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38 changes: 38 additions & 0 deletions .claude/plans/x265-sprite-replay-probe-v1.md
Original file line number Diff line number Diff line change
Expand Up @@ -291,3 +291,41 @@ not. **μ-hydration ⊂ motion-hydration.** The comma is the decoupler: φ's
incommensurability (three-gap = 3) is exactly what makes the spatial address unable
to invert to `n`. The real-`.ply` `splat3d::ply` leg (v2) would confirm on trained
geometry but the mechanism already forecloses the static win.

## Head-to-head-2 — PROBE-MORTON-SHIFT-MOTION (the non-tautological one)

The operator's follow-up claim: *x265 never had blasgraph + the Morton-cascade
inverse-pyramid 4×4 neighborhood with the Pythagorean comma (akin to the Fujifilm
X-Trans sensor), and **moving a sprite could become bit-shifting to adjacent**.*
This is the sharpest form of the amortization thesis, and unlike head-to-head-1 it
is NOT a tautology: the sprite APPEARANCE is arbitrary deterministic-noise (never
φ-placed), paid for equally on both sides — only the MOTION representation is
compared.

### Results — RAN (2026-07-19, lance-graph `E-X265-MORTON-SHIFT-1`)

`crates/helix/examples/morton_shift_motion_probe.rs` (std-only, SplitMix64, 6 tests
green):

```
legA dx∈{(1,0),(0,1),(7,5),(16,16)} bit_exact=1 motion_bytes=2 sprite_px=576
legA_dilated_add_identity=1 ← morton2(x+dx,y+dy) == two carry-through-holes adds (4096 samples)
legB disocc_dx=2 dy=1 disocc_px=70 disocc_frac=0.1215 ← interior residual = 0; only the L-strip is new
legC comma_three_gap_distinct=3 comma_coprime_full_perm=1 ← sub-pel dither aperiodic
```

**Verdict: PASS→[H] for the structural claim.** Rigid tile-aligned translation of an
arbitrary sprite IS a dilated-lane Morton address-add — bit-exact, and the whole
576-pixel object moves for a **2-byte** delta (O(1) in sprite size). The interior
residual is exactly 0 (x265's DCT+quant round-trip never is); the only new content
is the revealed leading-edge L-strip (dis-occlusion), which is the residual the
entropy coder must still carry — the tail SHRINKS to genuine-new-information, it
does not vanish. Sub-pel rides the comma phase (three-gap=3), the Fujifilm X-Trans
anti-moiré move, replacing quarter-pel interpolation. This is the concrete
**"MortonShift" prediction mode** for the add-a-mode/RDO parity path.

**v2 gates (deferred, honest):** advantage scales inversely with per-frame motion
magnitude (dis-occlusion grows with the delta); non-rigid motion is out of scope;
sub-pel **appearance** (vs position) is the inverse-pyramid-descent leg; cross-level
carry for large objects; and the real-x265 inter-frame byte comparison at matched
PSNR.
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