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.