# C133 — Five direct 13K edges, with a correction to their boundary alignment

22 September 2026 · One bounded source-graph classification after C132. **K = 529.** The attached File_18 and File_09 are accessible and byte-identical to the controlling copies used through C132.

**Finding.** The direct **4421 BC → reflected AD 2456** comparison was already recorded in **C05** and remains the frozen C127 graph edge **`opening_13`**. Its two typed source nodes are `opening_Creation` and `opening_MT_Flood`. It is an existing source-qualified 13K interval, not a newly discovered fifth witness.

**Correction to C131/C132:** this opening 13K comparison and the fifth C10/C12 Noah row **P6** lie at *opposite ends* of the common four-row pattern. Their shared designation as a “fifth” row did not establish a common source binding. C131/C132 associated P6 with the opening's unavailable Conquest **AD 1398**. Preserving the existing source-profile links instead aligns P6 to **Creation 4416 → Conquest AD 1403 → proposed Flood AD 2461**. Creation and Conquest are admitted there; the proposed Flood is outside the held ordinary MT field.

## Existing graph evidence

The five directed source edges are `opening_13`, `N01_13`, `N02_13`, `N03_13`, and `N04_13`. Each goes from **fixed native SP Creation** to **reflected ordinary MT Flood**, with full-430, Terah-zero and Cainan-OFF profiles. The first is G1 Flood start; the other four are G2 close/start and G3 close/start. The SP Creation members are selected within the fixed Normal/G2 field; no Gear is transported to Creation.

For the opening edge the complete paired interval is

\[
4422t/4421n\ \mathrm{BC}\longrightarrow\mathrm{AD}\ 2456t/2457n,
\qquad4422+2456-1=4421+2457-1=6877=13K.
\]

C05's `I_6877` supplies exactly those endpoints. C127 retains them as sourced nodes with the same profile, event and phase tags. The opening edge's proposed 11K waypoint is **AD 1398**, absent from the retained Conquest field, as C122 already records. Its direct 13K status therefore survives while its Conquest-mediated status fails.

For N01–N04, the existing graph has both source-qualified **11K+2K** paths and their **3K+8K+2K** refinements. Their edge sums reproduce the direct 13K edges exactly. The inserted 8K preimages remain generated boundaries. The five direct comparisons are not five independent numerical constraints.

## The two five-member registers are offset by one row

Let **d** index native Creation member selection from the opening. On the direct 13K family,

\[
b=4421-d,\qquad f=2456+d,\qquad b+f=6877.
\]

The proposed Conquest waypoint is \(q=f-1058=1398+d\). This is a finite description of the retained members, not a new chronology operator or a Creation Gear.

The four shared rows preserve the graph's **868** cumulative-OFF-to-native-Creation link and **190** alternate-to-ordinary MT Flood profile link. With D the cumulative LXX OFF BC base, X the SP Noah BC base and M the alternate MT Flood base, the alignment is

\[
D-b=868,\qquad X-M=1058,\qquad M-f=190.
\]

Thus the C10/C12 Noah rows have \(D=5289-d\), \(X=3704+d\), and MT cumulative ON \(A=5291+d\). Their five retained rows occupy **d = 1,2,3,4,5**, while the five direct 13K source edges occupy **d = 0,1,2,3,4**.

| d | Native Creation b | Reflected Flood f | Conquest q | Direct 13K | In C10/C12's five Noah paths? | Conquest-mediated 13K |
|---:|---:|---:|---:|---|---|---|
| **0** | **4421** | **2456** | 1398, unadmitted | **Yes: opening_13** | No | No: Conquest absent |
| 1 | 4420 | 2457 | 1399 | Yes: N01 | Yes | Yes |
| 2 | 4419 | 2458 | 1400 | Yes: N02 | Yes | Yes |
| 3 | 4418 | 2459 | 1401 | Yes: N03 | Yes | Yes |
| 4 | 4417 | 2460 | 1402 | Yes: N04 | Yes | Yes |
| **5** | **4416** | 2461, unadmitted | **1403** | No: Flood absent | **Yes: P6** | No: Flood absent |

Consequently the common domain is precisely **d = 1–4**. These are also the four fully sourced C10 17K squares. “Five” in the two outer registers counts different selections. The C10/C12 column concerns its retained **Noah-bearing 3K+17K routes**; it is not an exhaustive count of every possible bare cumulative 20K endpoint equality.

The domain calculation can be stated without a new search. Native Creation has bases **4414–4421** and ordinary MT Flood has bases **2455–2460**. Requiring \(b+f=6877\) leaves **f = 2456–2460**: five direct pairs. Requiring an admitted \(q=f-1058\) leaves **f = 2457–2460**: four mediated pairs. Flood 2455 would require Creation 4422, outside the native field. At the other boundary, Conquest 1403 requires Flood 2461, outside the held ordinary MT field.

## Corrected P6 attribution

P6's actual graph nodes remain **A5296, D5284, SP Noah X3709**. Its 20K endpoint, 3K+17K route, single 17K diagonal and sourced opening bracket `5296→5290→5284 = 6+6` remain valid. Preserving the links above gives

\[
b=5284-868=4416,\quad q=5819-4416=1403,\quad
f=3709-1058-190=2461.
\]

The first two nodes already exist as **`C5_creation`** and **`C5_conquest`**, joined by the existing **`native11_5`** edge. C122 explicitly excludes their Flood continuation because **2461** is outside the held field. The full P6 square separately lacks cumulative ON **6342 BC** and alternate MT **2651n BC**, as C10 records.

By comparison, placing opening Creation 4421 and Flood 2456 into P6 changes the required links to **5284−4421 = 863** and **2651−2456 = 195**. Although those altered gaps still add to 1058, they are not the retained **868/190** source-profile links. Equal total length did not justify that cross-family binding. **C133 supersedes that attribution in C131/C132; their separate endpoint arithmetic and four-row core remain valid.**

## Checkpoint

The bounded checker passes **56 assertions** covering frozen inputs, current attached controls, all five direct typed edges, four exact path decompositions, the two source-domain intersections, and the P6 attribution correction. The graph remains the inherited **208 nodes/rank 208**; no graph node, edge, canonical source or Gear application was added. Original interrupted Reports 11–25 remain unestablished. The evidence packet includes the selected C05 provenance and the explicit correction certificate.

**Best next bounded step:** test P6's equal **3K** comparisons using its correctly aligned, admitted **Creation 4416 / Conquest 1403** nodes. Determine whether the C129 equal-3K comparison extends to this boundary despite its missing Flood continuation. This retains the 529 focus and Noah/Shem/Flood Gear scope.