nx_room_fec.nx

nx_room_fec.nx -- X-ROOM (overseas-grade): sovereign DETERMINISTIC Reed-Solomon systematic ERASURE CODE over GF(256) -- Forward Error Correction for high-RTT, lossy intercontinental video calls. WHY (the overseas-call performance axis): at ~250ms intercontinental RTT a retransmit (ARQ) costs a full round-trip = an audible/visible STALL. FEC recovers lost packets from PARITY already in flight -> ZERO added latency, NO retransmit. k data shards + m parity shards (n=k+m). ANY m losses out of n reconstruct exactly. EXCEED axis (honest) vs Zoom/Teams/WebRTC FlexFEC: a PROVABLE MDS guarantee -- deterministic, integer-exact, audit-replayable recovery of EVERY <=m erasure pattern (the gate proves all C(n,m) of them), sovereign (own GF(256), no library). HONEST SCOPE: ERASURE coding (lost-packet positions known from RTP seq numbers) -- not error correction of silently-corrupted survivors; rate-adaptive FEC = deeper rung. CONSTRUCTION: generator G (n x k) = [ I_k ; Cauchy ]. Cauchy[j][i] = 1/((k+j) ^ i) in GF(256) -> every k x k submatrix invertible (MDS). Decode = pick any k surviving rows, solve the k x k GF system by Gauss-Jordan -> the original data shards. main() is the SELF-VALIDATING GATE. Evidence -> knowledge/status/room_fec.log. license_tier: ORIGINAL