{
  "approach": "Preserves the base's tiny probes, sub-tick probability filter, inside quotes and cheap YES crossing bids. Main quotes are split into four equal FIFO slices so downsizing can retain earlier queue positions. When the inferred competitor spread exceeds one tick, small extra bids and asks join the competitor's own prices after subtracting the core quote size and a $24 queue allowance; extra bid collateral and uncovered ask collateral are capped at 15% of remaining cash, with covered YES accounted for separately. Overflow is disabled in one-tick markets, while slicing remains active. The original refilling and downsizing thresholds are retained. Selected only on seeds 1000-1599, then frozen before the untouched holdout.",
  "blocked": null,
  "python_version": "3.12.3",
  "base_mean_edge": 102.33197908899267,
  "score": {
    "mean_edge": 108.42885016453633,
    "retail_edge": 136.803363239503,
    "arb_edge": -28.37451307498033,
    "simulations": 600,
    "seed_start": 1000,
    "failures": 0
  },
  "holdout": {
    "mean_edge": 96.32372908023733,
    "simulations": 600,
    "seed_start": 30000,
    "failures": 0
  },
  "code": "\"\"\"Stale-quote defence with tick probes, a sub-tick belief and cheap YES stock.\n\nEvery step the arbitrageur removes any order on the wrong side of p, so tiny\ntwo-sided probes around the estimate locate p to a tick; a grid filter narrows\nthat further.  Quotes sit one tick inside the competitor and are sized by the\nmarginal rule: one more share is worth quoting while the chance a retail order\nreaches it, times its edge, exceeds the expected arbitrage loss.  Near p=0 a\nretail buy pays almost its whole notional as edge, so YES is held to cover low\nasks.  That YES is bought when it is cheap: a large bid rests at tick 1 while p\nis above it, so the arbitrageur fills it on the crossing for about 0.1 tick a\nshare instead of nearly a full tick once p is near zero, and smaller bids sit on\nwhichever tick p is within 0.15 of.  Below tick 1 the estimate of p decays with\nthe time spent there, since no probe can see it.\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=0.7, 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\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        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            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 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 = 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            q1 = max(0.0, P['ydf1'] * min(H, P['Wf']) / (self.s / 100.0) - 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        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        # A small second level can collect retail overflow past finite competitor liquidity.\n        if self.s > 1 and 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 self.s > 1 and 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": "11786b375d91e18da0c3dea7df02c7e1f19a50ce01b2a4d6b6ed4f2d3016561d",
  "tried": [
    "Unmodified public simulator commit b244530ee2a6247b5f930830eeca9dd950da0e7e. Strategy imports only math and the provided strategy/types API; no additional runtime dependency.",
    "Scorer check, original downloaded base, seeds 0-599: mean 102.33197908899267; author reference 102.33197908899267. All means use the simulator's unmodified BatchResult properties on its JSON simulation results.",
    "All search used only seeds 1000-1599; no seed recognition or path replay. Code was frozen before any seed 30000-30599 evaluation.",
    "$12 queue allowance: mean 127.22704169152667, retail 154.95678004651919, arb -27.729738355054167; 120 simulations, seeds 1000-1119, failures 0.",
    "$48 queue allowance: mean 126.93579747502251, retail 153.86548802155167, arb -26.9296905466075; 120 simulations, seeds 1000-1119, failures 0.",
    "$72 queue allowance: mean 126.9539004960625, retail 153.88248284358832, arb -26.9285823475975; 120 simulations, seeds 1000-1119, failures 0.",
    "30% overflow cash cap: mean 127.5882457046625, retail 154.178727865985, arb -26.590482161384166; 120 simulations, seeds 1000-1119, failures 0.",
    "5% overflow cash cap: mean 127.5421087534775, retail 154.159139879665, arb -26.617031126251668; 120 simulations, seeds 1000-1119, failures 0.",
    "Ablation: four slices without overflow: mean 126.9661476238075, retail 153.86238479463833, arb -26.8962371709025; 120 simulations, seeds 1000-1119, failures 0.",
    "Ablation: overflow without slicing: mean 126.2295269839375, retail 153.26562571322498, arb -27.036098729361665; 120 simulations, seeds 1000-1119, failures 0.",
    "Ask-only overflow plus four slices: mean 127.02241450936167, retail 153.92638131881915, arb -26.903966809525834; 120 simulations, seeds 1000-1119, failures 0.",
    "Bid-only overflow plus four slices: mean 127.53852660144666, retail 154.1358246488442, arb -26.597298047468332; 120 simulations, seeds 1000-1119, failures 0.",
    "Direct graft: $24 queue allowance, 15% cash cap, four main FIFO slices: mean 127.58517782361668, retail 154.17237844593083, arb -26.587200622375835; 120 simulations, seeds 1000-1119, failures 0.",
    "Downsize ceiling 1.0 times desired: mean 126.22435418780417, retail 152.24320344374166, arb -26.018849256004167; 120 simulations, seeds 1000-1119, failures 0.",
    "Downsize ceiling 1.2 times desired: mean 127.54303525018416, retail 153.28824551703335, arb -25.745210266914167; 120 simulations, seeds 1000-1119, failures 0.",
    "Downsize ceiling 2.0 times desired: mean 127.38850836307667, retail 154.99598759247834, arb -27.60747922947; 120 simulations, seeds 1000-1119, failures 0.",
    "Eight main FIFO slices: mean 127.6877300509225, retail 154.40935318521585, arb -26.7216231343725; 120 simulations, seeds 1000-1119, failures 0.",
    "Four geometric FIFO slices: mean 127.30080667498001, retail 153.88312358130668, arb -26.58231690638; 120 simulations, seeds 1000-1119, failures 0.",
    "Overflow asks require existing YES coverage: mean 127.53931261056583, retail 154.16696258056834, arb -26.627649970071666; 120 simulations, seeds 1000-1119, failures 0.",
    "Promote surviving overflow orders into core quotes: mean 127.65497401557417, retail 154.2055295768875, arb -26.550555561379166; 120 simulations, seeds 1000-1119, failures 0.",
    "Refill below 50% of desired: mean 127.68792322930418, retail 152.53772053639335, arb -24.849797307166668; 120 simulations, seeds 1000-1119, failures 0.",
    "Refill below 90% of desired: mean 127.29834148615251, retail 154.90235841284417, arb -27.604016926739167; 120 simulations, seeds 1000-1119, failures 0.",
    "Two main FIFO slices: mean 127.33411579568416, retail 153.72399886472834, arb -26.3898830691025; 120 simulations, seeds 1000-1119, failures 0.",
    "Unchanged base comparison: mean 125.69520508572083, retail 153.04067831998086, arb -27.345473234341668; 120 simulations, seeds 1000-1119, failures 0.",
    "Allow 12000-share overflow ask marginal target: mean 115.86172724429792, retail 140.83767580540706, arb -24.975948561137916; 240 simulations, seeds 1000-1239, failures 0.",
    "Allow 6000-share overflow ask marginal target: mean 115.86172727795126, retail 140.83767580540706, arb -24.975948527484583; 240 simulations, seeds 1000-1239, failures 0.",
    "Retain and slice competitor-price overflow orders: mean 115.62949927979209, retail 140.79909020549167, arb -25.169590925730414; 240 simulations, seeds 1000-1239, failures 0.",
    "$12 queue allowance: mean 106.80242430536018, retail 137.59478190973502, arb -30.792357604386833; 600 simulations, seeds 1000-1599, failures 0.",
    "$48 queue allowance: mean 107.9394893155525, retail 136.59349075976348, arb -28.654001444225003; 600 simulations, seeds 1000-1599, failures 0.",
    "1% overflow cash cap: mean 107.81190760128, retail 136.81023194073333, arb -28.998324339467665; 600 simulations, seeds 1000-1599, failures 0.",
    "2% overflow cash cap: mean 107.9971982970085, retail 136.9199322773865, arb -28.922733980390166; 600 simulations, seeds 1000-1599, failures 0.",
    "5% overflow cash cap: mean 108.0265184352415, retail 136.99268779687665, arb -28.966169361648834; 600 simulations, seeds 1000-1599, failures 0.",
    "Ablation: four slices without overflow: mean 108.1039223982305, retail 136.56257430694333, arb -28.45865190872433; 600 simulations, seeds 1000-1599, failures 0.",
    "Ablation: overflow without slicing: mean 107.12681192719616, retail 136.258794162036, arb -29.13198223485917; 600 simulations, seeds 1000-1599, failures 0.",
    "Ask-only overflow plus four slices: mean 107.45569567391284, retail 136.60533909608583, arb -29.149643422184667; 600 simulations, seeds 1000-1599, failures 0.",
    "Bid-only overflow plus four slices: mean 108.22026839158849, retail 136.94926851712734, arb -28.729000125553835; 600 simulations, seeds 1000-1599, failures 0.",
    "Direct graft: $24 queue allowance, 15% cash cap, four main FIFO slices: mean 107.77941648794467, retail 137.01055490399065, arb -29.231138416059004; 600 simulations, seeds 1000-1599, failures 0.",
    "Disable added asks at competitor ask ticks 1-5: mean 108.27316115174699, retail 136.99450132664052, arb -28.721340174907667; 600 simulations, seeds 1000-1599, failures 0.",
    "Disable added asks at inferred one-tick spread: mean 108.23689994659134, retail 136.97037370128666, arb -28.733473754711667; 600 simulations, seeds 1000-1599, failures 0.",
    "Disable both additions at inferred one-tick spread: mean 108.23518925076917, retail 136.80257003045384, arb -28.56738077969667; 600 simulations, seeds 1000-1599, failures 0.",
    "Disable overflow at inferred one-tick spread: mean 108.42885016453633, retail 136.803363239503, arb -28.37451307498033; 600 simulations, seeds 1000-1599, failures 0.",
    "Disable slicing when inferred competitor spread is one tick: mean 107.79422866841867, retail 137.02861409042833, arb -29.23438542202117; 600 simulations, seeds 1000-1599, failures 0.",
    "Downsize ceiling 1.2 times desired: mean 107.53463893281832, retail 136.34352954769267, arb -28.808890614904666; 600 simulations, seeds 1000-1599, failures 0.",
    "Eight FIFO slices with no one-tick overflow: mean 108.40411290337983, retail 136.9599960685725, arb -28.555883165222998; 600 simulations, seeds 1000-1599, failures 0.",
    "Eight main FIFO slices: mean 107.78937137233667, retail 137.1799134422658, arb -29.3905420699595; 600 simulations, seeds 1000-1599, failures 0.",
    "No one-tick overflow; four slices, 1.2 downsize ceiling and 50% refill threshold: mean 106.5920064287895, retail 134.48859513342916, arb -27.89658870467017; 600 simulations, seeds 1000-1599, failures 0.",
    "Refill below 50% of desired: mean 106.91330123657251, retail 135.38151547406116, arb -28.468214237514996; 600 simulations, seeds 1000-1599, failures 0.",
    "Two FIFO slices with no one-tick overflow: mean 108.38417352163218, retail 136.57067664853383, arb -28.186503126919003; 600 simulations, seeds 1000-1599, failures 0.",
    "Unchanged base comparison: mean 107.2442092237515, retail 135.80165652288784, arb -28.557447299150834; 600 simulations, seeds 1000-1599, failures 0.",
    "Both queue conversion changes: mean 103.63006740421334, retail 127.09194949628834, arb -23.461882092066666; 120 simulations, seeds 1120-1239, failures 0.",
    "Convert bid queue allowance at the quoted bid: mean 103.63248776537166, retail 127.08457929555668, arb -23.452091530175; 120 simulations, seeds 1120-1239, failures 0.",
    "Convert main ask consumption into deeper-price notional: mean 104.08092550757, retail 127.444679665145, arb -23.363754157570835; 120 simulations, seeds 1120-1239, failures 0.",
    "Direct graft: $24 queue allowance, 15% cash cap, four main FIFO slices: mean 104.081143117255, retail 127.43731868677, arb -23.35617556951083; 120 simulations, seeds 1120-1239, failures 0.",
    "Subtract actually placed core size from overflow capacity: mean 104.09123183093084, retail 127.45455288075667, arb -23.363321049818335; 120 simulations, seeds 1120-1239, failures 0.",
    "Deduct stock-acquisition bids from overflow capacity: mean 106.91962503643832, retail 131.08737960077042, arb -24.16775456435625; 240 simulations, seeds 1120-1359, failures 0.",
    "No overflow bids below estimated probability 5%: mean 106.72175149414501, retail 130.86990975082668, arb -24.1481582567075; 240 simulations, seeds 1120-1359, failures 0.",
    "No tick-1 overflow bids: mean 106.92507608657542, retail 131.08596502834627, arb -24.160888941795; 240 simulations, seeds 1120-1359, failures 0.",
    "Skip tick-1 overflow bids when a stock-acquisition bid is placed there: mean 106.92017947214542, retail 131.08737960077042, arb -24.167200128649164; 240 simulations, seeds 1120-1359, failures 0.",
    "Disable both additions at inferred one-tick spread: mean 104.1545652094646, retail 135.87213407880458, arb -31.717568869392917; 240 simulations, seeds 1240-1479, failures 0.",
    "Disable overflow at inferred one-tick spread: mean 104.11190723790418, retail 135.82679518427375, arb -31.714887946423335; 240 simulations, seeds 1240-1479, failures 0.",
    "Disable slicing when inferred competitor spread is one tick: mean 104.14451388087583, retail 136.17434505245626, arb -32.029831171634164; 240 simulations, seeds 1240-1479, failures 0.",
    "Slice only main asks: mean 103.75794515692708, retail 135.71745925556917, arb -31.959514098707498; 240 simulations, seeds 1240-1479, failures 0.",
    "Slice only main bids: mean 103.96165139193666, retail 135.76352994871291, arb -31.801878556837085; 240 simulations, seeds 1240-1479, failures 0.",
    "1% overflow cash cap: mean 99.23299960336166, retail 134.16696761995874, arb -34.93396801656833; 240 simulations, seeds 1360-1599, failures 0.",
    "2% overflow cash cap: mean 99.37051721757793, retail 134.19932277066707, arb -34.8288055530625; 240 simulations, seeds 1360-1599, failures 0.",
    "Cap each overflow quote at 10 shares: mean 98.8920577464779, retail 133.97026737621917, arb -35.078209629714166; 240 simulations, seeds 1360-1599, failures 0.",
    "Observational fill attribution, combined, 600 tuning seeds 1000-1599: direct overflow edge -0.9881436755241678, bid edge -0.5711648241153344, ask edge -0.41697885140883334. This is not a causal strategy delta: inventory and cash paths change.",
    "Observational fill attribution, nodeep1, 600 tuning seeds 1000-1599: direct overflow edge -0.24914928773861383, bid edge -0.26708861322091443, ask edge 0.017939325482300594. This is not a causal strategy delta: inventory and cash paths change.",
    "final --sandbox check: 20 simulations, 20 failures. ImportError: Import of 'ntpath' is not allowed in sandbox mode.",
    "starter --sandbox check: 20 simulations, 20 failures. ImportError: Import of 'ntpath' is not allowed in sandbox mode.",
    "Frozen-code structural check passed: main quotes split into four valid same-price slices, and a forced reduction retained earlier FIFO slices. Imports are limited to math and the provided strategy/types API; no file or dynamic-code calls.",
    "The unmodified sandbox fails for both the final candidate and examples/starter_strategy.py before strategy loading because Python 3.12 pathlib imports disallowed ntpath; unsandboxed scores are reported, no sandbox patch used. Nothing was fabricated.",
    "Fresh full tuning paired candidate-minus-base mean 1.1846409407848328, paired standard error 0.31792630781541154; seeds 1000-1599, 600 simulations, zero failures.",
    "Holdout benchmark after freeze only: base mean 96.0405203261775, retail 124.3725985363135, arb -28.332078210128167; candidate-minus-base mean 0.2832087540598333, paired standard error 0.3651905827107454; 600 matched seeds 30000-30599, zero failures in both. No code changes or candidate reselection after holdout.",
    "Retained best eligible tuning candidate at freeze nodeep1; frozen sha256 11786b375d91e18da0c3dea7df02c7e1f19a50ce01b2a4d6b6ed4f2d3016561d; fresh full tuning mean 108.42885016453633, retail 136.803363239503, arb -28.37451307498033; untouched holdout mean 96.32372908023733, retail 125.01364997711549, arb -28.689920896869165; 600 simulations per range, zero unsandboxed failures."
  ],
  "next": "Test a matched-collateral ablation that reserves the modeled overflow cash without executing overflow orders, separating cash throttling from retail-burst capture. Direct overflow fill edge was negative even when total strategy edge improved. Validate any resulting mechanism on fresh preregistered seeds."
}