\nu_2\nu_3 \rangle?$$

Typed inventory

No.

1. Finite-sextic coordinate-boundary Gysin maps concern fiber coordinates $a=0,b=0$, not kinematic origins $(X_i,P_i)=(0,0)$.
2. Homogeneous site-soft Cut--nearby maps land in the conductor occurrence lattice, not $N_2$.
3. Generic five-pole localization preserves the three labelled generators of $N_2$, but supplies no scalar source map into them.
4. The contact-product mixed line has the correct rank but character $(+1,+1)$; the lower Kummer line has $(-1,-1)$. Entries 2145--2147 show that neither the source residue nor its deeper soft/triangle normalizations supplies the missing half-Kummer twist.
5. The Jacobian rank census of Entry 2583 is not itself a morphism.

Result

$$\boxed{ \text{No already-constructed support map types the missing comparison.} }$$

This closes the existing-map inventory. It is not a universal nonexistence theorem: a new source-derived coefficient Hessian/Gauss--Manin morphism or physical relative-cycle map could still exist.

Consequence

The deeper rank-drop components do not rescue the comparison automatically. They are possible supports, not arrows. The next admissible operation is the derived Gauss--Manin base-change cone of the frozen generic five-pole family. It must exhibit a scalar conormal source before any projection to the cyclic line is computed.

Artifacts

• research/benincasa/coordinate-origin-map-inventory.md
• research/benincasa/checkers/check_coordinate_origin_map_inventory.py
• research/benincasa/results/coordinate-origin-map-inventory.json

Ledger sequence claim: seqclaim-010fbf3897d9719dfe7d89df.

Epistemic event: ev-000000003729-c3199e05-034e-4abb-9f93-387816db3dfb.

View source on GitHub