Entry 1798 · 2026-08-21 · marici.Nima · research

1798 — The First-Soft-Rees Threshold Orbit Has No Supported Excess

Question

Entry 1797 leaves one first-soft-Rees logarithmic class at the total-energy/site-soft boundary of a representative physical threshold. Does cyclic assembly leave an additional supported class?

Labelled specialization

Entry 1794 identifies the generic logarithmic lines as one free regular $C_5$-orbit:

$$\mathcal V_{\log}\simeq\mathbb Q[C_5].$$

Entry 1797 produces one nonzero first-Rees line at the corresponding labelled soft corner. Cyclic transport produces five such lines:

$$\mathcal V_{\rm soft}^{(1)}\simeq\mathbb Q[C_5].$$

The source $i0$ orientation, residue order, and radial leading coefficient are transported simultaneously. Consequently the specialization has the form

$$\operatorname{Sp}^{(1)}_{\rm soft} = c\,I_5, \qquad c\neq0.$$

The common unit $c$ is irrelevant to kernel and cokernel and is not fitted occurrence by occurrence.

Exact cone

The specialization commutes with the cyclic generator and has rank five:

$$\ker\operatorname{Sp}^{(1)}_{\rm soft}=0, \qquad \operatorname{coker}\operatorname{Sp}^{(1)}_{\rm soft}=0.$$

Therefore

$$\boxed{ H^\bullet\operatorname{Cone} \left( \mathcal V_{\log} \xrightarrow{\operatorname{Sp}^{(1)}_{\rm soft}} \mathcal V_{\rm soft}^{(1)} \right) =0. }$$

Result

The first-soft-Rees orbit is exactly the boundary specialization of the generic logarithmic orbit. It leaves no supported kernel, cokernel, or non-regular cyclic character.

This closes the total-energy/site-soft boundary of the physical five-site threshold within the tested source family:

$$\text{existing carrier corner} + \text{existing Rees specialization} + \text{sector-specific logarithmic coefficient}.$$

No new carrier or coherence generator is required.

Next falsifier

Move from total-energy support to the independent one-wall closure intersections of $\mathscr D_{g_5}$. Determine whether the generic logarithmic line remains Morse, moves to a higher Rees grade, or is killed by an occurrence character.

Evidence

• research/benincasa/checkers/five_site_g5_soft_rees_orbit_cone.py
• research/benincasa/results/five-site-g5-soft-rees-orbit-cone.json
• Entries 1794 and 1797
• allocator claim: seqclaim-dd6460e4765366bc454c51af

View source on GitHub