{
  "approach": "Builds on the base probe orders, sub-tick probability filter, marginal sizing, FIFO retention and cheap YES collateral replenishment. The engine has finite competitor liquidity, so retail bursts can continue into a second price level even when the base has no reason to enlarge its best quote. This version keeps the core quotes and adds small bids/asks at competitor prices: desired overflow size subtracts the core quote and a $24 notional queue allowance, then each extra side's cash collateral is capped at 15% of remaining cash; YES coverage and uncovered ask collateral are accounted for separately. Main quotes are split into four FIFO slices so a reduction can cancel later slices while preserving earlier queue priority. Alternatives were screened on seeds 0-119 and the leading versions compared through seed 359. Code was then frozen before the full 600-run training score and the single held-out 600-run evaluation; there is no seed recognition.",
  "blocked": null,
  "python_version": "3.12.3",
  "base_mean_edge": 78.85441957511699,
  "score": {
    "mean_edge": 91.45548862403717,
    "retail_edge": 121.438310894165,
    "arb_edge": -29.98282227013267,
    "simulations": 600,
    "seed_start": 0,
    "failures": 0
  },
  "holdout": {
    "mean_edge": 88.57704157989234,
    "simulations": 600,
    "seed_start": 20000,
    "failures": 0
  },
  "code": "\"\"\"Probe-filter market maker with finite-queue retail overflow.\n\nThe original inside quotes and low-price YES replenishment remain the core.\nExtra orders at competitor prices deduct the core size and a $24 queue\nallowance from the marginal optimum, then use at most 15% of remaining cash\nper extra side. Covered YES is counted separately from cash collateral.\nMain orders are split into four FIFO slices so downsizing keeps older slices.\n\"\"\"\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=0.5, 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=1500.0, H1=100.0)\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\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        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 sb and eb:\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            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        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 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 not o.order_id.startswith('d') and o.side is Side.BUY and o.remaining_quantity > PROBE + 1e-9]\n        asks = [o for o in state.own_orders if not o.order_id.startswith('d') and 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 = 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 < P['ammo_pmax']:\n            wealth = state.cash + Y * phat\n            x = max(ask_t, ptick + 1) / 100.0\n            target = min(P['ydem'] * min(H, P['W']) / x, P['fy'] * wealth / max(phat, 0.005))\n            if Y < target:\n                t = max(1, min(99, int(math.ceil(ptick + 1e-9))))\n                if bid_t <= t < ask_t and t / 100.0 - phat < P['ammo_maxpay']:\n                    amt = t\n                    qam = min(P['ammo_q'], target - Y)\n\n        if P['pre'] > 0 and ca == 2 and phat < 0.01 and H > P['H1'] and Y < P['pre'] and not qam:\n            amt, qam = 1, min(P['ammo_q'], P['pre'] - 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 or o.order_id.startswith('d'):\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        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        # A small second level can collect retail overflow past finite competitor liquidity.\n        if cb >= 1 and cb < bid_t:\n            q = fl(max(0.0, min(qbid(cb) - 24 / max(phat, 0.05) - max(qb, kb), free * 0.15 / (cb / 100.0))))\n            if q >= 0.02:\n                out.append(PlaceOrder(side=Side.BUY, price_ticks=cb, quantity=q, client_order_id=self._oid('db')))\n                free -= q * cb / 100.0 + 1e-6\n        if ca <= 99 and ca > ask_t:\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            covnew = sum(o.quantity - self.res.get(o.client_order_id, 0.0)\n                         for o in out if o.side is Side.SELL and o.client_order_id)\n            cov = max(0.0, Y - covk - covnew - 0.1)\n            x = ca / 100.0\n            q = fl(max(0.0, min(qask(ca) - 24 / x - max(qa, ka), cov + max(0.0, free - 10.0) * 0.15 / (1 - x))))\n            if q >= 0.02:\n                oid = self._oid('da')\n                r = max(0.0, q - cov)\n                self.res[oid] = r\n                out.append(PlaceOrder(side=Side.SELL, price_ticks=ca, quantity=q, client_order_id=oid))\n                free -= r * (1 - x) + 1e-6\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        # Cancel oversized quotes in small pieces while retaining the oldest FIFO slice.\n        pieces = []\n        for order in out:\n            oid = order.client_order_id\n            if oid is None or oid.startswith('d') or order.quantity < 0.08:\n                pieces.append(order)\n                continue\n            cents = int(round(order.quantity * 100))\n            covered_left = order.quantity - self.res.pop(oid, 0.0)\n            ahead = oid in self.ahead\n            self.ahead.discard(oid)\n            for i in range(4):\n                q = (cents // 4 + (i < cents % 4)) / 100.0\n                child = oid + '_' + str(i)\n                pieces.append(PlaceOrder(side=order.side, price_ticks=order.price_ticks,\n                                         quantity=q, client_order_id=child))\n                if ahead:\n                    self.ahead.add(child)\n                if order.side is Side.SELL:\n                    covered = min(covered_left, q)\n                    covered_left -= covered\n                    self.res[child] = max(0.0, q - covered)\n        return actions + pieces\n",
  "code_sha256": "7c5c13f2dafd336547000c288fed67da5c9e62b1aafba5163dd78497e21ff4e9",
  "tried": [
    "Public simulator commit b244530ee2a6247b5f930830eeca9dd950da0e7e, unchanged. Base seeds 0-199: mean 78.85441957511699, retail 105.184836572219, arb -26.330416997007; 0 failures. Matched base seeds 0-119: 93.2985374865475. All search seeds were within 0-359; no seed/path recognition.",
    "Join finite competitor queue at the one-cent boundary and acquire YES there: mean 92.35711882426084, retail 122.14972982576666, arb -29.792611001457498; seeds 0-119, 0 failures.",
    "Join two-cent competitor asks while pre-buying, rather than wait without a quote: mean 93.173101174075, retail 122.52084790077583, arb -29.347746726663335; seeds 0-119, 0 failures.",
    "Join two-cent asks with a 100-share cap: mean 88.84368903745501, retail 116.69361363555332, arb -27.849924598090002; seeds 0-119, 0 failures.",
    "Quote more covered YES despite the usual marginal size limit: mean 90.82082436369, retail 124.52321861058, arb -33.70239424688584; seeds 0-119, 0 failures.",
    "Sell one-cent asks immediately rather than let two-cent competitor liquidity erode: mean 90.53069531296416, retail 117.32124510615083, arb -26.790549793130833; seeds 0-119, 0 failures.",
    "Join the 99-cent bid queue when improving would exceed the price limit: mean 93.2985374865475, retail 120.8182395590775, arb -27.51970207247583; seeds 0-119, 0 failures.",
    "Reduce irreversible cash lock into NO (fu=0.1, Hu=100): mean 93.1446400703, retail 121.42899029815166, arb -28.284350227795002; seeds 0-119, 0 failures.",
    "Permit uncovered low-price asks before the late-game collateral release: mean 90.66097391438751, retail 117.82132306422916, arb -27.160349149825; seeds 0-119, 0 failures.",
    "Higher flow allowance (lambda=0.30) for multiple arrivals within a step: mean 93.74487414915001, retail 122.5887117423075, arb -28.843837593114166; seeds 0-119, 0 failures.",
    "Use probability of at least one same-side arrival instead of arrival rate: mean 93.26114375301917, retail 120.3528404804175, arb -27.09169672741; seeds 0-119, 0 failures.",
    "Approximate the two-arrival compound-notional tail with moment-matched lognormal: mean 93.66139460012083, retail 121.14618815549834, arb -27.484793555353335; seeds 0-119, 0 failures.",
    "Use conditional probability above the bid for the retail sell cash-to-shares conversion: mean 93.3166835131, retail 120.8260015941775, arb -27.509318081039165; seeds 0-119, 0 failures.",
    "Split main quotes into four FIFO slices so downsizing retains earlier queue positions: mean 93.7466349772, retail 121.49400271120834, arb -27.7473677339775; seeds 0-119, 0 failures.",
    "Combine one-cent boundary joins with four FIFO quote slices: mean 92.86274950698333, retail 122.81677137228667, arb -29.95402186527583; seeds 0-119, 0 failures.",
    "Replace inside quotes with same-price competitor quotes in tight spreads, no queue allowance: mean 84.88927173284833, retail 116.48967099533, arb -31.600399262481666; seeds 0-119, 0 failures.",
    "Replace inside quotes in tight spreads; deduct $12 of competitor queue: mean 89.309227536465, retail 116.18904880943, arb -26.879821272976663; seeds 0-119, 0 failures.",
    "Replace inside quotes in tight spreads; deduct $24 of competitor queue: mean 89.26716574615168, retail 115.91090407668834, arb -26.643738330552498; seeds 0-119, 0 failures.",
    "Keep inside quotes; add competitor-price overflow quotes after $12 queue allowance and main size; cash cap 15% per added side: mean 96.84520272076584, retail 126.48073654474166, arb -29.635533823942502; seeds 0-119, 0 failures.",
    "Keep inside quotes; add competitor-price overflow quotes after $24 queue allowance and main size; cash cap 15% per added side: mean 97.118361028445, retail 125.79003964993667, arb -28.671678621455833; seeds 0-119, 0 failures.",
    "Additive $12-allowance overflow with 30% cash caps: mean 96.86672296213666, retail 126.48134518885917, arb -29.6146222266875; seeds 0-119, 0 failures.",
    "Additive overflow with $6 queue allowance and 15% cash caps: mean 94.79952115665333, retail 127.09935070905334, arb -32.299829552377496; seeds 0-119, 0 failures.",
    "Allocate bid/ask collateral proportionally to desired orders rather than bid-first budgeting: mean 93.29846804505334, retail 120.81820345092834, arb -27.519735405819997; seeds 0-119, 0 failures.",
    "Raise YES replenishment speed from 60 to 180 shares per step: mean 93.98581627083333, retail 121.91749356716667, arb -27.931677296305; seeds 0-119, 0 failures.",
    "Raise per-side maximum size from 3000 to 6000 shares: mean 93.52226921473749, retail 121.1380077500625, arb -27.615738535274165; seeds 0-119, 0 failures.",
    "Ablate additive overflow asks; keep only extra competitor-price bids: mean 93.36088468637084, retail 121.37183937638666, arb -28.010954689974167; seeds 0-119, 0 failures.",
    "Ablate additive overflow bids; keep only extra competitor-price asks: mean 96.470295801775, retail 125.34259381969834, arb -28.872298017878332; seeds 0-119, 0 failures.",
    "Permit low-price overflow asks only when covered by YES: mean 97.11598687786, retail 125.78907386592333, arb -28.673086988023332; seeds 0-119, 0 failures.",
    "Confirmation, base, untouched training seeds 120-359: mean 82.15752188448583, retail 110.25590729828083, arb -28.098385413782502; 0 failures.",
    "Confirmation, deep12, untouched training seeds 120-359: mean 85.43036945635792, retail 115.07965704440457, arb -29.649287588023334; 0 failures.",
    "Confirmation, deep24, untouched training seeds 120-359: mean 85.28122980217249, retail 114.3382604036754, arb -29.05703060149; 0 failures.",
    "Four FIFO slices plus $24-allowance overflow: mean 89.47983458476972, retail 118.76309346864889, arb -29.283258883869166; seeds 0-359, 0 failures. Candidate selected on training comparisons only; holdout started after code freeze.",
    "Selection on matched seeds 0-359: base mean 85.87119375183973; selected overflow plus FIFO slices mean 89.47983458476972; paired improvement 3.60864083293, paired standard error 0.7435466918485537. The $12 and $24 unsliced versions scored 89.23531387782722 and 89.22694021093001; selected before holdout.",
    "Final strategy --sandbox on 20 simulations: 20 failures; Python 3.12 pathlib imports ntpath, which the unmodified sandbox disallows before strategy loading. No sandbox workaround applied.",
    "Starter --sandbox on 20 simulations: 20 failures; Python 3.12 pathlib imports ntpath, which the unmodified sandbox disallows before strategy loading. No sandbox workaround applied.",
    "Frozen-code holdout benchmark only, no subsequent tuning: base mean 85.46780344973116; paired candidate-minus-base mean 3.1092381301611667, paired standard error 0.6153500934504534; seeds 20000-20599, 0 unsandboxed failures in either strategy. This remains one 600-run estimate, not a leaderboard result.",
    "Retained deepslices, frozen sha256 7c5c13f2dafd336547000c288fed67da5c9e62b1aafba5163dd78497e21ff4e9: full training mean 91.45548862403717, retail 121.438310894165, arb -29.98282227013267; holdout mean 88.57704157989234, retail 120.88134566640817, arb -32.30430408652567; 600 simulations per window and 0 unsandboxed failures."
  ],
  "next": "Infer remaining competitor queue from quote age and observed depletion, with censored retail-flow estimates, instead of a fixed notional allowance. Validate on new training runs and a newly reserved holdout. Also test combining the compound-arrival tail correction with the overflow mechanism; its standalone gain was small, so it was not automatically combined."
}