# 490d C322 — Whole-biography460 correspondence and joint support

24 September 2026. Step 9 of the ten-step authorization C314–C323.

**All three primary same-Gear Noah-bound biographies transfer uniformly by460 years**, from SP OFF/Terah0/full430 to MT CainanON/Terah60/full430. Every endpoint is in the frozen source register; all15 endpoint and30 component comparisons have zero residual.

| Gear | SP: Noah→Shem→Flood start→Noah death→Shem death, BC | Restored MT same-Gear chain, BC |
|---|---|---|
|G1|3706→3206→3106→2756→2606|3246→2746→2646→2296→2146|
|G2|3708→3208→3108→2758→2608|3248→2748→2648→2298→2148|
|G3|3710→3210→3110→2760→2610|3250→2750→2650→2300→2150|

Each chain retains500+100+350+150, Noah950 and Shem600. The success is qualified by the **Noah-bound/Flood-bound500/100 state**. SP primary death and MT target qualifications remain attached to their source records.

The initial hypothesis that same-Gear MT must instead give502 was rejected by the actual register and File_18 §1.3.5. That passage explicitly preserves both the Noah-bound harmonic state and Arphaxad-bound/textual state. For example, restored MTG2 Noah3248 with G1 Shem2746 gives502 and Shem→G2 Flood2648 gives98. This separately selected binding is valid in its own mode; it does not invalidate or replace the same-Gear500 correspondence. The failed initial assumption and its source correction are recorded in TEST_PLAN.json. No date or source instruction was changed to obtain the result.

The completed family has this joint support:

| i | OFF600 | NativeON600 | Reversed SP500 | C287 at i | C287 at j=10−i |
|---:|---|---|---|---|---|
|0|No|No|No|No|No|
|1|No|No|No|No|No|
|2|Yes|No|No|Yes|No|
|3|Yes|Yes|Yes|Yes|No|
|4|Yes|No|Yes|Yes|No|
|5|Yes|Yes|Yes|Yes|Yes|
|6|Yes|No|Yes|No|Yes|
|7|Yes|Yes|Yes|No|Yes|

OFF600 +ON600 +reversedSP500 +C287 at i coexist at i3 and5. Adding the **extra** requirement of C287 support also at j leaves onlyi=j5. That uniqueness is conditional on the listed criteria, not an independently preferred chronology. The configurations retain different traditions, variants and ancestor roles; co-existence does not collapse them into a single identity. C315's same-ancestor8395 failure and C313's same-phase-ancestry500 failure remain unrepaired.

## Verification and limits

39 main assertions and 16 frozen-input/predecessor checks passed. A second main replay produced byte-identical DATA and RESULTS. Separate review scope and agreement are recorded in the evidence. All frozen originals and standing controls remain unchanged. These are verification counts, not independent-witness counts.

Success isNoah-boundharmonic-state-specific. Conditionaljointuniqueness andalgebraicclosure are notsourceprescription orindependenthistoricalproof.

Mirror/529 remains the focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction x=1 January AD2; no civil year zero. Regular Gears remain Noah/Shem/Flood only. SP minus-one companion is local to SP Noah/Shem. No cumulative/upstream Gear, new endpoint or phase, fitted anchor, global axis, z-law, canonical or graph edit. Capture now; canonize later. Source state, event identity, generated coordinate and phase ancestry remain distinct. Exact arithmetic and source membership do not establish intention or independent historical witnesses.

## Decision after this result

**C323, proposed and unexecuted:** ConsolidateC314–C322 into the tenth bounded step: a source-qualified529 synthesis, minimal dependency and limitation ledger, verified report/evidence index and recovery packets. No new endpoint or anchor search.

The finite algebra, source domains, exact phases andwholebiography qualification are now resolved sufficiently for a reliable synthesis. Further transformations would add scope instead of closing this authorization.