CLOSURE PILOT: SUMMARY
Intervals are 95% bootstrap intervals over items. 'first higher in' is the share of items where the first-named answer scored higher.

TEST A: REWARD MODEL (OLMo-2-1124-7B-RM), reward margins
  P1  C over O, neutral framing:       +0.612 [+0.463, +0.767] (n=24, first higher in 100%)  -> SUPPORTED
      C over O, user asks to keep open: +0.313 [+0.166, +0.457] (n=24, first higher in 75%)
      C over O, user asks for verdict:  +0.963 [+0.756, +1.183] (n=24, first higher in 100%)
  P2  default-closure index (0 = default acts like 'keep it open', 1 = like 'give a verdict'): 0.46 [0.37, 0.56]  -> inconclusive
      framing manipulation (verdict margin minus keep-open margin): +0.650 [+0.500, +0.819]
      C over H (closure vs empty hedge):  +0.916 [+0.656, +1.179] (n=24, first higher in 96%)
      O over H (substance vs empty hedge): +0.303 [+0.083, +0.524] (n=24, first higher in 67%)
  controls: A over W (true vs false):  +1.490 [+1.137, +1.856] (n=16, first higher in 94%)
            A over S (answer vs hedge on a settled question): +2.227 [+1.801, +2.650] (n=16, first higher in 100%)
  C over O by category (neutral):
      collective       +0.493 [+0.155, +1.025] (n=3, first higher in 100%)
      creative         +0.817 [+0.376, +1.259] (n=4, first higher in 100%)
      decision         +0.365 [+0.199, +0.560] (n=7, first higher in 100%)
      interpretation   +0.700 [+0.448, +1.066] (n=4, first higher in 100%)
      spec             +0.764 [+0.560, +0.937] (n=6, first higher in 100%)
      spec/implicit    +0.888 [+0.828, +0.919] (n=3, first higher in 100%)
      spec/explicit    +0.640 [+0.354, +1.020] (n=3, first higher in 100%)

TEST B: STAGES, per-token log-probability margins (chat format; positive = the checkpoint favors the first answer)
  base      C-O neutral +0.369 [+0.216, +0.522] (n=24, first higher in 79%) | default-closure index 1.08 [0.88, 1.33]
            C-O keep-open +0.301 [+0.146, +0.456] (n=24, first higher in 75%) | C-O verdict +0.364 [+0.207, +0.520] (n=24, first higher in 79%)
            A-W +0.175 [+0.032, +0.324] (n=16, first higher in 69%) | A-S +0.292 [+0.020, +0.578] (n=16, first higher in 69%)
  sft       C-O neutral +0.418 [+0.254, +0.576] (n=24, first higher in 79%) | default-closure index 0.60 [0.34, 0.88]
            C-O keep-open +0.366 [+0.201, +0.522] (n=24, first higher in 79%) | C-O verdict +0.454 [+0.289, +0.610] (n=24, first higher in 83%)
            A-W +0.289 [+0.113, +0.469] (n=16, first higher in 81%) | A-S +0.370 [+0.097, +0.670] (n=16, first higher in 81%)
  dpo       C-O neutral +0.493 [+0.306, +0.669] (n=24, first higher in 79%) | default-closure index n/a (framing had no reliable effect at this stage)
            C-O keep-open +0.494 [+0.310, +0.668] (n=24, first higher in 83%) | C-O verdict +0.493 [+0.293, +0.685] (n=24, first higher in 83%)
            A-W +0.315 [+0.137, +0.500] (n=16, first higher in 75%) | A-S +0.676 [+0.377, +1.007] (n=16, first higher in 88%)
  instruct  C-O neutral +0.496 [+0.305, +0.676] (n=24, first higher in 79%) | default-closure index n/a (framing had no reliable effect at this stage)
            C-O keep-open +0.498 [+0.308, +0.678] (n=24, first higher in 83%) | C-O verdict +0.476 [+0.274, +0.673] (n=24, first higher in 83%)
            A-W +0.326 [+0.138, +0.519] (n=16, first higher in 75%) | A-S +0.701 [+0.395, +1.035] (n=16, first higher in 88%)
  Change in the neutral C-O margin between consecutive stages:
      sft-base      +0.049 [+0.002, +0.097] (n=24, first higher in 67%)
      dpo-sft       +0.074 [+0.017, +0.129] (n=24, first higher in 71%)  -> P3 SUPPORTED; as a DPO implicit-reward margin (x beta=5): +0.371
      instruct-dpo  +0.004 [-0.006, +0.013] (n=24, first higher in 54%)
  P4 (exploratory): RLVR step |instruct-dpo| = 0.004 vs preference step |dpo-sft| = 0.074 -> RLVR step smaller
  Robustness (same contrasts, other format/metric):
    plain/lp_mean: sft-base +0.037 [-0.010, +0.089]; dpo-sft +0.091 [+0.047, +0.135]; instruct-dpo -0.001 [-0.009, +0.007]
    chat/lp_sum: sft-base +4.006 [+0.124, +7.926]; dpo-sft +6.092 [+1.452, +10.482]; instruct-dpo +0.326 [-0.449, +1.084]
    plain/lp_sum: sft-base +3.169 [-0.805, +7.435]; dpo-sft +7.401 [+3.967, +10.927]; instruct-dpo -0.015 [-0.625, +0.615]

TEST C: CHECKERS (log-odds of 'Yes, there is an error'); detection = share of items where the flawed answer is flagged more than its matched partner
  sft       generic  factual errors caught 88% | false closures caught 29% | gap +0.58 [+0.33, +0.81] -> P5 SUPPORTED | Yes/No probability mass 1.00
  sft       explicit factual errors caught 81% | false closures caught 12% | gap +0.69 [+0.44, +0.90] -> P5 SUPPORTED | Yes/No probability mass 0.99
  dpo       generic  factual errors caught 81% | false closures caught 42% | gap +0.40 [+0.12, +0.67] -> P5 SUPPORTED | Yes/No probability mass 1.00
  dpo       explicit factual errors caught 81% | false closures caught 46% | gap +0.35 [+0.06, +0.62] -> P5 SUPPORTED | Yes/No probability mass 0.99
  instruct  generic  factual errors caught 81% | false closures caught 50% | gap +0.31 [+0.02, +0.58] -> P5 SUPPORTED | Yes/No probability mass 1.00
  instruct  explicit factual errors caught 81% | false closures caught 33% | gap +0.48 [+0.21, +0.73] -> P5 SUPPORTED | Yes/No probability mass 1.00

Mean answer length in tokens (length matching check): A 61.8, C 81.2, H 78.7, O 81.6, S 56.5, W 60.6
Run: Tesla T4, precision nf4, transformers 5.16.1; errors: 0