{"approach": "In spread 1 only, suppress planned bulk inventory-replenishment bids at ticks 2-5 by zeroing amt/qam before the existing short-horizon bridge. The bridge can still replenish toward its near-term ask-coverage target. Regular-bid and tick-1 stock sizing rules and ask formulas are retained; inventory and cash feedback can change later quantities. Base fill attribution showed that intermediate-price bulk stock purchases lost more to arbitrage than they earned from retail. Preserving the bridge retained more useful ask coverage than suppressing all replenishment at those prices. The candidate set and trading rules were fixed before any unseen scoring. The initial combined candidate lost on unseen; three already-defined alternatives were then validated, and the two with positive validation gains were scored unchanged. Three fixed trading policies were compared on the same unseen set; every comparison is disclosed in tried. Selection across those policies introduces selection bias, and the paired standard error does not adjust for multiple comparisons. The strongest trading policy initially measured slightly slower than the base. A subsequent performance-only fast path skips AB in qbid when the existing spread-1 dmin test already forces zero; it changes no trading rule or parameter. The final code was frozen before re-running all 2036 tuning, 1969 unseen and 900 other-spread seeds. A reference strategy ran alongside it for assertions; only final-code actions were applied by the unmodified engine. Every ordered action list at every step and every result field matched the original policy (and the base on other spreads). Reported scores are from those final-code runs. A fresh 200-run benchmark uses ordinary single-strategy factories, without the equivalence wrapper. Simulator b244530ee2a6247b5f930830eeca9dd950da0e7e; default configuration, 2000 steps, no sandbox, standard library only. Discovery: spread 1 within 8000-11999 (1027 seeds); validation: spread 1 within 12000-15999 (1009 seeds). Unseen: all spread-1 seeds within 60000-67999 (1969 seeds). The supplied CLI scorer check used 4000 simulations starting at seed 4000 and four workers. Every custom run instantiates SimulationEngine(sample_config(ChallengeConfig(), ParameterVariance(), seed=seed), factory, seed=seed), as run_batch does. All scores below come from the unmodified engine; fill attribution is diagnostic only. Other-spread equivalence compares every SimulationResult field on the first 300 seeds of each spread from 60000. Paired standard error is sample standard deviation of per-seed edge differences divided by sqrt(n); arb edge is signed. Timing reports 200 runs each for the base and returned file in one process, rotating execution order after warmups, on the first 200 spread-1 tuning seeds.", "blocked": null, "python_version": "3.13.5", "spread": 1, "base_mean_edge": 98.4694596619638, "runs": {"tuning": 2036, "unseen": 1969}, "base_unseen": {"mean_edge": 41.78494849744236, "retail_edge": 65.91107840022042, "arb_edge": -24.1261299027871}, "holdout": {"mean_edge": 42.221069666167644, "retail_edge": 65.30045934270161, "arb_edge": -23.079389676546114, "failures": 0}, "diff": {"mean": 0.436121168725292, "standard_error": 0.12893019771871916, "retail": -0.6106190575187915, "arb": 1.046740226240985}, "others_identical": {"runs": 900, "identical": true}, "seconds": {"base": 90.80524627608247, "yours": 90.33332743751816}, "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            if self.s == 1 and phat * 100 - t < P['dmin']:\n                return 0.0\n            a, b = AB(t / 100.0)\n            if phat * 100 - t < P['dmin']:\n                return 0.0\n            if P['nb1'] > 0 and self.s == 1 and t == 1 and ptk < 1.0:\n                return 0.0\n            if phat < P['pL']:\n                ytg = P['ydem'] * min(H, P['W']) / max(ca - 1, ptk + 1) * 100.0\n                a *= (P['kLb'] if state.yes_inventory < ytg else P['kLf']) / P['kL']\n            return qsize(a, b, max(phat, 0.05))\n\n        def qask(t):\n            if not 1 <= t <= 99:\n                return 0.0\n            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        # Avoid bulk stock purchases at intermediate low ticks in spread one.\n        if self.s == 1 and 2 <= amt <= 5:\n            amt, qam = 0, 0.0\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": "0eb7247fe76f8b732dde92ebe4975470599eb319a0cdf610d271d13ea86a3b7f", "tried": ["Bid-fill diagnostics on the first 400 discovery runs; per-run unrounded fill-edge sums, including probes: 01: retail_edge=0.4193717161657164, arb_edge=-13.604210625415169, retail_quantity=72.074425, arb_quantity=9267.518050000002; 02-05: retail_edge=1.937083529995673, arb_edge=-4.712331359371367, retail_quantity=304.12145, arb_quantity=2390.1918749999995; 06-10: retail_edge=0.3821454364112926, arb_edge=-0.5014369745811096, retail_quantity=52.896325, arb_quantity=183.28314999999998; 11-25: retail_edge=0.15256710851815267, arb_edge=-0.16265947674147227, retail_quantity=17.756149999999995, arb_quantity=43.01227499999996; 26-50: retail_edge=0.005354179091109586, arb_edge=-0.02616568372384592, retail_quantity=0.6230499999999995, arb_quantity=3.5065749999999785; 51-99: retail_edge=0.5999419997138956, arb_edge=-0.15711102670405303, retail_quantity=75.12854999999998, arb_quantity=40.12682499999995", "Frozen-candidate attribution on the same 400 discovery seeds, unrounded fill-edge sums per run; every SimulationResult field matched the ordinary-engine cached run. Changes: BUY/arb=0.8400484641534476; BUY/retail=0.0027334165444479197; SELL/arb=0.6847107605812042; SELL/retail=-0.9832288090353813", "Seed selection using the pinned runner sample_config with default ChallengeConfig and ParameterVariance. Tuning spread-1 seeds: 8005,8007,8009,8014,8016,8018,8019,8020,8021,8025,8029,8030,8034,8035,8036,8037,8043,8047,8048,8050,8051,8052,8057,8058,8062,8069,8074,8077,8078,8080,8083,8084,8086,8087,8091,8092,8096,8098,8100,8104,8108,8109,8110,8114,8116,8117,8119,8122,8124,8142,8148,8149,8153,8162,8167,8171,8178,8179,8181,8182,8183,8184,8185,8198,8206,8207,8222,8227,8228,8230,8234,8236,8245,8249,8250,8251,8256,8259,8262,8265,8268,8270,8275,8284,8293,8295,8298,8299,8300,8301,8303,8308,8311,8317,8323,8329,8339,8340,8341,8351,8354,8356,8365,8366,8370,8371,8374,8381,8383,8385,8387,8390,8397,8398,8400,8414,8425,8426,8428,8429,8430,8437,8438,8439,8446,8447,8450,8453,8458,8460,8461,8463,8464,8468,8471,8473,8474,8478,8485,8489,8490,8491,8492,8503,8508,8510,8514,8515,8517,8521,8523,8524,8531,8539,8541,8547,8552,8553,8557,8563,8571,8572,8575,8583,8592,8596,8598,8605,8608,8613,8614,8620,8629,8635,8636,8649,8653,8655,8656,8658,8665,8666,8672,8673,8678,8683,8684,8700,8703,8705,8716,8718,8722,8723,8724,8725,8729,8735,8740,8741,8746,8748,8750,8754,8755,8758,8760,8767,8770,8774,8775,8776,8779,8780,8782,8783,8785,8793,8796,8797,8804,8805,8808,8815,8816,8819,8822,8825,8831,8835,8840,8842,8845,8849,8850,8851,8854,8855,8859,8864,8869,8871,8874,8875,8883,8886,8890,8902,8904,8910,8911,8914,8916,8923,8934,8937,8941,8942,8944,8949,8954,8955,8956,8961,8963,8973,8978,8984,8986,8988,8996,8997,9004,9008,9016,9018,9023,9026,9028,9034,9036,9038,9044,9046,9051,9052,9054,9056,9061,9071,9074,9076,9085,9086,9087,9091,9093,9094,9095,9096,9097,9109,9110,9111,9113,9114,9121,9127,9142,9145,9155,9162,9163,9164,9166,9170,9174,9177,9188,9189,9195,9204,9205,9210,9215,9219,9225,9226,9229,9233,9234,9242,9244,9248,9254,9255,9262,9274,9275,9277,9279,9282,9285,9289,9290,9291,9297,9303,9314,9316,9329,9334,9348,9352,9353,9354,9355,9361,9362,9370,9371,9375,9383,9390,9392,9397,9400,9401,9406,9413,9416,9419,9422,9426,9429,9437,9447,9450,9451,9453,9459,9468,9475,9476,9477,9480,9484,9485,9486,9490,9494,9496,9500,9507,9512,9514,9515,9520,9522,9530,9534,9540,9544,9546,9551,9552,9553,9556,9558,9563,9565,9567,9568,9572,9579,9580,9582,9583,9584,9588,9596,9599,9610,9614,9616,9624,9628,9629,9630,9633,9636,9642,9650,9652,9653,9654,9656,9657,9660,9661,9664,9680,9681,9683,9686,9693,9694,9699,9701,9703,9714,9718,9725,9739,9740,9742,9744,9745,9752,9753,9757,9762,9763,9764,9766,9768,9770,9780,9781,9782,9783,9784,9787,9790,9791,9793,9795,9796,9804,9806,9807,9812,9815,9820,9824,9832,9838,9844,9845,9856,9865,9866,9867,9868,9872,9882,9884,9890,9899,9902,9903,9908,9909,9912,9917,9920,9928,9929,9943,9944,9954,9955,9958,9960,9961,9964,9965,9966,9967,9968,9970,9982,9984,9990,9994,10000,10003,10005,10006,10015,10021,10023,10032,10036,10039,10040,10051,10061,10065,10070,10071,10075,10089,10093,10099,10103,10107,10112,10114,10116,10136,10141,10145,10150,10156,10160,10176,10181,10182,10183,10190,10197,10198,10199,10205,10206,10214,10215,10224,10235,10244,10250,10255,10258,10264,10269,10273,10274,10283,10288,10289,10292,10299,10301,10304,10310,10311,10312,10313,10320,10322,10324,10326,10339,10343,10344,10346,10348,10350,10355,10359,10364,10366,10367,10371,10378,10379,10380,10387,10390,10397,10399,10400,10405,10407,10416,10418,10429,10439,10445,10446,10451,10453,10454,10457,10466,10468,10469,10474,10476,10480,10482,10483,10484,10485,10489,10490,10492,10493,10494,10495,10498,10499,10503,10506,10507,10511,10516,10523,10525,10528,10538,10543,10544,10548,10550,10553,10554,10555,10557,10560,10565,10569,10574,10575,10582,10584,10591,10596,10599,10600,10608,10610,10617,10619,10623,10624,10629,10631,10633,10634,10636,10639,10641,10642,10646,10647,10649,10651,10654,10655,10666,10667,10670,10672,10674,10675,10680,10681,10683,10685,10692,10693,10694,10695,10701,10702,10704,10707,10712,10715,10716,10721,10724,10726,10727,10728,10729,10736,10739,10741,10742,10743,10744,10748,10750,10751,10752,10760,10761,10766,10768,10773,10775,10782,10790,10793,10795,10819,10834,10835,10838,10839,10841,10842,10844,10847,10849,10850,10851,10852,10854,10855,10860,10862,10866,10867,10871,10884,10887,10889,10891,10906,10907,10913,10917,10919,10922,10927,10928,10936,10938,10940,10944,10945,10947,10949,10955,10956,10957,10958,10960,10965,10967,10968,10976,10983,10997,11017,11019,11025,11027,11033,11038,11047,11050,11053,11056,11059,11063,11067,11095,11096,11101,11114,11116,11122,11130,11132,11135,11136,11142,11145,11149,11151,11154,11157,11158,11160,11163,11164,11165,11166,11169,11170,11171,11176,11178,11189,11190,11193,11194,11195,11196,11201,11202,11203,11208,11210,11218,11220,11222,11227,11228,11237,11245,11252,11253,11258,11266,11279,11282,11286,11287,11299,11304,11307,11313,11315,11317,11325,11331,11332,11342,11346,11353,11363,11364,11365,11366,11368,11373,11379,11381,11383,11384,11395,11401,11406,11407,11408,11418,11422,11423,11425,11428,11432,11436,11438,11446,11451,11460,11461,11465,11467,11471,11472,11474,11480,11486,11500,11502,11504,11508,11509,11512,11516,11521,11534,11537,11540,11542,11548,11551,11554,11558,11562,11563,11566,11569,11570,11578,11582,11586,11592,11596,11598,11599,11601,11602,11604,11605,11609,11613,11617,11621,11628,11639,11642,11658,11662,11663,11664,11666,11668,11670,11673,11678,11681,11683,11684,11687,11689,11692,11702,11705,11707,11715,11717,11726,11727,11731,11736,11742,11763,11767,11768,11769,11770,11771,11773,11776,11780,11783,11786,11788,11791,11794,11795,11797,11805,11807,11809,11812,11817,11818,11820,11822,11828,11832,11837,11838,11839,11841,11848,11849,11850,11852,11853,11862,11867,11872,11881,11887,11890,11895,11896,11897,11909,11911,11917,11920,11922,11927,11937,11943,11945,11951,11957,11965,11966,11967,11968,11983,11987,11996,11998,12005,12013,12018,12029,12039,12047,12048,12058,12059,12060,12065,12067,12068,12069,12070,12078,12079,12082,12084,12085,12087,12092,12093,12094,12109,12111,12118,12119,12121,12122,12123,12124,12127,12129,12132,12135,12137,12140,12142,12143,12148,12162,12163,12167,12176,12179,12181,12182,12185,12187,12190,12196,12200,12201,12210,12213,12216,12218,12221,12228,12230,12242,12245,12247,12248,12251,12252,12255,12260,12261,12265,12268,12283,12284,12285,12286,12287,12299,12301,12303,12309,12310,12320,12324,12331,12334,12337,12339,12342,12348,12350,12356,12361,12362,12368,12372,12376,12384,12385,12387,12388,12390,12393,12395,12402,12405,12406,12414,12416,12418,12425,12429,12430,12431,12436,12438,12441,12442,12449,12452,12454,12455,12462,12463,12467,12477,12483,12486,12493,12496,12497,12503,12504,12509,12511,12512,12516,12520,12521,12522,12525,12528,12532,12538,12553,12554,12560,12561,12566,12567,12572,12577,12580,12583,12590,12599,12602,12615,12616,12617,12618,12623,12625,12630,12639,12641,12645,12647,12658,12660,12673,12678,12682,12688,12690,12693,12697,12701,12703,12704,12705,12717,12719,12720,12732,12733,12735,12743,12753,12759,12761,12767,12777,12783,12785,12786,12788,12799,12800,12807,12815,12816,12818,12819,12823,12829,12840,12848,12858,12871,12877,12881,12887,12890,12895,12897,12906,12910,12912,12928,12936,12939,12945,12947,12948,12960,12971,12973,12976,12990,12992,12995,13006,13009,13011,13013,13017,13019,13020,13021,13022,13030,13034,13037,13039,13042,13056,13064,13066,13067,13070,13072,13078,13079,13082,13090,13092,13093,13095,13097,13102,13103,13113,13117,13121,13127,13142,13146,13151,13154,13161,13166,13170,13171,13177,13180,13181,13184,13186,13192,13194,13198,13204,13205,13206,13207,13211,13212,13217,13224,13226,13229,13230,13235,13236,13237,13247,13253,13265,13266,13269,13272,13276,13280,13294,13297,13301,13304,13314,13320,13324,13331,13333,13336,13341,13348,13350,13351,13353,13358,13363,13364,13365,13366,13367,13368,13374,13375,13377,13378,13381,13386,13390,13392,13395,13396,13405,13407,13410,13414,13415,13416,13424,13429,13433,13438,13439,13441,13446,13451,13462,13463,13466,13476,13477,13487,13497,13504,13505,13506,13515,13518,13523,13525,13529,13531,13534,13536,13538,13544,13545,13550,13551,13552,13554,13556,13558,13563,13570,13577,13583,13586,13588,13589,13590,13591,13602,13605,13613,13616,13620,13628,13630,13633,13635,13637,13639,13641,13649,13656,13661,13666,13667,13668,13688,13690,13695,13697,13701,13708,13715,13717,13720,13727,13729,13733,13735,13737,13745,13746,13747,13749,13754,13756,13759,13762,13763,13775,13778,13779,13782,13785,13798,13800,13807,13811,13813,13814,13815,13821,13825,13830,13831,13838,13839,13841,13846,13849,13854,13856,13860,13864,13874,13877,13878,13879,13884,13888,13890,13894,13899,13905,13909,13911,13916,13918,13924,13928,13929,13930,13933,13937,13939,13942,13944,13948,13951,13952,13953,13954,13956,13960,13964,13967,13974,13981,13982,13985,13987,13989,13992,13998,13999,14000,14003,14009,14020,14026,14027,14037,14040,14041,14043,14045,14046,14051,14060,14062,14063,14067,14070,14077,14086,14105,14111,14113,14118,14125,14128,14130,14132,14134,14136,14139,14144,14145,14155,14156,14159,14164,14165,14166,14169,14176,14178,14184,14187,14192,14193,14196,14202,14208,14209,14215,14217,14219,14221,14232,14234,14237,14239,14242,14246,14249,14250,14251,14252,14254,14262,14265,14269,14281,14293,14294,14297,14298,14299,14303,14305,14308,14309,14312,14315,14319,14320,14324,14325,14327,14329,14333,14336,14337,14341,14342,14346,14347,14348,14353,14356,14360,14366,14371,14374,14375,14376,14383,14384,14386,14387,14397,14398,14402,14403,14408,14409,14416,14424,14430,14433,14434,14438,14449,14451,14452,14463,14466,14469,14473,14484,14489,14493,14496,14498,14499,14502,14503,14504,14509,14510,14512,14521,14524,14526,14530,14532,14533,14539,14540,14548,14550,14552,14560,14562,14571,14578,14581,14583,14587,14591,14598,14602,14613,14617,14619,14621,14632,14636,14637,14642,14650,14651,14659,14660,14662,14663,14665,14668,14674,14676,14683,14696,14697,14700,14706,14708,14711,14717,14718,14719,14720,14726,14727,14734,14738,14739,14743,14746,14757,14758,14763,14768,14769,14775,14776,14778,14781,14783,14787,14788,14790,14792,14794,14797,14799,14803,14806,14809,14817,14818,14819,14823,14828,14830,14838,14849,14850,14858,14859,14867,14870,14873,14876,14879,14880,14881,14882,14892,14894,14895,14908,14913,14915,14917,14918,14924,14925,14926,14928,14930,14932,14936,14937,14940,14942,14944,14946,14947,14952,14953,14954,14956,14962,14970,14972,14976,14978,14979,14986,14987,14988,14994,14997,15003,15013,15024,15025,15030,15032,15036,15043,15050,15053,15056,15060,15061,15063,15065,15066,15067,15068,15079,15088,15094,15097,15099,15105,15110,15113,15115,15117,15125,15131,15135,15136,15140,15148,15152,15157,15160,15165,15166,15168,15170,15175,15181,15188,15189,15202,15207,15209,15210,15214,15216,15226,15235,15242,15252,15256,15268,15269,15272,15279,15284,15285,15290,15291,15298,15299,15303,15307,15308,15312,15314,15317,15319,15322,15327,15342,15344,15345,15346,15347,15350,15351,15354,15357,15359,15366,15369,15374,15377,15384,15387,15390,15391,15392,15394,15399,15402,15403,15411,15414,15415,15418,15419,15420,15425,15434,15437,15438,15439,15442,15446,15450,15453,15454,15466,15473,15474,15476,15479,15486,15489,15494,15495,15497,15503,15504,15505,15510,15511,15523,15524,15527,15531,15535,15545,15550,15552,15558,15559,15565,15575,15577,15585,15598,15600,15607,15616,15617,15620,15634,15636,15638,15639,15648,15649,15650,15656,15659,15664,15667,15673,15675,15676,15680,15681,15685,15689,15692,15693,15698,15709,15710,15713,15715,15718,15719,15720,15722,15724,15732,15734,15735,15739,15742,15746,15757,15760,15765,15775,15779,15781,15788,15798,15800,15801,15803,15805,15811,15812,15813,15820,15823,15829,15831,15839,15841,15842,15843,15844,15848,15849,15857,15863,15868,15869,15872,15874,15879,15883,15890,15896,15907,15908,15909,15911,15917,15921,15924,15926,15931,15935,15942,15959,15960,15962,15965,15966,15968,15972,15981,15982,15984,15986,15988,15993,15995,15996. Unseen spread-1 seeds: 60004,60012,60014,60016,60021,60023,60027,60028,60044,60045,60056,60062,60067,60069,60075,60076,60079,60081,60082,60089,60090,60092,60094,60099,60103,60104,60113,60117,60127,60131,60132,60133,60141,60143,60147,60152,60153,60155,60156,60159,60165,60167,60175,60178,60180,60181,60189,60194,60195,60196,60210,60212,60214,60217,60218,60225,60232,60235,60243,60244,60249,60251,60253,60263,60265,60266,60268,60269,60273,60283,60285,60288,60289,60296,60297,60298,60301,60306,60309,60312,60316,60317,60320,60325,60329,60330,60334,60338,60341,60343,60344,60361,60362,60369,60370,60376,60377,60381,60393,60394,60396,60403,60404,60415,60416,60417,60421,60426,60433,60434,60436,60443,60446,60448,60454,60463,60465,60469,60473,60475,60478,60490,60494,60496,60498,60500,60501,60519,60521,60524,60526,60527,60529,60533,60543,60544,60553,60554,60555,60558,60560,60564,60573,60578,60579,60580,60583,60588,60590,60595,60604,60605,60612,60619,60620,60622,60623,60628,60632,60634,60636,60642,60643,60647,60656,60658,60659,60661,60663,60667,60668,60672,60674,60678,60679,60686,60688,60690,60691,60698,60704,60711,60712,60714,60719,60723,60724,60736,60738,60741,60743,60744,60746,60751,60753,60762,60780,60782,60787,60792,60798,60799,60802,60803,60805,60807,60808,60812,60819,60820,60821,60825,60829,60831,60834,60836,60852,60853,60860,60863,60864,60867,60868,60874,60875,60883,60887,60888,60894,60902,60903,60917,60930,60933,60934,60936,60949,60952,60956,60966,60972,60975,60984,60985,60990,60991,60992,60993,60997,61000,61007,61008,61009,61010,61018,61021,61024,61045,61047,61049,61053,61058,61071,61075,61078,61080,61083,61084,61092,61093,61104,61106,61114,61122,61134,61136,61140,61144,61146,61149,61150,61151,61160,61165,61174,61176,61180,61186,61187,61191,61199,61205,61206,61207,61208,61209,61213,61217,61218,61219,61221,61222,61227,61229,61235,61236,61238,61239,61241,61246,61259,61262,61264,61272,61273,61274,61275,61278,61283,61285,61293,61295,61296,61298,61299,61301,61311,61313,61314,61315,61318,61319,61321,61340,61342,61350,61353,61356,61359,61360,61365,61372,61373,61381,61385,61387,61388,61390,61393,61394,61401,61403,61408,61412,61420,61427,61428,61429,61432,61440,61441,61445,61446,61448,61460,61463,61466,61467,61474,61477,61480,61485,61491,61494,61496,61500,61511,61515,61519,61520,61522,61525,61532,61533,61537,61540,61545,61546,61553,61554,61556,61561,61563,61565,61566,61572,61573,61575,61576,61579,61585,61587,61588,61590,61599,61600,61602,61609,61615,61621,61622,61626,61636,61644,61658,61661,61663,61671,61672,61678,61682,61692,61693,61694,61701,61702,61704,61717,61725,61726,61736,61737,61738,61741,61747,61751,61755,61763,61765,61767,61768,61769,61770,61776,61777,61781,61784,61786,61790,61791,61800,61801,61803,61804,61806,61819,61823,61825,61827,61829,61833,61834,61835,61839,61840,61846,61854,61857,61863,61868,61870,61872,61873,61883,61891,61893,61898,61900,61901,61906,61915,61916,61919,61926,61927,61937,61941,61942,61947,61949,61952,61954,61955,61958,61969,61977,61980,61981,61994,61998,62003,62004,62008,62009,62015,62017,62018,62019,62020,62027,62032,62038,62039,62042,62048,62055,62065,62068,62072,62081,62088,62092,62094,62096,62106,62112,62120,62124,62128,62131,62141,62145,62147,62151,62152,62161,62165,62168,62170,62175,62183,62184,62186,62187,62211,62214,62217,62220,62222,62223,62226,62229,62230,62232,62233,62239,62241,62243,62244,62248,62249,62251,62253,62255,62258,62260,62262,62270,62282,62284,62285,62306,62307,62311,62315,62316,62320,62322,62326,62331,62341,62354,62364,62371,62376,62379,62383,62384,62392,62396,62399,62400,62403,62410,62414,62416,62417,62418,62439,62441,62445,62446,62452,62453,62456,62461,62462,62465,62466,62468,62470,62475,62476,62477,62488,62491,62493,62495,62508,62511,62536,62537,62552,62560,62564,62567,62571,62572,62573,62574,62577,62580,62582,62587,62589,62590,62592,62595,62604,62608,62609,62620,62623,62626,62632,62634,62637,62639,62643,62645,62646,62662,62663,62668,62672,62679,62682,62683,62684,62685,62689,62692,62693,62700,62701,62706,62707,62718,62719,62722,62743,62745,62751,62756,62759,62761,62763,62769,62774,62785,62788,62799,62804,62805,62806,62812,62813,62815,62821,62824,62825,62828,62829,62834,62838,62839,62842,62852,62867,62869,62876,62880,62881,62882,62887,62888,62890,62899,62905,62912,62913,62919,62920,62925,62927,62935,62938,62944,62946,62947,62952,62953,62970,62975,62976,62979,62986,62987,62989,62994,63004,63018,63021,63024,63026,63027,63036,63038,63039,63041,63044,63046,63049,63051,63052,63053,63054,63058,63062,63070,63077,63078,63079,63081,63084,63087,63090,63092,63096,63097,63102,63106,63113,63117,63119,63121,63122,63124,63128,63131,63135,63140,63150,63152,63157,63158,63162,63168,63171,63185,63195,63198,63200,63204,63210,63211,63213,63220,63222,63227,63239,63240,63241,63243,63248,63250,63252,63255,63260,63261,63267,63271,63275,63277,63279,63280,63282,63288,63289,63293,63295,63299,63300,63304,63306,63311,63312,63320,63323,63325,63328,63334,63337,63339,63345,63348,63350,63357,63367,63369,63379,63392,63398,63403,63407,63409,63412,63415,63425,63426,63427,63439,63442,63447,63457,63459,63466,63471,63473,63481,63484,63487,63505,63508,63518,63520,63523,63525,63535,63537,63539,63541,63549,63552,63559,63561,63562,63566,63567,63583,63585,63592,63598,63599,63600,63607,63610,63619,63620,63621,63622,63624,63626,63628,63634,63640,63649,63650,63655,63662,63670,63673,63679,63681,63682,63684,63687,63688,63698,63703,63708,63712,63721,63724,63730,63733,63745,63748,63751,63761,63764,63768,63769,63771,63772,63778,63779,63780,63786,63790,63803,63810,63811,63818,63826,63827,63837,63839,63851,63852,63857,63860,63862,63868,63871,63873,63875,63877,63882,63883,63886,63889,63891,63895,63896,63897,63899,63904,63906,63910,63912,63917,63920,63922,63925,63927,63931,63932,63934,63935,63958,63961,63966,63967,63970,63974,63979,63987,63997,64005,64006,64007,64014,64030,64033,64036,64038,64044,64046,64050,64060,64061,64063,64064,64070,64076,64080,64082,64083,64098,64104,64105,64106,64109,64110,64111,64113,64115,64116,64122,64127,64133,64134,64139,64140,64144,64151,64152,64159,64161,64165,64176,64177,64178,64180,64181,64188,64191,64192,64195,64200,64212,64216,64218,64219,64224,64225,64228,64229,64230,64237,64243,64245,64248,64249,64252,64255,64256,64257,64258,64259,64261,64268,64269,64273,64277,64280,64290,64292,64298,64300,64301,64306,64309,64316,64320,64321,64332,64335,64336,64339,64346,64351,64352,64355,64360,64363,64369,64375,64380,64381,64382,64388,64389,64401,64419,64421,64429,64433,64437,64444,64453,64459,64462,64464,64466,64467,64468,64476,64483,64485,64486,64488,64493,64494,64506,64512,64516,64517,64519,64527,64532,64533,64534,64538,64539,64544,64545,64547,64548,64550,64551,64556,64558,64566,64568,64575,64580,64582,64583,64587,64594,64596,64617,64623,64633,64638,64641,64643,64644,64648,64650,64653,64658,64663,64665,64674,64675,64677,64679,64682,64684,64687,64689,64697,64699,64703,64706,64710,64712,64718,64729,64736,64742,64743,64747,64748,64749,64752,64763,64764,64768,64774,64778,64782,64784,64793,64795,64798,64801,64805,64812,64829,64830,64833,64834,64838,64840,64845,64847,64851,64858,64861,64862,64863,64865,64868,64871,64872,64874,64875,64878,64879,64881,64885,64889,64892,64894,64900,64903,64904,64906,64908,64916,64924,64925,64926,64927,64931,64943,64945,64947,64948,64951,64954,64959,64961,64970,64973,64974,64978,64981,64998,64999,65004,65014,65021,65024,65026,65029,65030,65032,65034,65035,65051,65054,65056,65058,65060,65061,65063,65064,65067,65068,65071,65079,65080,65082,65083,65090,65097,65105,65106,65111,65114,65119,65120,65128,65133,65134,65137,65141,65142,65146,65152,65155,65158,65161,65164,65167,65172,65181,65182,65184,65188,65195,65202,65203,65211,65220,65225,65231,65239,65247,65256,65258,65260,65261,65267,65271,65273,65279,65283,65284,65285,65286,65293,65300,65310,65314,65320,65333,65334,65335,65337,65339,65341,65343,65346,65347,65348,65350,65352,65353,65360,65363,65376,65377,65389,65392,65394,65395,65396,65400,65401,65402,65404,65407,65415,65418,65422,65426,65435,65445,65446,65461,65464,65467,65468,65469,65471,65473,65478,65480,65481,65483,65486,65493,65495,65496,65501,65507,65510,65511,65516,65521,65523,65524,65542,65545,65546,65550,65553,65555,65557,65563,65584,65589,65590,65597,65600,65611,65618,65620,65627,65633,65638,65642,65644,65645,65646,65650,65652,65657,65662,65665,65666,65667,65671,65675,65677,65681,65682,65683,65685,65686,65694,65696,65698,65703,65704,65714,65723,65730,65731,65735,65738,65742,65748,65750,65753,65754,65756,65757,65762,65763,65765,65768,65772,65776,65784,65785,65788,65791,65799,65803,65812,65817,65818,65820,65822,65827,65829,65832,65834,65837,65838,65839,65840,65842,65851,65854,65856,65858,65863,65874,65875,65883,65884,65885,65888,65890,65892,65893,65895,65896,65909,65910,65915,65916,65920,65924,65934,65936,65937,65938,65944,65949,65951,65955,65961,65962,65966,65970,65977,65981,65992,66001,66004,66006,66007,66010,66012,66015,66019,66023,66025,66040,66041,66045,66066,66067,66072,66077,66079,66084,66086,66087,66088,66089,66091,66096,66098,66101,66109,66111,66112,66118,66129,66134,66140,66142,66152,66154,66155,66156,66158,66163,66166,66168,66172,66176,66177,66178,66191,66196,66200,66209,66215,66216,66219,66222,66223,66228,66229,66233,66234,66236,66240,66245,66251,66256,66261,66265,66269,66272,66275,66276,66278,66279,66282,66283,66287,66297,66298,66299,66305,66306,66313,66319,66322,66323,66325,66326,66328,66334,66342,66345,66347,66348,66349,66350,66352,66360,66362,66363,66372,66373,66374,66375,66377,66380,66392,66395,66397,66407,66413,66426,66432,66437,66444,66454,66455,66456,66457,66463,66464,66465,66467,66473,66479,66480,66486,66490,66501,66504,66507,66511,66513,66522,66529,66532,66533,66534,66538,66555,66558,66567,66568,66574,66575,66577,66580,66589,66596,66597,66599,66605,66610,66613,66618,66620,66622,66626,66629,66635,66640,66646,66656,66658,66660,66670,66671,66672,66675,66677,66686,66690,66694,66699,66701,66704,66705,66706,66707,66713,66718,66719,66720,66724,66732,66733,66734,66736,66737,66739,66746,66749,66751,66767,66769,66776,66777,66779,66780,66783,66787,66788,66791,66795,66796,66801,66804,66806,66809,66812,66822,66823,66824,66825,66832,66834,66835,66838,66839,66840,66842,66843,66844,66845,66855,66858,66860,66871,66875,66876,66877,66878,66879,66889,66898,66902,66910,66911,66912,66930,66932,66935,66936,66938,66939,66944,66947,66951,66954,66955,66959,66966,66968,66969,66972,66981,66984,66997,66998,67006,67012,67014,67018,67019,67022,67023,67035,67036,67039,67059,67063,67066,67069,67071,67072,67079,67081,67088,67100,67115,67118,67127,67129,67130,67131,67136,67139,67140,67143,67149,67150,67151,67152,67155,67156,67166,67167,67175,67185,67188,67191,67193,67198,67203,67210,67222,67235,67236,67242,67243,67248,67249,67251,67252,67256,67258,67260,67261,67268,67271,67274,67277,67278,67280,67284,67285,67286,67292,67293,67297,67303,67307,67311,67313,67323,67326,67337,67341,67345,67347,67352,67355,67356,67357,67361,67367,67368,67370,67374,67377,67378,67382,67384,67389,67392,67402,67414,67419,67430,67431,67433,67436,67443,67451,67463,67464,67467,67469,67473,67482,67489,67494,67497,67502,67503,67506,67511,67513,67514,67516,67517,67519,67520,67524,67525,67529,67530,67540,67546,67549,67552,67553,67554,67559,67576,67577,67595,67598,67601,67606,67608,67612,67613,67619,67623,67626,67636,67640,67645,67650,67654,67662,67665,67675,67687,67688,67692,67698,67705,67706,67712,67715,67718,67719,67721,67722,67727,67731,67732,67735,67741,67745,67746,67748,67750,67752,67754,67757,67763,67764,67769,67783,67785,67793,67798,67801,67807,67816,67826,67830,67838,67841,67843,67851,67854,67861,67863,67864,67865,67866,67876,67877,67880,67881,67882,67886,67887,67891,67899,67900,67901,67910,67914,67924,67930,67932,67937,67938,67945,67946,67948,67952,67955,67957,67963,67973,67975,67979,67982,67985,67987,67991,67998.", "Remove regular bids at ticks 1-5, leaving stock and bridge orders intact: discovery n=1027, paired mean=-1.2747881468555988, SE=1.2489075766860536, retail=-5.128278043347809, arb=3.8534898964788704, failures=0", "Remove the short-horizon inventory bridge at estimated probability 2-10 cents: discovery n=1027, paired mean=0.48590745908480987, SE=1.15023599733213, retail=-0.42766837841898714, arb=0.9135758375014605, failures=0", "Restrict the large tick-1 stock bid to estimated probability between 1 and 2 cents: discovery n=1027, paired mean=1.7631663192111005, SE=1.250336903877562, retail=-0.681605106115969, arb=2.44477142532668, failures=0; validation n=1009, paired mean=-1.1740792941819624, SE=0.49237787237172287, retail=-0.9374807552216055, arb=-0.23659853895966307, failures=0", "Restrict the large tick-1 stock bid to estimated probability between 1 and 1.5 cents: discovery n=400, paired mean=1.1648021833037503, SE=3.1644702917459133, retail=-2.6388913370532503, arb=3.80369352036225, failures=0", "Restrict the large tick-1 stock bid to estimated probability between 1 and 3 cents: discovery n=1027, paired mean=1.1707932752875365, SE=1.1991428412049945, retail=-0.49139636984771184, arb=1.6621896451356377, failures=0", "Raise low-price regular-bid loss penalty from 0.08 to 0.7 without changing asks: discovery n=400, paired mean=2.6073829727855, SE=3.0879832230476696, retail=-3.0309161016477497, arb=5.6382990744285, failures=0", "Quote regular bids at floor(estimated probability in ticks minus 0.3) between 1 and 5 cents, allowing joins behind the rival: discovery n=400, paired mean=-2.215876976356, SE=1.1751735340295684, retail=0.4582987415345001, arb=-2.6741757178910013, failures=0", "Suppress inventory-replenishment bids at ticks >=2 when their price does not improve the rival best bid: discovery n=1027, paired mean=0.9923970862178185, SE=1.1506530093915512, retail=-0.5426706951980524, arb=1.5350677814138265, failures=0", "Track priority of inventory bids placed ahead of the rival in the existing sticky-order logic: discovery n=300, paired mean=0.00909925087466666, SE=0.008402954583395789, retail=0.008774843594999939, arb=0.00032440727900000965, failures=0", "Remove inventory-replenishment bids at ticks 2-5 after bridge sizing, while preserving regular bids and tick-1 stock orders: discovery n=1027, paired mean=1.6248231541422589, SE=1.176892134327785, retail=-1.5264384478870499, arb=3.151261602028724, failures=0; validation n=1009, paired mean=1.5332965627712587, SE=1.2590404376259898, retail=-1.4973603077559958, arb=3.030656870528741, failures=0; unseen n=1969, paired mean=0.13540334258247821, SE=0.21404449104558204, retail=-1.7881271626539867, arb=1.9235305052359066, failures=0", "Keep the full tick-1 stock bid below 2 cents, taper it to zero between 2 and 3 cents: discovery n=400, paired mean=3.0547752664762498, SE=2.9231457891042996, retail=-0.9032561592147499, arb=3.9580314256915, failures=0", "Combine removal of inventory-replenishment bids at ticks 2-5 with a 1-2-cent window for the large tick-1 stock bid: discovery n=1027, paired mean=2.1203748843633887, SE=1.2666155526705556, retail=-2.085858782695132, arb=4.206233667057936, failures=0; validation n=1009, paired mean=0.6866675539327058, SE=1.319428544703334, retail=-2.322276367421308, arb=3.0089439213548066, failures=0; unseen n=1969, paired mean=-0.14939334252092448, SE=0.459577693639384, retail=-2.9579687033834943, arb=2.8085753608600306, failures=0", "Remove bulk inventory-replenishment bids at ticks 2-5 before bridge sizing, retaining the short-horizon bridge: discovery n=1027, paired mean=0.5080998905718597, SE=0.2326774413382024, retail=-0.6138365245735151, arb=1.1219364151431352, failures=0; validation n=1009, paired mean=1.828980274813479, SE=1.0610890323065365, retail=-0.3409499431419227, arb=2.169930217954014, failures=0; unseen n=1969, paired mean=0.436121168725292, SE=0.12893019771871916, retail=-0.6106190575187915, arb=1.046740226240985, failures=0", "Performance-only equivalent of no_bulk_low_ammo: skip pure AB payoff integrals when the existing spread-1 bid-gap check forces zero size. Every ordered action list at every step and every SimulationResult field matched on all 4905 required runs: discovery n=1027, paired mean=0.5080998905718597, SE=0.2326774413382024, retail=-0.6138365245735151, arb=1.1219364151431352, failures=0; validation n=1009, paired mean=1.828980274813479, SE=1.0610890323065365, retail=-0.3409499431419227, arb=2.169930217954014, failures=0; unseen n=1969, paired mean=0.436121168725292, SE=0.12893019771871916, retail=-0.6106190575187915, arb=1.046740226240985, failures=0", "Initial single-process 200-run timing, with rotating order on identical seeds: base=93.37296490813605 seconds, no_low_ammo=92.96062008710578 seconds, no_bulk_low_ammo=93.50435302895494 seconds. The stronger unchanged policy missed the speed criterion; the final performance-only equivalent was retimed separately.", "FINAL FROZEN CODE: all 2036 tuning runs paired mean=1.1627012204833498, SE=0.5388570435601362; unseen n=1969, paired mean=0.436121168725292, SE=0.12893019771871916; zero failed runs. Frozen before unseen evaluation at 2026-11-06T09:04:30.599455+00:00."], "next": "Use a new untouched seed range. Break bulk refill and bridge fills down by price, inventory coverage and remaining horizon, then test a small replacement for the suppressed bulk bids only where retail edge repays adverse selection. Both assigned ranges have been consumed, and the unseen set compared three fixed policies."}