C287 — The four-node 529 normal form
24 September2026. Integration of the17K and19K endpoint families.
The supported source rows reduce to four coefficients:−12,−10,5,7, all in units K=529 with one shared annual offset i. This exposes a second source-qualified2K edge and the relationship among15K,17K and19K.
| Node | Qualified source role | Signed coordinate |
|---|---|---|
| S | Cumulative LXX ON Shem, index i+2 | −12K+i |
| F | Cumulative LXX OFF Flood, index i | −10K+i |
| R | Regular MT ON/Terah+60/full430 Flood | 5K+i |
| N | Regular SP OFF/full430 Noah birth; selected LXX OFF primary aliases | 7K+i |
The first three nodes exist for i0–5. N is supplied by SP for i2–5 and additionally by LXX OFF at i3/5. At i0/1 the required Noah3703/3704 remains absent. Consequently there are four complete numerical rows and six complete labeled realizations.
Both same-side separations are2K: F−S=N−R=1058. The cumulative-to-regular width matrix is:
| From / to | R | N |
|---|---|---|
| S | 17K | 19K |
| F | 15K | 17K |
The17K correspondences form the two matching sides. The off-diagonal15K and19K widths lie2K below and above17K. Their difference is4K=2116, but that difference of widths is not itself an edge between the four admitted nodes.
The additional regular2K edge has explicit source roles: restored MT G2 close/start to SP G1 companion/primary, and restored MT G3 close/start to SP G2 companion/primary. These are cross-tradition comparisons; no single individual's age is changed. The LXX aliases retain their own primary labels and do not inherit SP companions.
All matched source components have coordinate coefficient×K+i±1/4. Each permitted route preserves the same component offset; reflecting later would reverse ancestry in the usual way. The matrix is a comparison table, not a physical two-dimensional space or a new global axis.
The compact form reduces several observed widths to two increments,2K and17K, once the state and selector choices are fixed. It does not make those choices historically necessary or turn six aliases into independent witnesses. Thirty-eight mathematical/domain checks and six source-authentication checks pass; exact replay agrees. Author review only; C127 unchanged.
Best next bounded step — C288: audit the actual composable paths in this finite four-node structure. Separate its source-supported widths from formal integer combinations that could generate K or4K without supplying a corresponding source edge. High is sufficient.