{"approach": "Started with the priced per-run Bayesian retail-rate and order-size flow estimator. Then added the original s3-clock rule before the bridge logic: if H>500, suppress ammunition bids at ticks >=2 above estimated fair value; bridge logic remains unchanged. Copied trading rules only; omitted the pieces' optional belief-loop speed refactors. All trading changes are gated by self.s == 3. No constants tuned, no seed recognition. Choosing and confirming use disjoint prescribed seed windows; means and paired sample-standard-error estimates are local measurements, not Paradigm pricing. Work files stayed in test/scratch/.cache under the scratch exception; only result.json and sources.json are delivered.", "blocked": null, "spread": 3, "base_mean_edge": 108.63974289615767, "contains": ["s3-flow", "s3-clock"], "holdout": {"mean_edge": 115.89562063046318, "retail_edge": 147.16254600357766, "arb_edge": -31.266925373125552, "failures": 0}, "diff": {"mean": 3.041444306678269, "standard_error": 0.9323195936655891, "retail": -1.423968732666096, "arb": 4.465413039345876}, "vs_priced": {"mean": 0.43899751404466797, "standard_error": 0.06254419195348541}, "others_identical": {"runs": 450, "identical": true}, "seconds": {"base": 146.9139512560796, "yours": 148.38329777796753}, "code": "\"\"\"Crossing-cover base with isolated spread overrides; spread 3 sizes on this run's own estimated retail flow.\"\"\"\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\n# Spread 3 only: grids over the simulator's public bands for retail rate and mean order size.\nLAM_NODES = [0.154 + (i + 0.5) * 0.022 for i in range(9)]\nLAM_LOGS = [math.log(v) for v in LAM_NODES]\nM_NODES = [2.64 + (i + 0.5) * 3.696 / 9.0 for i in range(9)]\nM_MUS = [math.log(v) - 0.72 for v in M_NODES]\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_ll = [0.0] * 9   # log likelihood of each M_NODES value\n        self.flow_events = 0       # retail orders seen\n        self.flow_exposed = 0      # side-steps on which one would have been seen\n        self.flow_lam = 0.253      # posterior means, starting at the prior's\n        self.flow_m = 4.488\n        self.flow_ask = None       # (shares, price, rival quote) we showed last step\n        self.flow_bid = None\n        self.params = P.copy()\n\n    def _oid(self, tag):\n        self.n += 1\n        return tag + str(self.n)\n\n    def _flow_side(self, seen, filled):\n        # One side's last step: an order under our displayed size shows its whole notional, one\n        # that used it up only shows a lower bound. Such bounds also come from the arbitrageur,\n        # so they are weighted down by adding 0.5 to their likelihood.\n        self.flow_exposed += 1\n        if filled <= 0.1:\n            return False\n        self.flow_events += 1\n        cap, price = seen[0], seen[1]\n        ll = self.flow_ll\n        if filled < cap - 0.01:\n            ln = math.log(filled * price)\n            for j in range(9):\n                d = (ln - M_MUS[j]) / 1.2\n                ll[j] -= 0.5 * d * d\n        else:\n            ln = math.log(cap * price)\n            for j in range(9):\n                ll[j] += math.log(0.5 + 0.5 * math.erfc((ln - M_MUS[j]) / (1.2 * SQ2)))\n        return True\n\n    def _flow_update(self, state, cb, ca):\n        new = False\n        seen = self.flow_ask\n        if seen is not None and ca <= seen[2] + 1:\n            new = self._flow_side(seen, state.sell_filled_quantity)\n        seen = self.flow_bid\n        if seen is not None and cb >= seen[2] - 1:\n            new = self._flow_side(seen, state.buy_filled_quantity) or new\n        if new:\n            ev = self.flow_events\n            ex = 0.5 * self.flow_exposed\n            lg = [ev * a - ex * b for a, b in zip(LAM_LOGS, LAM_NODES)]\n            top = max(lg)\n            ws = [math.exp(v - top) for v in lg]\n            self.flow_lam = sum(w * v for w, v in zip(ws, LAM_NODES)) / sum(ws)\n            top = max(self.flow_ll)\n            ws = [math.exp(v - top) for v in self.flow_ll]\n            self.flow_m = sum(w * v for w, v in zip(ws, M_NODES)) / sum(ws)\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_level': 0.6, 'flow_safety': 2.0})\n        P = self.params\n        if self.s == 3:\n            self._flow_update(state, cb, ca)\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        fscale = 1.0\n        if self.s == 3:\n            rho = self.flow_lam * 0.5\n            mu = math.log(self.flow_m) - 0.5 * P['sig_n'] ** 2\n            fscale = self.flow_lam * self.flow_m * 0.5 / P['flow_level']\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(fscale * P['ydem'] * min(H, P['W']) / x, capw)\n            full = min(fscale * 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                stock_rate *= max(0.5, min(2.0, fscale))\n            q1 = max(0.0, stock_rate * min(H, P['Wf']) / (self.s / 100.0) - Y)\n\n        if self.s == 3 and H > 500 and amt >= 2 and amt / 100.0 > phat:\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            margin = max(0.005, P['flow_safety'] * self.st / 100.0)\n            q = ka + sum(o.quantity for o in out if o.side is Side.SELL and o.quantity > PROBE)\n            self.flow_ask = (q, ask_t / 100.0, ca) if q * ask_t >= 50.0 and ask_t / 100.0 > phat + margin else None\n            q = 0.0\n            tb = 0\n            if kb > 0:\n                q, tb = kb, bid_t\n            for o in out:\n                if o.side is Side.BUY and o.quantity > PROBE and o.price_ticks > cb:\n                    q += o.quantity\n                    tb = max(tb, o.price_ticks)\n            x = max(phat, 0.05)\n            self.flow_bid = (q, x, cb) if q * x >= 0.5 and tb / 100.0 < phat - margin else None\n        return actions + out\n", "code_sha256": "2d763767160f2791f9e92e18300f49a5fce7ce7e99a717c463c3e8c081920550", "tried": ["Calibration: parent, seeds 1000..1599, 600 simulations, CLI --workers 4 --json, no sandbox; mean=108.63974289615767, failures=0, seconds=382.04293986596167. Over five minutes: all requested counts halved (rounding down): choosing first 1020 of 2041 spread-3 seeds in [20000,28000), confirming first 994 of 1988 in [80000,88000), other spreads 150 each from 80000, timing 100 per strategy.", "Choosing n=1020, flow + s3-asks minus priced flow: {'mean': -0.7963580444730389, 'standard_error': 0.8694739606602105, 'retail': 1.1646048153936286, 'arb': -1.9609628598711766}; rejected.", "Choosing n=1020, flow + s3-asks + s3-clock: versus flow + s3-asks {'mean': 0.3603429829233334, 'standard_error': 0.0701132353166557, 'retail': -0.11076634221725555, 'arb': 0.47110932514009807}; versus priced flow {'mean': -0.4360150615497056, 'standard_error': 0.8703672612513013, 'retail': 1.053838473176373, 'arb': -1.4898535347310784}. Discarded because the preceding front-ask addition failed its gain test; tested clock separately on retained flow.", "Choosing n=1020, flow_clock minus priced: {'mean': 0.2643145625191177, 'standard_error': 0.11252652046932754, 'retail': -0.08507077939833342, 'arb': 0.3493853419181373}; kept.", "Counting correction before confirming outcomes were available: initial jobs used half-width seed windows (1061 choosing, 1000 confirming). Aggregation and decisions corrected to the first floor(n/2) matching spread-3 seeds, 1020 choosing and 994 confirming; extra 41 choosing and 6 confirming runs excluded. The chosen code and hash did not change.", "Initial supplemental choosing n=1061: flow + asks minus flow {'mean': -0.7434662733156453, 'standard_error': 0.8359498586284283, 'retail': 1.1425828337683328, 'arb': -1.886049107087936}; flow + asks + clock minus flow + asks {'mean': 0.38888412974655984, 'standard_error': 0.07010720921731918, 'retail': -0.10671162861856803, 'arb': 0.4955957583644675}; flow + clock minus flow {'mean': 0.2975817290795477, 'standard_error': 0.10991288578039043, 'retail': -0.08089188887879369, 'arb': 0.37847361795900103}. These larger-window figures did not select a different code.", "Frozen flow_clock: confirming n=994, candidate-minus-priced={'mean': 0.43899751404466797, 'standard_error': 0.06254419195348541, 'retail': -0.0932503857858147, 'arb': 0.5322478998288732}; positive, retained frozen combination.", "Final confirming spread 3 n=994; base mean=112.85417632378491; priced mean=115.45662311641851; failures base/priced/final=0/0/0.", "Full SimulationResult dictionaries identical on 450 non-target runs (150 each of spreads 1,2,4, first matching seeds from 80000); simulator commit b244530ee2a6247b5f930830eeca9dd950da0e7e unmodified. Timing: 100 spread-3 runs each, first matching confirming seeds, one process, alternating execution order, ratio=1.0100014090515255."], "next": "Have the operator price this exact flow-plus-clock code on Paradigm before merging it with other spreads. Next seat: audit spread-3 low-price FIFO events to explain why the front-ask rule added more arbitrage loss than retail edge when combined with flow on choosing seeds; evaluate any revised mechanism on fresh disjoint seeds without tuning constants. Do not infer a leaderboard gain from unseen-seed results."}