# Independent C270 induced-map audit

24 September 2026. Uses only C269’s three-point source-qualified8993 correspondence and C266’s inherited maps. No new scale, event search, additional Gear campaign, or C271 work.

## Fixed source correspondence

T(q)=q+8993 carries:

| Cumulative LXX OFF source q | Reflected regular SP image y |
|---:|---|
| −5883, Shem closing | 3110, G3 Flood start |
| −5285, N04 interior Flood member | 3708, G2 primary Noah birth |
| −5283, Flood closing | 3710, G3 primary Noah birth |

Both columns have598+2 separation. The600 endpoint separation is same-index cumulative Shem/Flood on the left and same-Gear reflected SP Flood/Noah on the right. The existing middle G2 record is retained only to audit the already admitted subdivision.

## Induced regular maps

The cumulative branch maps are F(q)=q+5290 and RH(q)=−(q+5888). Composing each with T⁻¹(y)=y−8993 uniquely gives

F_R(y)=F(T⁻¹(y))=y−3703,

RH_R(y)=RH(T⁻¹(y))=3105−y.

The constants are forced by8993−5290=3703 and8993−5888=3105. Their arithmetic derivation gives no additional event identity to the constants. Both maps have unit absolute slope and preserve the half-year width; RH_R reverses its order. The inherited comparison dilation remains eta(x)=1000(x−1).

F_R∘T=F and RH_R∘T=RH hold as affine coefficient identities. On the three retained rows they give an exact transport of the source projection, including both actual seasonal components. No phase restoration is needed for this unit-slope transport.

## Exact component table

| Reflected regular component | Induced branch | Local image | eta image |
|---|---|---|---:|
| AD3710t, x=3710−1/4 | F_R | AD7t, x=27/4 | 5750 |
| AD3711n, x=3710+1/4 | F_R | AD8n, x=29/4 | 6250 |
| AD3110t, x=3110−1/4 | RH_R | 5n BC, x=−19/4 | −5750 |
| AD3111n, x=3110+1/4 | RH_R | 6t BC, x=−21/4 | −6250 |

Thus the regular G3 Noah pair displays locally as AD7t/8n, while the regular G3 Flood pair displays chronologically as6t/5n BC. The negative branch’s chronological order reverses: its input Tishri maps to local Nisan, and its input Nisan maps to local Tishri. The pair centers are7 and−5, whose eta images are±6000; both seasonal brackets are precisely6000±250 in absolute radius.

The original native SP sources remain the G3 Noah birth pair3711t/3710n BC and G3 Flood start pair3111t/3110n BC. The table operates on their already reflected AD pairs, as the C269 correspondence requires. Their native source phases must not be silently substituted for the table’s reflected input phases.

## Bilateral J₁ relation

The regular closing endpoints satisfy H=N−600. Therefore

RH_R(y−600)=3705−y=2−F_R(y)=J₁(F_R(y)).

On the retained same-Gear pair this holds for center and both matching input components. Applying eta gives opposite signed comparison values:

eta(RH_R(y−600))=−eta(F_R(y)).

The reflected positive inner component27/4 corresponds to the negative inner component−19/4; the positive outer29/4 corresponds to negative outer−21/4. This is exactly the existing local reflection about1. It does not move the global Mirror origin or create a new universal axis.

## Intermediate record confirms branch assignments

The N04 cumulative Flood member−5285 maps by T to regular G2 Noah3708 and then by F_R to local center5, with components AD5t/6n at19/4 and21/4. Their eta values are3750 and4250. This uses the Flood-source projection branch, despite the regular target’s Noah label.

For the Shem-source branch, the induced map before reflection is U_R(y)=y−3105. It sends regular G3 Flood3110 to the same local center5. Thus

F_R(3708)=U_R(3110)=5,

while F_R(3710)=7. The two branch constants differ by598 and absorb the existing regular598 comparison, just as the inherited cumulative translations do. Applying reflection to the Shem-source branch sends its5 to−5.

This co-location does not identify the regular G2 Noah birth with the G3 Flood. The maps are selected by the inherited source branch, not simply by the regular target’s person/event name. Applying the other formula indiscriminately would leave the declared finite comparison.

## Scope of the result

The two G3 endpoint pairs have an exact component-preserving counterpart to the bilateral LXX bracket under maps forced by the existing17K translation. This is a genuine finite commuting correspondence and requires no newly fitted scale. Its source qualification is inherited from C269’s dependent rectangle; it does not add independent17K witnesses.

The formulas are defined algebraically beyond the displayed points, but source support is asserted only for these admitted records and branch assignments. They do not identify different source events, prove a global transformation of all regular chronology, generate additional Gear endpoints, supply a regular Shem299 midpoint closure, or extend C268’s phase-to-center rescaling to a universal source-preserving action. The two operations retain their separate purposes.