06-ilang-source / 06-own-mark
06own markverified
Determines what the field change made by a body itself does to the cost of its levels, its clock spacings and its inertia, and whether these change in proportion to the gaps of all levels.
# Review: 06-own-mark v1 - **Subproject:** 06-ilang-source - **Package:** 06-own-mark - **Reviewed version:** v1 - **Date:** 2026-10-19 --- VERDICT: minor issues ## Issues ### I1. The isolation condition (6.4) is dropped from the spacing and inertia results - **Location:** Result (6.8), (6.9), (6.12), (6.13) (rest-only spacings and inertia); Step 5 (last paragraph); twin entries 6.8, 6.9, 6.12, 6.13 - **Severity:** minor - **Problem:** (6.8), (6.10) and (6.12) rest on the second-order expansion (6.5), which is established only under (6.4). The Result states (6.10) "under (6.4)", but (6.8), (6.9), (6.12) and the second-order parts of (6.13) are stated with only the conditions $2t_f<m$ (c), $4t_f\le m$ (a) or $2t_f<M_k$, for every $N_f\ge1$. For $N_f\ge2$ these conditions do not imply (6.4): by Step 3 the excitation energies reach $4t_fN_f$, so for $\sigma=+$ an excitation with two or more objects can meet $M_k+\omega_k(Q)$ when $2t_f<M_k\le2t_fN_f$, and Step 3 itself gives only $2t_fN_f<M_k$ as sufficient. At such a coincidence the start is degenerate at $\gamma=0$ and the Rayleigh–Schrödinger second order of (6.5) is not established. - **Fix:** State every second-order result under (6.4) (or under the sufficient condition $2t_fN_f<M_k$ at $P=0$ for $\sigma=+$), in the steps, the Result and the twin.