# 490d C342 — Double-E dependency, prior art and selector audit

24 September2026. Step9 of10 in the C334–C343 authorization.

**The complete regular E ladder adds a useful source realization, but it does not select the unresolved cumulative a choice.** In the frozen C319 menu it leaves exactly the same four source-admitted configurations as C332's death criteria:02 and22 at i3 andi5. Adding the17K cross-span condition still selects22; that condition remains additional.

The ladder follows from a small source dependency set. Let δ be the base SP→MT Noah separation, u the base MT Noah→Shem span, v the base MT Noah→Flood span, and w the restored-context plus next-Gear Flood displacement. The primary same-Gear source rows give

`δ=650, u=500, v=600, w=130+60+2=192`.

Then the three distances from SP Noah are

`δ+v−w=1058`, `δ+u=1150`, `δ+v=1250`.

The second E step is equivalent to `δ=(v−E·u)/(E−1)=650`. Once that holds, the first step requires `w=1250−1150/E=192`. These equations expose the precise source values supporting the pattern. They do not prove that the source author selected those values to encode the pattern. The two primary Gear realizations differ by a uniform two-year translation of the complete comparison field; they are not separate numerical calibrations of E.

| Provenance layer | Established result |
|---|---|
| C01/C09 | The scalar1058→1150→1250 ladder was already recorded |
| File_46 §6A.3 | A23²-multiple admits two integral25/23 expansions |
| C89, retrieved by locator and matching its recorded report hash | A different complete endpoint realization; its final1250 interval is shared here |
| C338–C341 | The Noah-held source realization, primary/companion and modal controls, death refinement, and exact phase/map limits |
| C334 and this dependency audit | No reviewed source instruction couples the exact cumulative/regular choices or prescribes this particular endpoint sequence |

C89's first two stages use different event pairs. The same scalar values and shared final interval do not identify its source map with the Noah-held construction. No Creation, Joseph or Conquest campaign has been reopened here.

The regular ladder knows N,R,H,F; changing the cumulative S while holding these regular endpoints cannot change its truth. The20 frozen C319 controls verify this directly and agree with C332's existing selector. Thus the positive E result strengthens the description of the regular structure while leaving the original source-binding question open.

The batch is ready for synthesis. The last authorized step will consolidate these findings and verify the saved evidence and recovery packages, without beginning a further research question.

## Verification and limits

96 main checks and 23 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.

No independent historical-witness, source-prescription or global-dilation claim. Conditional source realization and its current controls are preserved; no new source anchor or endpoint is adopted.

Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.

## Decision after this result

**C343, proposed and unexecuted:** Complete C343 as the synthesis and recovery step: consolidate C334–C342, verify all sealed evidence packets and predecessor links, and publish the final reading index, checkpoint, compact restart kit, continuation archive and integrity record. Do not execute C344.

The bounded source, sign, pair, factorization, expansion, modal, death, phase and dependency questions have been answered. Consolidation and recovery are now the best use of the last authorized step.