# C132 — Which source attachments sustain the 20K, 17K, and 13K Mirror claims?

22 September 2026 · One bounded audit of the four C122 paths and the fifth C10/C12 boundary row. Here **K = 529**. File_18 controls the event fields, File_09 the paired reflection and absence of year zero. C10, C12, C122, and the frozen C127 graph supply the existing records; C131 supplies the immediately preceding result. Regular Gears remain restricted to **Noah, Shem, and Flood**.

**Finding.** The three statements have different minimum sets of *source roles*. A direct 13K Creation→reflected-Flood comparison also exists at the fifth boundary, even though its proposed Conquest waypoint **AD 1398** is outside the retained source field. Calling that direct endpoint comparison an admitted **Creation–Conquest–Flood path** would add an unsupported waypoint.

## The incidence question

For each N01–N04 row, use these typed attachments: **A**, MT cumulative Cainan ON Flood; **D**, LXX cumulative derived-OFF Flood and its paired reflection; **O**, sourced 5290 BC LXX-OFF opening; **U**, LXX cumulative ON Shem-birth/Noah-death; **X**, SP regular Noah birth, with its Gear and companion tag; **M**, alternate MT regular Cainan ON/Terah +60 Flood start/close; **b**, fixed native SP Creation; **q**, reflected Conquest source member; **f**, reflected ordinary MT regular Flood start/close. The 8K preimage **z = 4232 − q** is generated, with no independent source role. Source identity includes profile, event, Gear, start/close, companion, projection, and phase; an equal number alone is insufficient.

| Claim being tested | Minimum sourced roles in this selected construction | Arithmetic once those roles are present |
|---|---|---|
| **Mixed 20K endpoint** | **A, D** | \(A+D=10580=20K\), with both paired phases checked. |
| **Full cumulative 17K square** | **U, D, X, M** | \(U-D=X-M=1058\); \(U+M=D+X=8993=17K\). These are the four sides and both equal diagonals of C10's comparison. |
| **Conquest-mediated 13K prefix** | **b, q, f** | \(b+q=5819=11K\), \(f-q=1058=2K\), hence \(b+f=6877=13K\). The refinement through generated \(z\) is 3K+8K+2K. |

Here BC and reflected AD coordinates are **paired bases**. For example, `4422t/4421n BC → AD2456t/2457n` gives \(4422+2456-1=4421+2457-1=6877\). The symbol \(U+D\) is *not* substituted for the square relation: the actual equal 17K diagonals are \(U+M\) and \(D+X\). Bare 20K needs no Noah or midpoint node; its **3K+17K route** additionally needs X, and its *sourced opening midpoint* additionally needs O. The one-diagonal 17K comparison needs D and X. The direct 13K endpoint comparison needs b and f, while the Conquest route needs q as well.

## Four rows and the one-source deletion control

Each of N01–N04 has all nine sourced roles, and the above claims pass their exact phase and type checks. The four values of `(A,D;U,X,M;b,q,f)` are:

| Row | A,D | U,X,M | b,q,f | Boundary and SP Noah |
|---|---|---|---|---|
| N01 | 5292, 5288 | 6346, 3705, 2647 | 4420, 1399, 2457 | MT G2 **close**; SP G1 companion |
| N02 | 5293, 5287 | 6345, 3706, 2648 | 4419, 1400, 2458 | MT G2 **start**; SP G1 primary |
| N03 | 5294, 5286 | 6344, 3707, 2649 | 4418, 1401, 2459 | MT G3 **close**; SP G2 companion |
| N04 | 5295, 5285 | 6343, 3708, 2650 | 4417, 1402, 2460 | MT G3 **start**; SP G2 primary |

Delete one **selected source attachment** per row, keeping all coordinates and other roles fixed. “Yes” means the stated *source-qualified construction* survives; it does not assert that a different historical selector could never yield the same number.

| Selected role withheld | Mixed 20K endpoint | Full 17K square | Conquest-mediated 13K prefix |
|---|---|---|---|
| A | **No** | Yes | Yes |
| D | **No** | **No** | Yes |
| O | Yes | Yes | Yes |
| U | Yes | **No** | Yes |
| X | Yes | **No** | Yes |
| M | Yes | **No** | Yes |
| b | Yes | Yes | **No** |
| q | Yes | Yes | **No** |
| f | Yes | Yes | **No** |
| generated z value omitted | Yes | Yes | Yes |

These are incidence counterfactuals, **not** deletions from the historical graph. If O is withheld, the separately sourced `A→O→D` equal-leg statement loses its opening witness, though the A→D 20K comparison remains. If X is withheld, the A→X→D 3K+17K route and the D→reflected-X 17K diagonal lose their Noah witness, though the bare 20K endpoints remain. With q withheld, a direct b→f 13K endpoint span can remain but the 11K+2K route cannot. Dropping generated z alone removes no source witness: it can be recomputed from an *admitted* q.

## Why the fifth boundary behaves differently

C10/C12's fifth selection has sourced **A=5296, D=5284, O=5290, X=3709**, and the direct source endpoints **b=4421, f=2456**. Thus:

| Fifth-row comparison | Exact result | Source status |
|---|---|---|
| A→reflected D | \(5296+5284=10580=20K\) | **Admitted**, including its `5296→5290→5284 = 6+6` opening bracket. |
| A→X→reflected D | \(5296-3709=1587=3K\); \(5284+3709=8993=17K\) | **Admitted** with SP G3 *companion* Noah. |
| D→reflected X | \(5284+3709=8993=17K\) | **Admitted single diagonal**; does not complete the square. |
| b→reflected f | \(4421+2456=6877=13K\) | **Admitted direct endpoint comparison**: SP native Creation opening and ordinary MT G1 Flood start are both sourced. |
| U,D,X,M full square | Proposed \(U=6342, M=2651\) would give the same 17K arithmetic. | **Unadmitted:** cumulative ON **6342 BC** is outside 6350–6343; alternate MT **2651n BC** is outside its Nisan Flood field. The supported **2651t BC** belongs to a different phase and selection. |
| b→q→f | Proposed \(q=1398\) gives 11K+2K arithmetically. | **Unadmitted:** reflected Conquest **AD 1398** is outside the retained Conquest field. A formal \(z=2834\) derived from it cannot supply that missing event. |

The direct fifth 13K is a **source-qualified endpoint equality**, and the four retained 13K *Conquest-mediated prefixes* remain exactly four. Likewise there are **five** source-qualified mixed 20K endpoint comparisons and **four** fully sourced 17K squares. These counts answer different incidence questions. The fifth direct 13K does not establish a full earlier expansion, a Shem join, or a fifth Conquest path. N01/N03 remain partial expansions and N03 has no complete Shem join.

## Status and boundary

The checker verifies **91** frozen-input, typed-role, endpoint, componentwise phase, and single-removal assertions over four rows plus the fifth control. This is a finite audit of the existing selected constructions, **not** an exhaustive search for alternative chronologies. It changes no File_18/File_09 control, historical graph edge, rank (**208 nodes/rank 208**), or source Gear. Original interrupted Reports 11–25 are still unestablished. Evidence includes the input hashes, executable audit and results, and the explicit claim matrix.

**Next bounded step, if requested:** compare the fifth direct 13K endpoint with the four mediated 13K rows as a *typed two-way classification*; check whether its SP Creation opening and MT G1 Flood start are already represented by the current source graph, without creating a Conquest waypoint or extending the full expansions.