C154 — Source intersections explain the nested seven, five and four counts

23 September 2026 · Bounded step 19 of 20 (C136–C155).

Three different questions give three different finite counts: seven bare 20K endpoint pairs, five Noah-supported rows, and four exact Flood-square rows. These counts must not be used interchangeably.

Intersect the retained cumulative MT ON A=5296…5289 field with the LXX OFF D=5290…5283 field under A+D=20K. Then impose the Noah endpoint X=A−3K and finally alternate Flood M=X−2K:

The first two bare pairs require Noah 3703 and 3704, absent from the held SP birth field. At the other end, SP G3 primary Noah 3710 exists, but its required cumulative A=5297 falls outside the held field. P6 retains Noah 3709 and loses the exact Flood M=2651. These are distinct boundary failures.

The numerical A=D=5290 pair still consists of different cumulative tradition/profile roles; it is not a license to merge them with the historical LXX opening self-comparison. Likewise, the bare d=0 alignment does not supply the missing Noah 3704 or Conquest 1398.

The native direct13 family separately has five admitted Creation→ordinary-Flood endpoint pairs (b=4421…4417), while its common complete Noah/Conquest/square core is four. This step takes analytic intersections of retained fields; it does not reopen the old 20K or endpoint-search campaigns.

Source and scope control

All numerical bases in this packet stand for paired coordinates: BC base B is (B+1)t/Bn BC; reflected AD base A is AD At/(A+1)n. Thus a cross-Mirror same-season span is B+A, after the civil no-year-zero subtraction. AD stations are reflected source events, not historical AD occurrences. K=529 throughout.

Regular Gears remain restricted to Noah/Shem/Flood. Creation and Conquest are fixed source-field selections. C133–C135 corrections remain controlling. The C127 graph and canonical controls are frozen; source-field admission is distinguished from an existing graph node and from a generated comparison coordinate. No wider N01/N03 expansion or missing N03 Shem join is repaired. Original Reports 01–10 remain previously verified references; interrupted original Reports 11–25 remain unestablished. Check counts are computational assertions, not independent historical witnesses.

Evidence: CERTIFICATE.json; 24 passing assertions in RESULTS.json. The assertion list identifies the actual tests.