490d C349 — Finite partial endpoint relations for E and300/299
24 September 2026. Step 6 of 10 in the C344–C353 authorization.
The supported structure is a small collection of partial, invertible endpoint relations. Within each primary path, the longest nontrivial E chain is R→H→F; the300/299 repairs form separate one-step relations.
Use the already established N,M,D,R,H,F, add S=SP same-Gear Shem, U=next-Gear restored MT Noah, V=old-Gear restored MT Flood, and the old/new MT Noah deaths B,C. All eleven nodes are existing source records.
| Comparison expression | Exact forward moves within this field | Fixed source point |
|---|---|---|
| E=25/23, fixing N | M→S; R→H→F | N |
| 300/299, fixing R | M→U | R |
| 300/299, fixing M | R→V | M |
Every listed arrow has an exact inverse within the same field. Every other input in this eleven-node domain was checked and did not match a field node. In particular, a second E step after M→S and a second300/299 step after either repair leave the field. The SP and MT death nodes remain source records but are not transported to another field node by these expressions.
The two Gear placements reproduce the same labelled relations. The132 forward/inverse input checks and32 matches include fixed points and inverses; they are not independent historical evidence. A nonmatch means outside this declared field, not absent from every chronology or archive. Diagnostic outputs are not adopted as new endpoints.
The inverse relations make the local algebra precise, but do not establish a total group action on the source register. The next check asks whether changing the order of the two distinct, fixed-endpoint expressions produces any additional source-supported composition.
Verification and limits
142 main checks and 18 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.
Only the eleven-node field and its two primary placements are covered. No new source node, global action or canonical graph edit.
Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.
Decision after this result
C350, proposed and unexecuted: Audit the order of the three existing fixed-endpoint expressions. Compute their exact coordinate commutators and test whether both composition orders remain inside the declared source field, keeping scalar algebra separate from source permission.
The partial relation table is now complete. Composition order is the next unresolved structural issue; its fixed anchors are already declared, so no new anchor is needed.