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.