{"variant":"small Gaussian-mixture posterior of z=ln(p/spot) (<=4 components, ADF moment-matched truncation, Runnalls-cost merge), replicate B; not an RS2 overlay","status":"complete on replica; engine (Rust) run, Solidity port, and RS2 pairing NOT done (out of item scope/time)","engine_setup":"amm-challenge @6b6921f8 cloned and research/setup.sh ran OK (StarterStrategy validated); all scoring here is on replica.py (pure Python), compare paired only","seeds":{"train":"128..255 (64-seed sweep on 128..191 only, 8 configs)","eval":"10000..10255 (256 seeds, 10000 steps, replica's own per-seed config draws)","ablation":"10000..10063 router-off","never_touched":"5148000..5151999"},"inputs":{"urls":{"https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/replica.py":"d079712fa1f4850ad8337e656e7ee8dbdde806cd4762d597fae50f547ef9c7c4","https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/oracle_table.json":"3e9d1fc8874c6d796d4c26948d486b587f2a6b5610b20fba99923a60954cf4b5","https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/filter-brief.md":"0ef2200226b68aa58de6aad268442ba09ada710c54b3fb0ec35c77b491f78a4b","https://raw.githubusercontent.com/gtmcknight/amm-sim/main/research/setup.sh":"dc7fa6a1e59f5b043d3954cf68d538318b7affaf5c0db3ca69a1822680f300d4"}},"harness_changes":"none to replica.py; arms are policy wrappers. Filter (MixFilter.update) receives only (is_buy, amount_x, amount_y, t, x, y) plus its own stored fees and init reserves; replica's init(sigma,lam,size) and on_trade's arb,p,s2 are ignored except p used for logging error and by oracle/diag table arms.","arms":{"oracle":"table(true p, true arb flag)","filter":"table(p_hat=spot*exp(E[z]), inferred flag parb>0.5)","diag":"table(true p, inferred flag)"},"parameters":"{\"KMAX\": 4, \"SIG0\": 0.000945, \"N0\": 200.0, \"TAU_ROUTER\": 0.0015, \"ROUTER\": 1, \"PRETAIL\": 0.27, \"RET_MU\": 2.2757322735539907, \"RET_SD\": 1.3, \"PIN_VAR\": 1e-12, \"MINVAR\": 1e-12, \"ARB_CONF\": 0.9}","source":{"mf.py":"\"\"\"Small Gaussian-mixture posterior of z=ln(p/spot) for the AMM fee challenge (replica B).\nFilter sees only: init reserves, and per own-pool callback (is_buy, amount_x, amount_y, t, x, y)\nplus its own stored fees. Policy = frozen oracle_table driven by p_hat=spot*exp(E[z]).\"\"\"\nimport math, json, os\nSQ2 = math.sqrt(2.0)\ndef Phi(u): return 0.5 * (1.0 + math.erf(u / SQ2))\ndef phi(u): return math.exp(-0.5 * u * u) / 2.5066282746310002\nP = dict(KMAX=4, SIG0=0.000945, N0=200.0, TAU_ROUTER=0.0015, ROUTER=1, PRETAIL=0.27,\n         RET_MU=math.log(20.0) - 0.72, RET_SD=1.3, PIN_VAR=1e-12, MINVAR=1e-12, ARB_CONF=0.9)\nTAB = json.load(open(os.path.join(os.path.dirname(os.path.abspath(__file__)), 'oracle_table.json')))\n\ndef interp(arr, u):\n    u = (u + 8.0)\n    if u <= 0: return arr[0]\n    if u >= 16: return arr[16]\n    i = int(u); f = u - i\n    return arr[i] * (1 - f) + arr[i + 1] * f\n\ndef table_fees(spot, p, arbflag):\n    d = math.log(spot / p); u = d / 0.003\n    a = interp(TAB['ask'], u) + (TAB['arb_flag'] if arbflag else 0.0)\n    b = interp(TAB['bid'], u) + (TAB['arb_flag'] if arbflag else 0.0)\n    fa = 1 - math.exp(d - a * 0.003); fb = 1 - math.exp(-b * 0.003 - d)\n    return min(max(fb, 0.0), 0.1), min(max(fa, 0.0), 0.1)\n\ndef soft_upper(m, v, b, tau2):\n    \"\"\"Gaussian(m,v) times Phi((b-z)/sqrt(tau2)) (tau2=0: hard truncation z<=b).\n    Returns (mass, mean, var).\"\"\"\n    s = math.sqrt(v + tau2); a = (b - m) / s\n    Z = Phi(a)\n    if Z < 1e-300: return 0.0, b, P['MINVAR']\n    lam = phi(a) / Z\n    mean = m - v / s * lam\n    var = v - v * v / (v + tau2) * lam * (a + lam)\n    return Z, mean, max(var, P['MINVAR'])\n\ndef soft_lower(m, v, b, tau2):\n    Z, mean, var = soft_upper(-m, v, -b, tau2)\n    return Z, -mean, var\n\ndef trunc(m, v, lo, hi):\n    \"\"\"hard truncate to [lo,hi]\"\"\"\n    s = math.sqrt(v); A = (lo - m) / s; B = (hi - m) / s\n    Z = Phi(B) - Phi(A)\n    if Z < 1e-14:  # numerically empty: put at nearest edge\n        e = lo if m < lo else hi\n        return 1e-300, min(max(e, lo), hi), P['MINVAR']\n    pa, pb = phi(A), phi(B)\n    mu = m + s * (pa - pb) / Z\n    var = v * (1 + (A * pa - B * pb) / Z - ((pa - pb) / Z) ** 2)\n    return Z, mu, max(var, P['MINVAR'])\n\nclass MixFilter:\n    def __init__(self, x0, y0, router=None):\n        self.x, self.y = x0, y0\n        self.c = [[1.0, 0.0, 1e-10]]  # weight, mean, var  (p0 == initial spot)\n        self.t = -1; self.fb = self.fa = 0.003\n        self.sig2 = P['SIG0'] ** 2; self.sq = 0.0; self.dt = 0.0\n        self.lastpin = None; self.router = P['ROUTER'] if router is None else router\n        self.merge_err = 0.0; self.nmerge = 0; self.parb = 0.0\n    def _diffuse(self, n=1):\n        d = self.sig2 * n\n        for c in self.c: c[1] += -0.5 * self.sig2 * n; c[2] += d\n    def _band(self):\n        lo = math.log(1 - self.fb) if self.fb < 1 else -50; hi = -math.log(1 - self.fa)\n        out = []; tot = 0.0\n        for w, m, v in self.c:\n            Z, mu, var = trunc(m, v, lo, hi); out.append([w * Z, mu, var]); tot += w * Z\n        return out, tot\n    def _silent(self, n):\n        # fully silent steps: diffuse+truncate each step; long gaps: after 64 steps truncation\n        # is near stationary, cap per-step loop and do remaining in chunks of diffusion+trunc\n        for _ in range(min(n, 400)):\n            self._diffuse(1)\n            out, tot = self._band()\n            if tot > 0: self.c = [[w / tot, m, v] for w, m, v in out]\n        if n > 400:\n            self._diffuse(n - 400); out, tot = self._band()\n            if tot > 0: self.c = [[w / tot, m, v] for w, m, v in out]\n    def _norm_prune(self):\n        tot = sum(c[0] for c in self.c)\n        self.c = [[w / tot, m, v] for w, m, v in self.c if w / tot > 1e-9]\n        while len(self.c) > P['KMAX']:\n            best = None\n            for i in range(len(self.c)):\n                for j in range(i + 1, len(self.c)):\n                    wi, mi, vi = self.c[i]; wj, mj, vj = self.c[j]\n                    w = wi + wj; m = (wi * mi + wj * mj) / w\n                    v = (wi * (vi + (mi - m) ** 2) + wj * (vj + (mj - m) ** 2)) / w\n                    # Runnalls KL upper bound of the merge\n                    cost = 0.5 * (w * math.log(v) - wi * math.log(vi) - wj * math.log(vj))\n                    if best is None or cost < best[0]: best = (cost, i, j, [w, m, v])\n            cost, i, j, nc = best\n            self.merge_err += cost; self.nmerge += 1\n            self.c = [c for k, c in enumerate(self.c) if k not in (i, j)] + [nc]\n    def mean(self): return sum(w * m for w, m, v in self.c)\n    def var(self):\n        mu = self.mean(); return sum(w * (v + (m - mu) ** 2) for w, m, v in self.c)\n    def update(self, is_buy, ax, ay, t, x, y):\n        \"\"\"is_buy: AMM bought X (trader sold X). Returns (p_hat, arb_prob).\"\"\"\n        ls0 = math.log(self.y / self.x); ls1 = math.log(y / x)\n        first = t != self.t\n        parb = 0.0\n        if first:\n            if t > self.t + 1: self._silent(t - self.t - 1)\n            self._diffuse(1)\n            lo = math.log(1 - self.fb); hi = -math.log(1 - self.fa)\n            # arb hypothesis: pinned z (relative to post spot), mapped back to pre-spot coords\n            if not is_buy:  # AMM sold X: arb bought X, spot_after = p(1-fa)\n                zpost = -math.log(1 - self.fa); xn = x; a = ax\n                consistent = True\n            else:            # AMM bought X: spot_after = p/(1-fb)\n                zpost = math.log(1 - self.fb); xn = x; a = ax\n                consistent = True\n            zpre = zpost + ls1 - ls0\n            dens = 0.0\n            ok = (zpre > hi) if not is_buy else (zpre < lo)\n            if ok and consistent:\n                for w, m, v in self.c:\n                    dens += w * phi((zpre - m) / math.sqrt(v)) / math.sqrt(v)\n                dens *= 2.0 * a / xn  # |dz/dln a|\n            # retail hypothesis: no-arb band, then retail density of ln(amount in Y)\n            out, tot = self._band()\n            ly = math.log(max(ay, 1e-9))\n            dret = P['PRETAIL'] * phi((ly - P['RET_MU']) / P['RET_SD']) / P['RET_SD']\n            Larb = dens; Lret = tot * dret\n            parb = Larb / (Larb + Lret) if Larb + Lret > 0 else 0.0\n            ret = [[w * (1 - parb) / max(tot, 1e-300), m - (ls1 - ls0), v] for w, m, v in out] if tot > 0 else []\n            comps = ret + ([[parb, zpost, P['PIN_VAR']]] if parb > 1e-9 else [])\n            if not comps: comps = [[1.0, zpost, P['PIN_VAR']]]\n            self.c = comps\n            if parb > P['ARB_CONF']:\n                lp = ls1 + zpost\n                if self.lastpin is not None:\n                    tp, lpp = self.lastpin; dtp = t - tp\n                    if dtp > 0:\n                        self.sq += (lp - lpp + 0.5 * self.sig2 * dtp) ** 2; self.dt += dtp\n                        self.sig2 = (P['N0'] * P['SIG0'] ** 2 + self.sq) / (P['N0'] + self.dt)\n                self.lastpin = (t, lp)\n        else:\n            for c in self.c: c[1] -= (ls1 - ls0)\n        if parb < 0.5 and self.router:\n            # weak router observation: rival marginal >= p-band => z <= -ln(1-fa) after buy-X fill\n            tau2 = P['TAU_ROUTER'] ** 2; new = []\n            for w, m, v in self.c:\n                if v <= P['PIN_VAR'] * 1.01: new.append([w, m, v]); continue\n                if not is_buy: Z, mu, var = soft_upper(m, v, -math.log(1 - self.fa), tau2)\n                else: Z, mu, var = soft_lower(m, v, math.log(1 - self.fb), tau2)\n                new.append([w * Z, mu, var])\n            if sum(c[0] for c in new) > 0: self.c = new\n        self._norm_prune()\n        self.x, self.y, self.t = x, y, t; self.parb = parb\n        return (y / x) * math.exp(self.mean()), parb\n    def set_fees(self, fb, fa): self.fb, self.fa = fb, fa\n\nclass Arm:\n    \"\"\"mode: 'oracle' (true p, true flag), 'filter' (p_hat, inferred flag),\n    'diag' (true p, inferred flag). Oracle values are passed to the filter NEVER.\"\"\"\n    def __init__(self, mode, router=None):\n        self.mode = mode; self.router = router\n    def init(self, sigma, lam, size):  # hidden params ignored\n        self.f = MixFilter(100.0, 10000.0, self.router)\n        self.se = 0.0; self.n = 0; self.cov = 0; self.parb_err = 0\n        return 0.003, 0.003\n    def on_trade(self, is_buy, ax, ay, t, x, y, arb, p, s2):\n        ph, parb = self.f.update(is_buy, ax, ay, t, x, y)\n        e = math.log(ph / p); self.se += e * e; self.n += 1\n        sd = math.sqrt(self.f.var()); self.cov += abs(e) <= 1.96 * sd + 1e-12\n        flag = parb > 0.5; self.parb_err += flag != arb\n        s = y / x\n        if self.mode == 'oracle': fb, fa = table_fees(s, p, arb)\n        elif self.mode == 'diag': fb, fa = table_fees(s, p, flag)\n        else: fb, fa = table_fees(s, ph, flag)\n        self.f.set_fees(fb, fa)\n        return fb, fa\n","run.py":"import sys, json, os, time\nsys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))\nimport replica, mf\nfrom multiprocessing import Pool\ndef one(args):\n    seed, mode, router, nsteps = args\n    a = mf.Arm(mode, router); r = replica.run(seed, a, n_steps=nsteps)\n    return dict(seed=seed, mode=mode, edge=r['edge'], retail=r['retail'], arb=r['arb'], rv=r['rv'], av=r['av'],\n                se=a.se, n=a.n, cov=a.cov, flagerr=a.parb_err, merge=a.f.merge_err, sig=a.f.sig2 ** .5, tsig=r['sigma'])\nif __name__ == '__main__':\n    lo, hi, modes, router, nsteps, out = int(sys.argv[1]), int(sys.argv[2]), sys.argv[3].split(','), int(sys.argv[4]), int(sys.argv[5]), sys.argv[6]\n    t0 = time.time()\n    jobs = [(s, m, router, nsteps) for s in range(lo, hi) for m in modes]\n    with Pool(8) as pool: res = pool.map(one, jobs, chunksize=1)\n    json.dump(res, open(out, 'w')); print('secs', time.time() - t0)\n","agg.py":"import json, math\nr = json.load(open('e1.json')) + json.load(open('e2.json')); a = json.load(open('abl.json'))\nby = {}\nfor x in r: by.setdefault(x['seed'], {})[x['mode']] = x\ndef st(v):\n    n=len(v); m=sum(v)/n; sd=(sum((u-m)**2 for u in v)/(n-1))**.5; se=sd/n**.5; return dict(n=n,mean=round(m,3),se=round(se,3),ci95=[round(m-1.96*se,3),round(m+1.96*se,3)])\nS=sorted(by)\nout=dict(gap_oracle_minus_filter=st([by[s]['oracle']['edge']-by[s]['filter']['edge'] for s in S]),\n gap_oracle_minus_diag_trueP_inferredFlag=st([by[s]['oracle']['edge']-by[s]['diag']['edge'] for s in S]),\n gap_diag_minus_filter=st([by[s]['diag']['edge']-by[s]['filter']['edge'] for s in S]))\ndef agg(m,k): return round(sum(by[s][m][k] for s in S)/len(S),2)\nfor m in ('oracle','filter','diag'):\n    out[m]=dict(edge=agg(m,'edge'),retail_edge=agg(m,'retail'),arb_edge=agg(m,'arb'),retail_volY=agg(m,'rv'),arb_volY=agg(m,'av'),\n      rms_bps=round(1e4*math.sqrt(sum(by[s][m]['se'] for s in S)/sum(by[s][m]['n'] for s in S)),3),\n      coverage_95pct_interval=round(sum(by[s][m]['cov'] for s in S)/sum(by[s][m]['n'] for s in S),4),\n      arbflag_error_rate_per_callback=round(sum(by[s][m]['flagerr'] for s in S)/sum(by[s][m]['n'] for s in S),4),\n      merge_runnalls_cost_per_seed=agg(m,'merge'))\nab={x['seed']:x for x in a}; S2=sorted(ab)\nout['ablation_router_off_10000_10063']=dict(filter_on_minus_off=st([by[s]['filter']['edge']-ab[s]['edge'] for s in S2]),\n  rms_bps_off=round(1e4*math.sqrt(sum(ab[s]['se'] for s in S2)/sum(ab[s]['n'] for s in S2)),3),\n  rms_bps_on=round(1e4*math.sqrt(sum(by[s]['filter']['se'] for s in S2)/sum(by[s]['filter']['n'] for s in S2)),3))\nout['sigma_estimate_rms_err_bps']=round(1e4*math.sqrt(sum((by[s]['filter']['sig']-by[s]['filter']['tsig'])**2 for s in S)/len(S)),4)\njson.dump(out,open('agg.json','w')); print(json.dumps(out))\ncols=['seed','filt_edge','orc_edge','diag_edge','f_ret','f_arb','f_rvY','f_avY','o_ret','o_arb','o_rvY','o_avY','f_sqlog_sum','f_n','f_cov95_hits','f_flagerr']\nrows=[[s]+[round(by[s][m]['edge'],2) for m in ('filter','oracle','diag')]+[round(by[s][m][k],1) for m in ('filter','oracle') for k in ('retail','arb','rv','av')]+[round(by[s]['filter']['se'],5),by[s]['filter']['n'],by[s]['filter']['cov'],by[s]['filter']['flagerr']] for s in S]\njson.dump(dict(columns=cols,rows=rows),open('perseed.json','w'),separators=(',',':'))\n","test_mf.py":"import math, replica, mf, inspect\n# 1 isolation: update() signature has no oracle args; replaying recorded callbacks with garbage p gives same fees\nassert list(inspect.signature(mf.MixFilter.update).parameters) == ['self','is_buy','ax','ay','t','x','y']\nclass Rec(mf.Arm):\n    def on_trade(self, *a):\n        self.log = getattr(self, 'log', []); r = super().on_trade(*a); self.log.append((a[:6], r)); return r\narm = Rec('filter'); replica.run(130, arm, 2000)\nf = mf.MixFilter(100., 10000.)\nfor args, fees in arm.log:\n    ph, pa = f.update(*args); fb, fa = mf.table_fees(args[5]/args[4], ph, pa > .5); f.set_fees(fb, fa)\n    assert (fb, fa) == fees\nprint('isolation ok', len(arm.log))\n# 2 signs: arb buys X from us at ask fee fa; spot_after = p(1-fa) -> p_hat = p\nK = 1e6; p = 100.45; fa = 0.004; g = 1 - fa\nf = mf.MixFilter(100., 10000.); f.set_fees(0.003, fa)\nnx = math.sqrt(K / (g * p)); ny = K / nx\nph, pa = f.update(False, 100 - nx, (ny - 10000) / g, 50, nx, ny)\nprint('sell-X pin', ph, pa); pin=[c for c in f.c if c[2]<1e-11]; assert pin and abs(math.exp(pin[0][1])*f.y/f.x/p-1)<1e-9; print('pinned comp ok, parb',pa)\np = 99.45; fb = 0.005; g = 1 - fb\nf = mf.MixFilter(100., 10000.); f.set_fees(fb, 0.003)\nxv = math.sqrt(K * g / p); ax = (xv - 100) / g; nrx = 100 + ax * g; nry = K / nrx\nph, pa = f.update(True, ax, 10000 - nry, 50, nrx, nry)\nprint('buy-X pin', ph, pa); pin=[c for c in f.c if c[2]<1e-11]; assert pin and abs(math.exp(pin[0][1])*f.y/f.x/p-1)<1e-9; print('pinned comp ok, parb',pa)\n# 3 repeated callback at same t: retail, mean shifts with spot only (router off)\nf = mf.MixFilter(100., 10000., router=0); f.set_fees(0.003, 0.003)\nph1, _ = f.update(False, 0.1, 10.0, 5, 99.9, K / 99.9); z1 = f.mean()\nph2, pa2 = f.update(False, 0.1, 10.0, 5, 99.8, K / 99.8)\nassert pa2 == 0.0 and abs(ph2 - ph1) < 1e-9; print('repeat ok', ph1, ph2)\n# 4 silent truncation keeps mean within band\nf = mf.MixFilter(100., 10000.); f.set_fees(0.003, 0.003); f._silent(500)\nassert abs(f.mean()) < 0.003 and len(f.c) <= 4; print('silent ok', f.mean(), f.var() ** .5)\n","sweep.py":"import sys, json, replica, mf\nfrom multiprocessing import Pool\ndef one(a):\n    seed, kv = a\n    mf.P.update(kv); r = {}\n    for m in ('oracle', 'filter'):\n        arm = mf.Arm(m); r[m] = replica.run(seed, arm, 10000)['edge']\n    return r['oracle'] - r['filter'], 1e4 * (arm.se / arm.n) ** .5\ngrid = [dict(), dict(TAU_ROUTER=0.0005), dict(TAU_ROUTER=0.004), dict(ROUTER=0), dict(PRETAIL=0.1), dict(PRETAIL=0.6), dict(KMAX=2), dict(N0=1000.0)]\nwith Pool(8) as p:\n    for kv in grid:\n        res = p.map(one, [(s, kv) for s in range(128, 192)])\n        print(kv, round(sum(r[0] for r in res) / len(res), 2), round(sum(r[1] for r in res) / len(res), 2), flush=True)\n"},"source_sha256":{"mf.py":"8adbd509efdac3e77ccde38d07a7272e9706b42ea4ecc926f77963e2a332445e","run.py":"7d7026c48cea6901ff3debebe5f552a7c263fa330a7f14448338a3df41837d33","agg.py":"d0e2f71bb48ab1467ca63d3af31d63f739678ce839408712f0165a3e69f77479","test_mf.py":"4192217a4bc758a6c0e5308d59224ea02a24dd217da012bd13fe5df824782ddc","sweep.py":"8e6613ef40efa930307bbea6a95acf4c438c15ce26b89afab127ee1b49b6efe5"},"aggregate":{"gap_oracle_minus_filter":{"n":256,"mean":6.273,"se":0.082,"ci95":[6.112,6.433]},"gap_oracle_minus_diag_trueP_inferredFlag":{"n":256,"mean":0.323,"se":0.014,"ci95":[0.294,0.351]},"gap_diag_minus_filter":{"n":256,"mean":5.95,"se":0.081,"ci95":[5.791,6.109]},"oracle":{"edge":535.22,"retail_edge":566.71,"arb_edge":-31.5,"retail_volY":76276.1,"arb_volY":23965.94,"rms_bps":14.17,"coverage_95pct_interval":0.9465,"arbflag_error_rate_per_callback":0.094,"merge_runnalls_cost_per_seed":6.11},"filter":{"edge":528.94,"retail_edge":563.86,"arb_edge":-34.91,"retail_volY":75340.41,"arb_volY":24720.97,"rms_bps":15.206,"coverage_95pct_interval":0.9473,"arbflag_error_rate_per_callback":0.1019,"merge_runnalls_cost_per_seed":9.5},"diag":{"edge":534.89,"retail_edge":566.29,"arb_edge":-31.39,"retail_volY":75758.83,"arb_volY":23835.54,"rms_bps":14.334,"coverage_95pct_interval":0.9453,"arbflag_error_rate_per_callback":0.094,"merge_runnalls_cost_per_seed":6.05},"ablation_router_off_10000_10063":{"filter_on_minus_off":{"n":64,"mean":-0.044,"se":0.069,"ci95":[-0.18,0.091]},"rms_bps_off":15.235,"rms_bps_on":15.245},"sigma_estimate_rms_err_bps":0.4562},"headline":"eval 256 seeds: oracle-minus-filter gap 6.27 (SE 0.08, CI 6.11..6.43) vs target <=2: TARGET MISSED. Filter RMS 15.2 bps, 95% interval coverage 0.947. Inferred-flag cost with true p only 0.32, so ~5.95 of the gap is price error. Router likelihood ablation: on-off = -0.04 (SE 0.07), i.e. no measurable value.","train_sweep_128_191":{"default":[6.55,15.23],"TAU_ROUTER=0.0005":[6.69,15.34],"TAU_ROUTER=0.004":[6.43,15.21],"ROUTER=0":[6.52,15.21],"PRETAIL=0.1":[6.77,17.0],"PRETAIL=0.6":[8.49,16.4],"KMAX=2":[8.63,16.54],"N0=1000":[8.59,16.5],"_cols":"[mean gap oracle-filter, rms bps]; defaults frozen"},"tests":{"command":". scratch/env.sh && python3 test_mf.py (in source dir with replica.py, oracle_table.json)","result":"isolation ok 1866\nsell-X pin 100.11883385171149 0.185031113125793\npinned comp ok, parb 0.185031113125793\nbuy-X pin 99.83901289001993 0.1464623481102429\npinned comp ok, parb 0.1464623481102429\nrepeat ok 100.0343108243682 100.03431082436818\nsilent ok -1.4847619393627061e-06 0.0017232303915676735\nrc=0\n","notes":"isolation: update() signature has no oracle args and replaying the recorded callbacks gives bit-identical fees; signs: pinned component equals ln(p/spot_after) for both directions; repeated same-t callback treated as retail (parb=0, mean shifts with spot only); silent truncation bounded; gap propagation: aggregate gap equals mean of per-seed gaps (computed from per_seed)."},"per_seed":{"columns":["seed","filt_edge","orc_edge","diag_edge","f_ret","f_arb","f_rvY","f_avY","o_ret","o_arb","o_rvY","o_avY","f_sqlog_sum","f_n","f_cov95_hits","f_flagerr"],"rows":[[10000,439.03,445.68,445.55,461.5,-22.5,61645.4,21382.2,465.4,-19.7,62676.2,20750.2,0.01991,8438,7995,962],[10001,568.88,572.59,572.4,598.2,-29.4,87853.1,26742.3,598.4,-25.8,88628.8,26003.6,0.02402,11705,11123,1037],[10002,522.55,527.97,527.44,553.2,-30.7,68253.9,24871.5,555.5,-27.5,69315.7,23991.7,0.02352,9636,9126,1060],[10003,564.65,573.64,573.58,594.0,-29.3,81787.3,26687.5,599.4,-25.8,82803.6,25935.9,0.02523,11111,10479,1003],[10004,519.86,524.59,524.35,545.8,-26.0,72688.2,24386.8,547.6,-23.0,73741.7,23809.0,0.02046,9921,9420,966],[10005,523.17,527.73,527.88,550.1,-27.0,72728.4,24023.7,551.0,-23.3,73539.1,23414.9,0.02204,9936,9461,964],[10006,481.51,487.62,487.33,507.5,-26.0,74485.7,23742.5,510.1,-22.5,75295.7,22987.8,0.02083,10272,9783,941],[10007,519.87,527.21,526.91,546.7,-26.8,76389.4,24161.2,551.2,-24.0,77242.6,23734.9,0.02369,10478,9869,1039],[10008,654.73,664.11,663.66,687.1,-32.3,95121.7,28256.6,692.1,-28.0,96183.9,27361.3,0.02714,11968,11309,1148],[10009,646.44,653.73,653.62,677.7,-31.2,91698.4,27860.3,681.6,-27.8,92585.7,27194.9,0.02796,12024,11274,1143],[10010,473.8,479.56,479.5,499.2,-25.4,75330.6,23504.9,501.6,-22.0,76561.4,22847.1,0.02414,10642,10060,1116],[10011,365.43,371.52,371.12,385.5,-20.1,58279.6,19173.4,388.9,-17.4,58837.5,18499.1,0.01849,8365,7942,934],[10012,452.88,459.0,458.31,479.0,-26.2,74243.2,23575.7,481.2,-22.2,75282.7,22751.5,0.02623,10288,9573,1163],[10013,397.26,402.85,402.44,417.4,-20.2,57111.1,19450.4,420.5,-17.6,58205.9,18876.1,0.01835,8242,7808,866],[10014,697.37,702.86,702.74,733.5,-36.1,86968.8,27218.9,735.2,-32.4,87675.9,26631.5,0.02252,11225,10720,1031],[10015,621.86,632.33,632.17,654.5,-32.6,92091.9,28482.9,660.9,-28.6,93499.3,27734.4,0.03096,11760,11010,1194],[10016,560.8,569.34,569.16,630.5,-69.7,70890.4,24141.1,635.5,-66.1,71952.9,23389.4,0.02439,9634,9111,1121],[10017,490.02,494.51,494.25,516.9,-26.9,72166.8,24266.6,518.8,-24.3,73105.0,23875.2,0.02126,10079,9588,993],[10018,476.61,482.17,482.07,502.8,-26.2,69531.5,24199.5,504.8,-22.6,70468.5,23389.6,0.02057,9500,9079,982],[10019,450.39,455.47,455.09,472.7,-22.3,61095.8,21025.7,475.0,-19.5,62126.4,20408.1,0.0191,8450,8082,950],[10020,493.01,498.15,497.64,518.8,-25.8,67805.1,23828.4,521.0,-22.9,68460.0,23205.9,0.01888,9327,8913,944],[10021,407.16,413.41,412.41,427.7,-20.5,56647.0,20248.2,431.3,-17.9,57695.8,19503.5,0.02068,8398,7947,991],[10022,435.76,442.04,441.51,458.6,-22.8,61047.5,21015.4,461.9,-19.8,61812.7,20259.0,0.02239,8720,8164,1056],[10023,630.2,635.3,634.72,663.1,-32.9,86819.3,27218.5,664.3,-29.0,87931.0,26225.6,0.02404,10944,10389,1037],[10024,475.71,483.68,483.23,502.4,-26.7,72698.6,24533.6,507.0,-23.3,73874.8,23743.3,0.0257,10574,10059,1140],[10025,442.14,447.67,447.17,465.8,-23.7,61688.0,21276.4,468.1,-20.5,62444.3,20480.2,0.02328,9164,8704,1031],[10026,341.71,347.39,346.96,361.1,-19.4,53761.7,18965.7,364.6,-17.2,54625.3,18425.5,0.02011,8376,7897,965],[10027,543.65,549.71,549.59,572.0,-28.4,73009.7,24969.6,574.4,-24.7,73914.1,24197.1,0.02535,10076,9564,1104],[10028,522.33,527.77,527.6,552.4,-30.1,67708.4,23436.2,554.8,-27.1,68637.9,23007.4,0.02159,9215,8810,967],[10029,438.06,444.58,443.77,461.2,-23.1,72057.7,21959.3,464.8,-20.2,72760.7,21296.2,0.02442,10252,9610,1070],[10030,590.55,597.82,597.29,622.5,-31.9,89023.4,28016.9,625.6,-27.7,89760.2,27047.2,0.02735,11668,11061,1144],[10031,336.53,343.56,343.24,358.4,-21.9,56927.1,20580.6,361.7,-18.2,58012.4,19671.4,0.02344,8580,8202,1077],[10032,632.05,637.94,637.84,662.9,-30.8,85923.5,27057.2,664.7,-26.8,86666.4,26072.1,0.0241,11012,10441,1009],[10033,529.68,536.45,536.22,559.0,-29.3,81247.9,25980.5,561.4,-24.9,82155.9,25100.0,0.02694,10787,10213,1084],[10034,559.55,566.54,565.99,587.5,-28.0,83811.2,25377.5,590.9,-24.3,84709.8,24618.8,0.02657,11410,10757,1134],[10035,627.51,636.15,635.79,661.0,-33.5,93738.1,28612.9,664.6,-28.5,95096.7,27580.4,0.03051,12175,11519,1235],[10036,540.5,546.64,546.18,569.0,-28.5,81501.9,25537.2,571.1,-24.5,82299.0,24462.0,0.02639,10960,10335,1142],[10037,439.28,445.18,444.89,463.6,-24.3,66517.2,22393.8,466.1,-20.9,67465.9,21411.8,0.02258,9332,8859,1013],[10038,614.68,620.61,620.16,645.5,-30.8,91388.1,27699.2,647.6,-27.0,92527.8,26776.4,0.02937,12403,11693,1202],[10039,584.86,590.59,590.15,618.0,-33.2,78325.9,25048.3,620.0,-29.4,79366.8,24324.4,0.02679,10633,10013,1191],[10040,603.08,609.99,610.04,633.2,-30.2,90642.8,27583.1,636.9,-26.9,91586.2,27149.3,0.02408,12147,11500,1008],[10041,625.75,632.28,632.09,655.0,-29.2,86047.1,26701.2,657.8,-25.5,86756.3,25889.8,0.02216,11258,10757,956],[10042,706.95,711.21,711.24,740.9,-34.0,93227.8,29559.4,741.0,-29.8,94009.7,28685.1,0.02371,12047,11484,1040],[10043,631.92,639.26,638.98,662.9,-30.9,88423.7,27232.3,666.8,-27.5,89319.8,26457.0,0.02722,11462,10761,1155],[10044,415.26,421.89,421.57,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6,10587,1190],[10229,426.6,433.69,433.42,449.6,-23.0,69234.6,22019.7,454.3,-20.6,70287.3,21562.4,0.02227,9882,9325,1084],[10230,625.05,633.96,633.74,658.2,-33.2,92494.8,28464.2,662.6,-28.6,93846.3,27757.7,0.02791,11578,10952,1149],[10231,689.46,696.75,696.45,723.5,-34.1,89739.2,29005.3,726.7,-30.0,90643.8,28098.2,0.02757,11726,11068,1060],[10232,497.51,502.62,502.14,523.8,-26.3,71324.9,23657.1,525.8,-23.2,72286.6,22899.7,0.02604,10105,9498,1121],[10233,443.27,448.73,448.52,467.8,-24.5,67144.4,22999.6,470.4,-21.7,67777.6,22528.9,0.01872,9308,8833,918],[10234,533.59,539.9,539.73,563.0,-29.4,73682.7,24901.4,566.2,-26.3,74716.2,24415.3,0.02371,10151,9610,1002],[10235,658.47,663.13,663.07,692.1,-33.7,84552.4,26694.1,693.2,-30.0,85025.1,25802.7,0.02261,10548,10033,997],[10236,438.21,445.66,445.09,462.0,-23.8,69015.9,22082.2,466.3,-20.7,70214.0,21227.6,0.02513,9901,9326,1048],[10237,639.74,645.7,645.62,671.7,-31.9,86555.8,28158.6,673.9,-28.2,87370.2,27178.6,0.02338,11428,10847,1034],[10238,449.56,454.82,454.59,479.7,-30.1,57954.1,22713.8,481.6,-26.8,58866.1,21768.1,0.0217,8483,8089,1022],[10239,596.75,603.9,603.62,627.9,-31.1,82324.2,27141.3,631.3,-27.4,83416.7,26225.9,0.02939,11155,10492,1198],[10240,595.71,603.95,603.93,635.4,-39.7,82725.6,26208.0,639.5,-35.6,83500.6,25211.5,0.0291,11219,10503,1194],[10241,401.16,406.79,406.24,424.4,-23.3,59437.3,20609.8,427.6,-20.8,60364.7,19996.3,0.02117,8738,8261,1006],[10242,418.75,425.49,425.37,441.0,-22.3,59064.4,20216.6,444.8,-19.3,59467.6,19572.6,0.01898,8707,8279,896],[10243,615.68,621.37,621.23,685.2,-69.5,73112.8,25595.0,687.7,-66.3,73658.5,24733.5,0.02044,9908,9430,881],[10244,435.85,440.85,441.01,460.0,-24.2,63912.4,22416.9,462.2,-21.3,64502.8,21798.4,0.02031,9399,8929,955],[10245,593.85,600.11,599.79,624.1,-30.2,82756.0,26469.9,626.3,-26.2,84022.8,25643.2,0.02799,11003,10310,1179],[10246,556.74,563.34,562.7,586.3,-29.6,82400.6,26394.5,588.9,-25.6,83032.8,25591.1,0.02508,11241,10653,1065],[10247,495.56,504.92,504.18,523.4,-27.8,76332.7,24912.0,528.6,-23.7,77279.5,23845.7,0.02647,10412,9831,1151],[10248,491.69,499.5,499.1,518.6,-26.9,78275.1,24583.2,522.9,-23.4,79585.5,23742.4,0.02895,10473,9864,1183],[10249,531.39,536.98,536.67,558.8,-27.5,76769.5,25258.9,561.3,-24.3,77631.5,24631.6,0.02094,10573,10096,939],[10250,400.59,407.05,406.2,422.4,-21.8,60290.5,20455.3,426.2,-19.1,61403.8,19933.5,0.02119,8957,8504,1003],[10251,381.57,386.21,385.65,404.5,-22.9,59120.5,21663.5,406.1,-19.8,59863.9,20962.2,0.0213,8892,8413,1008],[10252,394.88,399.77,399.3,417.5,-22.7,59136.5,20859.0,419.6,-19.9,60195.8,20226.4,0.02287,8470,8033,1041],[10253,575.09,581.53,581.13,603.6,-28.5,88460.9,26373.2,606.8,-25.3,89486.8,25796.6,0.02432,11936,11353,1032],[10254,495.62,502.47,502.44,522.6,-27.0,65476.6,24431.9,527.2,-24.7,66520.5,23957.2,0.02186,8998,8576,1041],[10255,596.71,601.81,601.53,626.1,-29.4,86360.3,26943.7,627.8,-26.0,87227.9,26136.0,0.02463,11307,10704,1060]]},"runtime":{"eval_256x3arms_sec":345.6,"ablation_64_sec":25.3,"sweep_sec":417,"cpus":8},"port_cost_estimate":"bounded state: 4 comps x (w,mean,var) + sigma accumulators + last pin + t = ~17 slots; per callback per silent step 4 erf/exp evaluations (needs fixed-point Phi/phi approximations, ~1.5-3k gas each) -> silent loop must be capped (e.g. 16 steps then closed-form) to stay under 245k; merge pass O(K^2)=10 pairs with ln: estimate 80-200k gas per afterSwap, unverified (no Solidity written).","dead_ends":["KMAX=2: gap 8.63 vs 6.55 at KMAX=4 (train 64 seeds)","PRETAIL 0.6: 8.49; 0.1: 6.77","sigma prior weight N0=1000: 8.59 (surprising; possibly noisy)","router likelihood (soft band, tau 5-40 bps): no effect, ablation -0.04+-0.07"],"limitations":["Arb/retail classifier undercalls arbs: in unit test a just-outside-band arb got parb 0.15-0.19 because retail amount density (lognormal guess mu=ln20-0.72, sd 1.3, PRETAIL 0.27) dominates the narrow pin density; flag error 10.2% of callbacks (oracle-run diag 9.4%). This is the most likely source of the 6.3 gap and the next thing to fix (e.g. use exact retail split-amount model, or arb amount-implied pin consistency with band).","Moment-matched (ADF) truncation per component loses tail shape; merge cost ~9.5 Runnalls nats/seed.","Long silent gaps >400 steps collapsed to one diffuse+truncate.","Sigma from pins with parb>0.9 only (selection biased toward large moves); RMS sigma error 0.46 bps/step.","Uncapped-arb assumption: 0.99x cap not modelled.","Replica only; no engine, no RS2 pairing, no 4000-seed confirm; replica reads ~3-5 above board."]}