{"approach":"For spread 1 only, omit the tiny information probes when inferred probability is 25..75 cents. These central probes incurred arbitrage losses with little retail edge. Cap the belief grid at eight nodes when its entire interval lies in 25..75 cents, recovering the computation otherwise added by wider intervals without probes. Main sizing and inventory rules are retained, though changed beliefs can affect later orders. The fixed rule gained on 128 training seeds and a separate 256-seed tuning validation, then an additional untouched 256-seed tuning slice after final freeze. Final code was frozen before its unseen runs; earlier candidate unseen scores were not inspected for selection. Base was scored on all 2036 spread-1 tuning seeds; runs.tuning counts the 640 distinct paired final-candidate tuning runs at tuning-list indices 0..383 and 1024..1279. Full scoring uses PyPy Python 3.11.13; reported runtime uses CPython Python 3.12.3 CPU seconds for 200 runs per strategy in one process. The measured reference mean is 0.001835162758013098 below the supplied reference; cross-interpreter differences were observed on two spread-2 reference seeds, while tested spread-1 replays matched. Exact cause of the reference mismatch was not isolated.","blocked":null,"python_version":"3.11.13","spread":1,"base_mean_edge":98.46762449920578,"runs":{"tuning":640,"unseen":1969},"base_unseen":{"mean_edge":41.78494849744246,"retail_edge":65.91107840022042,"arb_edge":-24.1261299027871},"holdout":{"mean_edge":41.853282578798726,"retail_edge":65.88832036780244,"arb_edge":-24.035037789012446,"failures":0},"diff":{"mean":0.06833408135627202,"standard_error":0.006536226241850507,"retail":-0.022758032417978743,"arb":0.09109211377465704},"others_identical":{"runs":900,"identical":true},"seconds":{"base":198.93443038600012,"yours":168.59853242000003},"code":"\"\"\"Crossing-cover base with isolated, untuned spread overrides.\"\"\"\nimport math\nfrom orderbook_pm_challenge.strategy import BaseStrategy\nfrom orderbook_pm_challenge.types import CancelOrder, PlaceOrder, Side\n\nP = dict(lam_r=0.25, m=5.0, sig_n=1.2, lam_j=0.0019, sig_j=0.35, sig=0.02,\n         qmax=3000.0, rmin=2, kA=0.7, kL=0.15, pL=0.05,\n         ammo=1.0, ydem=0.4, W=200.0, fy=0.6, ammo_q=60.0, ammo_pmax=0.05, ammo_maxpay=0.02,\n         fb=0.9, fu=0.7, xu=0.1, sticky=1.0, min_ahead=2.0, keep_hi=1.5, keep_lo=0.7, Hu=300.0, bins=8.0, filt=1.0, uni=0.01, jumpinfo=1.0, dmin=0.0, kLb=0.08, kLf=0.08, pinf=1.0, pre=0.0, H1=100.0,\n         ydf=0.6, Wf=2000.0, g_hi=0.15, g_lo=0.15, qf=400.0, pmaxf=0.05, pre_gap=1.0,\n         ydf1=0.6, g1=5.0, f1=0.6, a1=100.0, nb1=0.0, gs=1.0, p1t=1.0, m1=1.0, zd=1.0, pfl=0.0005)\nSQ2 = math.sqrt(2.0)\nSQ2PI = math.sqrt(2.0 * math.pi)\ndef cdf(x): return 0.5 * (1.0 + math.erf(x / SQ2))\ndef pdf(x): return math.exp(-0.5 * x * x) / SQ2PI\ndef inv(p):\n    p = min(max(p, 1e-9), 1 - 1e-9)\n    t = math.sqrt(-2.0 * math.log(min(p, 1 - p)))\n    x = t - (2.515517 + 0.802853 * t + 0.010328 * t * t) / (1 + 1.432788 * t + 0.189269 * t * t + 0.001308 * t ** 3)\n    x = -x if p < 0.5 else x\n    for _ in range(2):\n        d = pdf(x)\n        if d < 1e-12:\n            break\n        x -= (cdf(x) - p) / d\n    return x\ndef lpm(k):\n    return pdf(k) + k * cdf(k)\ndef fl(q):\n    return math.floor(q * 100 + 1e-9) / 100\n\nNODES = [(-2.2, .06), (-1.3, .17), (-0.6, .27), (0.6, .27), (1.3, .17), (2.2, .06)]\nPROBE = 0.01\n\n\nclass Strategy(BaseStrategy):\n    def __init__(self):\n        self.n = 0\n        self.ahead = set()     # main orders placed strictly ahead of any competitor order at their tick\n        self.res = {}          # order id -> uncovered quantity at placement\n        self.bc = None         # belief: sub-tick grid centres (ticks)\n        self.bw = None         # belief: weights\n        self.st = 0.5          # last one-step sd in ticks\n        self.pcb = self.pca = None\n        self.pb = set()\n        self.pa = set()\n        self.tb = 0\n        self.s = None          # competitor spread parameter\n        self.flow_notional = 0.0\n        self.flow_exposure = 0\n        self.last_ask_tick = None\n        self.last_quote_exposed = False\n        self.last_flow_ca = None\n        self.last_flow_cap = 0.0\n        self.last_flow_correction = 1.0\n        self.params = P.copy()\n\n    def _oid(self, tag):\n        self.n += 1\n        return tag + str(self.n)\n\n    def on_step(self, state):\n        H = max(1, state.steps_remaining)\n        cb = state.competitor_best_bid_ticks or 0\n        ca = state.competitor_best_ask_ticks or 100\n        if self.s is None:\n            self.s = max(1, (ca - cb + 1) // 2)\n            if self.s == 1:\n                self.params.update({'dmin': 0.3, 'pfl': 1e-06})\n            if self.s == 3:\n                self.params.update({'flow_prior': 200, 'flow_level': 0.6, 'flow_strength': 1.0, 'flow_safety': 2.0, 'flow_exposure_min': 5.0})\n        P = self.params\n        if self.s == 3 and self.last_quote_exposed and ca <= self.last_flow_ca + 1:\n            self.flow_exposure += 1\n            self.flow_notional += min(self.last_flow_cap, state.sell_filled_quantity * self.last_ask_tick / 100.0) * self.last_flow_correction\n        lo, hi = cb, ca\n        for o in state.own_orders:\n            if o.side is Side.BUY:\n                lo = max(lo, o.price_ticks)\n            else:\n                hi = min(hi, o.price_ticks)\n        if P['pinf'] > 0:\n            sb = {o.price_ticks for o in state.own_orders if o.side is Side.BUY and o.remaining_quantity <= PROBE + 1e-9}\n            sa = {o.price_ticks for o in state.own_orders if o.side is Side.SELL and o.remaining_quantity <= PROBE + 1e-9}\n            ea = self.pa - sa\n            eb = self.pb - sb\n            if sa and ea:\n                lo = max(lo, min(max(ea), hi))\n            if eb and (sb or min(eb) <= P['p1t']):\n                hi = min(hi, max(min(eb), lo))\n        if P['jumpinfo'] > 0 and self.pcb is not None:\n            if ca > self.pca + 1:\n                lo = max(lo, ca - 1)\n            if cb < self.pcb - 1:\n                hi = min(hi, cb + 1)\n        self.pcb, self.pca = cb, ca\n        if lo > hi:\n            lo, hi = hi, lo\n        # sub-tick belief over p_(t-1): predict with one-step noise, truncate to [lo, hi]\n        wid = max(hi - lo, 1e-6)\n        nb = max(2, min(48, int(round(wid * P['bins']))))\n        if self.s == 1 and 25 <= lo <= hi <= 75:\n            nb = min(nb, 8)\n        cs = [lo + (i + 0.5) * wid / nb for i in range(nb)]\n        if self.bc is None or P['filt'] <= 0:\n            ws = [1.0 / nb] * nb\n        else:\n            sg = max(self.st, 0.6 * wid / nb)\n            k = -0.5 / (sg * sg)\n            ws = []\n            uni = P['uni'] * sg\n            for c in cs:\n                t = uni\n                for ci, wi in zip(self.bc, self.bw):\n                    d = c - ci\n                    d2 = d * d * k\n                    if d2 > -12.5:\n                        t += wi * math.exp(d2)\n                ws.append(t)\n            tot = sum(ws)\n            ws = [w / tot for w in ws]\n        self.bc, self.bw = cs, ws\n        mean_t = sum(c * w for c, w in zip(cs, ws))\n        var_t = max(sum(c * c * w for c, w in zip(cs, ws)) - mean_t * mean_t, 0.0)\n        phat = min(max(mean_t / 100.0, 0.002), 0.998)\n        var = P['sig'] ** 2 + P['lam_j'] * P['sig_j'] ** 2\n        sd = math.sqrt(H * var)\n        self.tb = self.tb + 1 if hi <= 1 else 0\n        if self.tb > 0 and P['zd'] > 0:\n            # below the last tick there is no probe: the score keeps walking away from it\n            phat = min(phat, max(P['pfl'], cdf(inv(0.01) - P['zd'] * 0.02 * math.sqrt(self.tb) / sd)))\n        z = inv(phat)\n        Z = z * sd\n        sp = pdf(z) / sd * P['sig']\n        self.st = sp * 100.0\n        s = math.sqrt(sp * sp + var_t / 1e4 + 1e-8)\n        sd1 = math.sqrt(max(1.0, H - 1.0) * var)\n        jp = [(cdf((Z + n * P['sig_j']) / sd1), w) for n, w in NODES]\n        lj = P['lam_j']\n\n        def AB(x):\n            k = (x - phat) / s\n            a = s * lpm(k)\n            b = a - (x - phat)\n            ja = sum(w * max(0.0, x - p) for p, w in jp)\n            jb = sum(w * max(0.0, p - x) for p, w in jp)\n            return (1 - lj) * a + lj * ja, (1 - lj) * b + lj * jb\n\n        if H == 1:\n            def AB(x):\n                return (1 - phat) * x, phat * (1 - x)\n        rho = P['lam_r'] * 0.5\n        mu = math.log(P['m']) - 0.5 * P['sig_n'] ** 2\n        kA = P['kL'] if phat < P['pL'] else P['kA']\n\n        def qsize(loss, gain, px):\n            loss *= kA\n            if gain <= 0:\n                return 0.0\n            tail = loss / (rho * gain)\n            if tail >= 1.0:\n                return 0.0\n            return min(P['qmax'], math.exp(mu + P['sig_n'] * inv(1 - max(tail, 1e-6))) / px)\n\n        ptk = phat * 100\n        def qbid(t):\n            if not 1 <= t <= 99:\n                return 0.0\n            a, b = AB(t / 100.0)\n            if phat * 100 - t < P['dmin']:\n                return 0.0\n            if P['nb1'] > 0 and self.s == 1 and t == 1 and ptk < 1.0:\n                return 0.0\n            if phat < P['pL']:\n                ytg = P['ydem'] * min(H, P['W']) / max(ca - 1, ptk + 1) * 100.0\n                a *= (P['kLb'] if state.yes_inventory < ytg else P['kLf']) / P['kL']\n            return qsize(a, b, max(phat, 0.05))\n\n        def qask(t):\n            if not 1 <= t <= 99:\n                return 0.0\n            a, b = AB(t / 100.0)\n            if t - phat * 100 < P['dmin']:\n                return 0.0\n            return qsize(b, a, t / 100.0)\n\n        bids = [o for o in state.own_orders if o.side is Side.BUY and o.remaining_quantity > PROBE + 1e-9]\n        asks = [o for o in state.own_orders if o.side is Side.SELL and o.remaining_quantity > PROBE + 1e-9]\n        sticky = P['sticky'] > 0\n        def top(orders, comp, step):\n            if sticky and sum(o.remaining_quantity for o in orders if o.price_ticks == comp and o.order_id in self.ahead) >= P['min_ahead']:\n                return comp\n            return comp + step\n        bid_t = top(bids, cb, 1)\n        ask_t = top(asks, ca, -1)\n        qb = qbid(bid_t)\n        qa = qask(ask_t)\n\n        Y = state.yes_inventory\n        if ask_t == 1 and H > P['H1'] and P['pre'] > 0:\n            qa = qa if Y >= P['a1'] > 0 else 0.0          # let the competitor's 2-tick ask erode instead of fronting it for nothing\n        # ammunition: hold YES so that low asks are covered\n        ptick = phat * 100\n        amt = 0\n        qam = 0.0\n        if P['ammo'] > 0 and ask_t >= 2 and phat < max(P['ammo_pmax'], P['pmaxf']):\n            wealth = state.cash + Y * phat\n            x = max(ask_t, ptick + 1) / 100.0\n            capw = P['fy'] * wealth / max(phat, 0.005)\n            target = min(P['ydem'] * min(H, P['W']) / x, capw)\n            full = min(P['ydf'] * min(H, P['Wf']) / x, capw) if phat < P['pmaxf'] else 0.0\n            t = max(1, min(99, int(math.ceil(ptick + 1e-9))))\n            g = t - ptick\n            if Y < full and g <= P['g_hi'] and bid_t <= t < ask_t:\n                amt, qam = t, min(P['qf'], full - Y)     # a tick p has just crossed: nearly free\n            elif Y < target and phat < P['ammo_pmax'] and bid_t <= t < ask_t and t / 100.0 - phat < P['ammo_maxpay']:\n                amt, qam = t, min(P['ammo_q'], target - Y)\n            elif Y < full and t >= 2 and 1.0 - g <= P['g_lo']:\n                amt, qam = t - 1, min(P['qf'], full - Y)  # rest just under p: filled only on the crossing, or by retail\n\n        if P['pre'] > 0 and ca == 2 and phat < 0.01 and H > P['H1'] and Y < P['pre'] and not qam and 1.0 - ptick < P['pre_gap']:\n            amt, qam = 1, min(P['ammo_q'], P['pre'] - Y)\n        q1 = 0.0\n        if P['ydf1'] > 0 and P['m1'] < ptick < P['g1'] + 1.0 and amt != 1:\n            stock_rate = P['ydf1']\n            if self.s == 3:\n                flow = (self.flow_notional + P['flow_prior'] * P['flow_level']) / (P['flow_prior'] + self.flow_exposure)\n                scale = max(0.5, min(2.0, flow / P['flow_level']))\n                stock_rate *= 1.0 + P['flow_strength'] * (scale - 1.0)\n            q1 = max(0.0, stock_rate * min(H, P['Wf']) / (self.s / 100.0) - Y)\n\n        # Bridge expected retail demand until another tick crossing is available.\n        if 0.02 < phat < 0.1:\n            ct = max(2, min(99, int(math.floor(ptick))))\n            wealth = state.cash + Y * phat\n            goal = min(1 * qa, 0.3 * max(wealth, 0.0) / phat)\n            if Y < goal and ct < ask_t:\n                amt, qam = ct, min(3000.0, goal - Y)\n        # order management\n        actions = []\n        free = state.free_cash - 2.0\n        keep_ask = 0.0\n        new_b = []\n        new_a = []\n        def cancel(o):\n            nonlocal free\n            actions.append(CancelOrder(o.order_id))\n            x = o.price_ticks / 100.0\n            if o.side is Side.BUY:\n                free += x * o.remaining_quantity\n            else:\n                free += (1 - x) * min(self.res.get(o.order_id, 0.0), o.remaining_quantity)\n            self.ahead.discard(o.order_id)\n            self.res.pop(o.order_id, None)\n        for o in state.own_orders:\n            if o.remaining_quantity <= PROBE + 1e-9:\n                cancel(o)\n        kept_ids = set()\n        def manage(orders, t, q, comp):\n            kept = 0.0\n            for o in orders:\n                if o.price_ticks == t and q > 0 and kept + o.remaining_quantity <= max(q * P['keep_hi'], 1.0):\n                    kept += o.remaining_quantity\n                    kept_ids.add(o.order_id)\n                else:\n                    cancel(o)\n            return kept\n        kb = manage(bids, bid_t, qb, cb)\n        ka = manage(asks, ask_t, qa, ca)\n        add_b = (qb - kb) if (kb < qb * P['keep_lo'] and bid_t != cb) else 0.0\n        add_a = (qa - ka) if (ka < qa * P['keep_lo'] and ask_t != ca) else 0.0\n\n        budget = P['fb'] * max(free, 0.0)\n        cost = add_b * bid_t / 100.0 + qam * amt / 100.0\n        if cost > budget:\n            f = budget / cost\n            add_b *= f\n            qam *= f\n            cost = budget\n        out = []\n        q1 = min(q1, P['f1'] * max(budget - cost, 0.0) * 100.0)\n        if q1 >= 0.01:\n            out.append(PlaceOrder(side=Side.BUY, price_ticks=1, quantity=fl(q1)))\n            free -= fl(q1) / 100.0 + 1e-6\n        if amt and qam >= 0.01:\n            q = fl(qam)\n            out.append(PlaceOrder(side=Side.BUY, price_ticks=amt, quantity=q))\n            free -= q * amt / 100.0 + 1e-6\n        if bid_t >= 1 and add_b >= 0.01:\n            q = fl(add_b)\n            oid = self._oid('b')\n            out.append(PlaceOrder(side=Side.BUY, price_ticks=bid_t, quantity=q, client_order_id=oid))\n            free -= q * bid_t / 100.0 + 1e-6\n            if bid_t > cb:\n                self.ahead.add(oid)\n        if ask_t <= 99 and add_a >= 0.01:\n            x = ask_t / 100.0\n            covk = sum(o.remaining_quantity - min(self.res.get(o.order_id, 0.0), o.remaining_quantity)\n                       for o in asks if o.order_id in kept_ids)\n            cov = max(0.0, Y - covk - 0.1)\n            unc = max(0.0, add_a - cov)\n            if unc > 0:\n                ub = max(0.0, free - (1 - P['fu']) * max(state.cash, 0.0)) if x >= P['xu'] else 0.0\n                if H < P['Hu'] and phat < 0.05:\n                    ub = max(0.0, free * (1 - H / P['Hu']))\n                unc = min(unc, ub / (1 - x))\n            q = fl(min(add_a, cov + unc))\n            if q >= 0.01:\n                oid = self._oid('a')\n                out.append(PlaceOrder(side=Side.SELL, price_ticks=ask_t, quantity=q, client_order_id=oid))\n                r = max(0.0, q - cov)\n                self.res[oid] = r\n                free -= r * (1 - x) + 1e-6\n                if ask_t < ca:\n                    self.ahead.add(oid)\n\n        # probes: tiny orders that the arbitrageur removes when p crosses them\n        f = int(math.floor(ptick + 1e-9))\n        r = max(int(P['rmin']), int(math.ceil(2.0 * s * 100)))\n        self.pb = set()\n        self.pa = set()\n        if free > 1.0 and not (self.s == 1 and 25 <= ptick <= 75):\n            for t in range(f, f + r + 1):\n                if cb < t < ca and 1 <= t <= 99:\n                    out.append(PlaceOrder(side=Side.BUY, price_ticks=t, quantity=PROBE))\n                    self.pb.add(t)\n            for t in range(f + 1 - r, f + 2):\n                if cb < t < ca and 1 <= t <= 99:\n                    out.append(PlaceOrder(side=Side.SELL, price_ticks=t, quantity=PROBE))\n                    self.pa.add(t)\n        if self.s == 3:\n            self.last_ask_tick = ask_t\n            self.last_flow_ca = ca\n            exposed_qty = ka + sum(o.quantity for o in out if o.side is Side.SELL and o.price_ticks == ask_t and o.quantity > PROBE)\n            self.last_flow_cap = exposed_qty * ask_t / 100.0\n            self.last_quote_exposed = ask_t / 100.0 > phat + max(0.005, P['flow_safety'] * self.st / 100.0) and self.last_flow_cap >= P['flow_exposure_min']\n            if self.last_quote_exposed:\n                logcap = math.log(self.last_flow_cap)\n                mu_flow = math.log(P['m']) - 0.5 * P['sig_n'] ** 2\n                clipped = P['m'] * cdf((logcap - mu_flow - P['sig_n'] ** 2) / P['sig_n']) + self.last_flow_cap * (1.0 - cdf((logcap - mu_flow) / P['sig_n']))\n                self.last_flow_correction = min(3.0, P['m'] / max(clipped, 0.01))\n        return actions + out\n","code_sha256":"9b03f7f0d050475d5c6d0abf0424b828b73f5f99e86a49d66d52000d18caa48f","tried":["Simulator revision b244530ee2a6247b5f930830eeca9dd950da0e7e; seed lists sampled from ChallengeConfig and ParameterVariance with sample_config, not recognized by strategy.","Spread-1 tuning seeds, 8000..15999: 8005,8007,8009,8014,8016,8018,8019,8020,8021,8025,8029,8030,8034,8035,8036,8037,8043,8047,8048,8050,8051,8052,8057,8058,8062,8069,8074,8077,8078,8080,8083,8084,8086,8087,8091,8092,8096,8098,8100,8104,8108,8109,8110,8114,8116,8117,8119,8122,8124,8142,8148,8149,8153,8162,8167,8171,8178,8179,8181,8182,8183,8184,8185,8198,8206,8207,8222,8227,8228,8230,8234,8236,8245,8249,8250,8251,8256,8259,8262,8265,8268,8270,8275,8284,8293,8295,8298,8299,8300,8301,8303,8308,8311,8317,8323,8329,8339,8340,8341,8351,8354,8356,8365,8366,8370,8371,8374,8381,8383,8385,8387,8390,8397,8398,8400,8414,8425,8426,8428,8429,8430,8437,8438,8439,8446,8447,8450,8453,8458,8460,8461,8463,8464,8468,8471,8473,8474,8478,8485,8489,8490,8491,8492,8503,8508,8510,8514,8515,8517,8521,8523,8524,8531,8539,8541,8547,8552,8553,8557,8563,8571,8572,8575,8583,8592,8596,8598,8605,8608,8613,8614,8620,8629,8635,8636,8649,8653,8655,8656,8658,8665,8666,8672,8673,8678,8683,8684,8700,8703,8705,8716,8718,8722,8723,8724,8725,8729,8735,8740,8741,8746,8748,8750,8754,8755,8758,8760,8767,8770,8774,8775,8776,8779,8780,8782,8783,8785,8793,8796,8797,8804,8805,8808,8815,8816,8819,8822,8825,8831,8835,8840,8842,8845,8849,8850,8851,8854,8855,8859,8864,8869,8871,8874,8875,8883,8886,8890,8902,8904,8910,8911,8914,8916,8923,8934,8937,8941,8942,8944,8949,8954,8955,8956,8961,8963,8973,8978,8984,8986,8988,8996,8997,9004,9008,9016,9018,9023,9026,9028,9034,9036,9038,9044,9046,9051,9052,9054,9056,9061,9071,9074,9076,9085,9086,9087,9091,9093,9094,9095,9096,9097,9109,9110,9111,9113,9114,9121,9127,9142,9145,9155,9162,9163,9164,9166,9170,9174,9177,9188,9189,9195,9204,9205,9210,9215,9219,9225,9226,9229,9233,9234,9242,9244,9248,9254,9255,9262,9274,9275,9277,9279,9282,9285,9289,9290,9291,9297,9303,9314,9316,9329,9334,9348,9352,9353,9354,9355,9361,9362,9370,9371,9375,9383,9390,9392,9397,9400,9401,9406,9413,9416,9419,9422,9426,9429,9437,9447,9450,9451,9453,9459,9468,9475,9476,9477,9480,9484,9485,9486,9490,9494,9496,9500,9507,9512,9514,9515,9520,9522,9530,9534,9540,9544,9546,9551,9552,9553,9556,9558,9563,9565,9567,9568,9572,9579,9580,9582,9583,9584,9588,9596,9599,9610,9614,9616,9624,9628,9629,9630,9633,9636,9642,9650,9652,9653,9654,9656,9657,9660,9661,9664,9680,9681,9683,9686,9693,9694,9699,9701,9703,9714,9718,9725,9739,9740,9742,9744,9745,9752,9753,9757,9762,9763,9764,9766,9768,9770,9780,9781,9782,9783,9784,9787,9790,9791,9793,9795,9796,9804,9806,9807,9812,9815,9820,9824,9832,9838,9844,9845,9856,9865,9866,9867,9868,9872,9882,9884,9890,9899,9902,9903,9908,9909,9912,9917,9920,9928,9929,9943,9944,9954,9955,9958,9960,9961,9964,9965,9966,9967,9968,9970,9982,9984,9990,9994,10000,10003,10005,10006,10015,10021,10023,10032,10036,10039,10040,10051,10061,10065,10070,10071,10075,10089,10093,10099,10103,10107,10112,10114,10116,10136,10141,10145,10150,10156,10160,10176,10181,10182,10183,10190,10197,10198,10199,10205,10206,10214,10215,10224,10235,10244,10250,10255,10258,10264,10269,10273,10274,10283,10288,10289,10292,10299,10301,10304,10310,10311,10312,10313,10320,10322,10324,10326,10339,10343,10344,10346,10348,10350,10355,10359,10364,10366,10367,10371,10378,10379,10380,10387,10390,10397,10399,10400,10405,10407,10416,10418,10429,10439,10445,10446,10451,10453,10454,10457,10466,10468,10469,10474,10476,10480,10482,10483,10484,10485,10489,10490,10492,10493,10494,10495,10498,10499,10503,10506,10507,10511,10516,10523,10525,10528,10538,10543,10544,10548,10550,10553,10554,10555,10557,10560,10565,10569,10574,10575,10582,10584,10591,10596,10599,10600,10608,10610,10617,10619,10623,10624,10629,10631,10633,10634,10636,10639,10641,10642,10646,10647,10649,10651,10654,10655,10666,10667,10670,10672,10674,10675,10680,10681,10683,10685,10692,10693,10694,10695,10701,10702,10704,10707,10712,10715,10716,10721,10724,10726,10727,10728,10729,10736,10739,10741,10742,10743,10744,10748,10750,10751,10752,10760,10761,10766,10768,10773,10775,10782,10790,10793,10795,10819,10834,10835,10838,10839,10841,10842,10844,10847,10849,10850,10851,10852,10854,10855,10860,10862,10866,10867,10871,10884,10887,10889,10891,10906,10907,10913,10917,10919,10922,10927,10928,10936,10938,10940,10944,10945,10947,10949,10955,10956,10957,10958,10960,10965,10967,10968,10976,10983,10997,11017,11019,11025,11027,11033,11038,11047,11050,11053,11056,11059,11063,11067,11095,11096,11101,11114,11116,11122,11130,11132,11135,11136,11142,11145,11149,11151,11154,11157,11158,11160,11163,11164,11165,11166,11169,11170,11171,11176,11178,11189,11190,11193,11194,11195,11196,11201,11202,11203,11208,11210,11218,11220,11222,11227,11228,11237,11245,11252,11253,11258,11266,11279,11282,11286,11287,11299,11304,11307,11313,11315,11317,11325,11331,11332,11342,11346,11353,11363,11364,11365,11366,11368,11373,11379,11381,11383,11384,11395,11401,11406,11407,11408,11418,11422,11423,11425,11428,11432,11436,11438,11446,11451,11460,11461,11465,11467,11471,11472,11474,11480,11486,11500,11502,11504,11508,11509,11512,11516,11521,11534,11537,11540,11542,11548,11551,11554,11558,11562,11563,11566,11569,11570,11578,11582,11586,11592,11596,11598,11599,11601,11602,11604,11605,11609,11613,11617,11621,11628,11639,11642,11658,11662,11663,11664,11666,11668,11670,11673,11678,11681,11683,11684,11687,11689,11692,11702,11705,11707,11715,11717,11726,11727,11731,11736,11742,11763,11767,11768,11769,11770,11771,11773,11776,11780,11783,11786,11788,11791,11794,11795,11797,11805,11807,11809,11812,11817,11818,11820,11822,11828,11832,11837,11838,11839,11841,11848,11849,11850,11852,11853,11862,11867,11872,11881,11887,11890,11895,11896,11897,11909,11911,11917,11920,11922,11927,11937,11943,11945,11951,11957,11965,11966,11967,11968,11983,11987,11996,11998,12005,12013,12018,12029,12039,12047,12048,12058,12059,12060,12065,12067,12068,12069,12070,12078,12079,12082,12084,12085,12087,12092,12093,12094,12109,12111,12118,12119,12121,12122,12123,12124,12127,12129,12132,12135,12137,12140,12142,12143,12148,12162,12163,12167,12176,12179,12181,12182,12185,12187,12190,12196,12200,12201,12210,12213,12216,12218,12221,12228,12230,12242,12245,12247,12248,12251,12252,12255,12260,12261,12265,12268,12283,12284,12285,12286,12287,12299,12301,12303,12309,12310,12320,12324,12331,12334,12337,12339,12342,12348,12350,12356,12361,12362,12368,12372,12376,12384,12385,12387,12388,12390,12393,12395,12402,12405,12406,12414,12416,12418,12425,12429,12430,12431,12436,12438,12441,12442,12449,12452,12454,12455,12462,12463,12467,12477,12483,12486,12493,12496,12497,12503,12504,12509,12511,12512,12516,12520,12521,12522,12525,12528,12532,12538,12553,12554,12560,12561,12566,12567,12572,12577,12580,12583,12590,12599,12602,12615,12616,12617,12618,12623,12625,12630,12639,12641,12645,12647,12658,12660,12673,12678,12682,12688,12690,12693,12697,12701,12703,12704,12705,12717,12719,12720,12732,12733,12735,12743,12753,12759,12761,12767,12777,12783,12785,12786,12788,12799,12800,12807,12815,12816,12818,12819,12823,12829,12840,12848,12858,12871,12877,12881,12887,12890,12895,12897,12906,12910,12912,12928,12936,12939,12945,12947,12948,12960,12971,12973,12976,12990,12992,12995,13006,13009,13011,13013,13017,13019,13020,13021,13022,13030,13034,13037,13039,13042,13056,13064,13066,13067,13070,13072,13078,13079,13082,13090,13092,13093,13095,13097,13102,13103,13113,13117,13121,13127,13142,13146,13151,13154,13161,13166,13170,13171,13177,13180,13181,13184,13186,13192,13194,13198,13204,13205,13206,13207,13211,13212,13217,13224,13226,13229,13230,13235,13236,13237,13247,13253,13265,13266,13269,13272,13276,13280,13294,13297,13301,13304,13314,13320,13324,13331,13333,13336,13341,13348,13350,13351,13353,13358,13363,13364,13365,13366,13367,13368,13374,13375,13377,13378,13381,13386,13390,13392,13395,13396,13405,13407,13410,13414,13415,13416,13424,13429,13433,13438,13439,13441,13446,13451,13462,13463,13466,13476,13477,13487,13497,13504,13505,13506,13515,13518,13523,13525,13529,13531,13534,13536,13538,13544,13545,13550,13551,13552,13554,13556,13558,13563,13570,13577,13583,13586,13588,13589,13590,13591,13602,13605,13613,13616,13620,13628,13630,13633,13635,13637,13639,13641,13649,13656,13661,13666,13667,13668,13688,13690,13695,13697,13701,13708,13715,13717,13720,13727,13729,13733,13735,13737,13745,13746,13747,13749,13754,13756,13759,13762,13763,13775,13778,13779,13782,13785,13798,13800,13807,13811,13813,13814,13815,13821,13825,13830,13831,13838,13839,13841,13846,13849,13854,13856,13860,13864,13874,13877,13878,13879,13884,13888,13890,13894,13899,13905,13909,13911,13916,13918,13924,13928,13929,13930,13933,13937,13939,13942,13944,13948,13951,13952,13953,13954,13956,13960,13964,13967,13974,13981,13982,13985,13987,13989,13992,13998,13999,14000,14003,14009,14020,14026,14027,14037,14040,14041,14043,14045,14046,14051,14060,14062,14063,14067,14070,14077,14086,14105,14111,14113,14118,14125,14128,14130,14132,14134,14136,14139,14144,14145,14155,14156,14159,14164,14165,14166,14169,14176,14178,14184,14187,14192,14193,14196,14202,14208,14209,14215,14217,14219,14221,14232,14234,14237,14239,14242,14246,14249,14250,14251,14252,14254,14262,14265,14269,14281,14293,14294,14297,14298,14299,14303,14305,14308,14309,14312,14315,14319,14320,14324,14325,14327,14329,14333,14336,14337,14341,14342,14346,14347,14348,14353,14356,14360,14366,14371,14374,14375,14376,14383,14384,14386,14387,14397,14398,14402,14403,14408,14409,14416,14424,14430,14433,14434,14438,14449,14451,14452,14463,14466,14469,14473,14484,14489,14493,14496,14498,14499,14502,14503,14504,14509,14510,14512,14521,14524,14526,14530,14532,14533,14539,14540,14548,14550,14552,14560,14562,14571,14578,14581,14583,14587,14591,14598,14602,14613,14617,14619,14621,14632,14636,14637,14642,14650,14651,14659,14660,14662,14663,14665,14668,14674,14676,14683,14696,14697,14700,14706,14708,14711,14717,14718,14719,14720,14726,14727,14734,14738,14739,14743,14746,14757,14758,14763,14768,14769,14775,14776,14778,14781,14783,14787,14788,14790,14792,14794,14797,14799,14803,14806,14809,14817,14818,14819,14823,14828,14830,14838,14849,14850,14858,14859,14867,14870,14873,14876,14879,14880,14881,14882,14892,14894,14895,14908,14913,14915,14917,14918,14924,14925,14926,14928,14930,14932,14936,14937,14940,14942,14944,14946,14947,14952,14953,14954,14956,14962,14970,14972,14976,14978,14979,14986,14987,14988,14994,14997,15003,15013,15024,15025,15030,15032,15036,15043,15050,15053,15056,15060,15061,15063,15065,15066,15067,15068,15079,15088,15094,15097,15099,15105,15110,15113,15115,15117,15125,15131,15135,15136,15140,15148,15152,15157,15160,15165,15166,15168,15170,15175,15181,15188,15189,15202,15207,15209,15210,15214,15216,15226,15235,15242,15252,15256,15268,15269,15272,15279,15284,15285,15290,15291,15298,15299,15303,15307,15308,15312,15314,15317,15319,15322,15327,15342,15344,15345,15346,15347,15350,15351,15354,15357,15359,15366,15369,15374,15377,15384,15387,15390,15391,15392,15394,15399,15402,15403,15411,15414,15415,15418,15419,15420,15425,15434,15437,15438,15439,15442,15446,15450,15453,15454,15466,15473,15474,15476,15479,15486,15489,15494,15495,15497,15503,15504,15505,15510,15511,15523,15524,15527,15531,15535,15545,15550,15552,15558,15559,15565,15575,15577,15585,15598,15600,15607,15616,15617,15620,15634,15636,15638,15639,15648,15649,15650,15656,15659,15664,15667,15673,15675,15676,15680,15681,15685,15689,15692,15693,15698,15709,15710,15713,15715,15718,15719,15720,15722,15724,15732,15734,15735,15739,15742,15746,15757,15760,15765,15775,15779,15781,15788,15798,15800,15801,15803,15805,15811,15812,15813,15820,15823,15829,15831,15839,15841,15842,15843,15844,15848,15849,15857,15863,15868,15869,15872,15874,15879,15883,15890,15896,15907,15908,15909,15911,15917,15921,15924,15926,15931,15935,15942,15959,15960,15962,15965,15966,15968,15972,15981,15982,15984,15986,15988,15993,15995,15996","Spread-1 unseen seeds, 60000..67999: 60004,60012,60014,60016,60021,60023,60027,60028,60044,60045,60056,60062,60067,60069,60075,60076,60079,60081,60082,60089,60090,60092,60094,60099,60103,60104,60113,60117,60127,60131,60132,60133,60141,60143,60147,60152,60153,60155,60156,60159,60165,60167,60175,60178,60180,60181,60189,60194,60195,60196,60210,60212,60214,60217,60218,60225,60232,60235,60243,60244,60249,60251,60253,60263,60265,60266,60268,60269,60273,60283,60285,60288,60289,60296,60297,60298,60301,60306,60309,60312,60316,60317,60320,60325,60329,60330,60334,60338,60341,60343,60344,60361,60362,60369,60370,60376,60377,60381,60393,60394,60396,60403,60404,60415,60416,60417,60421,60426,60433,60434,60436,60443,60446,60448,60454,60463,60465,60469,60473,60475,60478,60490,60494,60496,60498,60500,60501,60519,60521,60524,60526,60527,60529,60533,60543,60544,60553,60554,60555,60558,60560,60564,60573,60578,60579,60580,60583,60588,60590,60595,60604,60605,60612,60619,60620,60622,60623,60628,60632,60634,60636,60642,60643,60647,60656,60658,60659,60661,60663,60667,60668,60672,60674,60678,60679,60686,60688,60690,60691,60698,60704,60711,60712,60714,60719,60723,60724,60736,60738,60741,60743,60744,60746,60751,60753,60762,60780,60782,60787,60792,60798,60799,60802,60803,60805,60807,60808,60812,60819,60820,60821,60825,60829,60831,60834,60836,60852,60853,60860,60863,60864,60867,60868,60874,60875,60883,60887,60888,60894,60902,60903,60917,60930,60933,60934,60936,60949,60952,60956,60966,60972,60975,60984,60985,60990,60991,60992,60993,60997,61000,61007,61008,61009,61010,61018,61021,61024,61045,61047,61049,61053,61058,61071,61075,61078,61080,61083,61084,61092,61093,61104,61106,61114,61122,61134,61136,61140,61144,61146,61149,61150,61151,61160,61165,61174,61176,61180,61186,61187,61191,61199,61205,61206,61207,61208,61209,61213,61217,61218,61219,61221,61222,61227,61229,61235,61236,61238,61239,61241,61246,61259,61262,61264,61272,61273,61274,61275,61278,61283,61285,61293,61295,61296,61298,61299,61301,61311,61313,61314,61315,61318,61319,61321,61340,61342,61350,61353,61356,61359,61360,61365,61372,61373,61381,61385,61387,61388,61390,61393,61394,61401,61403,61408,61412,61420,61427,61428,61429,61432,61440,61441,61445,61446,61448,61460,61463,61466,61467,61474,61477,61480,61485,61491,61494,61496,61500,61511,61515,61519,61520,61522,61525,61532,61533,61537,61540,61545,61546,61553,61554,61556,61561,61563,61565,61566,61572,61573,61575,61576,61579,61585,61587,61588,61590,61599,61600,61602,61609,61615,61621,61622,61626,61636,61644,61658,61661,61663,61671,61672,61678,61682,61692,61693,61694,61701,61702,61704,61717,61725,61726,61736,61737,61738,61741,61747,61751,61755,61763,61765,61767,61768,61769,61770,61776,61777,61781,61784,61786,61790,61791,61800,61801,61803,61804,61806,61819,61823,61825,61827,61829,61833,61834,61835,61839,61840,61846,61854,61857,61863,61868,61870,61872,61873,61883,61891,61893,61898,61900,61901,61906,61915,61916,61919,61926,61927,61937,61941,61942,61947,61949,61952,61954,61955,61958,61969,61977,61980,61981,61994,61998,62003,62004,62008,62009,62015,62017,62018,62019,62020,62027,62032,62038,62039,62042,62048,62055,62065,62068,62072,62081,62088,62092,62094,62096,62106,62112,62120,62124,62128,62131,62141,62145,62147,62151,62152,62161,62165,62168,62170,62175,62183,62184,62186,62187,62211,62214,62217,62220,62222,62223,62226,62229,62230,62232,62233,62239,62241,62243,62244,62248,62249,62251,62253,62255,62258,62260,62262,62270,62282,62284,62285,62306,62307,62311,62315,62316,62320,62322,62326,62331,62341,62354,62364,62371,62376,62379,62383,62384,62392,62396,62399,62400,62403,62410,62414,62416,62417,62418,62439,62441,62445,62446,62452,62453,62456,62461,62462,62465,62466,62468,62470,62475,62476,62477,62488,62491,62493,62495,62508,62511,62536,62537,62552,62560,62564,62567,62571,62572,62573,62574,62577,62580,62582,62587,62589,62590,62592,62595,62604,62608,62609,62620,62623,62626,62632,62634,62637,62639,62643,62645,62646,62662,62663,62668,62672,62679,62682,62683,62684,62685,62689,62692,62693,62700,62701,62706,62707,62718,62719,62722,62743,62745,62751,62756,62759,62761,62763,62769,62774,62785,62788,62799,62804,62805,62806,62812,62813,62815,62821,62824,62825,62828,62829,62834,62838,62839,62842,62852,62867,62869,62876,62880,62881,62882,62887,62888,62890,62899,62905,62912,62913,62919,62920,62925,62927,62935,62938,62944,62946,62947,62952,62953,62970,62975,62976,62979,62986,62987,62989,62994,63004,63018,63021,63024,63026,63027,63036,63038,63039,63041,63044,63046,63049,63051,63052,63053,63054,63058,63062,63070,63077,63078,63079,63081,63084,63087,63090,63092,63096,63097,63102,63106,63113,63117,63119,63121,63122,63124,63128,63131,63135,63140,63150,63152,63157,63158,63162,63168,63171,63185,63195,63198,63200,63204,63210,63211,63213,63220,63222,63227,63239,63240,63241,63243,63248,63250,63252,63255,63260,63261,63267,63271,63275,63277,63279,63280,63282,63288,63289,63293,63295,63299,63300,63304,63306,63311,63312,63320,63323,63325,63328,63334,63337,63339,63345,63348,63350,63357,63367,63369,63379,63392,63398,63403,63407,63409,63412,63415,63425,63426,63427,63439,63442,63447,63457,63459,63466,63471,63473,63481,63484,63487,63505,63508,63518,63520,63523,63525,63535,63537,63539,63541,63549,63552,63559,63561,63562,63566,63567,63583,63585,63592,63598,63599,63600,63607,63610,63619,63620,63621,63622,63624,63626,63628,63634,63640,63649,63650,63655,63662,63670,63673,63679,63681,63682,63684,63687,63688,63698,63703,63708,63712,63721,63724,63730,63733,63745,63748,63751,63761,63764,63768,63769,63771,63772,63778,63779,63780,63786,63790,63803,63810,63811,63818,63826,63827,63837,63839,63851,63852,63857,63860,63862,63868,63871,63873,63875,63877,63882,63883,63886,63889,63891,63895,63896,63897,63899,63904,63906,63910,63912,63917,63920,63922,63925,63927,63931,63932,63934,63935,63958,63961,63966,63967,63970,63974,63979,63987,63997,64005,64006,64007,64014,64030,64033,64036,64038,64044,64046,64050,64060,64061,64063,64064,64070,64076,64080,64082,64083,64098,64104,64105,64106,64109,64110,64111,64113,64115,64116,64122,64127,64133,64134,64139,64140,64144,64151,64152,64159,64161,64165,64176,64177,64178,64180,64181,64188,64191,64192,64195,64200,64212,64216,64218,64219,64224,64225,64228,64229,64230,64237,64243,64245,64248,64249,64252,64255,64256,64257,64258,64259,64261,64268,64269,64273,64277,64280,64290,64292,64298,64300,64301,64306,64309,64316,64320,64321,64332,64335,64336,64339,64346,64351,64352,64355,64360,64363,64369,64375,64380,64381,64382,64388,64389,64401,64419,64421,64429,64433,64437,64444,64453,64459,64462,64464,64466,64467,64468,64476,64483,64485,64486,64488,64493,64494,64506,64512,64516,64517,64519,64527,64532,64533,64534,64538,64539,64544,64545,64547,64548,64550,64551,64556,64558,64566,64568,64575,64580,64582,64583,64587,64594,64596,64617,64623,64633,64638,64641,64643,64644,64648,64650,64653,64658,64663,64665,64674,64675,64677,64679,64682,64684,64687,64689,64697,64699,64703,64706,64710,64712,64718,64729,64736,64742,64743,64747,64748,64749,64752,64763,64764,64768,64774,64778,64782,64784,64793,64795,64798,64801,64805,64812,64829,64830,64833,64834,64838,64840,64845,64847,64851,64858,64861,64862,64863,64865,64868,64871,64872,64874,64875,64878,64879,64881,64885,64889,64892,64894,64900,64903,64904,64906,64908,64916,64924,64925,64926,64927,64931,64943,64945,64947,64948,64951,64954,64959,64961,64970,64973,64974,64978,64981,64998,64999,65004,65014,65021,65024,65026,65029,65030,65032,65034,65035,65051,65054,65056,65058,65060,65061,65063,65064,65067,65068,65071,65079,65080,65082,65083,65090,65097,65105,65106,65111,65114,65119,65120,65128,65133,65134,65137,65141,65142,65146,65152,65155,65158,65161,65164,65167,65172,65181,65182,65184,65188,65195,65202,65203,65211,65220,65225,65231,65239,65247,65256,65258,65260,65261,65267,65271,65273,65279,65283,65284,65285,65286,65293,65300,65310,65314,65320,65333,65334,65335,65337,65339,65341,65343,65346,65347,65348,65350,65352,65353,65360,65363,65376,65377,65389,65392,65394,65395,65396,65400,65401,65402,65404,65407,65415,65418,65422,65426,65435,65445,65446,65461,65464,65467,65468,65469,65471,65473,65478,65480,65481,65483,65486,65493,65495,65496,65501,65507,65510,65511,65516,65521,65523,65524,65542,65545,65546,65550,65553,65555,65557,65563,65584,65589,65590,65597,65600,65611,65618,65620,65627,65633,65638,65642,65644,65645,65646,65650,65652,65657,65662,65665,65666,65667,65671,65675,65677,65681,65682,65683,65685,65686,65694,65696,65698,65703,65704,65714,65723,65730,65731,65735,65738,65742,65748,65750,65753,65754,65756,65757,65762,65763,65765,65768,65772,65776,65784,65785,65788,65791,65799,65803,65812,65817,65818,65820,65822,65827,65829,65832,65834,65837,65838,65839,65840,65842,65851,65854,65856,65858,65863,65874,65875,65883,65884,65885,65888,65890,65892,65893,65895,65896,65909,65910,65915,65916,65920,65924,65934,65936,65937,65938,65944,65949,65951,65955,65961,65962,65966,65970,65977,65981,65992,66001,66004,66006,66007,66010,66012,66015,66019,66023,66025,66040,66041,66045,66066,66067,66072,66077,66079,66084,66086,66087,66088,66089,66091,66096,66098,66101,66109,66111,66112,66118,66129,66134,66140,66142,66152,66154,66155,66156,66158,66163,66166,66168,66172,66176,66177,66178,66191,66196,66200,66209,66215,66216,66219,66222,66223,66228,66229,66233,66234,66236,66240,66245,66251,66256,66261,66265,66269,66272,66275,66276,66278,66279,66282,66283,66287,66297,66298,66299,66305,66306,66313,66319,66322,66323,66325,66326,66328,66334,66342,66345,66347,66348,66349,66350,66352,66360,66362,66363,66372,66373,66374,66375,66377,66380,66392,66395,66397,66407,66413,66426,66432,66437,66444,66454,66455,66456,66457,66463,66464,66465,66467,66473,66479,66480,66486,66490,66501,66504,66507,66511,66513,66522,66529,66532,66533,66534,66538,66555,66558,66567,66568,66574,66575,66577,66580,66589,66596,66597,66599,66605,66610,66613,66618,66620,66622,66626,66629,66635,66640,66646,66656,66658,66660,66670,66671,66672,66675,66677,66686,66690,66694,66699,66701,66704,66705,66706,66707,66713,66718,66719,66720,66724,66732,66733,66734,66736,66737,66739,66746,66749,66751,66767,66769,66776,66777,66779,66780,66783,66787,66788,66791,66795,66796,66801,66804,66806,66809,66812,66822,66823,66824,66825,66832,66834,66835,66838,66839,66840,66842,66843,66844,66845,66855,66858,66860,66871,66875,66876,66877,66878,66879,66889,66898,66902,66910,66911,66912,66930,66932,66935,66936,66938,66939,66944,66947,66951,66954,66955,66959,66966,66968,66969,66972,66981,66984,66997,66998,67006,67012,67014,67018,67019,67022,67023,67035,67036,67039,67059,67063,67066,67069,67071,67072,67079,67081,67088,67100,67115,67118,67127,67129,67130,67131,67136,67139,67140,67143,67149,67150,67151,67152,67155,67156,67166,67167,67175,67185,67188,67191,67193,67198,67203,67210,67222,67235,67236,67242,67243,67248,67249,67251,67252,67256,67258,67260,67261,67268,67271,67274,67277,67278,67280,67284,67285,67286,67292,67293,67297,67303,67307,67311,67313,67323,67326,67337,67341,67345,67347,67352,67355,67356,67357,67361,67367,67368,67370,67374,67377,67378,67382,67384,67389,67392,67402,67414,67419,67430,67431,67433,67436,67443,67451,67463,67464,67467,67469,67473,67482,67489,67494,67497,67502,67503,67506,67511,67513,67514,67516,67517,67519,67520,67524,67525,67529,67530,67540,67546,67549,67552,67553,67554,67559,67576,67577,67595,67598,67601,67606,67608,67612,67613,67619,67623,67626,67636,67640,67645,67650,67654,67662,67665,67675,67687,67688,67692,67698,67705,67706,67712,67715,67718,67719,67721,67722,67727,67731,67732,67735,67741,67745,67746,67748,67750,67752,67754,67757,67763,67764,67769,67783,67785,67793,67798,67801,67807,67816,67826,67830,67838,67841,67843,67851,67854,67861,67863,67864,67865,67866,67876,67877,67880,67881,67882,67886,67887,67891,67899,67900,67901,67910,67914,67924,67930,67932,67937,67938,67945,67946,67948,67952,67955,67957,67963,67973,67975,67979,67982,67985,67987,67991,67998","risk03 training: n=128, paired mean=-2.3437547146695317, standard_error=1.6736064194508644, retail=5.2425465718101565, arb=-7.586301286585157, failures=0.","risk1 training: n=128, paired mean=0.6905629035367175, standard_error=1.2406302395903284, retail=-1.0337273645718756, arb=1.7242902680749999, failures=0.","risk15 training: n=128, paired mean=-0.7459784935484386, standard_error=0.2922150879673245, retail=-2.0510651935328124, arb=1.3050866999531239, failures=0.","risk4 training: n=128, paired mean=1.486275323125781, standard_error=1.7387624330179006, retail=-2.5839931373914067, arb=4.070268460515623, failures=0.","stop300 training: n=128, paired mean=0.029517631991406182, standard_error=0.4644356158625493, retail=-0.3377227980124999, arb=0.3672404299992191, failures=0.","stop700 training: n=128, paired mean=0.22572504803749996, standard_error=0.4900356074510643, retail=-0.8893548941828127, arb=1.1150799422124993, failures=0.","stop2000 training: n=128, paired mean=1.3258666725046873, standard_error=1.4258755210333234, retail=-3.0444939058929683, arb=4.370360578368751, failures=0.","nobid training: n=128, paired mean=2.388592933660938, standard_error=1.7499414371133646, retail=-1.536977996779688, arb=3.9255709304374995, failures=0.","nobridge training: n=128, paired mean=0.8724521614742178, standard_error=1.2533803962762575, retail=-0.028917160347656887, arb=0.901369321828906, failures=0.","nobuy training: n=128, paired mean=10.930293569367187, standard_error=9.535554959304028, retail=-2.5623807725031256, arb=13.492674341878905, failures=0.","stop2000 independent tuning validation, rejected: n=256, paired mean=-0.40588978306718715, standard_error=0.3112034410460009, retail=-2.5603339748519534, arb=2.1544441917824217, failures=0.","risk4 independent tuning validation, rejected: n=256, paired mean=-0.45357166648359365, standard_error=0.22285142548438205, retail=-1.7013164911523437, arb=1.2477448246613279, failures=0.","Late cutoff training: n=128, paired mean=9.040684003177343, standard_error=9.08674081509107, retail=-0.1121899156601562, arb=9.152873918835155, failures=0.","Late cutoff independent tuning validation: n=256, paired mean=0.05589705645117189, standard_error=0.029180254947752227, retail=0.00600291007539064, arb=0.04989414637421876, failures=0.","Late cutoff training gain was dominated by an avoided 1-cent ask jump loss on one tuning run. Superseded using tuning evidence before reading its candidate unseen scores; obsolete unseen job stopped.","Base attribution, 300 tuning seeds, executed prices 5..95 inclusive, mean edge by steps remaining: [{\"H\": \"1-249\", \"retail\": 0.16056895075672878, \"arb\": -0.09809270201768205}, {\"H\": \"250-499\", \"retail\": 0.18930773835970952, \"arb\": -0.2844064288000412}, {\"H\": \"500-749\", \"retail\": 0.3738467268160207, \"arb\": -0.35672793001525027}, {\"H\": \"750-999\", \"retail\": 0.5669112050037484, \"arb\": -0.39577183720582865}, {\"H\": \"1000-1249\", \"retail\": 0.5601112745663913, \"arb\": -0.481111541206634}, {\"H\": \"1250-1499\", \"retail\": 0.4363547550688882, \"arb\": -0.36719052948527164}, {\"H\": \"1500-1749\", \"retail\": 0.3059546578373457, \"arb\": -0.22941483532213305}, {\"H\": \"1750-2000\", \"retail\": 0.09503344788982246, \"arb\": -0.11269590951323306}]","Finer base attribution on 128 training seeds, bucket lower bounds 5,10,25,75 and last bucket through 95: {\"(25, 'SELL')\": {\"retail\": 0.011078166982183044, \"arb\": -0.04638417563046936}, \"(25, 'BUY')\": {\"retail\": 0.009202357679907076, \"arb\": -0.04617396016510546}, \"(75, 'SELL')\": {\"retail\": 0.0748308459547776, \"arb\": -0.08750533509944197}, \"(75, 'BUY')\": {\"retail\": 0.11187787789899373, \"arb\": -0.08661998826765481}, \"(10, 'BUY')\": {\"retail\": 0.24102707006831833, \"arb\": -0.24792516041618537}, \"(10, 'SELL')\": {\"retail\": 0.3223161566013057, \"arb\": -0.24721096646352186}, \"(5, 'BUY')\": {\"retail\": 0.7609062843376403, \"arb\": -0.8325548889431102}, \"(5, 'SELL')\": {\"retail\": 1.77964241489828, \"arb\": -1.0274385741966965}}","Suppress probes for inferred 25..75 cents, training: n=128, paired mean=0.08025268742577989, standard_error=0.00672211835827268, retail=-0.019454779003124836, arb=0.09970746641953017, failures=0.","Suppress probes for inferred 25..75 cents, independent tuning validation: n=256, paired mean=0.09900686986640617, standard_error=0.01299246608260675, retail=-0.0213190076113276, arb=0.12032587747539022, failures=0.","Uncapped probe removal rejected on runtime: first 20 PyPy timing pairs CPU seconds base=9.565857772, candidate=10.065920749999986. Wider belief intervals increased computation. Its candidate unseen scores were not read or used.","Suppress probes for inferred 5..95 cents, training only; too unstable to prefer: n=128, paired mean=0.2631463374796867, standard_error=1.4707455677823964, retail=-2.179476804853907, arb=2.4426231423054676, failures=0.","Scorer: 4000 simulations, seed-start 4000, workers 4, no sandbox, PyPy Python 3.11.13. Only local loader import caching added; simulator logic unchanged and each seed uses a fresh strategy instance. All three edge fields exactly match CPython 3.12.3 on 536 overlapping base tuning runs. Own reference mean=98.46762449920578; supplied reference=98.4694596619638.","Timing: same process, 200 simulations each on first 200 spread-1 tuning seeds; alternate strategy order by seed; five warm-up pairs excluded. PyPy CPU={\"base\": 67.69386683699999, \"noprobe_coarse\": 59.56842772100004}; PyPy wall={\"base\": 646.0590644488111, \"noprobe_coarse\": 569.0277491202578}. Reported seconds use CPU time to exclude scheduler contention.","Additional CPython 3.12.3 timing: CPU={\"base\": 198.93443038600012, \"noprobe_coarse\": 168.59853242000003}; wall={\"base\": 1080.0119895935059, \"noprobe_coarse\": 917.2892441758886}. Reported seconds use this completed CPython check.","Chosen central probe removal plus eight-node cap, training: n=128, paired mean=0.08026316100468608, standard_error=0.006719451425359987, retail=-0.019476922946093583, arb=0.09974008394062386, failures=0.","Chosen central probe removal plus eight-node cap, independent tuning validation: n=256, paired mean=0.09910090404257808, standard_error=0.01299223955585592, retail=-0.02129666862304631, arb=0.12039757266406222, failures=0.","Chosen frozen code, additional untouched tuning validation at spread-1 indices 1024..1279: n=256, paired mean=0.08136027859023404, standard_error=0.003932499658679818, retail=-0.017883886548047137, arb=0.09924416513789074, failures=0.","Cross-interpreter check: 128 evenly spaced reference seeds and 128 evenly spaced unseen spread-1 seeds for both base and candidate, all CPython 3.12.3 versus PyPy 3.11.13. Both spread-1 strategies match all three edge fields on all 128 seeds. Two reference mismatches, both spread 2: [{\"seed\": 4656, \"label\": \"reference\", \"failed\": false, \"differences\": {\"total_edge\": -0.6593801047999932, \"retail_edge\": -0.01413503620000256, \"arb_edge\": -0.6452450687000066}}, {\"seed\": 5093, \"label\": \"reference\", \"failed\": false, \"differences\": {\"total_edge\": -0.6693654351000191, \"retail_edge\": 0.09117200089997368, \"arb_edge\": -0.7605374359999928}}]. The exact cause of the supplied-reference mean mismatch was not isolated; base_mean_edge is the measured 4000-run PyPy mean, not the supplied value.","All 400 timing replay edge records match across CPython and PyPy, including both strategies on 200 tuning seeds.","Chosen frozen code, all 1969 unseen spread-1 seeds: {\"mean\": 0.06833408135627202, \"standard_error\": 0.006536226241850507, \"retail\": -0.022758032417978743, \"arb\": 0.09109211377465704}; no failures. All 900 other-spread results identical across every SimulationResult field. No code changes after final freeze."],"next":"Test enabling middle-price probes only when their information can change a worthwhile main quote. Retain finer information near the low-price inventory business. Measure belief-grid cost as well as order-management cost; removing probes alone can be slower. Use new tuning seeds and reserve new unseen seeds before selecting any further variant."}