# C327 — Complete positive residual census: source review

**The 40-year residual is one member of a larger, source-qualified structure.** The held five-role biographies yield eighteen positive annual residuals: six role patterns repeated across three Gears, with residual values 40, 140, 490, and 640. All are partitions of already admitted source-biography durations after the same 460-year context leg.

This source review checks all 75 ordered role choices against frozen C322 identities, contexts, and modal bindings, plus their 150 coherent same-phase realizations. It records 382 passing checks in `C327_Source_Results.json`. Thirty-six coherent phase realizations have a positive residual. The other 57 annual choices have negative residuals; none is zero. This review does not claim to independently enumerate every mixed-phase combination.

## Source-role inventory

A is the SP first-role endpoint. B is its MT same-role counterpart, so A−B=460. C is another held SP endpoint. The original SP duration is d=A−C, and the cross-context remainder is r=B−C=d−460. A positive remainder places B between A and C in the declared BC order.

| SP first role A → SP terminal C | Original d | Cross-context r | Partition | Meaning of d |
|---|---:|---:|---|---|
| Noah birth → Shem birth | 500 | 40 | 500 = 460 + 40 | Noah-bound begetting relation |
| Noah birth → Flood start | 600 | 140 | 600 = 460 + 140 | Noah's age at the selected Flood start |
| Noah birth → Noah death | 950 | 490 | 950 = 460 + 490 | Matched Noah biography, with SP primary-death qualification |
| Noah birth → Shem death | 1100 | 640 | 1100 = 460 + 640 | Cross-person span, not a lifespan |
| Shem birth → Shem death | 600 | 140 | 600 = 460 + 140 | Shem's matched lifespan |
| Flood start → Shem death | 500 | 40 | 500 = 460 + 40 | Shem's post-Flood interval in the Noah-bound state |

Each row occurs at G1, G2, and G3 without changing its event meaning or duration. The two 600 rows are different source intervals; the two 500 rows are also different source intervals. Equal numbers do not merge those roles. In particular, 490 is the interval from **MT Noah birth to SP Noah death**, not a revised Noah lifespan. Likewise, 640 is not Shem's lifespan, and 1100 is not Noah's lifespan.

For example, the held G2 Noah biography uses SP Noah birth 3708 and death 2758, with MT Noah birth 3248 between them. Its 950 source duration is partitioned as 3708→3248→2758. This uses the same source-qualified dates already admitted in C322; 2758 was not selected by subtracting a desired 490 from an anchor.

## Modal, inclusive, and event controls

SP remains Cainan OFF/Terah0/full430; MT remains restored Cainan ON/Terah60/full430. The same Gear is held throughout each triple. B has A's event role; it does not inherit C's role simply because it divides the SP interval. Source admission is inherited from C322's five-role records and independently checked here; no source row was altered.

File18 §3, lines1444–1488, explicitly supplies the SP primary Noah 950 row and the primary Noah-to-Flood 600 path. It also distinguishes the one-year Flood event span from person-station alternatives. Line1460 states that inclusive cap counting does not add an extra year to every lifespan. Therefore the 950 partition is not changed to 951 by a blanket inclusive convention.

File18 §3.2.1, lines1571–1594, keeps the SP primary Noah-death column's inclusive/harmonic qualification while stating that matched endpoints preserve Noah 950, Shem 600, and Noah/Shem 500. That qualification remains attached to the new 490 residual's terminal endpoint. The residual arithmetic does not erase it or silently substitute the ordinary-companion death.

File18 §1.3.5, lines755–771, preserves both Noah-bound/Flood-bound Shem 100 and Arphaxad-bound/textual Shem 100. The present same-Gear modal state uses Noah 500/Shem 100/Flood 600. C322's separately recorded MT Noah G2→Shem G1 gap 502 remains valid under its different binding. It is not inserted into this fixed same-Gear census, and the census does not correct or disprove it.

Flood start retains its event identity. No close was substituted, no Flood companion was created, and SP's person-only companion was not transferred to MT. No upstream or cumulative Gear operation was opened.

## Phases, dependence, and prior work

The integer partitions remain exact when A, B, and C use the same already admitted quarter-year component. The review reads those components from frozen C322 rather than assigning fresh phases. File18 line1488 expressly says its annual coordinates do not supply an unstated birthday or fractional-year phase; the inherited exact component system is not newly claimed as textual birthday evidence.

The recorded C325/C314 ancestry distinctions remain unchanged. Equal actual component offsets do not identify opposite cumulative ancestry labels. This census does not invent a new cumulative path for a death endpoint or merge antecedents merely because output coordinates form an exact partition.

Every residual follows from the two held equalities A−B=460 and A−C=d. The census adds complete finite coverage and validates the endpoint labels. It does not add an independent numerical equation for every subtraction, an independent witness for every Gear, or a source-prescribed E expansion.

The prior-work locator reports a bounded failure to find these exact cross-context death/residual partitions explicitly stated before this census. It also records older regular-context 460 derivations and differently typed 490,1100, and460→500 motifs. Those are prior context, not interchangeable evidence for these event paths. This review makes no archive-wide novelty claim and does not rerun those earlier campaigns. File09's cumulative 460+30=490 motif, for example, must not replace the present regular 950=460+490 endpoint partition.

## Consequence and possible next question

Removing the 500-only filter shows why the 40 residual should not be presented as an isolated or uniquely selected source signal. The same admitted biography supports the 140, 490, and 640 remainders under precisely the same context translation. C324's missing E prescription and C326's whole-field mismatch remain unchanged.

A useful next bounded question would arrange the ten existing SP/MT biography endpoints into a complete source-labelled order for each Gear and determine whether the residual families are consequences of one coherent interleaving. Such a ledger must preserve event roles and context, add no endpoints or phases, and carry no new E or historical-intention claim. **No C328 calculation was performed.**