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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"## Observations\n\nThese are **weight-only inferences, not measured attention patterns**. Exact distances and character identities remain uncertain.\n\nDefine \\(A_{lh}=D_lW_{q,lh}^{T}W_{k,lh}D_l\\) and \\(B_{lh}=W_{o,lh}W_{v,lh}D_l\\), where \\(D_l=\\operatorname{diag}(\\text{ln1_w.l})\\).\n\n- **One exceptional positional-selector candidate:** L0H2 has \\(\\|A\\|_F=32.627\\), versus 0.236–3.157 for the other first-layer heads. Its substantial complex eigenpairs, including \\(5.058\\pm6.513i\\), suggest a shift-like positional circuit. “Previous character” is plausible, but the missing position embeddings prevent identifying its lag conclusively.\n- **Four shared positional-summary heads:** L0H0/H1/H4/H5 put respectively **91.2%, 93.9%, 85.3%, 93.5%** of their OV energy into the same two-dimensional write subspace, called \\(C\\) below. Their two dominant shared read directions overlap the L0H2 QK subspace by **98.3% and 94.9%**. This suggests positional summaries subsequently used for routing.\n- **A particularly strong induction-like connection:** L3H1 uniquely aligns with L0H2’s OV map: normalized \\(\\operatorname{tr}(A_{31}B_{02})=0.0949\\). Restricted to the strongest 16 read directions, the symmetric composition has positive eigenvalue mass **3.2621**, versus negative mass **0.0039**. Conditional on L0H2 transporting the previous character, this is compelling successor-matching evidence.\n- **Corpus identification is much weaker.** `W_proj.3` has singular values \\(s_1=26.309,\\ s_{23}=10.367,\\ s_{28}=7.166\\): substantial, diverse learned output directions. This does not recover letters or uniquely identify a language. Weight-row clustering also did not reveal clean character identities.\n\n## Heads\n\nRoles below are provisional. “Clock-key energy” means QK energy reading the shared subspace \\(C\\); bias alignment refers to the key-linear weight direction generated by `ln1_b`.\n\nL0H0: **broad** — small QK norm 0.437; 91.2% shared positional-summary write energy.  \nL0H1: **broad** — smallest QK norm, 0.236; 93.9% shared write energy.  \nL0H2: **previous** — exceptional, shift-like QK structure and the downstream induction-like connection; exact lag unverified.  \nL0H3: **local** — QK matrix cosine 0.239 with L0H2; weaker, lower-rank positional selection.  \nL0H4: **broad** — QK norm 0.851; 85.3% shared write energy.  \nL0H5: **broad** — QK norm 0.621; 93.5% shared write energy.\n\nL1H0: **local** — clock-key energy 57.5%; bias alignment 77.3%.  \nL1H1: **local** — clock-key energy 53.6%; bias alignment 81.5%.  \nL1H2: **local** — clock-key energy 54.9%; strong clock-aligned key bias, norm 20.70.  \nL1H3: **local** — clock-key energy 55.5%; bias alignment 79.3%.  \nL1H4: **local** — highest L1 clock-key energy, 60.3%; bias alignment 82.7%.  \nL1H5: **local** — clock-key energy 54.9%; bias alignment 78.4%.\n\nL2H0: **local** — strong key bias, norm 13.59, with 85.4% clock alignment.  \nL2H1: **local** — weaker positional bias, norm 5.96; 79.3% clock alignment. Lower-confidence assignment.  \nL2H2: **local** — largest L2 clock-key energy, 17.7%; bias alignment 80.2%.  \nL2H3: **local** — key-bias norm 11.70; clock alignment 86.8%.  \nL2H4: **local** — key-bias norm 12.62; clock alignment 86.2%.  \nL2H5: **local** — key-bias norm 12.07; clock alignment 85.4%.\n\nL3H0: **unclear** — positive QK trace 27.30 suggests content matching, but no clear successor-matching composition.  \nL3H1: **copy** — uniquely strong, predominantly positive composition with L0H2; strongest induction candidate.  \nL3H2: **unclear** — modest clock-key energy, 6.9%; neither distance nor induction is established.  \nL3H3: **unclear** — modest clock-key energy, 6.5%; weak successor-composition evidence.  \nL3H4: **unclear** — clock-key energy 4.4%; content-dependent routing likely, but its range is unresolved.  \nL3H5: **broad** — weakest final-layer QK norm, 6.679, and only 0.84% clock-key energy; strong OV map suggests aggregation.\n\n## Reasoning\n\nThe strongest interpretation is **positional summaries → nearby-character composition → later content matching and copying**. Such an organized successor-matching circuit is substantially more useful for intact text than for independently shuffled lines.\n\n**English is a weak corpus preference**, not a decoded identification. The diverse feature structure is compatible with English spelling and repeated words; Python remains a substantial alternative. The spectrum provides, at most, weak evidence against romaji’s more restricted orthography. The ordered-versus-shuffled conclusion is much stronger than the corpus choice.\n\ncorpus: english  \norder: as is  \nprobabilities: python=0.35 romaji=0.17 english=0.48; as is=0.98 shuffled=0.02"}}
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