# C139 — Source-field membership does not require a stored graph node

23 September 2026 · Bounded step 4 of 20 (C136–C155).

**The six-square result has two provenance levels: four U vertices already exist as typed graph nodes; two are admitted members of the explicit retained field.** No graph node is added.

| Cumulative U pair | Existing typed graph node | Admission |
|---|---|---|
| 6349t/6348n BC | None | Retained field member |
| 6348t/6347n BC | None | Retained field member |
| 6347t/6346n BC | N01_u | Retained field member |
| 6346t/6345n BC | N02_u | Retained field member |
| 6345t/6344n BC | N03_u | Retained field member |
| 6344t/6343n BC | N04_u | Retained field member |

C10 explicitly states the cumulative ON Shem-birth/Noah-death field 6350–6343 and OFF Flood/Shem-death field 5290–5283. File_18 §6D supplies native cumulative Flood 5750–5743. The retained comparisons use the 600-year Shem span for the first field and the 460-year cumulative Cainan removal for the second. These operations belong to cumulative architecture; neither is a regular Gear.

Thus U=6347/6348 is not rejected merely because it lacks a stored C127 node. Conversely, arithmetic U=6342 is not admitted merely because it would complete an exact 1058 square: it is outside the retained field. This step checks retained field membership, not a fresh historical attestation of each generated pairing. The six-square language means sourced endpoints available for comparison; it does not certify a larger joined chronology or source-preserving transformation.

## 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`; **29 passing assertions** in `RESULTS.json`. The assertion list identifies the actual tests.