{"approach": "Retains the base passive quoter, queue-priority management and low-price YES inventory policy, but replaces the probability-space grid filter with a censored latent-score filter. Each step propagates a diffusion/jump Gaussian mixture, maps integer-price bounds through the compound-Poisson terminal-probability formula, and uses complete and partial own-order fills to weight arbitrage versus lognormal retail explanations. The estimate uses three-node conditional-CDF quadrature of the truncated mixture components; quote sizing uses the improved point estimate and one-step process noise without the former additional posterior-variance term. This combination was selected on allowed tuning seeds, with the code frozen before the independent 600-run holdout.", "blocked": null, "python_version": "3.12.3", "base_mean_edge": 78.85441957511699, "score": {"mean_edge": 93.445515230491, "retail_edge": 123.45701001467084, "arb_edge": -30.0114947841895, "simulations": 600, "seed_start": 0, "failures": 0}, "holdout": {"mean_edge": 89.58847361470433, "simulations": 600, "seed_start": 20000, "failures": 0}, "code": "\"\"\"Stale-quote defence with tick probes, a sub-tick belief and YES ammunition.\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.  That rule pulls\nquotes by itself when a move would hurt most.  Near p=0 a retail buy pays almost\nits whole notional as edge, so YES is held to cover low asks.\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\nBLAM = 0.0019\nBJS = 0.4\nLAT_LIK = 1.0\nLAT_JUMPINFO = 1.0\nMIXES = {}\nZTICKS = {}\ndef mixture(H):\n    if H not in MIXES:\n        v=math.exp(-H*BLAM)\n        arr=[]\n        for n in range(16):\n            arr.append((v,1.0/math.sqrt(max(H,1)*0.0004+n*BJS*BJS)))\n            v*=H*BLAM/(n+1)\n        MIXES[H]=arr\n    return MIXES[H]\ndef latent_tick(H,t):\n    if t<=0: return -12.0\n    if t>=100: return 12.0\n    key=(H,t)\n    if key not in ZTICKS:\n        mix=mixture(H)\n        z=inv(t/100.0)*math.sqrt(H*(0.0004+BLAM*BJS*BJS))\n        for _ in range(10):\n            prob=sum(w*cdf(z*r) for w,r in mix)\n            d=sum(w*r*pdf(z*r) for w,r in mix)\n            dz=max(-0.5,min(0.5,(prob-t/100.0)/max(d,1e-12)))\n            z-=dz\n            if abs(dz)<1e-8: break\n        ZTICKS[key]=z\n    return ZTICKS[key]\ndef normal_piece(mean,var,lo,hi):\n    sd=math.sqrt(max(var,1e-12))\n    a=(lo-mean)/sd;b=(hi-mean)/sd\n    if a>0:\n        mass=0.5*(math.erfc(a/SQ2)-math.erfc(b/SQ2))\n    elif b<0:\n        mass=0.5*(math.erfc(-b/SQ2)-math.erfc(-a/SQ2))\n    else:\n        mass=cdf(b)-cdf(a)\n    if mass<1e-200: return 0.0,mean,var\n    pa=pdf(a);pb=pdf(b)\n    shift=(pa-pb)/mass\n    m=mean+sd*shift\n    v=var*max(1e-8,1+(a*pa-b*pb)/mass-shift*shift)\n    return mass,m,v\n\n\ndef inverse_survival(q):\n    q=min(0.5,max(1e-300,q))\n    t=math.sqrt(-2.0*math.log(q))\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    for _ in range(5):\n        x+=(0.5*math.erfc(x/SQ2)-q)/max(pdf(x),1e-300)\n    return max(0.0,x)\n\ndef truncated_quantile(mean,sd,lo,hi,u):\n    a=(lo-mean)/sd;b=(hi-mean)/sd\n    if a>0:\n        qa=0.5*math.erfc(a/SQ2);qb=0.5*math.erfc(b/SQ2)\n        z=inverse_survival(qa+u*(qb-qa))\n    elif b<0:\n        qa=0.5*math.erfc(-a/SQ2);qb=0.5*math.erfc(-b/SQ2)\n        z=-inverse_survival(qa+u*(qb-qa))\n    else:\n        z=inv(cdf(a)+u*(cdf(b)-cdf(a)))\n    return min(hi,max(lo,mean+sd*z))\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 remember(self, state, actions):\n        prev = {o.order_id:(o.side,o.price_ticks,o.remaining_quantity) for o in state.own_orders}\n        for action in actions:\n            if isinstance(action, CancelOrder):\n                prev.pop(action.order_id,None)\n            elif isinstance(action, PlaceOrder):\n                prev[action.client_order_id]=(action.side,action.price_ticks,action.quantity)\n        self.previous_orders = prev\n\n    def belief(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.pcb is None:\n            spread=max(1,(ca-cb+1)//2)\n            lo,hi=cb+spread-1,ca-spread+1\n        else:\n            lo,hi=min(cb,self.pcb),max(ca,self.pca)\n        for o in state.own_orders:\n            if o.side is Side.BUY: lo=max(lo,o.price_ticks)\n            else: hi=min(hi,o.price_ticks)\n        if LAT_JUMPINFO and self.pcb is not None:\n            if ca>self.pca+1: lo=max(lo,ca-1)\n            if cb<self.pcb-1: hi=min(hi,cb+1)\n        self.pcb,self.pca=cb,ca\n        if lo>=hi: lo,hi=min(lo,hi)-0.001,max(lo,hi)+0.001\n        prev=getattr(self,'previous_orders',{})\n        survivors={o.order_id:o.remaining_quantity for o in state.own_orders}\n        filled=[[],[]]\n        cuts={lo,hi}\n        for oid,(side,tick,qty) in prev.items():\n            rest=survivors.get(oid,0.0)\n            if qty-rest>0.005:\n                filled[0 if side is Side.BUY else 1].append((tick,qty-rest,rest))\n                if lo<tick<hi: cuts.add(tick)\n        bounds=sorted(cuts)\n        if not hasattr(self,'zm'):\n            zl=latent_tick(H,lo);zh=latent_tick(H,hi)\n            self.zm=(zl+zh)/2; self.zv=(zh-zl)**2/12\n        components=[]\n        points=[]\n        for l,h in zip(bounds,bounds[1:]):\n            c=(l+h)/2\n            like=1.0\n            if LAT_LIK:\n                for side,records in enumerate(filled):\n                    rq=cash=0.0\n                    for tick,qty,rest in records:\n                        isarb=tick>c if side==0 else tick<c\n                        if not isarb:\n                            rq+=qty;cash+=qty*tick/100.0\n                    if rq<=0.005:\n                        like*=0.875\n                    else:\n                        value=rq*max(c/100.0,0.05) if side==0 else cash\n                        k=(math.log(max(value,1e-9))-(math.log(4.5)-0.72))/1.2\n                        tail=1-cdf(k)\n                        if any(rest>0.005 for tick,qty,rest in records):\n                            tail=pdf(k)/max(value*1.2,1e-9)\n                        like*=max(1e-8,0.125*tail)\n            zl=latent_tick(H,l);zh=latent_tick(H,h)\n            for jump,weight in [(0,1-BLAM),(BJS*BJS,BLAM)]:\n                mass,m,v=normal_piece(self.zm,self.zv+0.0004+jump,zl,zh)\n                components.append((weight*mass*like,m,v))\n                if mass > 1e-100:\n                    sd=math.sqrt(self.zv+0.0004+jump)\n                    aa=cdf((zl-self.zm)/sd)\n                    bb=cdf((zh-self.zm)/sd)\n                    for u,qw in [(0.1127016654,5/18),(0.5,4/9),(0.8872983346,5/18)]:\n                        zz=truncated_quantile(self.zm,sd,zl,zh,u)\n                        pp=sum(w*cdf(zz*r) for w,r in mixture(H))\n                        points.append((weight*mass*like*qw,pp))\n        total=sum(w for w,m,v in components)\n        if total<=1e-150:\n            zl=latent_tick(H,lo);zh=latent_tick(H,hi)\n            self.zm=max(zl,min(zh,self.zm));self.zv=0.0004\n        else:\n            m=sum(w*m for w,m,v in components)/total\n            v=sum(w*(v+(mm-m)**2) for w,mm,v in components)/total\n            self.zm,self.zv=m,max(v,1e-10)\n        mean=sum(w*cdf(self.zm/math.sqrt(1/r**2+self.zv)) for w,r in mixture(H))\n        if total > 1e-150 and points:\n            mean=sum(w*pp for w,pp in points)/total\n            v=max(0,sum(w*(pp-mean)**2 for w,pp in points)/total)\n        else:\n            deriv=sum(w*r*pdf(self.zm*r) for w,r in mixture(H))\n            v=deriv**2*self.zv\n        return min(0.999999,max(0.000001,mean)),v\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        phat, var_p = self.belief(state)\n        var_t = 0.0\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 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 = 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:\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, client_order_id=self._oid('m')))\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:\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, client_order_id=self._oid('p')))\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, client_order_id=self._oid('p')))\n                    self.pa.add(t)\n        self.remember(state, actions+out)\n        return actions + out\n", "code_sha256": "bedc511f82b2631a74848dbb41ba284399fd373c305bbb28639f1b8ad32b01a3", "tried": ["Unmodified public simulator commit b244530ee2a6247b5f930830eeca9dd950da0e7e.", "Base reproduction: seeds 0-199, mean_edge=78.85441957511699, retail_edge=105.184836572219, arb_edge=-26.330416997007, failures=0.", "Diagnostic oracle on seeds 0-79: true current probability before the next process move, posterior variance removed; hidden state used only in the scratch harness, never in candidate code: 103.50546918421375 on 80 seeds starting 0; failures=0; paired gap versus base=1.199275357668752; paired standard error=1.8070059573773884.", "Diagnostic oracle: exact current p before the next process move, posterior variance removed; hidden state used only in the scratch evaluation harness, never in candidate code: 85.78094321710999 on 200 seeds starting 0; failures=0; paired gap versus base=6.926523641993; paired standard error=1.496986080248015.", "Probability grid with soft competitor bounds and endpoint probes: mean_edge=95.09660957287625, retail_edge=122.5600791568575, arb_edge=-27.46346958396, seeds 0-79, failures=0.", "Widen probes to two ticks beyond competitor quotes: mean_edge=99.6647322721, retail_edge=130.72659550560624, arb_edge=-31.061863233445003, seeds 0-79, failures=0.", "Latent filter with soft competitor bounds and endpoint probes: mean_edge=99.98030696810625, retail_edge=130.43749195365248, arb_edge=-30.457184985507503, seeds 0-79, failures=0.", "Endpoint probes plus latent filter and exact local pricing model: mean_edge=100.84065323814625, retail_edge=130.88632415321374, arb_edge=-30.0456709149875, seeds 0-79, failures=0.", "Latent point estimate with original probability-grid sizing variance: mean_edge=100.85259174822001, retail_edge=130.23344109885124, arb_edge=-29.380849350618753, seeds 0-79, failures=0.", "Use latent point estimate only below 0.1 or above 0.9: mean_edge=101.03843682440501, retail_edge=130.12488909362, arb_edge=-29.086452269188747, seeds 0-79, failures=0.", "Full-fill likelihood using retail notional tails: mean_edge=101.43831072068875, retail_edge=130.53219450700377, arb_edge=-29.093883786219997, seeds 0-79, failures=0.", "Also use a lognormal density for partial retail fills: mean_edge=101.43999098862125, retail_edge=130.532639633995, arb_edge=-29.0926486453025, seeds 0-79, failures=0.", "Original grid with one-tick competitor movement likelihood and exact initial tick interval: mean_edge=101.5084954282975, retail_edge=130.51698971597625, arb_edge=-29.00849428757875, seeds 0-79, failures=0.", "Fill likelihood with conservative competitor bounds: mean_edge=101.686448483715, retail_edge=130.39637249953876, arb_edge=-28.709924015730003, seeds 0-79, failures=0.", "Latent-score censored Gaussian-mixture filter with fill-size likelihoods: mean_edge=101.7759139052925, retail_edge=130.43336821808626, arb_edge=-28.65745431270875, seeds 0-79, failures=0.", "Same latent filter without fill-size likelihoods: mean_edge=101.80440702413125, retail_edge=130.57123123663, arb_edge=-28.7668242124525, seeds 0-79, failures=0.", "Latent filter with soft competitor movement likelihoods: mean_edge=101.82737751959624, retail_edge=130.12340128505375, arb_edge=-28.29602376539375, seeds 0-79, failures=0.", "Latent filter plus exact local process derivative and jump probabilities for pricing: mean_edge=101.85583815474, retail_edge=130.94387182658625, arb_edge=-29.088033671764997, seeds 0-79, failures=0.", "Equal blend of latent and original point estimates, original sizing variance: mean_edge=101.87149974525501, retail_edge=130.46180259628375, arb_edge=-28.590302851031247, seeds 0-79, failures=0.", "Tempered Bayesian ensemble over three jump regimes: mean_edge=102.04484342039, retail_edge=130.6639850626475, arb_edge=-28.619141642160002, seeds 0-79, failures=0.", "Widen inside-spread probes from minimum radius 2 to 8 ticks: mean_edge=102.06761032526501, retail_edge=130.74961450482374, arb_edge=-28.68200417951125, seeds 0-79, failures=0.", "Use conservative previous/current competitor bounds: mean_edge=102.08823173820625, retail_edge=130.82400129481874, arb_edge=-28.73576955654125, seeds 0-79, failures=0.", "Remove probability clipping at 0.002 and 0.998: mean_edge=102.306193826545, retail_edge=130.83550361629875, arb_edge=-28.5293097896925, seeds 0-79, failures=0.", "Compound-Poisson mapping and derivative for quote risk: mean_edge=102.30633137377, retail_edge=131.28263920809624, arb_edge=-28.976307834255, seeds 0-79, failures=0.", "Latent filter with three-node quadrature of truncated components: mean_edge=102.67623347013375, retail_edge=130.78020147892875, arb_edge=-28.10396800873125, seeds 0-79, failures=0.", "Latent filter with half its posterior variance in quote risk: mean_edge=103.49561369725375, retail_edge=131.7938502346225, arb_edge=-28.298236537292503, seeds 0-79, failures=0.", "Integrate conditional Gaussian quote losses across original posterior grid: mean_edge=103.53003724934123, retail_edge=131.0500961143425, arb_edge=-27.520058864955, seeds 0-79, failures=0.", "Latent filter with quadrature and full-posterior expected quote losses: mean_edge=103.57730051988376, retail_edge=131.00589645891, arb_edge=-27.4285959389575, seeds 0-79, failures=0.", "Base filter, omit posterior variance from quote-risk kernel: mean_edge=103.8877459694775, retail_edge=132.41974233589625, arb_edge=-28.53199636634625, seeds 0-79, failures=0.", "Latent filter without sizing variance; exact process mapping for quote risk and one-step conditional mean: mean_edge=105.18279494551125, retail_edge=134.068786180785, arb_edge=-28.88599123520125, seeds 0-79, failures=0.", "Latent filter without sizing variance; assumed jump sigma 0.5: mean_edge=105.75182601239752, retail_edge=133.66953810678623, arb_edge=-27.917712094261248, seeds 0-79, failures=0.", "Latent filter, omit posterior variance from quote-risk kernel: mean_edge=106.03181633287375, retail_edge=133.65367914546, arb_edge=-27.621862812515, seeds 0-79, failures=0.", "Adaptive three-regime filter, choose one regime after posterior concentration: mean_edge=106.140992716385, retail_edge=133.97562492551998, arb_edge=-27.834632209017503, seeds 0-79, failures=0.", "Three-regime ensemble without posterior variance in sizing: mean_edge=106.29629770530126, retail_edge=134.04844296824373, arb_edge=-27.752145262828748, seeds 0-79, failures=0.", "Latent filter without sizing variance, soft competitor bounds and no extra probes: mean_edge=106.34657364844375, retail_edge=133.4397324727825, arb_edge=-27.09315882425375, seeds 0-79, failures=0.", "Latent filter without sizing variance; assumed jump sigma 0.3: mean_edge=106.42947523256251, retail_edge=133.90020549019, arb_edge=-27.4707302575175, seeds 0-79, failures=0.", "Shadow test on 40 base market paths (seeds 0-39): probability MSE base=1.682090466480573e-05, latent=1.4733850066893329e-05; below 0.01: base=1.601545634094883e-05, latent=3.1651488052364123e-06. Improved MSE alone did not reliably improve trading edge before removing the sizing variance penalty.", "Fresh tuning range, basevar0: mean_edge=103.04500233508651, retail_edge=134.04370700349548, arb_edge=-30.9987046683525, seeds 200-399, failures=0.", "Fresh tuning range, quadvar0: mean_edge=105.01681924175901, retail_edge=134.871368266129, arb_edge=-29.8545490243545, seeds 200-399, failures=0.", "Fresh tuning range, latentvar0: mean_edge=104.7287859569225, retail_edge=134.81716811187948, arb_edge=-30.0883821549175, seeds 200-399, failures=0.", "Fresh tuning range, posterior: mean_edge=100.236113963013, retail_edge=129.7878203585525, arb_edge=-29.5517063954985, seeds 200-399, failures=0.", "Full training comparison recorded after final selection, latentvar0: mean_edge=93.39623949441433, retail_edge=123.43135429950834, arb_edge=-30.035114805090664, seeds 0-599, failures=0.", "Full training comparison recorded after final selection, latentjs30: mean_edge=93.990494373242, retail_edge=123.58203911757766, arb_edge=-29.591544744339334, seeds 0-599, failures=0.", "Final candidate --sandbox: 0/20 successful simulations. Python 3.12 pathlib imports ntpath, which the framework sandbox import allowlist rejects before strategy loading.", "Unmodified examples/starter_strategy.py --sandbox: 0/20 successful simulations. Python 3.12 pathlib imports ntpath, which the framework sandbox import allowlist rejects before strategy loading.", "Base on all tuning seeds 0-599: mean_edge=87.41650726068066, retail_edge=116.13125849331949, arb_edge=-28.714751232636335, failures=0. Selected candidate paired training gain=6.029007969810333, paired standard error=0.8566271757666162.", "Selected code on matched seeds 0-199: mean_edge=84.8538367091625 versus base 78.85441957511699. This subset is from the frozen 600-run training pass, not a separate retuning run.", "Selected frozen quadsafe: seeds 0-599 mean_edge=93.445515230491, retail_edge=123.45701001467084, arb_edge=-30.0114947841895, failures=0; untouched seeds 20000-20599 mean_edge=89.58847361470433, retail_edge=122.69526589614732, arb_edge=-33.106792281423836, failures=0. No tuning used the holdout."], "next": "A late sigma=0.3 moment-filter comparison scored 93.990494373242 on seeds 0-599 but finished after final selection and holdout launch, so this entry stayed frozen. Reproduce that variant by setting BJS=0.3 and returning the Gaussian-moment probability computed before the quadrature override; evaluate it on new seeds before adopting it. Also try the exact retail-sell quantity Jacobian and multiple-arrival likelihood. The small 80-run oracle gap was misleading compared with the full 200-run gap."}