| # Mirror Dimension: Persistent KV Cache (Six-Proof Build) |
|
|
| The MirrorDimension object from the Mirror Dimension paper (Heylel Yaka, v0.2), |
| upgraded with **embedded position tags** and a **sixth proof: shuffle-invariance**. |
|
|
| ## The discovery (Sept 21, 2026 session) |
|
|
| The original five tests are real and reproduce bit-for-bit (Test 1 identical to |
| the paper on an RTX GPU). But a sixth attack permuting every stored entry |
| across slots, values intact — exposed that the position lived in the **array |
| slot**, not the payload: |
|
|
| ``` |
| [before shuffle] recover(10) max err = 5.96e-08 (exact) |
| [after shuffle] recover(10) max err = 7.62e-01 (garbage — address destroyed) |
| ``` |
|
|
| The fix: every entry now carries its own position tag (`t`, one long per slot). |
| `recover()` finds entries **by tag**, and takes the un-rotation angle from the |
| entry itself. The slot is parking, not addressing. Same attack, after the fix: |
|
|
| ``` |
| [before shuffle] recover(10) max err = 5.96e-08 |
| [after shuffle] recover(10) max err = 5.96e-08 (SURVIVED) |
| ``` |
|
|
| The mirror is now genuinely self-describing: lossless AND order-independent. |
|
|
| ## Files |
|
|
| | File | What it is | |
| |---|---| |
| | `mirror_dimension.py` | The tagged MirrorDimension + all six tests (`python mirror_dimension.py`) | |
| | `test6_shuffle.py` | The shuffle attack, standalone — the before/after evidence | |
| | `mirror_test.pt` | Persistence-test artifact (written by Test 5) | |
|
|
| ## Reproduce |
|
|
| ```bash |
| pip install torch # CUDA optional; CPU works |
| python mirror_dimension.py # runs all six tests |
| python test6_shuffle.py # runs the shuffle attack standalone |
| ``` |
|
|
| Measured results this machine (RTX GPU, torch 2.8.0+cu126, Windows): |
|
|
| | Test | Property | Result | |
| |---|---|---| |
| | 1 | Isometry (norm preservation) | diff **0.00e+00** | |
| | 2 | Conjugate recovery | **0.00e+00** both parts | |
| | 3 | Cross-distance (4990 writes) | **5.96e-08** = float32 eps | |
| | 4 | Relative-offset invariance | diff **1.00e-05** | |
| | 5 | Save/load persistence | **5.96e-08** | |
| | 6 | **Shuffle-invariance (new)** | **5.96e-08 after full permutation** | |
|
|
| Legacy saves (no tags) load cleanly slots become tags automatically. |
|
|
| ## Cost of the upgrade |
|
|
| One int64 per entry (~4 bytes vs 2×head_dim float32s) plus a tag lookup on |
| read. Zero change to the rotation, the isometry, or the attention math. |
| |
| **License:** AGPL-3.0 — see [LICENSE](LICENSE) |
| |
