{
  "arm": "Fable 5",
  "provider": "anthropic",
  "benchmark": "postcutoff_pilot_v1",
  "freeze_tag": "postcutoff-pilot-v1-freeze-20260705",
  "note": "Frontier comparator. Single public model; full per-task output included.",
  "tasks": [
    {
      "task_id": "PILOT-N2",
      "task_type": "math",
      "answer": "30907",
      "gold": "30907",
      "correct": true,
      "tokens_in": 219,
      "tokens_out": 13419,
      "cost_usd": 0.67314,
      "latency_s": 127.26,
      "timed_out": false,
      "solution": "## Setting Up a Transfer Matrix\n\nI'll count tilings of the 3\u00d710 strip column by column, tracking horizontal dominoes protruding into the next column. States are subsets of rows {1,2,3} already filled by protrusions. Within each column, free cells are filled by vertical dominoes, monomers (weight $t$), or new horizontal dominoes.\n\nFilling a set of column cells with vertical dominoes/monomers gives weights:\n- $\\{1\\},\\{2\\},\\{3\\}$: $t$;  $\\{1,2\\},\\{2,3\\}$: $1+t^2$;  $\\{1,3\\}$: $t^2$;  $\\{1,2,3\\}$: $2t+t^3$\n\nI iterate the vector $v_n$ (starting at state $\\varnothing$), keeping polynomials mod $t^3$ since we need exactly 2 monomers.\n\n**Iteration results** (state $\\varnothing$, $\\{1\\},\\{2\\},\\{3\\},\\{12\\},\\{13\\},\\{23\\},\\{123\\}$):\n\n| $n$ | $\\varnothing$ | 1 | 2 | 3 | 12 | 13 | 23 | 123 |\n|---|---|---|---|---|---|---|---|---|\n| 2 | $3+11t^2$ | $4t$ | $3t$ | $4t$ | $1+3t^2$ | $3t^2$ | $1+3t^2$ | $2t$ |\n| 4 | $11+123t^2$ | $29t$ | $14t$ | $29t$ | $4+42t^2$ | $32t^2$ | $4+42t^2$ | $18t$ |\n| 6 | $41+908t^2$ | $161t$ | $55t$ | $161t$ | $15+325t^2$ | $207t^2$ | $15+325t^2$ | $106t$ |\n| 8 | $153+5580t^2$ | $798t$ | $208t$ | $798t$ | $56+2030t^2$ | $1110t^2$ | $56+2030t^2$ | $540t$ |\n\nAt $n=9$: $\\varnothing: 2554t$, $1,3: 209+8769t^2$, $2: 2859t^2$, $12,23: 951t$, $13: 361t$, $123: 153+5580t^2$.\n\n**Checks:** Constant terms $3, 11, 41, 153$ match known domino tilings of $3\\times 2n$ \u2713. The one-monomer count $18$ for $3\\times 3$ matches direct enumeration (4 per corner + 2 for center) \u2713. Direct enumeration of $3\\times 2$ with two monomers gives $11$ \u2713.\n\n## Final Step\n\n$$v_{10}[\\varnothing] = 2554t\\cdot 2t + 2(209+8769t^2)(1+t^2) + 2859t^2\\cdot t^2 + 2\\cdot 951t\\cdot t + 361t\\cdot t + (153+5580t^2)$$\n\n- Constant: $209+209+153 = 571$ (correct domino count for $3\\times 10$ \u2713)\n- Coefficient of $t^2$:\n$$5108 + 8978 + 8978 + 951 + 361 + 951 + 5580 = 30907$$\n\nANSWER: 30907"
    },
    {
      "task_id": "PILOT-K1",
      "task_type": "code",
      "answer": null,
      "gold": "121090",
      "correct": false,
      "tokens_in": 171,
      "tokens_out": 32768,
      "cost_usd": 1.64011,
      "latency_s": 267.33,
      "timed_out": false,
      "solution": ""
    },
    {
      "task_id": "PILOT-Q1",
      "task_type": "simple_qa",
      "answer": "10152",
      "gold": "10152",
      "correct": true,
      "tokens_in": 222,
      "tokens_out": 420,
      "cost_usd": 0.02322,
      "latency_s": 7.31,
      "timed_out": false,
      "solution": "**Daily crates:** Mon 48, Tue 54, Wed 60, Thu 66, Fri 72.\n\n- **Monday:** 48 \u00d7 36 = 1728\n- **Tuesday:** 54 \u00d7 36 = 1944\n- **Wednesday:** one third of 60 = 20 crates at 18 units, 40 crates at 36 units \u2192 20 \u00d7 18 + 40 \u00d7 36 = 360 + 1440 = 1800\n- **Thursday:** 66 \u00d7 36 = 2376\n- **Friday:** 72 \u2212 8 = 64 delivered crates \u2192 64 \u00d7 36 = 2304\n\n**Total:** 1728 + 1944 + 1800 + 2376 + 2304 = 10152\n\nANSWER: 10152"
    },
    {
      "task_id": "PILOT-R1",
      "task_type": "reasoning",
      "answer": "12",
      "gold": "12",
      "correct": true,
      "tokens_in": 260,
      "tokens_out": 2760,
      "cost_usd": 0.1406,
      "latency_s": 31.26,
      "timed_out": false,
      "solution": "**Setting up:** Let each statement's truth depend on who lies. Test liar pair {Ben, Eve} (others tested fail):\n\n- Truth-tellers: Ava, Cleo, Dan\n- Cleo says \"Cleo < Ava\" (true), Ava says \"Ava = Ben \u2212 1\" (true), Dan says \"Eve \u2260 1st\" (true)\n- Ben lies: Cleo is NOT last. Eve lies: Dan is NOT 3rd.\n\nSince Cleo < Ava and Ava is immediately ahead of Ben, try:\n- Cleo = 1, Ava = 2, Ben = 3, Eve = 4, Dan = 5.\n\n**Verify all conditions:**\n- Ava (truthful): \"I finished immediately ahead of Ben\" \u2014 2 vs 3 \u2713\n- Ben (liar): \"Cleo finished last\" \u2014 Cleo is 1st, false \u2713\n- Cleo (truthful): \"I finished ahead of Ava\" \u2014 1 < 2 \u2713\n- Dan (truthful): \"Eve did not finish first\" \u2014 Eve is 4th \u2713\n- Eve (liar): \"Dan finished third\" \u2014 Dan is 5th, false \u2713\n- Ava (2nd) ahead of Dan (5th) \u2713\n- Liars Ben (3rd) and Eve (4th) are in consecutive positions \u2713\n\nChecking all other liar pairs leads to contradictions (e.g., Cleo truthfully saying she's ahead of Ava conflicts with Cleo being 5th, or liars end up non-consecutive).\n\nProduct of liars' positions: 3 \u00d7 4 = 12.\n\nANSWER: 12"
    },
    {
      "task_id": "PILOT-C1",
      "task_type": "code",
      "answer": null,
      "gold": "300062",
      "correct": false,
      "tokens_in": 152,
      "tokens_out": 259,
      "cost_usd": 0.01447,
      "latency_s": 5.95,
      "timed_out": false,
      "solution": ""
    }
  ]
}