Commit 7d09f75
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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.1 parent 1cb2576 commit 7d09f75
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