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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
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.