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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"## Observations\n\nThese are **weight-based hypotheses, not measured attention patterns**. Missing embeddings make corpus identification and exact attention distances uncertain.\n\nDefine \\(M=PDW_q^\\top W_kDP/8\\) and \\(B=PW_oW_vDP\\) for each head, where \\(D=\\operatorname{diag}(\\texttt{ln1_w})\\) and \\(P\\) subtracts the coordinate mean. These are linear weight products, not layer evaluations.\n\n- **A broad aggregation head:** L0H4 has \\(\\|M\\|_F=0.0093\\), versus **0.8775** for L0H1 and **0.9704** for L0H5. Its \\(B\\) has dominant singular values **13.877, 9.644**, suggesting weakly selective aggregation into a small feature space.\n- **Two likely positional character-routing heads:** L0H1 and L0H5 read largely outside their shared value-input subspace. Their generalized-eigenvalue phases support an approximately **2:1 shift relationship**—consistent with two-characters-back and previous-character heads, respectively. The absolute offsets remain inferred.\n- **Directional, induction-like composition:** Let\n  \\[\n  C_k=\\frac{\\operatorname{tr}(M_{\\rm later}B_{\\rm earlier})}\n  {\\|M_{\\rm later}\\|_F\\|B_{\\rm earlier}\\|_F},\n  \\qquad\n  C_q=\\frac{\\operatorname{tr}(M_{\\rm later}B_{\\rm earlier}^{\\top})}\n  {\\|M_{\\rm later}\\|_F\\|B_{\\rm earlier}\\|_F}.\n  \\]\n  The strongest relevant pairs are:\n  - L0H5 → L2H1: **\\(C_k=0.0776,\\ C_q=-0.0398\\)**\n  - L2H2 → L3H1: **\\(0.1104,\\ -0.0164\\)**\n  - L2H2 → L3H5: **\\(0.1836,\\ -0.0354\\)**\n\n  This key-specific matching supports successor/context-copying circuits, although it does not establish their complete behavior.\n- **Shared routing in layer 1:** The leading three output directions of L0H4 account for **53–68%** of key-side QK energy in L1H1–L1H5. Their query-bias-induced key preferences also align strongly. This suggests shared positional routing, but does not independently establish locality.\n\n## Heads\n\nHere, \\(r_{90}\\) is the number of singular values accounting for 90% of \\(M\\)'s squared norm.\n\nL0H0: **unclear** — \\(r_{90}=2\\); low-dimensional selector, but no identifiable distance.  \nL0H1: **local** — phase relationship with L0H5 suggests a two-character shift.  \nL0H2: **unclear** — \\(r_{90}=5\\); mixed positional and content-selective weight directions.  \nL0H3: **unclear** — \\(r_{90}=3\\); structured selector without a reliable lag signature.  \nL0H4: **broad** — exceptionally weak QK product and strong, low-dimensional OV aggregation.  \nL0H5: **previous** — strongest one-character-shift candidate; also supplies the L2H1 matching circuit.\n\nL1H0: **unclear** — weaker shared-routing component; distance and selectivity remain ambiguous.  \nL1H1: **local** — tentative; 63% key-side energy reads L0H4’s leading output subspace.  \nL1H2: **local** — tentative; corresponding fraction 63%, with substantial downstream matching composition.  \nL1H3: **local** — tentative; strongest shared-routing fraction, 68%.  \nL1H4: **local** — tentative; 65% shared-routing fraction and aligned key preference.  \nL1H5: **local** — tentative; 53% shared-routing fraction; exact offset unresolved.\n\nL2H0: **unclear** — distributed QK structure, \\(r_{90}=39\\), without a decisive routing signature.  \nL2H1: **copy** — positive, key-specific composition with the likely previous-character head L0H5.  \nL2H2: **unclear** — important precursor to both late copy candidates; its own attention distance is unverified.  \nL2H3: **unclear** — some shared positional-carrier dependence, insufficient to distinguish local from broad.  \nL2H4: **unclear** — mixed routing structure; no decisive predecessor or induction signature.  \nL2H5: **unclear** — distributed QK structure, \\(r_{90}=42\\).\n\nL3H0: **unclear** — modest composition signals, not enough to establish copying or locality.  \nL3H1: **copy** — strong directional composition with L2H2: \\(C_k=0.1104\\).  \nL3H2: **unclear** — distributed selector without a clear distance or copying signature.  \nL3H3: **unclear** — weaker QK magnitude alone cannot establish broad attention.  \nL3H4: **unclear** — no sufficiently diagnostic composition.  \nL3H5: **copy** — strongest induction-like candidate: \\(C_k=0.1836\\), versus \\(C_q=-0.0354\\).\n\n## Reasoning\n\nThe likely short-offset character routing and directional copying circuits favor **as-is text** substantially over independently shuffled lines.\n\nI weakly favor **Python**: repeated identifiers and recurring code fragments offer a particularly useful role for this hierarchy of local features and context matching. English is a substantial alternative; these circuits are not code-specific. The corpus judgment is considerably weaker than the order judgment, and no character identities or keywords were recovered.\n\ncorpus: python  \norder: as is  \nprobabilities: python=0.56 romaji=0.13 english=0.31; as is=0.96 shuffled=0.04"}}
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