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plans/x265: record PROBE-SPLAT-μ-HYDRATION-RHO leg 1 results (DROP for static μ) #251

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plans/x265: record PROBE-SPLAT-μ-HYDRATION-RHO leg 1 results (DROP for static μ) #251

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25 changes: 25 additions & 0 deletions .claude/plans/x265-sprite-replay-probe-v1.md
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Expand Up @@ -266,3 +266,28 @@ temporal tautology). "EWA = blasgraph semiring" DROPPED (depth-sorted Porter-Duf
runs on a real trained Inria `.ply` (non-φ input via `splat3d::ply`): μ-hydration
ratio + semiring-matches-EWA (commutative-⊕ vs sorted-over) + SoA-sweep throughput.
PASS→[H] / KILL→DROP bands in the board entry.

### Results — leg 1 RAN (2026-07-19, `E-3DGS-MU-HYDRATION-2`)

Leg 1 (the synthetic-structured falsifier, before the real-`.ply` v2) ran on
lance-graph `crates/helix/examples/mu_hydration_probe.rs` (std-only,
`helix::placement` public API, SplitMix64, 5 tests green):

```
set=ctrl_naddr rho=1.0000 residual=0.0000 escalation=0.0000 ← φ-phase at GENERATION index: perfect
set=ctrl rho=-0.0198 escalation=0.9978 ← SAME cloud, MORTON spatial address: collapses
set=nonphi rho=-0.0676 escalation=1.0000 ← structured cloud, spatial address: no win
comma_phi_three_gap_distinct=3 comma_coprime_full_perm=1 ← comma fence green (Steinhaus ≤3 + coprime full-perm)
```

**Verdict: KILL→DROP for STATIC spatially-addressed μ-hydration** — escalation ≈1.0
is precisely the KILL band; a spatially-addressed static cloud collapses to the
ordinary float-SoA `splat3d` already ships (no positions-free win). The
`ctrl_naddr` contrast (same data, `rho=1.0` at the generation index vs `rho≈0` at
the Morton address) proves hydration is **addressing-dependent, not data-dependent**:
the win needs a transmitted sequential generation index, which motion has (the
frame/path counter — the `E-X265-HEADTOHEAD-1` ∞-PSNR case) and a static cloud does
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.
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