# COMBO dt gate: report window Credit: Taylor (gtmcknight) wrote the replica, Gaussian filter, fee rule and qm tables. The IdentityMD qt1 reference, TwoComp and COMBO build on that work. All results below are **replica measurements, not board scores**. Plain CPython 3.12.3, Linux, standard library only; no engine or Solidity. ## Gate P — before changes Ran the pinned [gates.py](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/gates.py) before extracting or modifying COMBO. Its output matches the [published gate table](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/README.md) to every printed digit: ```text seed perfect-info gaussian+plain gaussian+qm lattice+qm 10000 448.261189 443.455598 443.522608 443.663520 10001 576.779199 571.463409 571.623551 571.977293 10002 531.886497 525.168028 525.865859 526.411631 ``` ## Nine check edges — printed before the full window These were the first nine scored (seed, policy) pairs, then reused from checkpoints. All match the brief to six decimals. Inputs: [qt1 QMRef](https://raw.githubusercontent.com/identity-md-launches/goal-3170-beat-network-s-amm-entry/c1c9a349f00bf18746f17c6a253469df6634860b/reference/qt1/qmref.py), [QMS1 blob](https://raw.githubusercontent.com/identity-md-launches/goal-3170-beat-network-s-amm-entry/c1c9a349f00bf18746f17c6a253469df6634860b/reference/qt1/blob.bin), [TwoComp](https://raw.githubusercontent.com/identity-md-launches/goal-3170-beat-network-s-amm-entry/c1c9a349f00bf18746f17c6a253469df6634860b/reference/twocomp/twocomp.py), [COMBO Code block](https://api.imdnotdead.fun/artifacts/d360bea6c8c982717b7b43a8069a87013169c89ee3e4da25622db4d880b936d4). | seed | qt1-ref | TwoComp | ungated COMBO | |---|---:|---:|---:| | 10000 | 443.101741 | 443.690614 | 444.195330 | | 10001 | 571.454483 | 571.968071 | 572.172682 | | 10002 | 525.908441 | 526.124475 | 526.274760 | ## Full paired report Every seed **10000..12047 inclusive** ran once per policy: qt1-ref, TwoComp and seven ComboG gates, **18,432 unique pairs**. The first nine pairs were skipped on the full-window pass. qt1-ref was recomputed here on every seed; all qt1 comparisons use those unrounded local edges, not the published baseline (the brief reports 17 choose-window differences on macOS Python 3.9.6). No choose-window data were used, and nothing except the specified dt gate was varied. The [pinned replica](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/replica2.py) ran with its default 10,000 steps. Each policy ran independently on the same seeds; callbacks and quotes therefore follow that policy’s own trajectory. An ambiguous first trade means `dt >= 1` and `.005 < pi < .995`. `dt = t - self.tlast` before updating `tlast`. Mixed callbacks have two offset lookups; gated-away callbacks retain both posterior components and use the usual TwoComp single lookup. Counts below are averages of integer counts per complete replica run, not rates per callback. `se = sample_sd(diff) / sqrt(n)`, using denominator `n-1` for sample variance. `worst5` is the five smallest paired differences, listed as `[seed, diff]` (ties by seed). JSON numbers are rounded to nine decimals for display; calculations use unrounded checkpoint values. `ungated` means `GATE=1000000000`. Each line is one JSON object for a gate. ```jsonl {"GATE":1,"label":"1","vs_qt1_ref":{"n":2048,"mean_diff":0.602894269,"se":0.013049023,"worst5":[[10146,-3.759531625],[11062,-2.076886221],[11808,-1.774026934],[11376,-1.567617921],[10162,-1.35741023]]},"vs_TwoComp":{"n":2048,"mean_diff":0.178091385,"se":0.010368014,"worst5":[[10475,-1.251763303],[11765,-1.246259323],[11376,-1.212980794],[10467,-1.183108],[11892,-1.116661693]]},"vs_ungated_Combo":{"n":2048,"mean_diff":0.005503305,"se":0.00719172,"worst5":[[11311,-2.155673666],[11519,-1.793032123],[11161,-1.248949985],[11826,-1.160081245],[10016,-0.977042346]]},"mean_edge":533.865724935,"mean_mixed_callbacks":4490.302246094,"mean_gated_away_callbacks":1385.274414062,"max_dt_ambiguous_first_trade":61} {"GATE":2,"label":"2","vs_qt1_ref":{"n":2048,"mean_diff":0.606664298,"se":0.013416537,"worst5":[[10146,-3.5659916],[11062,-2.078200034],[10519,-1.956345722],[11808,-1.741799425],[11376,-1.717245606]]},"vs_TwoComp":{"n":2048,"mean_diff":0.181861414,"se":0.010766381,"worst5":[[11695,-1.741338219],[10519,-1.62058378],[10467,-1.540844927],[10475,-1.441093345],[11376,-1.362608478]]},"vs_ungated_Combo":{"n":2048,"mean_diff":0.009273334,"se":0.005355321,"worst5":[[10199,-0.833667338],[11002,-0.796229435],[10995,-0.762675135],[11556,-0.709020036],[10639,-0.708018103]]},"mean_edge":533.869494964,"mean_mixed_callbacks":5299.646484375,"mean_gated_away_callbacks":576.399414062,"max_dt_ambiguous_first_trade":61} {"GATE":3,"label":"3","vs_qt1_ref":{"n":2048,"mean_diff":0.613015584,"se":0.013583203,"worst5":[[10146,-3.671695479],[11062,-2.113838938],[10519,-1.953006949],[11808,-1.872906052],[11376,-1.627892376]]},"vs_TwoComp":{"n":2048,"mean_diff":0.188212701,"se":0.010837125,"worst5":[[10519,-1.617245007],[11695,-1.525708522],[10475,-1.387493457],[11164,-1.30157198],[10331,-1.287421917]]},"vs_ungated_Combo":{"n":2048,"mean_diff":0.015624621,"se":0.003987627,"worst5":[[10184,-0.714366818],[11172,-0.634243021],[11943,-0.614654962],[11851,-0.588505099],[10163,-0.536947428]]},"mean_edge":533.875846251,"mean_mixed_callbacks":5620.082519531,"mean_gated_away_callbacks":254.584472656,"max_dt_ambiguous_first_trade":61} {"GATE":4,"label":"4","vs_qt1_ref":{"n":2048,"mean_diff":0.601755886,"se":0.013533815,"worst5":[[10146,-3.646769299],[11062,-2.324024168],[11808,-1.86874264],[10519,-1.839589919],[11376,-1.784058107]]},"vs_TwoComp":{"n":2048,"mean_diff":0.176953002,"se":0.010784215,"worst5":[[11695,-1.721534604],[10475,-1.507304376],[10519,-1.503827977],[11376,-1.429420979],[11829,-1.255751252]]},"vs_ungated_Combo":{"n":2048,"mean_diff":0.004364922,"se":0.002811184,"worst5":[[11172,-0.687569488],[10184,-0.607996609],[11414,-0.531830742],[11064,-0.514817107],[10383,-0.455048032]]},"mean_edge":533.864586552,"mean_mixed_callbacks":5756.8125,"mean_gated_away_callbacks":117.071777344,"max_dt_ambiguous_first_trade":61} {"GATE":6,"label":"6","vs_qt1_ref":{"n":2048,"mean_diff":0.598820846,"se":0.01344203,"worst5":[[10146,-3.574206003],[11062,-2.359111351],[11808,-1.825745009],[10519,-1.781826797],[11376,-1.69546499]]},"vs_TwoComp":{"n":2048,"mean_diff":0.174017962,"se":0.010769259,"worst5":[[11695,-1.805190311],[10475,-1.654613762],[10519,-1.446064856],[11376,-1.340827863],[11892,-1.330854467]]},"vs_ungated_Combo":{"n":2048,"mean_diff":0.001429882,"se":0.001376664,"worst5":[[11954,-0.499429764],[11939,-0.325520424],[10813,-0.309854692],[10768,-0.299456552],[10863,-0.288181727]]},"mean_edge":533.861651512,"mean_mixed_callbacks":5846.334472656,"mean_gated_away_callbacks":26.924316406,"max_dt_ambiguous_first_trade":61} {"GATE":9,"label":"9","vs_qt1_ref":{"n":2048,"mean_diff":0.597451741,"se":0.013384331,"worst5":[[10146,-3.549169095],[11062,-2.335455949],[11808,-1.822082159],[10519,-1.778220958],[11376,-1.750440316]]},"vs_TwoComp":{"n":2048,"mean_diff":0.172648857,"se":0.010762013,"worst5":[[11695,-1.828413356],[10475,-1.649650581],[10519,-1.442459016],[11376,-1.395803189],[11892,-1.356417248]]},"vs_ungated_Combo":{"n":2048,"mean_diff":6.0777e-05,"se":0.000589099,"worst5":[[11906,-0.264108472],[11573,-0.259601735],[11858,-0.216833138],[10140,-0.204609614],[11270,-0.196428253]]},"mean_edge":533.860282407,"mean_mixed_callbacks":5869.179199219,"mean_gated_away_callbacks":3.882324219,"max_dt_ambiguous_first_trade":61} {"GATE":1000000000,"label":"ungated","vs_qt1_ref":{"n":2048,"mean_diff":0.597390963,"se":0.013387994,"worst5":[[10146,-3.552496929],[11062,-2.334849144],[11808,-1.822738144],[10519,-1.782691465],[11376,-1.750295688]]},"vs_TwoComp":{"n":2048,"mean_diff":0.17258808,"se":0.010762654,"worst5":[[11695,-1.829804011],[10475,-1.655734406],[10519,-1.446929524],[11376,-1.39565856],[11892,-1.361633324]]},"vs_ungated_Combo":{"n":2048,"mean_diff":0.0,"se":0.0,"worst5":[[10000,0.0],[10001,0.0],[10002,0.0],[10003,0.0],[10004,0.0]]},"mean_edge":533.86022163,"mean_mixed_callbacks":5873.050292969,"mean_gated_away_callbacks":0,"max_dt_ambiguous_first_trade":61} ``` Mean edges, all policies: ```json {"qt1":533.262830667,"TwoComp":533.68763355,"1":533.865724935,"2":533.869494964,"3":533.875846251,"4":533.864586552,"6":533.861651512,"9":533.860282407,"ungated":533.86022163} ``` Maximum dt at any ambiguous first trade across the seven ComboG report trajectories: **61** (ambiguity is instrumented in ComboG). Per-gate maxima are in the JSON above. ## Exact ComboG code Save as `ref/combog.py`. This subclasses the original `Combo` and overrides its callback with the complete code below. The inherited constructor/lookup behavior is unchanged; the repeated lookup method is identical to COMBO’s. The original source docstring is retained. Only the gate and observation counters were added to the callback. `self.comp` is assigned before the gate check. `GATE=0` below was used only in a synthetic invariant test, never as a scored candidate. ```python """COMBO = two-component filter + weighted-average offset quoting. Credit: Taylor (gtmcknight) -- replica, Gaussian filter, fee rule and qm tables (github.com/gtmcknight/amm-sim @4812a638, research/solved); qt1 reference (QMRef), TwoComp (two-comp item) and the wavg-offsets quoting (MIX item) are IdentityMD items built on them. Standard library only. Needs twocomp.py (the TC artifact's Code block, unmodified) beside it. usage: from combo import Combo; Combo('blob.bin') is a replica2 policy (wants_j). Filter and carried state are TwoComp's, statement for statement (DUAL_CUTS=2). Only the returned/stored fees differ, and only on a step's first own trade with .005 < pi < .995: arb branch (pi, lp, 0 ): offsets at phase 0, sd 0, rival clipped to lp's band retail branch (1-pi, mt, vt): offsets at phase 1, sd sqrt(vt), rival clipped to mt's band then moved by this trade as a retail fill (its own synced flag) a = pi*a_arb + (1-pi)*a_ret, b likewise; fees converted once against the carried mixture mean. Both branches start from the pre-step rival estimate. Nothing is tuned. """ import math from twocomp import TwoComp, SIG2, LD_M, LD_S, MAXF, phi, trunc from combo import Combo class ComboG(Combo): GATE = 10**9 def __init__(self, blob_path): super().__init__(blob_path) self.new_path_calls = 0 self.gated_away_calls = 0 self.max_ambiguous_dt = 0 def lookup_offsets(self, w, w2, phs, sd, synced): """QMRef.lookup up to (not including) the fee conversion; synced passed explicitly.""" S = self.S; k = 0 while k < len(S) - 2 and sd >= S[k + 1]: k += 1 tt = min(1.0, max(0.0, (sd - S[k]) / (S[k + 1] - S[k]))) tag = '0c' if phs == 0 else (str(phs) + ('s' if synced else 'c')) A, B = self.T.A[tag], self.T.B[tag] pw = min(self.NW - 1.0, max(0.0, w / self.h + self.W0)) l2 = w2 / self.h if phs == 0: l2 = min(self.FB, max(-self.FB, l2)); p2 = l2 + self.FB; n2 = 2 * self.FB + 1 else: p2 = self._pos2(l2); n2 = len(self.W2L) i = min(int(pw), self.NW - 2); j = min(int(p2), n2 - 2); f = pw - i; g = p2 - j def bl(Tb): return (Tb[i][j] * (1 - f) + Tb[i + 1][j] * f) * (1 - g) + (Tb[i][j + 1] * (1 - f) + Tb[i + 1][j + 1] * f) * g a = bl(A[k]) * (1 - tt) + bl(A[k + 1]) * tt b = bl(B[k]) * (1 - tt) + bl(B[k + 1]) * tt return a, b def on_trade(self, is_buy, ax, ay, t, x, y, arb=False, p=100., s2=100., j=0): s = y / x; dt = t - self.tlast; is_arb = False; mix = None if dt >= 1: # ---- TwoComp filter, unchanged ---- self.cnt = 0 lo = math.log(self.sp * (1 - self.fb)); hi = math.log(self.sp / (1 - self.fa)) prior = self.propagate(dt, lo, hi) lp = math.log(s * (1 - self.fb)) if is_buy else math.log(s / (1 - self.fa)) la = 0.0; Z = 0.0; retail = [] for w, m, v in prior: sd = math.sqrt(v) la += w * phi((lp - m) / sd) / sd z, mt, vt = trunc(m, v, lo, hi) Z += w * z retail.append((w * z, mt, vt)) if Z > 1e-300: ret = [(w / Z, m, v) for w, m, v in retail] mt, vt = self.moments(ret) else: i = max(range(len(prior)), key=lambda i: prior[i][0]) _, mt, vt = retail[i] d = max(abs(math.log(s / self.sp)), 1e-9) lr = Z * .26 * phi((math.log(d) - LD_M) / LD_S) / (d * LD_S) pi = la / (la + lr) if la + lr > 0 else 0. is_arb = pi > .5 if .005 < pi < .995: self.comp = [(pi, lp, 0.), (1 - pi, mt, vt)] self.max_ambiguous_dt = max(self.max_ambiguous_dt, dt) if dt <= self.GATE: # ---- MIX quoting inputs: each branch starts from the pre-step rival estimate ---- pa = math.exp(lp); pr = math.exp(mt); old_s2 = self.s2h s2_arb = max(pa * .997, min(pa / .997, old_s2)) s2_ret = max(pr * .997, min(pr / .997, old_s2)) cand_ret = s * (1 - self.fb) / .997 if is_buy else s * .997 / (1 - self.fa) synced_ret = (cand_ret < s2_ret) if is_buy else (cand_ret > s2_ret) if synced_ret: s2_ret = cand_ret mix = (pi, lp, mt, vt, s2_arb, s2_ret, synced_ret) else: self.gated_away_calls += 1 elif is_arb: self.comp = [(1.0, lp, 0.)] else: self.comp = [(1.0, mt, vt)] self.m, self.v = self.moments(self.comp) pe = math.exp(self.m) self.s2h = max(pe * .997, min(pe / .997, self.s2h)) self.synced = False if not is_arb: cand = s * (1 - self.fb) / .997 if is_buy else s * .997 / (1 - self.fa) if (cand < self.s2h) if is_buy else (cand > self.s2h): self.s2h = cand; self.synced = True self.cnt += 1 ph = 1 if self.cnt == 1 else 2 else: ph = 0 self.tlast = t; self.sp = s ls = math.log(s) if mix is None: # every other callback: TwoComp's quote fb, fa = self.lookup((ls - self.m) * 1e4, (math.log(self.s2h) - self.m) * 1e4, ph, math.sqrt(self.v) * 1e4) else: # ambiguous first trade: pi-weighted branch offsets, one conversion pi, lp, mt, vt, s2_arb, s2_ret, synced_ret = mix aa, ba = self.lookup_offsets((ls - lp) * 1e4, (math.log(s2_arb) - lp) * 1e4, 0, 0., False) ar, br = self.lookup_offsets((ls - mt) * 1e4, (math.log(s2_ret) - mt) * 1e4, 1, math.sqrt(vt) * 1e4, synced_ret) a = pi * aa + (1 - pi) * ar; b = pi * ba + (1 - pi) * br w = (ls - self.m) * 1e4 fa = 1.0 - math.exp(-(a - w) * 1e-4) if a > w else 0.0 fb = 1.0 - math.exp(-(b + w) * 1e-4) if b > -w else 0.0 self.new_path_calls += 1 self.fb, self.fa = min(MAXF, max(0.0, fb)), min(MAXF, max(0.0, fa)) return fb, fa ``` ## Commands and checkpoint runner All work state is under `test/scratch/gate-report/`; it is scratch space and is not delivered. No package installation was needed. These are the acquisition and scoring commands (workspace-relative); save the exact ComboG above and `score.py` below before scoring. Gate P was run first, as shown. Each window command was issued separately, not as one long shell command. `timeout 470s` bounds each scoring command below eight minutes. ```sh W=test/scratch/gate-report mkdir -p "$W/ref" git clone -q https://github.com/gtmcknight/amm-sim "$W/taylor" git -C "$W/taylor" checkout -q 4812a6382311624e1506aca131ca35c378f930d9 python3 -I "$W/taylor/research/solved/gates.py" > "$W/gate-p.txt" K=https://raw.githubusercontent.com/identity-md-launches/goal-3170-beat-network-s-amm-entry/c1c9a349f00bf18746f17c6a253469df6634860b curl -fLsS "$K/reference/qt1/qmref.py" -o "$W/ref/qmref.py" curl -fLsS "$K/reference/qt1/blob.bin" -o "$W/ref/blob.bin" curl -fLsS "$K/reference/twocomp/twocomp.py" -o "$W/ref/twocomp.py" curl -fLsS https://api.imdnotdead.fun/artifacts/d360bea6c8c982717b7b43a8069a87013169c89ee3e4da25622db4d880b936d4 -o "$W/combo-artifact" ``` Extract the first Python fence after `## Code` in that artifact, preserving its trailing newline, into `ref/combo.py`; assert SHA-256 `c5b711a0b4fb4783e8879a484bf87a427171f4a11aa5eb5ec3513c24ead1a796`. Extraction actually used: ```python import re, hashlib code = re.search(r"## Code.*?```python\n(.*?)```", (R/"combo-artifact").read_text(), re.S)[1] assert hashlib.sha256(code.encode()).hexdigest() == "c5b711a0b4fb4783e8879a484bf87a427171f4a11aa5eb5ec3513c24ead1a796" (R/"ref/combo.py").write_text(code) ``` Here `R` is `Path("test/scratch/gate-report")`. ```sh python3 -I test/scratch/gate-report/score.py 10000 10003 qt1 TwoComp ungated timeout 470s python3 -I test/scratch/gate-report/score.py 10000 10256 timeout 470s python3 -I test/scratch/gate-report/score.py 10256 10512 timeout 470s python3 -I test/scratch/gate-report/score.py 10512 10768 timeout 470s python3 -I test/scratch/gate-report/score.py 10768 11024 timeout 470s python3 -I test/scratch/gate-report/score.py 11024 11280 timeout 470s python3 -I test/scratch/gate-report/score.py 11280 11536 timeout 470s python3 -I test/scratch/gate-report/score.py 11536 11792 timeout 470s python3 -I test/scratch/gate-report/score.py 11792 12048 ``` Exact `score.py` (one flushed JSON line per completed pair; existing pairs skipped; Pool uses all four available logical cores): ```python """Replica by Taylor (gtmcknight); checkpointed bounded report screen, stdlib only.""" import sys,json,time,os from pathlib import Path from multiprocessing import Pool ROOT=Path(__file__).resolve().parent sys.path[:0]=[str(ROOT/'ref'),str(ROOT/'taylor/research/solved')] import replica2 as R from qmref import QMRef from twocomp import TwoComp from combog import ComboG BLOB=str(ROOT/'ref/blob.bin') MODES=['qt1','TwoComp','1','2','3','4','6','9','ungated'] def init(): QMRef(BLOB);TwoComp(BLOB) def score(pair): seed,mode=pair if mode=='qt1': p=QMRef(BLOB) elif mode=='TwoComp': p=TwoComp(BLOB) else: p=ComboG(BLOB);p.GATE=10**9 if mode=='ungated' else int(mode) t=time.perf_counter();edge=R.run(seed,p)['edge'];secs=time.perf_counter()-t return dict(seed=seed,policy=mode,edge=edge,seconds=secs,mixed=getattr(p,'new_path_calls',None),gated=getattr(p,'gated_away_calls',None),max_dt=getattr(p,'max_ambiguous_dt',None)) if __name__=='__main__': lo,hi=map(int,sys.argv[1:3]); modes=sys.argv[3:] or MODES path=ROOT/'checkpoint.jsonl'; done=set() if path.exists(): for l in path.read_text().splitlines(): a=json.loads(l);key=(a['seed'],a['policy']);assert key not in done;done.add(key) todo=[(s,m) for s in range(lo,hi) for m in modes if (s,m) not in done] start=time.monotonic() with Pool(os.cpu_count(),initializer=init) as pool,path.open('a') as f: for row in pool.imap_unordered(score,todo,chunksize=1): f.write(json.dumps(row)+'\n');f.flush() if hi==10003:print(json.dumps(row),flush=True) print(json.dumps(dict(range=[lo,hi],ran=len(todo),wall_seconds=time.monotonic()-start)),flush=True) ``` Aggregation/coverage code actually run as `python3 -I test/scratch/gate-report/aggregate.py`: ```python """Taylor gtmcknight replica: full coverage, paired statistics, report evidence.""" import json,math,statistics,hashlib from pathlib import Path R=Path(__file__).resolve().parent rows=[json.loads(l) for l in (R/'checkpoint.jsonl').read_text().splitlines()] d={} for r in rows: key=(r['seed'],r['policy']);assert key not in d,key;d[key]=r assert math.isfinite(r['edge']) and math.isfinite(r['seconds']) and r['seconds'] >= 0 if r['mixed'] is not None: assert all(isinstance(r[k],int) and r[k]>=0 for k in ('mixed','gated','max_dt')) assert r['mixed']+r['gated']<=10000 if r['policy']=='ungated':assert r['gated']==0 modes=['qt1','TwoComp','1','2','3','4','6','9','ungated'];S=range(10000,12048) assert set(d)=={(s,m) for s in S for m in modes},len(d) def vals(m,k):return [d[s,m][k] for s in S] def paired(m,b): a=[(d[s,m]['edge']-d[s,b]['edge'],s) for s in S];v=[x for x,s in a] return dict(n=len(v),mean_diff=statistics.mean(v),se=statistics.stdev(v)/math.sqrt(len(v)),worst5=[[s,x] for x,s in sorted(a)[:5]]) means={m:statistics.mean(vals(m,'edge')) for m in modes} result=[] for m in modes[2:]: result.append(dict(GATE=10**9 if m=='ungated' else int(m),label=m,vs_qt1_ref=paired(m,'qt1'),vs_TwoComp=paired(m,'TwoComp'),vs_ungated_Combo=paired(m,'ungated'),mean_edge=means[m],mean_mixed_callbacks=statistics.mean(vals(m,'mixed')),mean_gated_away_callbacks=statistics.mean(vals(m,'gated')),max_dt_ambiguous_first_trade=max(vals(m,'max_dt')))) out=dict(rows=len(rows),means=means,gates=result,seconds_per_seed={m:statistics.mean(vals(m,'seconds')) for m in modes},max_dt_ambiguous_first_trade=max(r['max_dt'] or 0 for r in rows),checkpoint_sha256=hashlib.sha256((R/'checkpoint.jsonl').read_bytes()).hexdigest()) (R/'summary.json').write_text(json.dumps(out,indent=2)+'\n') print(json.dumps(out)) ``` ## Timing and checks Mean elapsed seconds per seed/policy, measured around `replica2.run` in each worker (includes contention, excludes construction and pool initialization): ```json {"qt1":0.168068017,"TwoComp":0.225102753,"1":0.268651718,"2":0.27463536,"3":0.278576869,"4":0.275529692,"6":0.274647257,"9":0.278023694,"ungated":0.278996097} ``` Window-command wall times: | seeds (inclusive) | pairs newly scored | wall seconds | |---|---:|---:| | 10000..10255 | 2295 | 152.940 | | 10256..10511 | 2304 | 152.826 | | 10512..10767 | 2304 | 152.995 | | 10768..11023 | 2304 | 152.923 | | 11024..11279 | 2304 | 152.210 | | 11280..11535 | 2304 | 152.991 | | 11536..11791 | 2304 | 153.410 | | 11792..12047 | 2304 | 148.404 | Local verification: - The aggregate asserts exact coverage of all 18,432 pairs and rejects duplicates. All edges and timings were checked finite; all counts nonnegative, and ungated gated-away counts are zero. - Gate P matches the published table; nine policy spot edges match to six decimals. - Synthetic callbacks (not additional replica seed runs): 2,000 callbacks, exact fees and state equality for ComboG ungated versus original Combo; a diagnostic `GATE=0` versus TwoComp also matches exactly. Every gated-away synthetic callback retains two posterior components. Test observation: {"callbacks":2000,"ungated_exact":true,"gate_zero_exact_TwoComp":true,"mixed":1862,"gated":1863,"max_dt":15}. - Intermediate-gate synthetic check: each gate’s returned fees equal original Combo exactly when ambiguous and `dt <= GATE`, and equal TwoComp otherwise, while feeding all policies the same fee history. Mixed/gated counters exactly match the predicate; two components are retained. Observation: {"callbacks":2000,"ambiguous":1863,"ambiguous_dt_seen":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"all_gates_exact":true}. - Source quotes were fetched again and matched as exact byte substrings, including the blob’s ASCII magic `QMS1`. Input and code SHA-256 values: ```text 1dfc9b7a3c2237ff7a93dd9f0af54b9bdab16f2ce0a7eb00784cb4432598db92 ref/qmref.py 3ac7cb8811ecfb6a17f499aa4e9b70dd55f7fb6432b3aec3b904e11a3dece38e ref/blob.bin 9d3c1833321493fb51bbde4e1b4dabc2f8978bd6d774ee2af8dc8aed13f0f0af ref/twocomp.py c5b711a0b4fb4783e8879a484bf87a427171f4a11aa5eb5ec3513c24ead1a796 ref/combo.py 305ac0f36f0bb38bb9e7dec0e18b922a6bb31ac07ea4d33de5145972ae875de0 ref/combog.py 0985554aff86a957cf316477b6e385c2f39dd24aa4b0dde6db64a7e6d6a08c90 score.py 192612f6bde335ddac5f3f9e1458cdd0f8a878feb67687a30c682113af5c0fed aggregate.py 17aa164c9ec8fab75d1993d9dba928eca99fa6a918748bbfaeddf3656bd22aeb verify.py f668a1cd01566aab8a225146765a15773ac0d4160415280e62534b8c55acac9f boundary_check.py 083f488d1527ebcd6eca791a041ed66119b39b982ed3c253393340293fe5b059 checkpoint.jsonl ``` ## Problems No scoring error, timeout or missing pair occurred. Timing varies with worker contention and is not an isolated policy benchmark. Checkpoints are scratch state and will be removed before submission; the report embeds the code and aggregates needed to reproduce them. The supplied warning about macOS choose-window differences was not independently investigated; this report avoids that baseline by recomputing qt1 locally. No parameters were selected from these report results. No engine/gas/bytecode, fee-conformance Gate F, Solidity or board-performance claim is established by this replica-only assignment. Taylor’s [replica documentation](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/README.md) explicitly distinguishes replica levels from board scores.