nx_teacher_synthesize_gate.nx

nx_teacher_synthesize_gate.nx -- proves the Teacher SYNTHESIS loop: a raw insight-ledger is consumed INTO the native team-capability store, the team can RECALL each insight, and the source is provably REDUNDANT only when every insight is absorbed. Hermetic /tmp fixtures (never touches the real store). Discriminating + liar-killed: T1 count: synthesizing a 3-row ledger stores exactly 3 insights. T2 recall: the team CONSUMES insight R2 from the store, byte-faithful to the source learning. T3 recall-absent: an unknown id recalls nothing (no phantom answer). T4 redundancy+: every learning of the synthesized ledger is recoverable -> redundant=1 (retirable). T5[neg] un-absorbed: a SUPERSET ledger (one extra un-synthesized row) is redundant=0 -- you CANNOT retire a source whose insight was not fully absorbed (the load-bearing control). T6[neg] no-fabrication: a rule never present in the source is ABSENT from the store (Rule 4 -- the synthesis copies real insight, it does not invent any). T7 idempotent: re-synthesizing the same ledger keeps count=3 and redundant=1. GREEN iff all hold. Sovereign: imports nx_teacher_synthesize + nx_syscalls. license_tier: ORIGINAL