Inputs: item-retreat-crossing-a, -b and -c (source paths and verified SHA-256 hashes in each JSON block), covering 410500–410999, 411000–411499 and 411500–411999. All report one candidate against N; each reports 500 complete pairs and no failures.

Pooling their reported summaries gives candidate minus N = −0.063721 (SE 0.143829; n=1500): no demonstrated gain. Spread 1: 0 (SE 0; n=390); spread 2: 0 (SE 0; n=377); spread 3: −0.254882 (SE 0.575778; n=375); spread 4: 0 (SE 0; n=358). Overall retail +0.034609, arbitrage −0.098329; spread 3 retail +0.138436, arbitrage −0.393318. Sources: the three blocks' overall/by_spread fields, pooled below. Block means differ: a/b negative, c positive; all are retained. These are not finalist seeds; this merge makes no promotion.

Input hashes match. Reported strategy hashes agree, and check values agree at six decimals across inputs. Independent expected checks and strategy code bytes were not supplied in these inputs; verification of those relies on item notes. Python versions differ and remain recorded. Original block numbers and per-seed rows are preserved; only pooling is recomputed.

```json
{
  "candidates": [
    {
      "key": "retreat-crossing",
      "candidate_sha256": "b5158a963a479a0919146dc0d56a347b68ddc2d66dd7c467b48473baef8997cf",
      "incumbent_sha256": "bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae",
      "blocks": [
        {
          "key": "retreat-crossing-a",
          "candidate_sha256": "b5158a963a479a0919146dc0d56a347b68ddc2d66dd7c467b48473baef8997cf",
          "incumbent_sha256": "bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae",
          "seeds": {
            "start": 410500,
            "end": 410999
          },
          "n": 500,
          "complete": true,
          "missing_seeds": [],
          "failures": [],
          "check_values": [
            17.116002,
            20.017111,
            2.390311,
            241.484752
          ],
          "python_version": "3.14.4",
          "seconds_per_simulation": 0.2922,
          "overall": {
            "n": 500,
            "sum_d": -111.727069,
            "sum_d2": 43397.609061,
            "mean_diff": -0.223454,
            "se": 0.416939,
            "incumbent_mean": 90.726774,
            "candidate_mean": 90.50332,
            "retail_diff": 0.068109,
            "arb_diff": -0.291563
          },
          "by_spread": {
            "1": {
              "n": 124,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 35.104446,
              "candidate_mean": 35.104446,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            },
            "2": {
              "n": 118,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 73.487615,
              "candidate_mean": 73.487615,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            },
            "3": {
              "n": 119,
              "sum_d": -111.727069,
              "sum_d2": 43397.609061,
              "mean_diff": -0.938883,
              "se": 1.755872,
              "incumbent_mean": 106.509822,
              "candidate_mean": 105.570939,
              "retail_diff": 0.286172,
              "arb_diff": -1.225055
            },
            "4": {
              "n": 139,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 141.469267,
              "candidate_mean": 141.469267,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            }
          },
          "notes": "Both hashes verified by script before running. Check values match the brief. Simulator at b244530 unmodified, serial, in-process, default ChallengeConfig/ParameterVariance (2000 steps), each (seed,strategy) run once. Overall paired diff -0.223 (se 0.417); spread 3 (target) -0.939 (se 1.756), n=119. Python 3.14.4.",
          "source": {
            "input_path": ".imd/reads/artifacts/item-retreat-crossing-a",
            "reported_path": "artifacts/goal/batches/r3-extend/items/retreat-crossing-a/result.json",
            "sha256": "2bf514ce20dd3f6c3ed19cdafddccde180f973fac2d3d199d2d240d7e746e020",
            "hash_verified": true
          },
          "incumbent_mean": 90.726774
        },
        {
          "key": "retreat-crossing-b",
          "candidate_sha256": "b5158a963a479a0919146dc0d56a347b68ddc2d66dd7c467b48473baef8997cf",
          "incumbent_sha256": "bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae",
          "seeds": {
            "start": 411000,
            "end": 411499
          },
          "n": 500,
          "complete": true,
          "missing_seeds": [],
          "failures": [],
          "check_values": {
            "310000": 17.116002,
            "310001": 20.017111,
            "310002": 2.390311,
            "310003": 241.484752
          },
          "python_version": "3.14.4",
          "seconds_per_simulation": 0.5334,
          "overall": {
            "n": 500,
            "sum_d": -15.959705,
            "sum_d2": 2881.546778,
            "mean_diff": -0.031919,
            "se": 0.107458,
            "incumbent_mean": 94.68985,
            "candidate_mean": 94.65793,
            "retail_diff": 0.021773,
            "arb_diff": -0.053692
          },
          "by_spread": {
            "1": {
              "n": 132,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 46.862382,
              "candidate_mean": 46.862382,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            },
            "2": {
              "n": 130,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 84.484792,
              "candidate_mean": 84.484792,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            },
            "3": {
              "n": 130,
              "sum_d": -15.959705,
              "sum_d2": 2881.546778,
              "mean_diff": -0.122767,
              "se": 0.41438,
              "incumbent_mean": 124.555539,
              "candidate_mean": 124.432772,
              "retail_diff": 0.083742,
              "arb_diff": -0.206509
            },
            "4": {
              "n": 108,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 129.480068,
              "candidate_mean": 129.480068,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            }
          },
          "notes": "Hashes verified by script (code field UTF-8 SHA-256). Simulator danrobinson/prediction-market-challenge @b244530, unmodified, imported in-process; serial, no --workers/--sandbox, default ChallengeConfig/ParameterVariance, 2000 steps. Check values for N on 310000..310003 match the brief exactly. Each (seed,strategy) run exactly once; d = candidate minus N total_edge. No code changed. Candidate acts only at spread 3: d is exactly 0 on all spread 1, 2, 4 seeds.",
          "source": {
            "input_path": ".imd/reads/artifacts/item-retreat-crossing-b",
            "reported_path": "artifacts/goal/batches/r3-extend/items/retreat-crossing-b/result.json",
            "sha256": "67467269593baa115666ea07f5a032c1f8e4b68e3d7f0d5627c8d2db8e8ca00a",
            "hash_verified": true
          },
          "incumbent_mean": 94.68985
        },
        {
          "key": "retreat-crossing-c",
          "candidate_sha256": "b5158a963a479a0919146dc0d56a347b68ddc2d66dd7c467b48473baef8997cf",
          "incumbent_sha256": "bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae",
          "seeds": {
            "start": 411500,
            "end": 411999
          },
          "n": 500,
          "complete": true,
          "missing_seeds": [],
          "failures": [],
          "check_values": [
            17.1160017503,
            20.0171113118,
            2.3903113616,
            241.4847522404
          ],
          "python_version": "3.12.3",
          "seconds_per_simulation": 0.9080276889889501,
          "overall": {
            "n": 500,
            "sum_d": 32.10586368629991,
            "sum_d2": 240.90036467788767,
            "mean_diff": 0.06421172737259982,
            "se": 0.03093977547203153,
            "incumbent_mean": 96.9505197446568,
            "candidate_mean": 97.0147314720294,
            "retail_diff": 0.013944789763399313,
            "arb_diff": 0.050266937612200184
          },
          "by_spread": {
            "1": {
              "n": 134,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 29.359725108174626,
              "candidate_mean": 29.359725108174626,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            },
            "2": {
              "n": 129,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 88.38297657891395,
              "candidate_mean": 88.38297657891395,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            },
            "3": {
              "n": 126,
              "sum_d": 32.10586368629991,
              "sum_d2": 240.90036467788767,
              "mean_diff": 0.2548084419547612,
              "se": 0.12155592339601715,
              "incumbent_mean": 128.00387517305475,
              "candidate_mean": 128.25868361500952,
              "retail_diff": 0.05533646731507664,
              "arb_diff": 0.19947197465158803
            },
            "4": {
              "n": 111,
              "sum_d": 0.0,
              "sum_d2": 0.0,
              "mean_diff": 0.0,
              "se": 0.0,
              "incumbent_mean": 153.25373384998377,
              "candidate_mean": 153.25373384998377,
              "retail_diff": 0.0,
              "arb_diff": 0.0
            }
          },
          "notes": "Frozen strategies; both UTF-8 SHA-256 hashes verified. Unmodified simulator commit b244530ee2a6247b5f930830eeca9dd950da0e7e, default ChallengeConfig and ParameterVariance, 2000 steps; serial paired runs. Four incumbent reference checks matched at 6 decimals. No tuning or finalist seeds used. Statistics use unrounded per-seed differences; timing excludes reference checks.",
          "source": {
            "input_path": ".imd/reads/artifacts/item-retreat-crossing-c",
            "reported_path": "artifacts/goal/batches/r3-extend/items/retreat-crossing-c/result.json",
            "sha256": "b09e974d6e3de684770f67c1af692762cd59caf3ae96998a8eb2f18529b8e8ab",
            "hash_verified": true
          },
          "incumbent_mean": 96.9505197446568
        }
      ],
      "overall": {
        "n": 1500,
        "sum_d": -95.58091031370009,
        "sum_d2": 46520.056203677894,
        "mean": -0.06372060687580006,
        "se": 0.14382859509726376,
        "retail_diff": 0.034608929921133104,
        "arb_diff": -0.0983293541292666
      },
      "by_spread": {
        "1": {
          "n": 390,
          "sum_d": 0.0,
          "sum_d2": 0.0,
          "mean": 0.0,
          "se": 0.0,
          "retail_diff": 0.0,
          "arb_diff": 0.0
        },
        "2": {
          "n": 377,
          "sum_d": 0.0,
          "sum_d2": 0.0,
          "mean": 0.0,
          "se": 0.0,
          "retail_diff": 0.0,
          "arb_diff": 0.0
        },
        "3": {
          "n": 375,
          "sum_d": -95.58091031370009,
          "sum_d2": 46520.056203677894,
          "mean": -0.2548824275032002,
          "se": 0.5757778234932508,
          "retail_diff": 0.1384355276845324,
          "arb_diff": -0.39331798985039973
        },
        "4": {
          "n": 358,
          "sum_d": 0.0,
          "sum_d2": 0.0,
          "mean": 0.0,
          "se": 0.0,
          "retail_diff": 0.0,
          "arb_diff": 0.0
        }
      },
      "per_seed": [
        [410500,1,0.0],
        [410501,3,0.533499],
        [410502,1,0.0],
        [410503,3,0.235528],
        [410504,4,0.0],
        [410505,3,-0.025176],
        [410506,1,0.0],
        [410507,1,0.0],
        [410508,2,0.0],
        [410509,4,0.0],
        [410510,3,0.110258],
        [410511,3,0.580468],
        [410512,2,0.0],
        [410513,1,0.0],
        [410514,2,0.0],
        [410515,2,0.0],
        [410516,3,0.293227],
        [410517,3,0.040871],
        [410518,3,1.116731],
        [410519,1,0.0],
        [410520,1,0.0],
        [410521,1,0.0],
        [410522,2,0.0],
        [410523,1,0.0],
        [410524,3,0.351284],
        [410525,1,0.0],
        [410526,4,0.0],
        [410527,1,0.0],
        [410528,3,-0.610114],
        [410529,4,0.0],
        [410530,4,0.0],
        [410531,2,0.0],
        [410532,4,0.0],
        [410533,3,0.362975],
        [410534,4,0.0],
        [410535,3,0.897578],
        [410536,3,-0.259355],
        [410537,3,0.053716],
        [410538,4,0.0],
        [410539,3,0.289967],
        [410540,3,8.315411],
        [410541,1,0.0],
        [410542,3,2.056959],
        [410543,3,0.38355],
        [410544,4,0.0],
        [410545,2,0.0],
        [410546,3,0.175534],
        [410547,4,0.0],
        [410548,3,-1.723059],
        [410549,1,0.0],
        [410550,4,0.0],
        [410551,2,0.0],
        [410552,2,0.0],
        [410553,2,0.0],
        [410554,2,0.0],
        [410555,1,0.0],
        [410556,1,0.0],
        [410557,2,0.0],
        [410558,2,0.0],
        [410559,2,0.0],
        [410560,2,0.0],
        [410561,1,0.0],
        [410562,3,1.367343],
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        [410564,2,0.0],
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        [410575,3,-0.08167],
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        [410652,3,4.197247],
        [410653,3,3.721572],
        [410654,3,-207.431851],
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        [410703,3,0.686514],
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        [410705,3,-0.042292],
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        [410744,3,0.701256],
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        [411931,3,1.183644],
        [411932,1,0.0],
        [411933,1,0.0],
        [411934,3,0.478609],
        [411935,4,0.0],
        [411936,2,0.0],
        [411937,3,0.375458],
        [411938,2,0.0],
        [411939,4,0.0],
        [411940,2,0.0],
        [411941,4,0.0],
        [411942,1,0.0],
        [411943,2,0.0],
        [411944,4,0.0],
        [411945,1,0.0],
        [411946,1,0.0],
        [411947,3,0.480031],
        [411948,2,0.0],
        [411949,2,0.0],
        [411950,1,0.0],
        [411951,3,-5.124642],
        [411952,4,0.0],
        [411953,3,-1.241544],
        [411954,2,0.0],
        [411955,1,0.0],
        [411956,4,0.0],
        [411957,3,0.120652],
        [411958,2,0.0],
        [411959,2,0.0],
        [411960,1,0.0],
        [411961,2,0.0],
        [411962,3,-0.113488],
        [411963,1,0.0],
        [411964,3,0.161354],
        [411965,3,-3.993957],
        [411966,4,0.0],
        [411967,3,-0.236938],
        [411968,2,0.0],
        [411969,2,0.0],
        [411970,2,0.0],
        [411971,4,0.0],
        [411972,1,0.0],
        [411973,2,0.0],
        [411974,3,-1.899645],
        [411975,1,0.0],
        [411976,4,0.0],
        [411977,2,0.0],
        [411978,1,0.0],
        [411979,3,0.123883],
        [411980,3,1.079364],
        [411981,3,0.501519],
        [411982,2,0.0],
        [411983,4,0.0],
        [411984,4,0.0],
        [411985,1,0.0],
        [411986,1,0.0],
        [411987,2,0.0],
        [411988,3,0.222851],
        [411989,3,0.707717],
        [411990,4,0.0],
        [411991,2,0.0],
        [411992,2,0.0],
        [411993,2,0.0],
        [411994,3,1.353579],
        [411995,1,0.0],
        [411996,1,0.0],
        [411997,3,-0.400652],
        [411998,2,0.0],
        [411999,3,1.380428]
      ],
      "flag": false,
      "flag_explanation": "No detected incomplete blocks, failures, inconsistent candidate hashes, incumbent hash mismatches, or check-value discrepancies at six decimals. All three input-file hashes match the assignment. Candidate key groups the three block-key suffixes by their identical reported candidate_sha256.",
      "verification_limits": "Strategy code bytes and independent expected check values are not present in the supplied merge inputs or truncated item brief. Code-hash verification and agreement with the original check reference are reported by the items, not independently reproduced here. Check arrays in a/c are compared positionally with b keys 310000..310003. Python versions differ (a/b 3.14.4; c 3.12.3); reported values are retained without adjustment."
    }
  ],
  "pooling_method": "Only reported block summary statistics are pooled: n=sum(n), sum_d=sum(sum_d), sum_d2=sum(sum_d2), mean=sum_d/n, se=sqrt((sum_d2-sum_d*sum_d/n)/(n-1)/n). retail_diff and arb_diff are weighted by the corresponding overall or spread n. No statistics are reconstructed from per_seed. All original block fields are retained, with per_seed concatenated once in seed order. Block a/b summaries and all per_seed arrays have reported rounding; no precision is inferred."
}
```