Fix: one symbol vocabulary across the optimizer cards

[NeoVand]

The inconsistencies

Reviewing all fifteen card equations side by side turned up five places where notation silently shifted meaning between cards:

1. The squared-gradient memory kept changing identity. AdaGrad and RMSProp wrote plain s, AdaDelta wrote bold 𝐬 for the same quantity, Adam wrote plain ŝ — while its own repair cards (Nadam, AdamW, RAdam) wrote bold ŝ right underneath it.
2. Prodigy resurrected v — the letter that meant velocity in the momentum act — for Adam's squared-gradient denominator, and used s for a different, paper-internal tally two symbols away from the family's s.
3. Prodigy alone spoke in subscripted recursion (d_{t+1} = max(d_t, …)) where every other card uses the ← update style.
4. Nesterov decorated one gradient with (θ) and left the other bare in the same line — inviting a hunt for a difference that doesn't exist.
5. Two minus signs: Nadam and Lion used the tight (1{-}β), everyone else the spaced (1-β).

The convention (now recorded in DEVIATIONS.md)

• Bold per-parameter state vectors (θ, m, v, s, u, h, c, w); plain scalars (γ, μ, ρ, β, λ, ε, t, d, r).
• One meaning per letter across the family tree: m = gradient memory, v = velocity, s = squared-gradient memory, u = AdaDelta's step memory, h = Sophia's curvature diagonal, c = Lion's blend, w = Prodigy's alignment tally. (Adam's paper calls its buffer v; the cards deliberately say s so it can't read as velocity — Prodigy now follows.)
• ← for updates, = for one-shot definitions; no time subscripts unless the quantity genuinely indexes time (β^t, ρₜ).
• Gradients never carry an argument — they're always at the current point.
• Collisions the papers own (RMSProp's decay ρ / Sophia's clip ρ / RAdam's ρₜ) are defused in prose — Sophia's card now carries the house "the alphabet is small and the field is greedy" note, its third verse.
• The reveal-the-code files keep each paper's own variable names — the card is the classroom, the code is the primary source; the ledger states that split explicitly.

Prodigy's prose also now names r and w as the two running tallies of the ⟨g, x₀−x⟩ alignment, so no symbol in its formula is unexplained.

Verified

All fifteen rendered formulas checked in the live DOM via their KaTeX annotation sources; Prodigy card eyeballed in dark mode; 194 tests green, svelte-check clean. Content-only — no optimizer behavior changes.

🤖 Generated with Claude Code

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