# C270 independent source and phase review

24 September 2026. Read C269's frozen `CLOSING_RECTANGLE.json`, C01's source event records in `C269/sources/C01_RESULTS.json`, the relevant C269 report, and selected C127 node metadata. Calculations below were independently checked with exact rational arithmetic. No canonical source, graph or previous evidence was changed; no wider endpoint campaign was performed.

## Induced maps

Let q denote a cumulative source component and y=q+8993 its corresponding reflected regular SP component. C266's inherited closing maps are

- Cumulative Flood: q→q+5290.
- Cumulative Shem: q→−(q+5888).

Consequently the regular SP maps are forced to be

**Noah:** hN(y)=y−(8993−5290)=y−3703.

**Flood:** hF(y)=−[y−(8993−5888)]=3105−y.

These identities hold for both components, not merely for the pair centers:

hN(q+8993)=q+5290; hF(q+8993)=−(q+5888).

They carry reflected SP G3 primary Noah center 3710 to local center 7, and reflected SP G3 Flood-start center 3110 to local center −5. Since the original correspondence and local maps are fixed, the induced translations are unique within these specified map types. This is conditional uniqueness, not a uniqueness theorem over arbitrary affine fits or chronology choices.

The coefficient magnitudes are 1, so actual half-year phase separation is preserved. The Flood map reverses phase order; Noah's map preserves the order of the already reflected regular pair. No center-phase reattachment or new scale is required.

## Full physical phase ancestry

The local chart remains η(x)=1000(x−1). Each regular row starts with an actual C01 BC source component, reflects it around global January AD1, and then uses the induced map above.

| Local marker | Exact local x and label | Cumulative source ancestry | Regular SP G3 source → reflection → local ancestry |
|---:|---|---|---|
| +5750 | 27/4 = AD 7t | Flood 5284t BC → translate 5290 | Noah 3710n BC → AD 3710t → subtract 3703 |
| +6250 | 29/4 = AD 8n | Flood 5283n BC → translate 5290 | Noah 3711t BC → AD 3711n → subtract 3703 |
| −6250 | −21/4 = 6t BC | Shem 5883n BC → translate 5888 → reflect | Flood 3111t BC → AD 3111n → apply 3105−y |
| −5750 | −19/4 = 5n BC | Shem 5884t BC → translate 5888 → reflect | Flood 3110n BC → AD 3110t → apply 3105−y |

The exact regular-component calculations are:

- Noah 3710n: −14839/4 → +14839/4 → 27/4.
- Noah 3711t: −14841/4 → +14841/4 → 29/4.
- Flood 3111t: −12441/4 → +12441/4 → −21/4.
- Flood 3110n: −12439/4 → +12439/4 → −19/4.

The reflected regular pairs are therefore **AD 3710t/3711n** and **AD 3110t/3111n**, exactly as C01 records. Their induced local pairs are **AD 7t/8n** and **6t/5n BC**, exactly as C266/C267 records.

The positive inner/outer radius ratio is (25/4)/(23/4)=25/23, and the negative pair has the same absolute radii in reversed chronological order. There is no civil year zero in any displayed source pair.

## Source roles and seasonal inversions

The original cumulative roles remain **Flood closing** and **Shem closing**. The regular roles remain **SP G3 primary Noah birth** and **SP G3 Flood start**. Thus cumulative Flood corresponds to regular Noah birth, while cumulative Shem corresponds to regular Flood start. The transported coordinates do not equate these events' identities.

The original source seasons likewise differ across the 8993 comparison. Cumulative Flood Tishri matches the reflected regular Tishri component descended from original SP Noah Nisan. Cumulative Shem Nisan supplies local negative Tishri, while original SP Flood Tishri reaches that same local component through two reflections overall. Both sides agree physically at the local coordinate; their histories must remain separately recorded.

In terms of original regular BC coordinates z, the complete maps simplify to −z−3703 for Noah and z+3105 for Flood. The Flood route has two reversals—original BC→reflected AD and the final local reflection—so its original Tishri/Nisan order is restored. The Noah route has one reversal overall.

The shift 3703 equals 7K; the constant 3105 is determined by 8993−5888. Its numerical coincidence with another SP Flood boundary must not change the selected source here: the endpoint remains G3 Flood **start 3110**, not a G1 closing selection or companion rail. No Gear transport is applied to cumulative sources or other regular nodes.

## Graph and novelty limits

- `N04_cm` stores the cumulative Shem closing source −5883; `N04_r` stores reflected SP G3 Flood start +3110. Their existing `N04_17opposite` edge has width 8993.
- C127 does not store Flood closing −5283 or reflected SP G3 primary Noah +3710. C254 and C269 certify the corresponding closing route without adding those nodes to frozen C127.
- C127's node at −5, `N04_Z`, has the different role `comparison_landing`. The new local image of SP G3 Flood or cumulative Shem must not be merged into that node by coordinate alone.
- C269 already established the 600-by-8993 source rectangle. C270's contribution is the induced regular-to-local transport and its actual component correspondence. It adds neither a second independent rectangle nor a new 17K witness.
- These piecewise role-specific isometries do not by themselves define a universal transformation for all regular chronology, all Gears, the entire source fields, or a new global Mirror axis.

## Review conclusion

Both regular SP G3 endpoint pairs give the exact existing bilateral 5750/6250 local bracket through maps forced by the inherited 8993 translation and C266 local operations. This is stronger than a fitted center correspondence because both physical components and their spacing agree. The cumulative and regular source-role labels, reflection histories, and frozen graph limits remain essential qualifications.