{
  "approach": "Returned the exact start file: no tested shrinking rule showed a broad discovery gain. Evaluated full modeled-loss sizing, suppressing ordinary quotes within one estimated tick, bid-only suppression, and pruning distant information probes, all guarded by self.s == 4 and quote ticks 5-95. No constants were swept and no strategy reads seeds. Froze the unchanged file before inspecting confirming seeds. The scorer exceeded five minutes, so final confirmation uses every second spread-4 seed in 90000-97999; other-spread checks use 150 per spread and timing uses 100 per file. The already-started full choosing loss map was retained as extra measurement.",
  "blocked": null,
  "spread": 4,
  "base_mean_edge": 108.64128535876738,
  "found": [
    "Measured start on 2050 spread-4 seeds in 30000-37999; price bands are quote ticks, Q1-Q4 are steps 0-499, 500-999, 1000-1499, 1500-1999; arb is signed edge.",
    "01-04/BUY/Q1: retail=0.07168052213802527; arb=-0.07631262097639736; net=-0.004632098838372095.",
    "01-04/BUY/Q2: retail=0.986998294364537; arb=-0.793614462149395; net=0.193383832215142.",
    "01-04/BUY/Q3: retail=2.76090692262651; arb=-2.0513697243577655; net=0.7095371982687446.",
    "01-04/BUY/Q4: retail=2.773503845546802; arb=-3.0246088796303954; net=-0.2511050340835932.",
    "01-04/SELL/Q1: retail=7.570077234986402e-06; arb=-3.6870078608737545e-05; net=-2.9300001373751143e-05.",
    "01-04/SELL/Q2: retail=1.2290292897747663; arb=-0.00254852398967054; net=1.2264807657850958.",
    "01-04/SELL/Q3: retail=9.663412368077477; arb=-0.2108579336574648; net=9.452554434420012.",
    "01-04/SELL/Q4: retail=48.263123035920806; arb=-1.4992435493748855; net=46.76387948654592.",
    "05-20/BUY/Q1: retail=1.4776439452229069; arb=-0.2370169745264084; net=1.2406269706964985.",
    "05-20/BUY/Q2: retail=3.811431916529045; arb=-0.7354726493433749; net=3.07595926718567.",
    "05-20/BUY/Q3: retail=4.197499762605294; arb=-0.8237867142206973; net=3.3737130483845967.",
    "05-20/BUY/Q4: retail=2.118753872906218; arb=-0.6721800755751663; net=1.4465737973310515.",
    "05-20/SELL/Q1: retail=2.3710132097571197; arb=-0.19472126701596598; net=2.1762919427411536.",
    "05-20/SELL/Q2: retail=9.85001351254699; arb=-0.7766572328394141; net=9.073356279707577.",
    "05-20/SELL/Q3: retail=18.956677155826533; arb=-1.5266644774375306; net=17.430012678389.",
    "05-20/SELL/Q4: retail=22.037514643516147; arb=-2.2395342707162067; net=19.79798037279994.",
    "21-40/BUY/Q1: retail=4.005824527896478; arb=-0.640846214048191; net=3.364978313848287.",
    "21-40/BUY/Q2: retail=2.6542156349968; arb=-0.4600830680761701; net=2.1941325669206297.",
    "21-40/BUY/Q3: retail=1.750659835523268; arb=-0.4470745580078713; net=1.3035852775153969.",
    "21-40/BUY/Q4: retail=0.6775947988639518; arb=-0.2802722876504346; net=0.3973225112135172.",
    "21-40/SELL/Q1: retail=4.322710978896685; arb=-0.6011256880099544; net=3.721585290886731.",
    "21-40/SELL/Q2: retail=3.492599209552277; arb=-0.47560294185467683; net=3.0169962676976003.",
    "21-40/SELL/Q3: retail=2.365520066825785; arb=-0.5470312602303243; net=1.8184888065954605.",
    "21-40/SELL/Q4: retail=0.9979836514696228; arb=-0.3673610712036379; net=0.6306225802659848.",
    "41-60/BUY/Q1: retail=2.9819597302618557; arb=-0.6234898737972793; net=2.3584698564645765.",
    "41-60/BUY/Q2: retail=1.8139372171468648; arb=-0.3751141550824306; net=1.4388230620644342.",
    "41-60/BUY/Q3: retail=1.0556407922363404; arb=-0.3112568688431777; net=0.7443839233931627.",
    "41-60/BUY/Q4: retail=0.3638257099830991; arb=-0.17216109181094222; net=0.19166461817215688.",
    "41-60/SELL/Q1: retail=3.1857422275638188; arb=-0.5116859437150831; net=2.674056283848736.",
    "41-60/SELL/Q2: retail=1.8478499872714564; arb=-0.33246113587581533; net=1.515388851395641.",
    "41-60/SELL/Q3: retail=1.1469742623875079; arb=-0.27910880961970086; net=0.867865452767807.",
    "41-60/SELL/Q4: retail=0.39818646975462374; arb=-0.17909088479917298; net=0.21909558495545076.",
    "61-80/BUY/Q1: retail=1.6917844372697746; arb=-0.2899876469259774; net=1.4017967903437971.",
    "61-80/BUY/Q2: retail=1.3530285706349603; arb=-0.24141125138427694; net=1.1116173192506833.",
    "61-80/BUY/Q3: retail=0.9180564593427986; arb=-0.28106605668768614; net=0.6369904026551124.",
    "61-80/BUY/Q4: retail=0.3840014648750545; arb=-0.16054497710746277; net=0.22345648776759172.",
    "61-80/SELL/Q1: retail=1.7029619966522571; arb=-0.23616663864378112; net=1.466795358008476.",
    "61-80/SELL/Q2: retail=1.1914787452491247; arb=-0.23842876813072406; net=0.9530499771184007.",
    "61-80/SELL/Q3: retail=0.8136134104682724; arb=-0.1919862403906852; net=0.6216271700775872.",
    "61-80/SELL/Q4: retail=0.30435369208067653; arb=-0.15101825387423928; net=0.15333543820643725.",
    "81-95/BUY/Q1: retail=0.2759814661742862; arb=-0.025584657233516987; net=0.2503968089407692.",
    "81-95/BUY/Q2: retail=0.8896586659736938; arb=-0.09043908760052685; net=0.7992195783731669.",
    "81-95/BUY/Q3: retail=1.3495797830590301; arb=-0.14654601354635502; net=1.2030337695126752.",
    "81-95/BUY/Q4: retail=1.2380863749725515; arb=-0.241824869815177; net=0.9962615051573744.",
    "81-95/SELL/Q1: retail=0.2238427776593563; arb=-0.0328480038796675; net=0.19099477377968882.",
    "81-95/SELL/Q2: retail=0.5554369000288819; arb=-0.07069132931455202; net=0.4847455707143299.",
    "81-95/SELL/Q3: retail=0.5376332747360898; arb=-0.10363637095231452; net=0.43399690378377526.",
    "81-95/SELL/Q4: retail=0.31132372222199833; arb=-0.08550573801008607; net=0.22581798421191226.",
    "96-99/BUY/Q1: retail=0.00013471115036194775; arb=-4.0644341474220386e-05; net=9.406680888772737e-05.",
    "96-99/BUY/Q2: retail=0.0784356587450312; arb=-0.000948205165497498; net=0.0774874535795337.",
    "96-99/BUY/Q3: retail=0.48352494629437376; arb=-0.018924154454932233; net=0.46460079183944153.",
    "96-99/BUY/Q4: retail=1.898204072532021; arb=-0.02892743948283676; net=1.8692766330491843.",
    "96-99/SELL/Q1: retail=0.002693275781457962; arb=-0.0006265021799747104; net=0.0020667736014832513.",
    "96-99/SELL/Q2: retail=0.060107564843049965; arb=-0.00883540905466247; net=0.051272155788387494.",
    "96-99/SELL/Q3: retail=0.14733123846141896; arb=-0.025758614585332896; net=0.12157262387608607.",
    "96-99/SELL/Q4: retail=0.15428143638342784; arb=-0.06059930364746467; net=0.09368213273596317.",
    "First 100 diagnostic seeds, ticks 5-95, estimated favorable distance <1 tick, ('ordinary', 'BUY'): retail=0.5480041671175796; arb=-1.20277705009787; net=-0.6547728829802905; tiny means fill quantity <=0.011 (not an order-type guarantee).",
    "First 100 diagnostic seeds, ticks 5-95, estimated favorable distance <1 tick, ('ordinary', 'SELL'): retail=0.29853216499954444; arb=-0.36271097722772877; net=-0.06417881222818433; tiny means fill quantity <=0.011 (not an order-type guarantee).",
    "First 100 diagnostic seeds, ticks 5-95, estimated favorable distance <1 tick, ('tiny', 'BUY'): retail=0.01490199414100466; arb=-0.3295345629267686; net=-0.3146325687857639; tiny means fill quantity <=0.011 (not an order-type guarantee).",
    "First 100 diagnostic seeds, ticks 5-95, estimated favorable distance <1 tick, ('tiny', 'SELL'): retail=0.015388884771190006; arb=-0.3293623075219269; net=-0.3139734227507369; tiny means fill quantity <=0.011 (not an order-type guarantee)."
  ],
  "holdout": {
    "mean_edge": 149.58875938279257,
    "retail_edge": 176.09510644082837,
    "arb_edge": -26.50634705805645,
    "failures": 0
  },
  "diff": {
    "mean": 0.0,
    "standard_error": 0.0,
    "retail": 0.0,
    "arb": 0.0,
    "trimmed": 0.0,
    "runs_up": 0,
    "runs_down": 0
  },
  "others_identical": {
    "runs": 450,
    "identical": true
  },
  "seconds": {
    "start": 163.0719555879332,
    "yours": 162.8405666820181
  },
  "code": "\"\"\"Crossing-cover base with isolated, untuned per-spread overrides stacked: each acts only in runs of its own competitor spread.\"\"\"\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 == 4:\n                # Censored compound-Poisson flow likelihood, using only our fills.\n                self.f4_exposure = [0, 0]\n                self.f4_events = [0, 0]\n                self.f4_weights = [[0.0] * 9, [0.0] * 9]\n                self.f4_means = [2.64 + i * (6.336 - 2.64) / 8 for i in range(9)]\n                # Positive aggregate flow is approximately lognormal; +0.065\n                # accounts for the occasional second arrival in a timestep.\n                self.f4_mu = [math.log(m) - 0.72 + 0.065 for m in self.f4_means]\n                self.f4_last = [None, None]\n                self.f4_rate = 0.1265\n                self.f4_mean = 4.488\n                self.f4_flow = self.f4_rate * self.f4_mean\n                self.f4_extreme = inv(1 - 1e-6)\n            if self.s == 2:\n                self.params.update(dict(W=150, ammo_pmax=0.02, fy=0.7, fu=0.25, Hu=500))\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 == 4:\n            for side, filled, bound in ((0, state.sell_filled_quantity, ca), (1, state.buy_filled_quantity, cb)):\n                last = self.f4_last[side]\n                if last is None:\n                    continue\n                tick, conv, cap, old_bound, ids = last\n                if (side == 0 and bound > old_bound + 1) or (side == 1 and bound < old_bound - 1):\n                    continue\n                # Track only the main quote, excluding probes and stock orders.\n                remaining = sum(o.remaining_quantity for o in state.own_orders if o.order_id in ids)\n                value = max(0.0, cap - remaining * conv)\n                self.f4_exposure[side] += 1\n                if value > 0.01:\n                    self.f4_events[side] += 1\n                    censored = remaining < 0.011\n                    logv = math.log(max(value, 0.01))\n                    weights = self.f4_weights[side]\n                    for i, mu4 in enumerate(self.f4_mu):\n                        z4 = (logv - mu4) / 1.2\n                        weights[i] += math.log(max(1e-12, 1.0 - cdf(z4))) if censored else -0.5 * z4 * z4\n            if state.step % 25 == 0:\n                exposure = sum(self.f4_exposure)\n                events = sum(self.f4_events)\n                event_probability = (events + 80.0 * (1.0 - math.exp(-0.1265))) / (exposure + 80.0)\n                self.f4_rate = max(0.077, min(0.176, -math.log(max(1e-6, 1.0 - event_probability))))\n                weights = [a + b for a, b in zip(*self.f4_weights)]\n                peak = max(weights)\n                weights = [math.exp(w - peak) for w in weights]\n                self.f4_mean = sum(m * w for m, w in zip(self.f4_means, weights)) / sum(weights)\n                self.f4_flow = self.f4_rate * self.f4_mean\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        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            if self.s == 4:\n                exp = math.exp\n                if self.bc == cs and 1.0 <= wid <= 6.0 and nb == 8 * wid:\n                    # On this stationary grid, spacing is exactly 1/8 tick.\n                    # Equal index distances therefore have bit-identical d*d*k.\n                    # Reuse exp values while retaining the original sum order.\n                    kernel = []\n                    c0 = cs[0]\n                    for ci in self.bc:\n                        d = c0 - ci\n                        d2 = d * d * k\n                        kernel.append(exp(d2) if d2 > -12.5 else 0.0)\n                    kernel = kernel[:0:-1] + kernel\n                    for i in range(nb):\n                        t = uni\n                        start = nb - 1 - i\n                        for wi, e in zip(self.bw, kernel[start:start + nb]):\n                            if e:\n                                t += wi * e\n                        ws.append(t)\n                else:\n                    previous = tuple(zip(self.bc, self.bw))\n                    for c in cs:\n                        t = uni\n                        for ci, wi in previous:\n                            d = c - ci\n                            d2 = d * d * k\n                            if d2 > -12.5:\n                                t += wi * exp(d2)\n                        ws.append(t)\n            else:\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            if self.s == 4:\n                ja = jb = 0.0\n                for p, w in jp:\n                    if x > p:\n                        ja += w * (x - p)\n                    else:\n                        jb += w * (p - x)\n            else:\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            if self.s == 4 and tail <= 1e-6:\n                return min(P['qmax'], math.exp(mu + P['sig_n'] * self.f4_extreme) / px)\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            if self.s == 4 and phat * 100 - t < P['dmin']:\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            if self.s == 4 and t - phat * 100 < P['dmin']:\n                return 0.0\n            a, b = AB(t / 100.0)\n            if t - phat * 100 < P['dmin']:\n                return 0.0\n            if self.s == 4:\n                tail = b * kA / max(self.f4_rate * a, 1e-30)\n                if a <= 0 or tail >= 1.0:\n                    return 0.0\n                return min(P['qmax'], math.exp(math.log(self.f4_mean) - 0.72 + 1.2 * (self.f4_extreme if tail <= 1e-6 else inv(1 - tail))) / (t / 100.0))\n            if self.s == 2 and phat < 0.1:\n                a = max(0.0, a - 0.0015 * (1 - min(1.0, state.yes_inventory / 3000.0)))\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            threshold = max(P['min_ahead'], 20 * 100.0 / comp) if self.s == 3 and step == -1 and 1 <= comp <= 5 else P['min_ahead']\n            if sticky and sum(o.remaining_quantity for o in orders if o.price_ticks == comp and o.order_id in self.ahead) >= threshold:\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        if self.s == 1 and ask_t == 2 and ask_t < ca and phat < 0.01:\n            qa *= 5\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            flow_scale = self.f4_flow / 0.6 if self.s == 4 else 1.0\n            target = min(flow_scale * P['ydem'] * min(H, P['W']) / x, capw)\n            full = min(flow_scale * 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 == 4:\n                stock_rate *= self.f4_flow / 0.6\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) or (self.s == 1 and (o.side is Side.SELL) and o.price_ticks <= 2 and o.order_id in self.ahead)):\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                if self.s == 2:\n                    ub = min(ub, max(0.0, free - 200 * min(1.0, H / 50.0)))\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:\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        if self.s == 4:\n            self.f4_last = [None, None]\n            # Eligibility is decided before observing fills, so depleted quotes\n            # remain in the sample as right-censored observations.\n            for side, tick, bound, conv, distance in (\n                (0, ask_t, ca, ask_t / 100.0, ask_t / 100.0 - phat),\n                (1, bid_t, cb, max(phat, 0.05), phat - bid_t / 100.0)):\n                if distance < max(0.01, 3.0 * self.st / 100.0):\n                    continue\n                if side == 0:\n                    if not (ask_t < ca or any(o.price_ticks == ask_t and o.order_id in self.ahead for o in asks)):\n                        continue\n                    orders = asks\n                    order_side = Side.SELL\n                else:\n                    if not (bid_t > cb or any(o.price_ticks == bid_t and o.order_id in self.ahead for o in bids)):\n                        continue\n                    if (qam > 0 and amt >= bid_t) or (q1 > 0 and bid_t <= 1):\n                        continue\n                    orders = bids\n                    order_side = Side.BUY\n                tracked = {o.order_id: o.remaining_quantity for o in orders if o.order_id in kept_ids and o.price_ticks == tick}\n                tracked.update({o.client_order_id: o.quantity for o in out if o.side is order_side and o.price_ticks == tick and o.client_order_id is not None})\n                cap = sum(tracked.values()) * conv\n                if cap >= 0.5:\n                    self.f4_last[side] = (tick, conv, cap, bound, tracked)\n        return actions + out\n",
  "code_sha256": "4bbf720ff34be09b441e84a7e0c1bf47cba036b5211c4118e44a597f941453db",
  "tried": [
    "Simulator pinned to https://github.com/danrobinson/prediction-market-challenge/tree/b244530ee2a6247b5f930830eeca9dd950da0e7e. No simulator execution or scoring rules changed; diagnostics wrap record_participant_fills and expose the strategy estimate only.",
    "Scorer: earlier artifact, python3 -m orderbook_pm_challenge run ../earlier.py --simulations 600 --seed-start 1000 --workers 4 --json; no sandbox; mean=108.64128535876738; reference=108.63974289615767; difference=0.001542462609705808; failures=0; wall_seconds=357.1153386980004. Cause of the small scorer-reference discrepancy was not established; exact reproduction is not claimed. Diagnostic jobs overlapped this timing. It exceeded 300 seconds, so final prescribed counts were halved; the already-running 2050-run choosing map was retained.",
    "Discovery uses all 516 actual spread-4 seeds in 30000-31999. The other choosing seeds were not used to invent a rule. All candidates act only when self.s == 4, and alter quotes only at ticks 5-95. No numerical constant sweep, seed access, or simulator-state access was used.",
    "Use full modeled marginal loss (kA=1 instead of the existing 0.7 weight, or 0.15 below estimated 5c) only when recomputing interior ordinary quote sizes, capped by original size; paired discovery n=516; mean=-3.1526353238062015; standard_error=0.6468124900668017; retail=-6.368976625063373; arb=3.2163413012323643; trimmed=-2.489832974647379; runs_up=189; runs_down=327; failures=0; rejected. Negative discovery means no candidate qualified to be kept; no confirming data was used to choose a change.",
    "Set ordinary bid and ask sizes to zero when favorable estimated distance is less than one full tick; paired discovery n=516; mean=-0.6041356469350775; standard_error=0.27035763483448205; retail=-1.2177203210527123; arb=0.6135846741054265; trimmed=-0.07750342001693582; runs_up=289; runs_down=227; failures=0; rejected. Negative discovery means no candidate qualified to be kept; no confirming data was used to choose a change.",
    "Set ordinary bid size to zero when favorable estimated distance is less than one full tick; retain asks and stock-cover rules; paired discovery n=516; mean=-1.2637687840753864; standard_error=0.31060358792312454; retail=-1.1641798541478685; arb=-0.09958892994089147; trimmed=-0.1857949210195555; runs_up=235; runs_down=281; failures=0; rejected. Negative discovery means no candidate qualified to be kept; no confirming data was used to choose a change.",
    "Skip interior BUY probes above ceil(hi) and SELL probes below floor(lo); retain probes at the interval boundary; paired discovery n=516; mean=-0.9216292464885655; standard_error=0.20980279718136155; retail=-0.5945587651383722; arb=-0.3270704814112403; trimmed=-0.49620100484455637; runs_up=212; runs_down=304; failures=0; rejected. Negative discovery means no candidate qualified to be kept; no confirming data was used to choose a change.",
    "Logging-only check: all 516 diagnostic runs exactly matched all start score/error fields; identical=True; largest difference between the sum of logged unrounded fill edges and total scored edge=3.744609955447231e-09. The map sum is divided by two because each fill is logged once by price and once by distance.",
    "Frozen output is byte-for-byte the start strategy, SHA256=4bbf720ff34be09b441e84a7e0c1bf47cba036b5211c4118e44a597f941453db. Final confirmation selects every second spread-4 seed in 90000-97999 (969 runs). Other-spread checks select the first 150 seeds of each actual spread 1, 2, 3 from 90000 onward (450 pairs). Timing uses 100 runs per file in one process, alternating evaluation order. All counts are explicit because the scorer exceeded five minutes.",
    "Rejected full-loss candidate also evaluated on the reserved every-second spread-4 seeds in 36000-37999, n=253; paired metrics={'mean': -1.5381469725177868, 'standard_error': 1.164015240331094, 'retail': -6.1131631144446645, 'arb': 4.575016141873913, 'trimmed': -1.6223600373648066, 'runs_up': 95, 'runs_down': 158}. This result was not used to tune any rule or select the output.",
    "Full start choosing map: n=2050; failures=0; mean_edge=155.99523135870106; retail_edge=180.19596961365767; arb_edge=-24.200738254963902. No coarse interior price-band/side/quarter bucket had negative net edge.",
    "Timing completed: {'runs_each': 100, 'identical': True, 'order': 'alternating', 'includes': 'SimulationEngine.run wall time, same process; factories and sampled configs prepared outside timed calls'}; seconds={'start': 163.0719555879332, 'yours': 162.8405666820181}; yours/start=0.9985810625433366. Other scoring jobs overlapped timing; alternating order controls shared load. All 100 complete SimulationResult objects matched.",
    "Sources: all five URLs were re-fetched and every quoted passage matched exactly; each quote is at most 500 characters."
  ],
  "next": "Study the inventory value of near-fair bids before removing them: direct fill losses do not capture the retail asks their YES inventory enables. Probe pruning also needs an information-value model; measure belief degradation and later retail loss, not only immediate probe cost."
}