# C130 — The N02/N04 20K midpoint and 17K circuit close dependently

22 September 2026 · One bounded continuation of C129, using only the retained primary N02 and N04 rows. Let **K=529**. The frozen C127 graph and controlling File_18/File_09 govern every endpoint and phase.

**Result.** C129's 6- and 10-year cross-cumulative remainders have an exact explanation inside the already retained **20K Mirror comparison**: each row places its MT cumulative ON and LXX cumulative OFF Flood members symmetrically around the **LXX cumulative OFF opening member 5290 BC**. Separately, the **17K** cumulative-to-reflected-Noah edge is the sum of five already encoded edges, including the 868 attachment and regular-profile 190. Both findings are **dependent graph relations**. Their event labels remain distinct.

## The doubled opening-member offset

Every BC number in the table is a Nisan pair base, so 5293 means `5294t/5293n BC`. The opening member \(O\) is the held LXX cumulative *derived Cainan OFF* source pair `5291t/5290n BC`, not an invented midpoint.

| Arc | MT cumulative ON Flood \(A\) | LXX cumulative OFF opening \(O\) | LXX cumulative OFF Flood \(C\) | Two equal BC legs | \(A-C\) |
|---|---|---|---|---:|---:|
| **N02** | 5294t/5293n | 5291t/5290n | 5288t/5287n | **3 + 3** | **6** |
| **N04** | 5296t/5295n | 5291t/5290n | 5286t/5285n | **5 + 5** | **10** |

The table's symmetry is a four-relation graph consequence. Using *signed paired centers*, \(A\) and \(c\) for the first and third columns, \(O=-5290\), and \(D=R(c)=-c\), the retained mixed **20K** path gives \(D-A=10580\). The opening self-Mirror path gives \(R(O)-O=10580\), with \(R(O)=-O\). Subtracting those two widths and the two reflection records yields

\[
\boxed{A+c=2O,\qquad c-A=2(c-O).}
\]

The *separately sourced* opening-to-member offsets \(c-O=3\) at N02 and \(c-O=5\) at N04 supply **6** and **10**. The relation alone would leave that member position free: the five-node 20K subgraph has rank **4** before its specific source-member attachment, and rank **5** after. A one-year perturbation of \(c\), with the appropriate changes to its reflection and the MT member, preserves the four 20K/reflection equations while changing the remainder by two. This is a mathematical omission witness, not an admitted chronology variant.

The C10 Christ-period landing remains the midpoint of each *mixed* 20K interval: the selected **3 BC** and **5 BC** pair bases give remainders \(2×3=6\) and \(2×5=10\). These are landing selections in the retained C10 field; the computation does not promote them to separate historical nativity claims.

## The 17K cycle and its source limits

For each primary row, the existing graph already has the following directed coordinate path. Its BC-to-AD legs follow File_09's paired suffix inversion; no civil year zero is counted.

| Segment in the retained graph | N02 pair bases | N04 pair bases | Width |
|---|---|---|---:|
| LXX cumulative OFF Flood \(c\) → SP Creation \(b\) | BC 5287 → BC 4419 | BC 5285 → BC 4417 | **868** |
| SP Creation \(b\) → reflected Conquest \(q\) | BC 4419 → AD 1400 | BC 4417 → AD 1402 | **5819 = 11K** |
| Reflected Conquest \(q\) → ordinary MT Flood \(f\) | AD 1400 → AD 2458 | AD 1402 → AD 2460 | **1058 = 2K** |
| Ordinary MT Flood \(f\) → alternate MT Flood \(v\) | AD 2458 → AD 2648 | AD 2460 → AD 2650 | **190** |
| Alternate MT Flood \(v\) → reflected SP Noah \(s\) | AD 2648 → AD 3706 | AD 2650 → AD 3708 | **1058 = 2K** |

The direct retained \(c\to s\) edge is **8993 = 17K**. Thus each graph circuit closes with the exact six-edge dependency

\[
\boxed{868+5819+1058+190+1058-8993=0.}
\]

The striking scalar compensation **868+190=1058=2K** uses different kinds of inputs: 868 is C12's retained cumulative/Creation attachment, while 190 is the *regular* MT Cainan-ON/Terah +60 Flood profile displacement from ordinary MT. The 868 and 190 segments are separated by the **11K and first 2K legs**; their sum is not a single contiguous event interval. The second 2K leg's BC Noah→alternate-Flood display is the reflection of the same regular AD interval, not another independent witness. The Conquest→ordinary-Flood 2K leg has its own source-qualified endpoints.

The pair checks hold componentwise. At N02, for example, the full 17K comparison gives `5288t BC → AD3706t` and `5287n BC → AD3707n`: **5288+3706−1 = 5287+3707−1 = 8993**. N04 gives **5286+3708−1 = 5285+3709−1 = 8993**. The two 20K intervals and the generated-preimage 8K leg pass both components as well.

## Effect on C129 and graph status

Combining the sourced 868 attachment with the doubled opening remainder recovers the two measured C129 displacements:

\[
\begin{array}{c|c}
\mathrm{N02}&868+6=874\\
\mathrm{N04}&868+10=878.
\end{array}
\]

The two separate 3K edges certify the equality of those displacements at both ends. They do **not** turn the generated 8K preimage into a Noah birth, nor identify MT cumulative ON with LXX cumulative OFF. The ordinary and alternate Flood nodes remain their declared profiles and Flood Gears. Creation and cumulative members acquire no regular Gear.

The C130 evidence checker verified **578 exact assertions**, including the frozen graph equations, source roles, both calendar components, explicit six- and four-edge dependency certificates, and the five-node omission witness. Four proposed summary relations per primary row each add **zero rank** to the unchanged **208-node, rank-208** graph. One isolated replay reproduced the result and certificate byte for byte. No prior campaign was run; original interrupted Reports 11–25 remain unestablished as completed.

**Best next bounded step:** extend this exact doubled opening-member check to the already retained **N01/N03 close rows**, testing their 2- and 4-year opening offsets, source phases, and partial-expansion limits without supplying the missing Shem join. **Sol Max is sufficient.**