{"approach": "Return the supplied base code unchanged: the frozen spread-2 clock candidate failed the unseen-gain criterion. Candidate: raise the quote-size ceiling in the original analytic size calculation from 3000 to 9000 shares only with H<1000, with an exactly equivalent spread-2-only belief-filter optimization to pass timing. It gained on discovery (240 seeds), threshold validation (727), and untouched tuning confirmation (1000), but on all 1987 unseen spread-2 runs its paired mean was -0.29353827974192226 with standard_error 0.5034197358961245. Retail gained 0.3966028741839454 while arb edge changed -0.6901411539251132. A single worst paired loss was -926.2801617855001. No policy was retuned after reading the unseen result. Final code and every final score field describe the unchanged base, so all diff fields are zero. Baseline calibration: 4000 runs from seed 4000, workers=4, exactly reproduced 98.4694596619638 with no failures. All trial p thresholds use the strategy pre-trade probability estimate. Tuning seeds: all spread-2 seeds in 8000..15999; unseen: all spread-2 seeds in 60000..67999, selected using sample_config. Final timing runs the unchanged base twice on 200 spread-2 seeds in one process with alternating order and three excluded warmup pairs; small differences are timing variation between identical implementations. Final other-spread checks run the unchanged base twice on 300 seeds each of spreads 1,3,4, from 60000 on. Each seed uses SimulationEngine(sample_config(ChallengeConfig(), ParameterVariance(), seed=seed), factory, seed=seed). Base time decomposition over the first 240 tuning runs, mean retail and signed arb edges by H range: [{'H': [2000, 1501], 'retail': 6.430141496343333, 'arb': -2.036037415780833}, {'H': [1500, 1001], 'retail': 11.123840591824584, 'arb': -3.727808528725417}, {'H': [1000, 501], 'retail': 23.57349320622083, 'arb': -7.030496134926249}, {'H': [500, 1], 'retail': 62.20182206805375, 'arb': -12.197217762413334}].", "blocked": null, "python_version": "3.12.3", "spread": 2, "base_mean_edge": 98.4694596619638, "runs": {"tuning": 1967, "unseen": 1987}, "base_unseen": {"mean_edge": 75.37891657984132, "retail_edge": 102.41461084785999, "arb_edge": -27.035694268030902}, "holdout": {"mean_edge": 75.37891657984132, "retail_edge": 102.41461084785999, "arb_edge": -27.035694268030902, "failures": 0}, "diff": {"mean": 0.0, "standard_error": 0.0, "retail": 0.0, "arb": 0.0}, "others_identical": {"runs": 900, "identical": true}, "seconds": {"base": 75.59783254703507, "yours": 75.62080980278552}, "code": "\"\"\"Crossing-cover base with isolated, untuned spread overrides.\"\"\"\nimport math\nfrom orderbook_pm_challenge.strategy import BaseStrategy\nfrom orderbook_pm_challenge.types import CancelOrder, PlaceOrder, Side\n\nP = dict(lam_r=0.25, m=5.0, sig_n=1.2, lam_j=0.0019, sig_j=0.35, sig=0.02,\n qmax=3000.0, rmin=2, kA=0.7, kL=0.15, pL=0.05,\n ammo=1.0, ydem=0.4, W=200.0, fy=0.6, ammo_q=60.0, ammo_pmax=0.05, ammo_maxpay=0.02,\n fb=0.9, fu=0.7, xu=0.1, sticky=1.0, min_ahead=2.0, keep_hi=1.5, keep_lo=0.7, Hu=300.0, bins=8.0, filt=1.0, uni=0.01, jumpinfo=1.0, dmin=0.0, kLb=0.08, kLf=0.08, pinf=1.0, pre=0.0, H1=100.0,\n ydf=0.6, Wf=2000.0, g_hi=0.15, g_lo=0.15, qf=400.0, pmaxf=0.05, pre_gap=1.0,\n ydf1=0.6, g1=5.0, f1=0.6, a1=100.0, nb1=0.0, gs=1.0, p1t=1.0, m1=1.0, zd=1.0, pfl=0.0005)\nSQ2 = math.sqrt(2.0)\nSQ2PI = math.sqrt(2.0 * math.pi)\ndef cdf(x): return 0.5 * (1.0 + math.erf(x / SQ2))\ndef pdf(x): return math.exp(-0.5 * x * x) / SQ2PI\ndef inv(p):\n p = min(max(p, 1e-9), 1 - 1e-9)\n t = math.sqrt(-2.0 * math.log(min(p, 1 - p)))\n x = t - (2.515517 + 0.802853 * t + 0.010328 * t * t) / (1 + 1.432788 * t + 0.189269 * t * t + 0.001308 * t ** 3)\n x = -x if p < 0.5 else x\n for _ in range(2):\n d = pdf(x)\n if d < 1e-12:\n break\n x -= (cdf(x) - p) / d\n return x\ndef lpm(k):\n return pdf(k) + k * cdf(k)\ndef fl(q):\n return math.floor(q * 100 + 1e-9) / 100\n\nNODES = [(-2.2, .06), (-1.3, .17), (-0.6, .27), (0.6, .27), (1.3, .17), (2.2, .06)]\nPROBE = 0.01\n\n\nclass Strategy(BaseStrategy):\n def __init__(self):\n self.n = 0\n self.ahead = set() # main orders placed strictly ahead of any competitor order at their tick\n self.res = {} # order id -> uncovered quantity at placement\n self.bc = None # belief: sub-tick grid centres (ticks)\n self.bw = None # belief: weights\n self.st = 0.5 # last one-step sd in ticks\n self.pcb = self.pca = None\n self.pb = set()\n self.pa = set()\n self.tb = 0\n self.s = None # competitor spread parameter\n self.flow_notional = 0.0\n self.flow_exposure = 0\n self.last_ask_tick = None\n self.last_quote_exposed = False\n self.last_flow_ca = None\n self.last_flow_cap = 0.0\n self.last_flow_correction = 1.0\n self.params = P.copy()\n\n def _oid(self, tag):\n self.n += 1\n return tag + str(self.n)\n\n def on_step(self, state):\n H = max(1, state.steps_remaining)\n cb = state.competitor_best_bid_ticks or 0\n ca = state.competitor_best_ask_ticks or 100\n if self.s is None:\n self.s = max(1, (ca - cb + 1) // 2)\n if self.s == 1:\n self.params.update({'dmin': 0.3, 'pfl': 1e-06})\n if self.s == 3:\n self.params.update({'flow_prior': 200, 'flow_level': 0.6, 'flow_strength': 1.0, 'flow_safety': 2.0, 'flow_exposure_min': 5.0})\n P = self.params\n if self.s == 3 and self.last_quote_exposed and ca <= self.last_flow_ca + 1:\n self.flow_exposure += 1\n self.flow_notional += min(self.last_flow_cap, state.sell_filled_quantity * self.last_ask_tick / 100.0) * self.last_flow_correction\n lo, hi = cb, ca\n for o in state.own_orders:\n if o.side is Side.BUY:\n lo = max(lo, o.price_ticks)\n else:\n hi = min(hi, o.price_ticks)\n if P['pinf'] > 0:\n sb = {o.price_ticks for o in state.own_orders if o.side is Side.BUY and o.remaining_quantity <= PROBE + 1e-9}\n sa = {o.price_ticks for o in state.own_orders if o.side is Side.SELL and o.remaining_quantity <= PROBE + 1e-9}\n ea = self.pa - sa\n eb = self.pb - sb\n if sa and ea:\n lo = max(lo, min(max(ea), hi))\n if eb and (sb or min(eb) <= P['p1t']):\n hi = min(hi, max(min(eb), lo))\n if P['jumpinfo'] > 0 and self.pcb is not None:\n if ca > self.pca + 1:\n lo = max(lo, ca - 1)\n if cb < self.pcb - 1:\n hi = min(hi, cb + 1)\n self.pcb, self.pca = cb, ca\n if lo > hi:\n lo, hi = hi, lo\n # sub-tick belief over p_(t-1): predict with one-step noise, truncate to [lo, hi]\n wid = max(hi - lo, 1e-6)\n nb = max(2, min(48, int(round(wid * P['bins']))))\n cs = [lo + (i + 0.5) * wid / nb for i in range(nb)]\n if self.bc is None or P['filt'] <= 0:\n ws = [1.0 / nb] * nb\n else:\n sg = max(self.st, 0.6 * wid / nb)\n k = -0.5 / (sg * sg)\n ws = []\n uni = P['uni'] * sg\n for c in cs:\n t = uni\n for ci, wi in zip(self.bc, self.bw):\n d = c - ci\n d2 = d * d * k\n if d2 > -12.5:\n t += wi * math.exp(d2)\n ws.append(t)\n tot = sum(ws)\n ws = [w / tot for w in ws]\n self.bc, self.bw = cs, ws\n mean_t = sum(c * w for c, w in zip(cs, ws))\n var_t = max(sum(c * c * w for c, w in zip(cs, ws)) - mean_t * mean_t, 0.0)\n phat = min(max(mean_t / 100.0, 0.002), 0.998)\n var = P['sig'] ** 2 + P['lam_j'] * P['sig_j'] ** 2\n sd = math.sqrt(H * var)\n self.tb = self.tb + 1 if hi <= 1 else 0\n if self.tb > 0 and P['zd'] > 0:\n # below the last tick there is no probe: the score keeps walking away from it\n phat = min(phat, max(P['pfl'], cdf(inv(0.01) - P['zd'] * 0.02 * math.sqrt(self.tb) / sd)))\n z = inv(phat)\n Z = z * sd\n sp = pdf(z) / sd * P['sig']\n self.st = sp * 100.0\n s = math.sqrt(sp * sp + var_t / 1e4 + 1e-8)\n sd1 = math.sqrt(max(1.0, H - 1.0) * var)\n jp = [(cdf((Z + n * P['sig_j']) / sd1), w) for n, w in NODES]\n lj = P['lam_j']\n\n def AB(x):\n k = (x - phat) / s\n a = s * lpm(k)\n b = a - (x - phat)\n ja = sum(w * max(0.0, x - p) for p, w in jp)\n jb = sum(w * max(0.0, p - x) for p, w in jp)\n return (1 - lj) * a + lj * ja, (1 - lj) * b + lj * jb\n\n if H == 1:\n def AB(x):\n return (1 - phat) * x, phat * (1 - x)\n rho = P['lam_r'] * 0.5\n mu = math.log(P['m']) - 0.5 * P['sig_n'] ** 2\n kA = P['kL'] if phat < P['pL'] else P['kA']\n\n def qsize(loss, gain, px):\n loss *= kA\n if gain <= 0:\n return 0.0\n tail = loss / (rho * gain)\n if tail >= 1.0:\n return 0.0\n return min(P['qmax'], math.exp(mu + P['sig_n'] * inv(1 - max(tail, 1e-6))) / px)\n\n ptk = phat * 100\n def qbid(t):\n if not 1 <= t <= 99:\n return 0.0\n a, b = AB(t / 100.0)\n if phat * 100 - t < P['dmin']:\n return 0.0\n if P['nb1'] > 0 and self.s == 1 and t == 1 and ptk < 1.0:\n return 0.0\n if phat < P['pL']:\n ytg = P['ydem'] * min(H, P['W']) / max(ca - 1, ptk + 1) * 100.0\n a *= (P['kLb'] if state.yes_inventory < ytg else P['kLf']) / P['kL']\n return qsize(a, b, max(phat, 0.05))\n\n def qask(t):\n if not 1 <= t <= 99:\n return 0.0\n a, b = AB(t / 100.0)\n if t - phat * 100 < P['dmin']:\n return 0.0\n return qsize(b, a, t / 100.0)\n\n bids = [o for o in state.own_orders if o.side is Side.BUY and o.remaining_quantity > PROBE + 1e-9]\n asks = [o for o in state.own_orders if o.side is Side.SELL and o.remaining_quantity > PROBE + 1e-9]\n sticky = P['sticky'] > 0\n def top(orders, comp, step):\n if sticky and sum(o.remaining_quantity for o in orders if o.price_ticks == comp and o.order_id in self.ahead) >= P['min_ahead']:\n return comp\n return comp + step\n bid_t = top(bids, cb, 1)\n ask_t = top(asks, ca, -1)\n qb = qbid(bid_t)\n qa = qask(ask_t)\n\n Y = state.yes_inventory\n if ask_t == 1 and H > P['H1'] and P['pre'] > 0:\n qa = qa if Y >= P['a1'] > 0 else 0.0 # let the competitor's 2-tick ask erode instead of fronting it for nothing\n # ammunition: hold YES so that low asks are covered\n ptick = phat * 100\n amt = 0\n qam = 0.0\n if P['ammo'] > 0 and ask_t >= 2 and phat < max(P['ammo_pmax'], P['pmaxf']):\n wealth = state.cash + Y * phat\n x = max(ask_t, ptick + 1) / 100.0\n capw = P['fy'] * wealth / max(phat, 0.005)\n target = min(P['ydem'] * min(H, P['W']) / x, capw)\n full = min(P['ydf'] * min(H, P['Wf']) / x, capw) if phat < P['pmaxf'] else 0.0\n t = max(1, min(99, int(math.ceil(ptick + 1e-9))))\n g = t - ptick\n if Y < full and g <= P['g_hi'] and bid_t <= t < ask_t:\n amt, qam = t, min(P['qf'], full - Y) # a tick p has just crossed: nearly free\n elif Y < target and phat < P['ammo_pmax'] and bid_t <= t < ask_t and t / 100.0 - phat < P['ammo_maxpay']:\n amt, qam = t, min(P['ammo_q'], target - Y)\n elif Y < full and t >= 2 and 1.0 - g <= P['g_lo']:\n amt, qam = t - 1, min(P['qf'], full - Y) # rest just under p: filled only on the crossing, or by retail\n\n if P['pre'] > 0 and ca == 2 and phat < 0.01 and H > P['H1'] and Y < P['pre'] and not qam and 1.0 - ptick < P['pre_gap']:\n amt, qam = 1, min(P['ammo_q'], P['pre'] - Y)\n q1 = 0.0\n if P['ydf1'] > 0 and P['m1'] < ptick < P['g1'] + 1.0 and amt != 1:\n stock_rate = P['ydf1']\n if self.s == 3:\n flow = (self.flow_notional + P['flow_prior'] * P['flow_level']) / (P['flow_prior'] + self.flow_exposure)\n scale = max(0.5, min(2.0, flow / P['flow_level']))\n stock_rate *= 1.0 + P['flow_strength'] * (scale - 1.0)\n q1 = max(0.0, stock_rate * min(H, P['Wf']) / (self.s / 100.0) - Y)\n\n # Bridge expected retail demand until another tick crossing is available.\n if 0.02 < phat < 0.1:\n ct = max(2, min(99, int(math.floor(ptick))))\n wealth = state.cash + Y * phat\n goal = min(1 * qa, 0.3 * max(wealth, 0.0) / phat)\n if Y < goal and ct < ask_t:\n amt, qam = ct, min(3000.0, goal - Y)\n # order management\n actions = []\n free = state.free_cash - 2.0\n keep_ask = 0.0\n new_b = []\n new_a = []\n def cancel(o):\n nonlocal free\n actions.append(CancelOrder(o.order_id))\n x = o.price_ticks / 100.0\n if o.side is Side.BUY:\n free += x * o.remaining_quantity\n else:\n free += (1 - x) * min(self.res.get(o.order_id, 0.0), o.remaining_quantity)\n self.ahead.discard(o.order_id)\n self.res.pop(o.order_id, None)\n for o in state.own_orders:\n if o.remaining_quantity <= PROBE + 1e-9:\n cancel(o)\n kept_ids = set()\n def manage(orders, t, q, comp):\n kept = 0.0\n for o in orders:\n if o.price_ticks == t and q > 0 and kept + o.remaining_quantity <= max(q * P['keep_hi'], 1.0):\n kept += o.remaining_quantity\n kept_ids.add(o.order_id)\n else:\n cancel(o)\n return kept\n kb = manage(bids, bid_t, qb, cb)\n ka = manage(asks, ask_t, qa, ca)\n add_b = (qb - kb) if (kb < qb * P['keep_lo'] and bid_t != cb) else 0.0\n add_a = (qa - ka) if (ka < qa * P['keep_lo'] and ask_t != ca) else 0.0\n\n budget = P['fb'] * max(free, 0.0)\n cost = add_b * bid_t / 100.0 + qam * amt / 100.0\n if cost > budget:\n f = budget / cost\n add_b *= f\n qam *= f\n cost = budget\n out = []\n q1 = min(q1, P['f1'] * max(budget - cost, 0.0) * 100.0)\n if q1 >= 0.01:\n out.append(PlaceOrder(side=Side.BUY, price_ticks=1, quantity=fl(q1)))\n free -= fl(q1) / 100.0 + 1e-6\n if amt and qam >= 0.01:\n q = fl(qam)\n out.append(PlaceOrder(side=Side.BUY, price_ticks=amt, quantity=q))\n free -= q * amt / 100.0 + 1e-6\n if bid_t >= 1 and add_b >= 0.01:\n q = fl(add_b)\n oid = self._oid('b')\n out.append(PlaceOrder(side=Side.BUY, price_ticks=bid_t, quantity=q, client_order_id=oid))\n free -= q * bid_t / 100.0 + 1e-6\n if bid_t > cb:\n self.ahead.add(oid)\n if ask_t <= 99 and add_a >= 0.01:\n x = ask_t / 100.0\n covk = sum(o.remaining_quantity - min(self.res.get(o.order_id, 0.0), o.remaining_quantity)\n for o in asks if o.order_id in kept_ids)\n cov = max(0.0, Y - covk - 0.1)\n unc = max(0.0, add_a - cov)\n if unc > 0:\n ub = max(0.0, free - (1 - P['fu']) * max(state.cash, 0.0)) if x >= P['xu'] else 0.0\n if H < P['Hu'] and phat < 0.05:\n ub = max(0.0, free * (1 - H / P['Hu']))\n unc = min(unc, ub / (1 - x))\n q = fl(min(add_a, cov + unc))\n if q >= 0.01:\n oid = self._oid('a')\n out.append(PlaceOrder(side=Side.SELL, price_ticks=ask_t, quantity=q, client_order_id=oid))\n r = max(0.0, q - cov)\n self.res[oid] = r\n free -= r * (1 - x) + 1e-6\n if ask_t < ca:\n self.ahead.add(oid)\n\n # probes: tiny orders that the arbitrageur removes when p crosses them\n f = int(math.floor(ptick + 1e-9))\n r = max(int(P['rmin']), int(math.ceil(2.0 * s * 100)))\n self.pb = set()\n self.pa = set()\n if free > 1.0:\n for t in range(f, f + r + 1):\n if cb < t < ca and 1 <= t <= 99:\n out.append(PlaceOrder(side=Side.BUY, price_ticks=t, quantity=PROBE))\n self.pb.add(t)\n for t in range(f + 1 - r, f + 2):\n if cb < t < ca and 1 <= t <= 99:\n out.append(PlaceOrder(side=Side.SELL, price_ticks=t, quantity=PROBE))\n self.pa.add(t)\n if self.s == 3:\n self.last_ask_tick = ask_t\n self.last_flow_ca = ca\n exposed_qty = ka + sum(o.quantity for o in out if o.side is Side.SELL and o.price_ticks == ask_t and o.quantity > PROBE)\n self.last_flow_cap = exposed_qty * ask_t / 100.0\n self.last_quote_exposed = ask_t / 100.0 > phat + max(0.005, P['flow_safety'] * self.st / 100.0) and self.last_flow_cap >= P['flow_exposure_min']\n if self.last_quote_exposed:\n logcap = math.log(self.last_flow_cap)\n mu_flow = math.log(P['m']) - 0.5 * P['sig_n'] ** 2\n clipped = P['m'] * cdf((logcap - mu_flow - P['sig_n'] ** 2) / P['sig_n']) + self.last_flow_cap * (1.0 - cdf((logcap - mu_flow) / P['sig_n']))\n self.last_flow_correction = min(3.0, P['m'] / max(clipped, 0.01))\n return actions + out\n", "code_sha256": "dcf68e0c9a7b06f90cf70a833357b60e2208b5b3e2971e7dddf02986d4747076", "tried": ["short_stock (cap Wf at 200): discovery n=240 paired mean=-7.525447739907084, standard_error=1.8374568240441793, failures=0.", "late_stock (stock rates 0.3 for H>500 and 1.2 otherwise): discovery n=240 paired mean=-4.225506033420417, standard_error=1.3934681010197167, failures=0.", "stock_ramp (stock rates 0.15 for H>1000, 0.3 for H>500, otherwise 0.6): discovery n=240 paired mean=-4.002366506829167, standard_error=1.3230122045527284, failures=0.", "late_size (double every ask size for H<500): discovery n=240 paired mean=-3.788672777959167, standard_error=2.2610725627043005, failures=0.", "all_uncovered (extend Hu to 2000): discovery n=240 paired mean=-3.6918022673295834, standard_error=1.846249900390694, failures=0.", "late_uncovered (extend uncovered ask window Hu from 300 to 1000): discovery n=240 paired mean=-2.96698403758875, standard_error=1.7567860620568938, failures=0.", "caution_size (halve main bid and ask sizes for H>1000; multiply ask size by 1.5 for H<500): discovery n=240 paired mean=-2.91502056963125, standard_error=1.1707818446596772, failures=0.", "risk_clock (double risk for H>1000, halve risk for H<300 and p<0.05): discovery n=240 paired mean=-2.7120294939729157, standard_error=0.9941190667609524, failures=0.", "latestockquarter (quarter those stock rates for H<500): discovery n=240 paired mean=-1.8380361467054172, standard_error=0.5247935673238775, failures=0.", "stock600 (cap full stock horizon Wf at 600): discovery n=240 paired mean=-1.4561822291670836, standard_error=0.6325963886278756, failures=0.", "latestockhalf (halve full and tick-1 stock rates for H<500): discovery n=240 paired mean=-0.9007738095833338, standard_error=0.3931714054841988, failures=0.", "midask4 (quadruple ask risk for H<1000 and p>0.05): discovery n=240 paired mean=-0.8577405570441664, standard_error=0.2606038485362174, failures=0.", "lateaskoff (suppress main asks for H<500 and p>0.05): discovery n=240 paired mean=-0.6923786625704167, standard_error=0.17990782943895708, failures=0.", "early_linear (multiply low-price risk weights by 1+H/1000): discovery n=240 paired mean=-0.6635519120966672, standard_error=1.3065304978622436, failures=0.", "lateask4 (quadruple ask risk for H<500 and p>0.05): discovery n=240 paired mean=-0.3192225755083338, standard_error=0.11738303887990896, failures=0.", "latelowask4 (quadruple ask risk for H<500 and 0.01700): discovery n=240 paired mean=-0.17885014697124993, standard_error=0.8966976641318596, failures=0.", "lastask4 (quadruple ask risk for H<250 and p>0.05): discovery n=240 paired mean=-0.09797053260750033, standard_error=0.04308253873278988, failures=0.", "lateask2 (double ask risk for H<500 and p>0.05): discovery n=240 paired mean=-0.09605055035833335, standard_error=0.09047368918481996, failures=0.", "uncovered30 (shorten Hu to 30): discovery n=240 paired mean=-0.0876546319174997, standard_error=0.19285298389185415, failures=0.", "latehighoff (suppress main asks for H<500 and p>0.2): discovery n=240 paired mean=-0.06952160909208377, standard_error=0.03618654814027958, failures=0.", "stock1000 (cap full stock horizon Wf at 1000): discovery n=240 paired mean=-0.0687405637108333, standard_error=0.09227916969370503, failures=0.", "uncovered100 (shorten Hu to 100): discovery n=240 paired mean=-0.005837766334583272, standard_error=0.1740540732046409, failures=0.", "last_depth (raise qmax to 12000 for H<100): discovery n=240 paired mean=0.0, standard_error=0.0, failures=0.", "early_caution4 (quadruple low-price risk weights for H>700): discovery n=240 paired mean=0.18910907911041638, standard_error=0.37676710703583, failures=0.", "lastlowask2 (double ask risk for H<200 and 0.01700): discovery n=240 paired mean=0.32910606601250075, standard_error=0.21717202341502323, failures=0.", "late_depth (raise qmax to 9000 for H<300): discovery n=240 paired mean=0.33180672905666647, standard_error=0.16083365011969558, failures=0.", "depth500 (raise qmax to 9000 for H<500): discovery n=240 paired mean=0.4038461345416666, standard_error=0.21265631499919543, failures=0.", "lowdepth500 (raise qmax to 9000 for H<500 and estimated p<0.01): discovery n=240 paired mean=0.4038461345416666, standard_error=0.21265631499919543, failures=0.", "depth1000 (raise qmax to 9000 for H<1000): discovery n=240 paired mean=0.414599999313333, standard_error=0.21284817688577232, failures=0.", "early_caution: independent validation n=727 paired mean=0.15032315176065988, standard_error=0.14593907502183337, failures=0.", "late_depth: independent validation n=727 paired mean=0.10383952480316386, standard_error=0.04497104369527749, failures=0.", "depth500: independent validation n=727 paired mean=0.2627081871148555, standard_error=0.16025509601031399, failures=0.", "depth1000: independent validation n=727 paired mean=0.40646617256464934, standard_error=0.16729869900305078, failures=0.", "Combined early caution H>700 and deeper ceiling H<300: validation n=727 paired mean=0.24471911476712485, standard_error=0.1507338564718177. Rejected in favor of one ceiling schedule.", "Initial emitted clock policy timing, 200 paired runs in one process: {'base': 70.99932690197602, 'yours': 71.04483156977221}. A 0.064% slowdown prompted runtime optimization without changing trading decisions.", "Repeated variance and inverse-normal constant cache: exact full-result equivalence on all 1967 tuning seeds, but rejected for slowdown; 200-pair seconds={'base': 71.47015131218359, 'yours': 72.04312426457182}.", "Spread-2-only belief-filter optimization reuses previous grid pairs and local math.exp binding; exact full-result equivalence on all 1967 tuning seeds. Frozen candidate timing 200 pairs={'base': 68.28434295672923, 'yours': 68.09812956117094}.", "Selected qmax=9000 only when H<1000 and s=2: untouched tuning confirmation n=1000 paired mean=0.5348215363022004, standard_error=0.1629970127024963, failures=0.", "Frozen rejected candidate over all tuning n=1967 paired mean=0.47271298606603984, standard_error=0.10657121953741786, failures=0.", "Rejected frozen candidate on unseen spread-2 n=1987 paired mean=-0.29353827974192226, standard_error=0.5034197358961245, failures=0; 900 complete results of other spreads identical; timing seconds={'base': 68.28434295672923, 'yours': 68.09812956117094}.", "Unseen failure mechanism: paired retail=0.3966028741839454, arb=-0.6901411539251132, worst per-run total-edge difference=-926.2801617855001. Larger depth exposed large arbitrage tail losses. No further policy was tuned on these unseen outcomes.", "FINAL: return the base code byte for byte, paired unseen mean=0.0, standard_error=0.0, retail=0.0, arb=0.0, failures=0; 900 final-code comparison runs identical; 200-pair unchanged-base timing seconds={'base': 75.59783254703507, 'yours': 75.62080980278552}."], "next": "On fresh unseen seeds, test a time-dependent ceiling confined to covered low-price asks, with an explicit jump-loss budget. Larger depth improved retail but rare arbitrage losses overwhelmed the frozen candidate. Do not select a threshold using this holdout."}