feat: M2 P1.5 (FEC) — nanors-exact Reed-Solomon recovery for the video stream

Moonlight now reconstructs lost video shards from our parity (verified live:
under induced packet loss the picture recovers cleanly instead of failing with
"network connection too bad"; 0% added loss in normal operation).

The decisive finding: Moonlight's nanors uses a CAUCHY generator matrix
(M[j][i] = inv[(m+i)^j], GF(2^8) poly 0x1d), while reed-solomon-erasure is
Vandermonde — so its parity was NOT Moonlight-decodable, despite the old
gf8.rs comment claiming equivalence.

lumen-core:
- Swap the GF(2^8) backend from reed-solomon-erasure to a vendored fec-rs
  (vendor/fec-rs, BSD-2), which builds the byte-identical Cauchy matrix. Pure
  Rust, no FFI — keeps the "one core" hot path. This makes both lumen's own
  protocol and the GameStream parity nanors-compatible.
- Lock it with a regression test against real nanors vectors
  (k=4,m=2 [10,20,30,40] -> parity [136,0]) + an independent matrix-derived
  cross-check + an erase/recover round-trip. Existing FEC/loopback tests stay
  green, so lumen's own protocol is unaffected.

lumen-host video.rs:
- Generate m = ceil(k*pct/100) parity shards per FEC block via Gf8Coder; stamp
  fecInfo with the recomputed wire pct (100*m/k) so the client derives the same
  count; cap per-block data to 255*100/(100+pct) so k+m <= 255.
- CRITICAL byte-exactness: RS runs over the whole `blocksize` shard (Moonlight
  decodes packetSize+16 bytes from the datagram start and PACKET_RECOVERY_FAILUREs
  on a bad reconstructed `flags` byte). So the NV header fields RS must reproduce
  (streamPacketIndex/frameIndex/flags/multiFec*) are written into data shards
  BEFORE encode, and only the transport fields (RTP header/seq/timestamp +
  fecInfo) are stamped AFTER — leaving the flags byte RS-covered. Matches
  Sunshine stream.cpp. Unit-tested incl. flags recovery.
- fec_percentage wired from stream.rs (Sunshine default 20, LUMEN_FEC_PCT
  override; 0 = data-only). LUMEN_VIDEO_DROP injects loss to test recovery.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

crates/lumen-core/Cargo.toml

@@ -23,7 +23,11 @@ quic = ["dep:quinn", "dep:tokio"]
 
 [dependencies]
 reed-solomon-simd = "3.1"      # GF(2^16) Leopard-RS, SIMD, O(n log n) — the wall-breaker (P2)
-reed-solomon-erasure = "6.0"   # GF(2^8) classic RS — GameStream/Moonlight compat (P1)
+# Vendored fork of fec-rs: GF(2^8) classic RS with the *Cauchy* generator matrix
+# (M[j][i] = inv[(m+i)^j]) — byte-identical to the `nanors` library Moonlight uses, so our
+# parity is decodable by a stock Moonlight client. (reed-solomon-erasure is Vandermonde and is
+# NOT interoperable.) See vendor/fec-rs/LICENSE (BSD-2-Clause).
+fec-rs = { path = "vendor/fec-rs" }
 aes-gcm = "0.10"               # AES-128-GCM session crypto, matches GameStream
 zerocopy = { version = "0.8", features = ["derive"] }
 bytes = "1"