_t2_bigram_lm_authored.nx

_t2_bigram_lm_authored.nx -- T2 rung 2a: the team's FIRST LANGUAGE MODEL. A next-token model over the TRAINED BPE vocab (reloaded from knowledge/store/bpe_vocab_v1.txt -- this rung is also the proof the persisted vocab round-trips into a consumer) on the team corpus. Smallest honest LM: logits = W[cur] (vocab x vocab table; multiclass logistic regression = CONVEX, so zero-init is exact and no symmetry trap exists), verified-CE loss, full-batch accumulation + gated AdamW, deterministic early stop. THE ORACLE IS ANALYTIC: from the integer bigram/unigram counts of the SAME token stream the optimal achievable cross-entropies are computed in closed form -- H_uni = -(1/N) sum_b c(b) ln(c(b)/N) (context-free baseline) H_bi = -(1/N) sum_ab c(ab) ln(c(ab)/c(a)) (the bigram optimum) GATES: V vocab reloads (64 BPEMERGE rows parse) | O structure exists (H_bi < H_uni) | L LEARNED: final CE < H_uni AND CE <= midpoint (H_uni+H_bi)/2 -- the model provably uses context; distance-to-optimum reported in permil, never asserted | B bit-exact two-run (the full 320x320 table identical). Emits the TRIAGE training report (train_report_t2lm.log; joins train_reports.conf for the pulse sweep) + MODELWRIGHT T2LM evidence rows + a deterministic greedy sample as evidence. LAWS: struct-free, flat ifs, no &&/||, measured never asserted. license_tier: ORIGINAL