# C277 — Coverage of the cross-index 598 alignment

24 September 2026. Continuation after C276. This is the first completed step of the authorized sequence through C310.

**All six selected cumulative alignments exist, but four have both regular SP counterparts.** The two lower rows require Noah centers absent from the held register. The extension preserves the distinction between a cumulative annual boundary and a registered regular event.

Let A_j=−5290+j be cumulative LXX OFF Flood and B_j=−5890+j be cumulative Shem. Both cumulative fields have indices0–7. The retained translations give F_j=j and H_j=j−2 before reflecting Shem. With a common additional translation u, they become j+u and j−2+u. Thus H_j=F_(j−2), independently of u, whenever both cumulative indices exist.

C271's regular counterpart register covers indices2–7 on both branches, with reflected Noah N_i=3703+i and reflected Flood R_j=3103+j. Therefore the translated-image alignment requires i=j−2 and source difference N_i−R_j=598.

| Shem j | Flood i | Regular Flood | Required regular Noah | Both regular records? |
|---:|---:|---|---|---|
|2|0|G1 close3105|3703|No|
|3|1|G1 start3106|3704|No|
|4|2|G2 close3107|G1 companion3705|Yes|
|5|3|G2 start3108|G1 primary3706|Yes|
|6|4|G3 close3109|G2 companion3707|Yes|
|7|5|G3 start3110|G2 primary3708|Yes|

The four complete regular comparisons lower the Noah Gear by one while retaining the matching selector: primary with start, companion with close. They do not move any cumulative record through a Gear. They are derived correspondences among retained records, not four newly certified graph paths or four independent determinations of598.

Both source seasonal offsets ±1/4 satisfy the same alignment. Reflecting the translated Shem branch reverses component order, yielding global image reflection between the selected cross-index partners. No phase reattachment or alternate offset is used.

The missing3703 and3704 are calculated requirements, not new Noah births. Their absence is restricted to the held Noah branch. A matching coordinate on another role cannot repair a missing event identity. Nor does the wider cumulative field authorize a fourth regular Gear.

C276's logical boundary survives: the source differences support the selected alignment, but requiring aligned images is an additional premise. This extension supplies coverage and source roles; it does not fix the common translation or prove historical necessity.

The evidence contains all six rows, including failures, and37 exact mathematical/domain checks. Nine separate source-authentication checks pass. Two generated readouts replay byte identically. Author review only. Standing sources and C127 remain unchanged.

**Best next bounded step — C278:** characterize the reverse602 comparison alongside598 and600, including the domain of the induced two-year shifts. This tests whether the extension is a finite partial correspondence or a closed action on the existing register. High is sufficient.