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GPT-6.1 Sol (effort default (no reasoning-effort override) · thinking on) on Pension claiming-age comparison: lifetime totals, present values and break-even ages

OGPT-6.1 Soldefault · thinking on · Codex CLI 0.163.0 (codex exec --json) · cloud · 2026-10-20 · by @bobsiopener

Trust 80%Fully autonomoussuccess · first try
Estimated cost
$0.05
Wall time
1m
Human step-ins
0
Outcome
Pass

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Summary

Exact prompt

# Pension claiming age: lifetime totals, present values and break-even ages `input.json` describes a worker's monthly benefit at full retirement age and the (synthetic, given) rules for claiming early or late. Write `solve.py` (Python 3 standard library only) so that `python solve.py input.json answer.json` compares claiming ages. We re-run it on fresh inputs, so do not hard-code anything. Use only the rules below and the numbers in the input. ## Input `pia_monthly` (monthly benefit if claimed exactly at full retirement age, before cost-of-living raises), `fra_months` (full retirement age in months, e.g. 800 = 66 years 8 months), `reduction_first_36_per_month`, `reduction_beyond_36_per_month`, `delayed_credit_per_month` (fractions), `cola` (yearly raise), `discount_rate`, `claim_ages`, `death_ages`, `max_age` (integers, whole years), `pairs` (list of [earlier, later] claim ages). ## Rules 1. Claiming at whole age A means the first payment is for the month the person turns A. Let m = A*12 - `fra_months`. 2. If m < 0, with k = -m: factor = 1 - (min(k, 36) * `reduction_first_36_per_month` + max(k - 36, 0) * `reduction_beyond_36_per_month`). If m >= 0: factor = 1 + m * `delayed_credit_per_month`. 3. The monthly payment during age-year t (the 12 months from birthday t to the day before birthday t+1) is `pia_monthly * factor * (1 + cola) ** (t - 62)`, for t >= A. Raises apply from age 62 whether or not the person has claimed yet. No rounding of payments. 4. `monthly_at_claim` = the monthly payment for age-year A. 5. `lifetime[D]` = sum of all monthly payments for age-years A .. D-1 (death at birthday D, nothing paid from then on). 6. `pv[D]` = sum over age-years t = A .. D-1 of (12 * monthly payment for t) / (1 + discount_rate) ** (t - 62). 7. Break-even for a pair [a, b]: go month by month from the month of birthday a up to (not including) the month of birthday `max_age`, keeping cumulative totals for both claim ages (the later one starts at birthday b). The break-even is the first month index M (months since birth, counting the birthday-a month as a*12) with M >= b*12 and cumulative(b) >= cumulative(a), reported as M / 12 rounded to 4 decimals; `null` if it never happens. 8. `best_by_pv[D]` = the claim age with the highest `pv[D]` (lower age on ties). 9. Round money to 2 decimals and `factor` to 6 decimals only when writing. ## Output `answer.json`: ``` {"claims": {"62": {"factor": ..., "monthly_at_claim": ..., "lifetime": {"72": ..., ...}, "pv": {"72": ..., ...}}, ... one entry per claim age}, "breakeven": {"62-67": ..., ...one key per pair "a-b"}, "best_by_pv": {"72": 70, ...one key per death age}} ``` Keys are strings of the integer ages. ## Scoring Hidden checks (partial credit = fraction passed; all must pass): `factors_and_monthly` (factor within 0.000001, money within 0.011), `lifetime_totals`, `present_values` (within 0.011), `breakeven_ages` (within 0.0001), `best_by_pv` (exact) on the given input; `fresh_run_1`, `fresh_run_2`: the whole answer on fresh inputs (tolerance 0.011; integers exact). Each run has a 60-second limit.

Two-tier early-claim reduction, delayed credits, raises from age 62 regardless of claiming, a month-by-month break-even search, and present values with a tie rule. Original benchmark task written for usecaserank.com. Headless, offline run on a reproducible fixture. Cost shown is a list-price API-equivalent estimate (run on a ChatGPT subscription, not billed).

These are synthetic test cases for comparing AI models, not financial advice.

Success criteria: 1. factors_and_monthly 2. lifetime_totals 3. present_values 4. breakeven_ages 5. best_by_pv 6. fresh_run_1 7. fresh_run_2

Setup notes: Batch 9 case j03-claiming-age-breakeven (offline fixture). Prepared with batch9/prepare.sh on the shared box; only TASK.md + starting files were copied to the agent machine, hidden key/tests stayed on the box. Prompt = TASK.md verbatim on stdin. Flags: --json -s workspace-write --skip-git-repo-check --ephemeral --ignore-user-config --ignore-rules -C <workdir>. Scored on the box with the case scorer using absolute paths: `python score.py WORKDIR KEYDIR`. Single run, no retries. A global user-level AGENTS.md was present on the agent machine and may have been in context. The served model id is not echoed in the event log. Serving model not confirmed: requested via -m; the event log does not echo the serving model id. Price source is secondary (pricing.json verification='secondary', https://www.actuia.com/en/news/ai-api-pricing-in-october-2026-050-to-50-for-output/), not an official OpenAI price page. Score: 7/7. Cost is an ESTIMATE: measured tokens x pricing.json list price (ChatGPT plan, nothing billed); input_tokens include cached reads; output_tokens include reasoning tokens. Tool calls 4 (1 failed, recovered). Single run.

Estimated cost List-price estimate; not actually billed.

Metrics

Estimated cost
$0.05
Wall time
1m
Human step-ins
0
Turns
1
Model usage
ModelInput tokOutput tokCost
OGPT-6.1 Solopenai/gpt-6.1-soleffort default (no reasoning-effort override) · thinking on83,0981,976$0.05

Reproduce this run

  1. Use the use case prompt on the use case page.
  2. Same setup: GPT-6.1 Sol (openai/gpt-6.1-sol, effort default (no reasoning-effort override) · thinking on) via Codex CLI 0.163.0 (codex exec --json), cloud.
  3. It counts as a success only if it meets every success criterion: 1. factors_and_monthly 2. lifetime_totals 3. present_values 4. breakeven_ages 5. best_by_pv 6. fresh_run_1 7. fresh_run_2
  4. Log model, tokens, wall time, human step-ins and the evidence log, then submit it as a reproduction. A different model? Submit a head-to-head rerun.

How runs are scored: Methodology.

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Evidence log
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{"type": "item.started", "item": {"id": "item_1", "type": "command_execution", "command": "/bin/bash -lc \"pwd && rg --files -g 'AGENTS.md' -g 'input.json' -g 'solve.py' -g '*test*'\"", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_1", "type": "command_execution", "command": "/bin/bash -lc \"pwd && rg --files -g 'AGENTS.md' -g 'input.json' -g 'solve.py' -g '*test*'\"", "aggregated_output": "/home/bob/usecase-runs/batch/out/gpt-6.1-sol/j03/work\ninput.json\n", "exit_code": 0, "status": "completed"}}
{"type": "item.started", "item": {"id": "item_2", "type": "command_execution", "command": "/bin/bash -lc 'cat input.json'", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_2", "type": "command_execution", "command": "/bin/bash -lc 'cat input.json'", "aggregated_output": "{\n \"note\": \"Synthetic pension rules for this exercise; all rule values are given here.\",\n \"pia_monthly\": 3143,\n \"fra_months\": 796,\n \"reduction_first_36_per_month\": 0.005555555555555556,\n \"reduction_beyond_36_per_month\": 0.004166666666666667,\n \"delayed_credit_per_month\": 0.006666666666666667,\n \"cola\": 0.0163,\n \"discount_rate\": 0.021,\n \"claim_ages\": [\n  62,\n  63,\n  64,\n  65,\n  66,\n  67,\n  68,\n  69,\n  70\n ],\n \"death_ages\": [\n  72,\n  78,\n  82,\n  86,\n  90,\n  95\n ],\n \"max_age\": 100,\n \"pairs\": [\n  [\n   62,\n   67\n  ],\n  [\n   62,\n   70\n  ],\n  [\n   67,\n   70\n  ],\n  [\n   65,\n   68\n  ]\n ]\n}", "exit_code": 0, "status": "completed"}}
{"type": "item.started", "item": {"id": "item_3", "type": "file_change", "changes": [{"path": "/home/bob/usecase-runs/batch/out/gpt-6.1-sol/j03/work/solve.py", "kind": "add"}], "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_3", "type": "file_change", "changes": [{"path": "/home/bob/usecase-runs/batch/out/gpt-6.1-sol/j03/work/solve.py", "kind": "add"}], "status": "completed"}}
{"type": "item.started", "item": {"id": "item_4", "type": "command_execution", "command": "/bin/bash -lc 'python solve.py input.json answer.json'", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_4", "type": "command_execution", "command": "/bin/bash -lc 'python solve.py input.json answer.json'", "aggregated_output": "/bin/bash: line 1: python: command not found\n", "exit_code": 127, "status": "failed"}}
{"type": "item.started", "item": {"id": "item_5", "type": "command_execution", "command": "/bin/bash -lc \"python3 solve.py input.json answer.json && python3 - <<'PY'\nimport json, math\nfrom solve import solve\nwith open('input.json') as f: d=json.load(f)\nwith open('answer.json') as f: out=json.load(f)\ndef factor(a):\n m=a*12-d['fra_months']; k=-m\n return 1-min(k,36)*d['reduction_first_36_per_month']-max(k-36,0)*d['reduction_beyond_36_per_month'] if m<0 else 1+m*d['delayed_credit_per_month']\ndef pay(a,t): return d['pia_monthly']*factor(a)*(1+d['cola'])**(t-62)\nfor a in d['claim_ages']:\n for death in d['death_ages']:\n  total=math.fsum(pay(a,m//12) for m in range(12*a,12*death))\n  pv=math.fsum(12*pay(a,t)/(1+d['discount_rate'])**(t-62) for t in range(a,death))\n  assert abs(out['claims'][str(a)]['lifetime'][str(death)]-total)<.011\n  assert abs(out['claims'][str(a)]['pv'][str(death)]-pv)<.011\nfor a,b in d['pairs']:\n totals=[0.,0.]; expected=None\n for m in range(a*12,d['max_age']*12):\n  totals[0]+=pay(a,m//12)\n  if m>=b*12:\n   totals[1]+=pay(b,m//12)\n   if totals[1]>=totals[0]: expected=round(m/12,4); break\n assert out['breakeven'][f'{a}-{b}']==expected\nprint('Independent lifetime, PV, and monthly break-even checks passed.')\nprint('Break-even:',out['breakeven'])\nx=dict(d,pia_monthly=100,fra_months=744,cola=0,discount_rate=0,reduction_first_36_per_month=0,reduction_beyond_36_per_month=0,delayed_credit_per_month=0,claim_ages=[63,62],death_ages=[61,62,63,64],pairs=[[62,63]],max_age=65)\nr=solve(x)\nassert r['best_by_pv']=={'61':62,'62':62,'63':62,'64':62}\nassert r['breakeven']['62-63'] is None\nassert r['claims']['62']['lifetime']['64']==2400\nprint('Zero rates, death before claiming, tie ordering, and no-crossing checks passed.')\nPY\"", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_5", "type": "command_execution", "command": "/bin/bash -lc \"python3 solve.py input.json answer.json && python3 - <<'PY'\nimport json, math\nfrom solve import solve\nwith open('input.json') as f: d=json.load(f)\nwith open('answer.json') as f: out=json.load(f)\ndef factor(a):\n m=a*12-d['fra_months']; k=-m\n return 1-min(k,36)*d['reduction_first_36_per_month']-max(k-36,0)*d['reduction_beyond_36_per_month'] if m<0 else 1+m*d['delayed_credit_per_month']\ndef pay(a,t): return d['pia_monthly']*factor(a)*(1+d['cola'])**(t-62)\nfor a in d['claim_ages']:\n for death in d['death_ages']:\n  total=math.fsum(pay(a,m//12) for m in range(12*a,12*death))\n  pv=math.fsum(12*pay(a,t)/(1+d['discount_rate'])**(t-62) for t in range(a,death))\n  assert abs(out['claims'][str(a)]['lifetime'][str(death)]-total)<.011\n  assert abs(out['claims'][str(a)]['pv'][str(death)]-pv)<.011\nfor a,b in d['pairs']:\n totals=[0.,0.]; expected=None\n for m in range(a*12,d['max_age']*12):\n  totals[0]+=pay(a,m//12)\n  if m>=b*12:\n   totals[1]+=pay(b,m//12)\n   if totals[1]>=totals[0]: expected=round(m/12,4); break\n assert out['breakeven'][f'{a}-{b}']==expected\nprint('Independent lifetime, PV, and monthly break-even checks passed.')\nprint('Break-even:',out['breakeven'])\nx=dict(d,pia_monthly=100,fra_months=744,cola=0,discount_rate=0,reduction_first_36_per_month=0,reduction_beyond_36_per_month=0,delayed_credit_per_month=0,claim_ages=[63,62],death_ages=[61,62,63,64],pairs=[[62,63]],max_age=65)\nr=solve(x)\nassert r['best_by_pv']=={'61':62,'62':62,'63':62,'64':62}\nassert r['breakeven']['62-63'] is None\nassert r['claims']['62']['lifetime']['64']==2400\nprint('Zero rates, death before claiming, tie ordering, and no-crossing checks passed.')\nPY\"", "aggregated_output": "Independent lifetime, PV, and monthly break-even checks passed.\nBreak-even: {'62-67': 77.0833, '62-70': 79.0833, '67-70': 81.6667, '65-68': 78.9167}\nZero rates, death before claiming, tie ordering, and no-crossing checks passed.\n", "exit_code": 0, "status": "completed"}}
{"type": "item.completed", "item": {"id": "item_6", "type": "agent_message", "text": "Created [solve.py](solve.py) and generated [answer.json](answer.json).\n\nVerified lifetime totals, present values, monthly break-even timing, and edge cases.\n\nRun with:\n```bash\npython3 solve.py input.json answer.json\n```\n\nThis environment provides `python3`; `python` is unavailable."}}
{"type": "turn.completed", "usage": {"input_tokens": 83098, "cached_input_tokens": 71680, "cache_write_input_tokens": 0, "output_tokens": 1976, "reasoning_output_tokens": 147}}

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