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 | , with both paired phases checked. |
| Full cumulative 17K square | U, D, X, M | ; . These are the four sides and both equal diagonals of C10's comparison. |
| Conquest-mediated 13K prefix | b, q, f | , , hence . The refinement through generated is 3K+8K+2K. |
Here BC and reflected AD coordinates are paired bases. For example, 4422t/4421n BC → AD2456t/2457n gives . The symbol is not substituted for the square relation: the actual equal 17K diagonals are and . 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 | Admitted, including its 5296→5290→5284 = 6+6 opening bracket. | |
| A→X→reflected D | ; | Admitted with SP G3 companion Noah. |
| D→reflected X | Admitted single diagonal; does not complete the square. | |
| b→reflected f | Admitted direct endpoint comparison: SP native Creation opening and ordinary MT G1 Flood start are both sourced. | |
| U,D,X,M full square | Proposed 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 gives 11K+2K arithmetically. | Unadmitted: reflected Conquest AD 1398 is outside the retained Conquest field. A formal 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.