# 2025 2222 / 4444 / 6666 / 8888 magic-square audit

## Result

The four numbers have a reproducible, natural referent: an author-published **16×16 factorization magic square**, first posted in 2018 and re-posted on 23 April 2025.  They do **not** yet supply a cipher key, a Page-23 extraction, or a new plaintext.

## Fixed source record

- 2018 source image: `twimg-DlclzejWwAAL7AU.jpg` — SHA-256 `278b887087f41432a8f8a1badd1a33b0f5e58cc51b8bdec88f8eed7ced8bfe03`
- 2025 re-post image: `twimg-GpMaU-NW8AAtwtj.jpg` — SHA-256 `2a7e1991019e1ff840907aef8470948d670a14464c806aab2cd925cd0ff4293c`
- Re-post: 2025-04-23T04:44:38.000Z — https://x.com/666ab731/status/1914903216644403468
- Hint: 2025-04-23T05:45:15.000Z — `@tactical_nook Seek also for 2222, 4444, 6666 and 8888.`
- The hint is 3,637 seconds after the re-post. Both are replies to `@tactical_nook`, but the preserved capture does not include their parent context.

## Arithmetic reproduced

- The values are every integer from **428 through 683**, exactly once.
- Every row, column, and every one of the 32 wrapped diagonals sums to **8,888**.
- At even-aligned starts, both orientations of the following rectangles are constant:

| block | sum |
|---|---:|
| 2×2 | 2,222 |
| 2×4 / 4×2 | 4,444 |
| 2×6 / 6×2 | 6,666 |
| 2×8 / 8×2 | 8,888 |

- The four visibly nested centre squares sum to `16×8888`, `9×8888`, `4×8888`, and `1×8888` for sides 16, 12, 8, and 4.
- Cyclic 2×4 and 2×8 blocks remain constant at 4,444 and 8,888. Cyclic 2×2 blocks do not, so the square is **not** most-perfect.

## Compact construction, not a new text

Subtracting 428 from each cell gives `n[r,c]`. The entire table obeys the
bitwise formula `n[r,c] = R[r] XOR C[c]`. After translating the row-mask set
by its first member, both the row and column masks are complementary
four-dimensional binary subspaces: each has 16 elements, they share only zero,
and their pairwise XORs cover all 256 byte values exactly once. This is a full,
repeatable generation rule for the square. It still does not select letters,
an extraction order, a key, or a plaintext.

## One bounded typo

Cell R03C05 is visibly printed as `3*3^2*31 = 837`. The reproduced square forces **558**, i.e. `2*3^2*31`. This is not a guessed correction: it is forced by the row sum and is the only way to restore canonical prime-power notation across the full table.

## Evidence boundary

The arithmetic result is investigator-derived and fully repeatable. The association between the hint and the square is a strong source-linked inference based on author, recipient, timing, and the exact ladder—not an explicit sentence from the author. Nothing in the preserved material selects a further text extraction.