{"approach":"The queue retention rules remain intact because all tested deletions lost paired edge on 125 choosing runs. Queue-first spread-2 combination: s2-queue, s2-stock, s2-bids, q2-bids. Each addition was compared run by run with its predecessor on fixed choosing seeds and kept only for positive mean gain. Stock and bid additions used 995 paired choosing runs; the completed file was frozen before 993 confirming runs. On confirmation, additional retail edge outweighed increased arbitrage losses. All changes are gated to spread 2; 450 full results from other spreads match the base exactly. These are local scores, not a leaderboard submission.","blocked":null,"spread":2,"base_mean_edge":108.63974289615767,"contains":["s2-queue","s2-stock","s2-bids","q2-bids"],"holdout":{"mean_edge":73.56546690853686,"retail_edge":101.34089702686012,"arb_edge":-27.775430118336555,"failures":0},"diff":{"mean":2.0015597964197385,"standard_error":0.43721099433183286,"retail":2.4149221962356497,"arb":-0.4133623998147029},"vs_priced":{"mean":1.2413501721502518,"standard_error":0.2535360118153212},"others_identical":{"runs":450,"identical":true},"seconds":{"base":280.492975549947,"yours":286.24650167889195},"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 == 2:\n                self.params.update(dict(flow_prior=200, flow_level=0.6, flow_strength=1.0, flow_safety=2.0, flow_exposure_min=5.0))\n            if self.s == 2:\n                self.params.update({'kLf': 0.16})\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 in (2, 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            # spread 2: a front order that one ordinary retail buy would use up is not worth holding the quote at the rival's tick ($4)\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'] if self.s != 2 else max(P['min_ahead'], 400.0 / max(comp, 1))):\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        s2f = self.s == 2 and bid_t == cb and qb > 0 and cb / 100.0 < phat\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 in (2, 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            if self.s == 2:\n                buy = comp == cb\n                held = {}\n                for o in orders:\n                    x = o.price_ticks\n                    gain = ptk - x if buy else x - ptk\n                    # under 10 cents a front order is kept whole for its life: resizing it would give up its place to the rival\n                    if x == t and q > 0 and (kept + o.remaining_quantity <= max(q * P['keep_hi'], 1.0) or (x == comp and o.order_id in self.ahead and ptk <= 10.0 and gain >= 0.0)):\n                        kept += o.remaining_quantity\n                        kept_ids.add(o.order_id)\n                        continue\n                    # a small front remainder stays behind the new inside quote: it still fills ahead of the rival on a large retail order\n                    if x == comp and x != t and o.order_id in self.ahead and gain >= 1.0:\n                        if x not in held:\n                            held[x] = [0.0, qbid(x) if buy else qask(x)]\n                        h = held[x]\n                        if h[0] + o.remaining_quantity <= max(h[1], 1.0) and h[1] > 0:\n                            h[0] += o.remaining_quantity\n                            kept_ids.add(o.order_id)\n                            continue\n                    cancel(o)\n                return kept\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        if s2f and 1:\n            kb = 0.0\n            for o in bids:\n                if o.price_ticks == bid_t and o.order_id in self.ahead:\n                    kb += o.remaining_quantity\n                    kept_ids.add(o.order_id)\n                else:\n                    cancel(o)\n        elif self.s == 2 and 1 and bid_t == cb + 1:\n            qf = qbid(cb) if 1 else 1.0\n            fr = [o for o in bids if o.price_ticks == cb and o.order_id in self.ahead and cb / 100.0 < phat - 0.0 and qf > 0]\n            for o in fr:\n                kept_ids.add(o.order_id)\n            kb = manage([o for o in bids if o not in fr], bid_t, qb, cb)\n        else:\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 in (2, 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":"5948bf6227f4224bb2358dd267a562f6459693eb32f134ba30eeb6771f9a7f0a","tried":["Original CLI parent check: n=600, seed_start=1000, workers=4, mean_edge=108.63974289615767, seconds=1498.3970484230085; author reference 108.63974289615767. Exceeded five minutes, so final choosing/confirming, other-spread, and timing counts halved: 995/993, 150 each, 100 per file.","Choosing diagnostics used the first 125 eligible spread-2 seeds in 20000-27999, fixed in advance; each stock/bid addition compared on the first 995 eligible seeds before freezing. No constants were tuned. Confirming uses the first 993 eligible spread-2 seeds in 80000-87999.","Direct fill trace, first 200 eligible choosing seeds: oversized retained BUY fronts retail=0.11200265188892569 arb=-0.22242601777090867; oversized SELL fronts retail=0.09843494509500586 arb=-0.266286455623531. This motivated testing removal of the whole-order resize exception only. Direct fills are diagnostic, not causal paired gains.","{\"stage\":\"remove whole-order resize exception\",\"against\":\"s2_queue\",\"n\":125,\"mean\":-0.4000447633704003,\"standard_error\":0.2593650643709737,\"retail\":-0.8636525260583988,\"arb\":0.46360776269359993,\"failures\":0}","{\"stage\":\"flow\",\"against\":\"s2_queue\",\"name\":\"s2_queue_flow\",\"n\":125,\"mean\":0.6006145022752012,\"standard_error\":0.48634772149050715,\"retail\":0.23485457905039994,\"arb\":0.36575992322399997,\"failures\":0}","{\"stage\":\"narrow repair\",\"name\":\"no_whole_bid\",\"against\":\"s2_queue\",\"n\":125,\"mean\":-0.2458782381407996,\"standard_error\":0.15980986701582803,\"retail\":-0.37877379326159977,\"arb\":0.13289555512000062,\"failures\":0}","{\"stage\":\"narrow repair\",\"name\":\"no_whole_ask\",\"against\":\"s2_queue\",\"n\":125,\"mean\":-0.12522171268159976,\"standard_error\":0.179707372466993,\"retail\":-0.48005654128879927,\"arb\":0.3548348286144003,\"failures\":0}","{\"stage\":\"narrow repair\",\"name\":\"whole_safe\",\"against\":\"s2_queue\",\"n\":125,\"mean\":-0.40935174950320036,\"standard_error\":0.25893045238998696,\"retail\":-0.8666812021511994,\"arb\":0.4573294526551999,\"failures\":0}","{\"stage\":\"narrow repair\",\"name\":\"ask_only\",\"against\":\"s2_queue\",\"n\":125,\"mean\":-0.34802088007279897,\"standard_error\":0.18277672555501778,\"retail\":-0.5817259411791991,\"arb\":0.2337050611048002,\"failures\":0}","{\"stage\":\"narrow repair\",\"name\":\"bid_only\",\"against\":\"s2_queue\",\"n\":125,\"mean\":-0.2836631625927983,\"standard_error\":0.2861461393564071,\"retail\":-0.7911495866760002,\"arb\":0.5074864240784007,\"failures\":0}","{\"stage\":\"narrow repair\",\"name\":\"threshold\",\"against\":\"s2_queue\",\"n\":125,\"mean\":-0.795565368984798,\"standard_error\":0.27278270940271265,\"retail\":-1.4308779748176015,\"arb\":0.6353126058320008,\"failures\":0}","{\"stage\":\"narrow repair\",\"name\":\"no_remainder\",\"against\":\"s2_queue\",\"n\":125,\"mean\":-0.3937226786343985,\"standard_error\":0.05763641241493211,\"retail\":-0.5643258447816004,\"arb\":0.17060316614080015,\"failures\":0}","{\"stage\":\"flow\",\"against\":\"s2_queue\",\"name\":\"s2_queue_flow\",\"n\":995,\"mean\":0.44913139023748744,\"standard_error\":0.26353360832830547,\"retail\":0.17516161132010058,\"arb\":0.27396977891809043,\"failures\":0}","{\"stage\":\"bids\",\"against\":\"s2_queue_flow\",\"name\":\"s2_queue_flow_bids\",\"n\":995,\"mean\":0.3464649139261305,\"standard_error\":0.07697208759753545,\"retail\":-0.12893200980904512,\"arb\":0.4753969237346734,\"failures\":0}","{\"stage\":\"lead\",\"against\":\"s2_queue_flow_bids\",\"name\":\"s2_queue_flow_bids_lead\",\"n\":995,\"mean\":0.03996440252572866,\"standard_error\":0.16145088231340582,\"retail\":0.5594536844627138,\"arb\":-0.5194892819394975,\"failures\":0}","Pre-freeze base comparison on discovery subset: {\"n\":125,\"mean\":1.906457216901601,\"standard_error\":0.6411389974319606,\"retail\":1.8756705199216002,\"arb\":0.030786696991999773,\"failures\":0}","Frozen candidate confirming comparison to base: {\"n\":993,\"mean\":2.0015597964197385,\"standard_error\":0.43721099433183286,\"retail\":2.4149221962356497,\"arb\":-0.4133623998147029,\"failures\":0}","Frozen candidate confirming comparison to priced: {\"n\":993,\"mean\":1.2413501721502518,\"standard_error\":0.2535360118153212,\"retail\":2.070578441567271,\"arb\":-0.8292282694174219,\"failures\":0}","Scoring uses unmodified simulator commit b244530ee2a6247b5f930830eeca9dd950da0e7e with test-harness-only exact heap priority indexes for order lookup; accounting, matching and strategy arithmetic unchanged. Every indexed priority lookup checked against the original in 32 complete base/queue runs across all spreads. Original CLI and final timing use original lookups.","Frozen confirming audit: every indexed lookup also checked against the original during 30 complete base/priced/candidate runs with seeds in 80000-80031; all passed.","Timing in one process alternates base/candidate order on 100 identical confirming spread-2 seeds, excluding configuration sampling and strategy loading; wall seconds={\"base\":280.492975549947,\"s2_queue_flow_bids_lead\":286.24650167889195}; process CPU seconds={\"base\":111.12490618999993,\"s2_queue_flow_bids_lead\":113.90859733799995}","Final delivery integrity: JSON shape/byte limits, syntax and code SHA-256 passed; the code extracted from result.json reproduced the entire cached SimulationResult in the unmodified simulator for one confirming seed from each of spreads 1, 2, 3 and 4."],"next":"Enter this exact code/hash on Paradigm before trusting its local gain. Next compare queue + stock + s2-bids without q2-bids on fresh choosing/confirming seeds. Bid lead added only 0.03996440252572866 (SE 0.16145088231340582) on choosing runs while increasing arbitrage losses. Also investigate coverage-aware retention of oversized ask fronts; broad cancellations lost more retail edge than they saved from arbitrage."}