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docs(splat-native): address codex P2 on #476 (SH band notation ℓ=3 → ℓ≤3)
Codex P2 finding on #476: my added text said "16 coeffs at ℓ=3" but a single SH band at ℓ=3 has 2ℓ+1 = 7 coefficients. The 16-coefficient carrier described in §3 D-SPLAT-1 is for all bands THROUGH ℓ≤3 (1 + 3 + 5 + 7 = 16). The "ℓ=3" shorthand could send a D-SPLAT-4 implementer toward the wrong palette cardinality / basis layout. ## Fix - Step 1 prefix: "SH basis index spanning the ℓ≤3 carrier" (was "ℓ=3 SH basis index"). - Step 2 palette domain: "16 coefficients spanning ℓ≤3 — degree 0: 1, degree 1: 3, degree 2: 5, degree 3: 7 — totaling 16, matching the §3 D-SPLAT-1 carrier shape" (was "16 coeffs at ℓ=3"). The expanded form mirrors the §0 executive summary line 23 wording "(spherical harmonics, ℓ≤3)" and pins the 16-coefficient count to a single source of truth via the cross-reference to §3 D-SPLAT-1. ## What this PR does NOT do - Does not touch pre-existing "ℓ=3" shorthand elsewhere in the plan (lines 72, 192, 438). Those use "ℓ=3" as informal shorthand for "up to degree ℓ=3" — common convention; out of scope for this fix. If the codex flags those as a follow-up, a separate normalization pass would touch them all together. ## Test plan - [x] Docs/plan only — no source code; no build/test invoked. - [x] Fix scoped to lines I added in #476 (157-158); does not modify pre-existing carrier-shape declarations elsewhere. - [x] Cross-references §3 D-SPLAT-1 carrier shape as the single source of truth for the 16-coefficient layout. - [ ] Codex re-review on this commit.
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.claude/plans/splat-native-ultrasound-v1.md

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@@ -154,8 +154,8 @@ The palette codec is currently `(centroid_palette: u8, edge_weight: u8, scent: u
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**ADR-024 adoption (palette256 + HHTL codec, OGAR #39).** D-SPLAT-4 is named in `OGAR/docs/ARCHITECTURAL-DECISIONS-2026-06-04.md § ADR-024 Consequences` as one of the two queued ADR-024 adopters (paired with D-OSM-2 — see `cesium-osm-substrate-v1.md §11` for the geographic-side adoption note). Mapping ADR-024's four-step adoption checklist onto D-SPLAT-4:
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1. **Prefix.** FMA NiblePath + SH basis-id — the per-region spatial frame (FMA class identity within the atlas + ℓ=3 SH basis index).
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2. **Palette domain.** Quantized SH coefficients (16 coeffs at ℓ=3) clustered per FMA region. Per-region palette captures dominant tissue echo signatures (planar fascia / spherical organ surfaces / Doppler-flow vascular).
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1. **Prefix.** FMA NiblePath + SH basis-id — the per-region spatial frame (FMA class identity within the atlas + SH basis index spanning the ℓ≤3 carrier).
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2. **Palette domain.** Quantized SH coefficients (16 coefficients spanning ℓ≤3 — degree 0: 1, degree 1: 3, degree 2: 5, degree 3: 7 — totaling 16, matching the §3 D-SPLAT-1 carrier shape) clustered per FMA region. Per-region palette captures dominant tissue echo signatures (planar fascia / spherical organ surfaces / Doppler-flow vascular).
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3. **ρ-vs-reference target ≥ 0.99**, matching the `lance-graph-arm-discovery` aerial-codebook empirical anchor (ρ = 0.9973 vs cosine). Reference: analytic SH evaluation at the same view direction (the same reference used in the D-SPLAT-4 test plan below). Report empirical ρ on the **first FMA-region palette build** (default region: femur cortical bone — smallest tractable corpus; cf. OGAR PR #30 §6 FMA-bones litmus).
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4. **Decode = const-table lookup.** Per-region SH palette is runtime const-table; decode path is zero-allocation. Compile-time HHTL where the palette is shared across regions (e.g. global basis-ID lookup for the 256 SH signatures).
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