C305 — Annual parity of the joint600-year comparison
24 September 2026. K=529; source bindings and anchors held fixed.
Result
The two joint positions established in C303–C304 select 599 and601 years, respectively, between SP Noah and the same-Gear SP counterpart of the fixed2832 MT Flood point. They do not select the matched-selector600-year interval. This is a precise compatibility boundary, not a contradiction in the source register.
Let q=−5290+i be the signed cumulative LXX_OFF Flood center. The17K source relation selects reflected SP Noah N=q+8993=3703+i. The fixed cross-bridge equality selects ordinary MT Flood B=−q−2832=2458−i. Its same-Gear, same-boundary SP counterpart is P=B+650=3108−i. Therefore
N−P = 595+2i.
The two maps have opposite dependence on the annual index. Exact600 would require i=5/2, outside the integer annual-center field. This is an algebraic statement over the held source domain; no new center or local axis is admitted.
Source support
MT Flood is available at indices0–3. The17K SP Noah requirement is available at indices2–7. Their intersection is indices2 and3, and both endpoints retain Gear1.
| Index | Stored branch | SP Noah | Same-Gear SP Flood | Width |
|---|---|---|---|---|
| 2 | N01 | 3705, companion | 3106, start | 599 |
| 3 | N02 | 3706, primary | 3105, close | 601 |
The matched600 comparisons in this Gear are primary Noah3706→Flood start3106 and companion Noah3705→Flood close3105. The joint selection instead uses the two opposite combinations. Flood start/close and the SP person companion remain independently tagged; numerical proximity does not authorize exchanging them without updating their source bindings.
These results do not weaken the stored17K edges verified by C304 or the complete600 segments in C302. Those results use their own endpoint bindings. C305 shows that imposing both particular interfaces does not also yield a600-year same-Gear comparison.
Evidence and next decision
Ten mathematical/domain checks and eight authentication checks passed; readouts reproduce byte identically. The annual ledger includes all eight cumulative indices and reports absent requirements without extending the regular domain. All canonical and graph controls remain unchanged. Author review only.
The next bounded step will test the existing phase components and all admitted Gear1 selector alternatives. It will record whether a600-year alternative preserves both fixed interface equations or instead changes one of them. This tests the only local source choices already available, without fitting a bridge or adding a companion.