{"key":"d-time-price","approach":"Copied simulator at b244530 to a separate dir; added a fill log (step, true p after that step's update, edge, aggressor) in record_participant_fills and a step counter in the engine. Default ChallengeConfig/ParameterVariance, 2000 steps, one process, no --workers/--sandbox, Python 3.12.3. Per-run edge summed per cell of step bucket x p bucket (p<0.05, 0.05-0.20, 0.20-0.80, 0.80-0.95, >=0.95), then averaged over the runs of each competitor spread. Table cells: mean per run (zeros included) of retail, arb, net=retail+arb, with net_se = standard error of per-run net; step buckets 0-199, 200-999, 1000-1599, 1600-1899, 1900-1999 by fill step.","tried":["sha256 of N code equals bf0d179f3e47d28819f6fa7e0d25548c2ced43374c216d36460b00a26a26ffae","Unmodified simulator, N on seed 310000: total edge 17.1160017503 (matches 17.116002)","Unmodified vs instrumented simulator, seeds 501500..501509: total, retail and arb edge identical on all 10","No fills with an aggressor other than retail or arb (edge 0 on all 500 runs); 0 failed runs","Ran only seeds 501500..501999; never 900000..903999"],"complete":true,"first_seed":501500,"last_seed":501999,"n":500,"incumbent_mean":99.8732,"retail_mean":124.22,"arb_mean":-24.3469,"by_spread":{"1":{"runs":134,"incumbent_mean":55.5166,"retail_mean":74.5489,"arb_mean":-19.0323,"table":{"steps 0-199 | p <5c":{"retail":0.0,"arb":0.0,"net":0.0,"net_se":0.0},"steps 0-199 | p 5-20c":{"retail":0.0187,"arb":-0.0152,"net":0.0035,"net_se":0.0076},"steps 0-199 | p 20-80c":{"retail":0.0288,"arb":-0.0458,"net":-0.017,"net_se":0.0034},"steps 0-199 | p 80-95c":{"retail":0.0049,"arb":-0.0045,"net":0.0004,"net_se":0.0008},"steps 0-199 | p >95c":{"retail":0.0,"arb":0.0,"net":0.0,"net_se":0.0},"steps 200-999 | p <5c":{"retail":2.8618,"arb":-4.4214,"net":-1.5596,"net_se":2.4715},"steps 200-999 | p 5-20c":{"retail":0.7296,"arb":-0.6945,"net":0.0351,"net_se":0.1847},"steps 200-999 | p 20-80c":{"retail":0.0353,"arb":-0.0856,"net":-0.0503,"net_se":0.0065},"steps 200-999 | p 80-95c":{"retail":0.1352,"arb":-0.0963,"net":0.0389,"net_se":0.015},"steps 200-999 | p >95c":{"retail":0.0425,"arb":-0.0179,"net":0.0246,"net_se":0.0107},"steps 1000-1599 | p <5c":{"retail":27.405,"arb":-7.2088,"net":20.1962,"net_se":6.2012},"steps 1000-1599 | p 5-20c":{"retail":0.5411,"arb":-1.4524,"net":-0.9113,"net_se":0.6934},"steps 1000-1599 | p 20-80c":{"retail":0.003,"arb":-0.1057,"net":-0.1027,"net_se":0.0634},"steps 1000-1599 | p 80-95c":{"retail":0.061,"arb":-0.0673,"net":-0.0062,"net_se":0.0093},"steps 1000-1599 | p >95c":{"retail":0.2684,"arb":-0.0535,"net":0.2149,"net_se":0.0468},"steps 1600-1899 | p <5c":{"retail":28.0482,"arb":-3.645,"net":24.4032,"net_se":5.2671},"steps 1600-1899 | p 5-20c":{"retail":0.0592,"arb":-0.1979,"net":-0.1388,"net_se":0.1114},"steps 1600-1899 | p 20-80c":{"retail":0.0012,"arb":-0.01,"net":-0.0087,"net_se":0.0013},"steps 1600-1899 | p 80-95c":{"retail":0.0039,"arb":-0.0066,"net":-0.0027,"net_se":0.0012},"steps 1600-1899 | p >95c":{"retail":0.3045,"arb":-0.0253,"net":0.2793,"net_se":0.0398},"steps 1900-1999 | p <5c":{"retail":13.9147,"arb":-0.8108,"net":13.104,"net_se":2.315},"steps 1900-1999 | p 5-20c":{"retail":0.0007,"arb":-0.0579,"net":-0.0573,"net_se":0.0318},"steps 1900-1999 | p 20-80c":{"retail":0.0004,"arb":-0.0036,"net":-0.0032,"net_se":0.0007},"steps 1900-1999 | p 80-95c":{"retail":0.0001,"arb":-0.001,"net":-0.0009,"net_se":0.0002},"steps 1900-1999 | p >95c":{"retail":0.0807,"arb":-0.0055,"net":0.0752,"net_se":0.0094}}},"2":{"runs":105,"incumbent_mean":80.9053,"retail_mean":112.2032,"arb_mean":-31.2979,"table":{"steps 0-199 | p <5c":{"retail":0.0,"arb":0.0,"net":0.0,"net_se":0.0},"steps 0-199 | p 5-20c":{"retail":0.0877,"arb":-0.048,"net":0.0397,"net_se":0.0654},"steps 0-199 | p 20-80c":{"retail":2.3471,"arb":-0.6157,"net":1.7313,"net_se":0.153},"steps 0-199 | p 80-95c":{"retail":0.0303,"arb":-0.0075,"net":0.0228,"net_se":0.0098},"steps 0-199 | p >95c":{"retail":0.0,"arb":0.0,"net":0.0,"net_se":0.0},"steps 200-999 | p <5c":{"retail":2.4505,"arb":-4.8527,"net":-2.4022,"net_se":3.3401},"steps 200-999 | p 5-20c":{"retail":5.9076,"arb":-1.578,"net":4.3295,"net_se":0.9245},"steps 200-999 | p 20-80c":{"retail":6.8858,"arb":-2.5692,"net":4.3166,"net_se":0.4612},"steps 200-999 | p 80-95c":{"retail":0.4868,"arb":-0.3638,"net":0.123,"net_se":0.2566},"steps 200-999 | p >95c":{"retail":0.1262,"arb":-0.0375,"net":0.0887,"net_se":0.0612},"steps 1000-1599 | p <5c":{"retail":30.078,"arb":-7.3103,"net":22.7677,"net_se":7.5738},"steps 1000-1599 | p 5-20c":{"retail":6.1476,"arb":-1.4863,"net":4.6613,"net_se":0.925},"steps 1000-1599 | p 20-80c":{"retail":2.0884,"arb":-2.982,"net":-0.8935,"net_se":1.5538},"steps 1000-1599 | p 80-95c":{"retail":0.4671,"arb":-0.1618,"net":0.3054,"net_se":0.0735},"steps 1000-1599 | p >95c":{"retail":0.701,"arb":-0.0707,"net":0.6304,"net_se":0.1542},"steps 1600-1899 | p <5c":{"retail":31.6625,"arb":-4.126,"net":27.5365,"net_se":5.2456},"steps 1600-1899 | p 5-20c":{"retail":1.3637,"arb":-3.6602,"net":-2.2965,"net_se":1.9252},"steps 1600-1899 | p 20-80c":{"retail":0.1675,"arb":-0.1978,"net":-0.0303,"net_se":0.0367},"steps 1600-1899 | p 80-95c":{"retail":0.0949,"arb":-0.03,"net":0.0649,"net_se":0.0226},"steps 1600-1899 | p >95c":{"retail":0.6926,"arb":-0.0418,"net":0.6508,"net_se":0.1176},"steps 1900-1999 | p <5c":{"retail":19.9177,"arb":-0.649,"net":19.2687,"net_se":2.5442},"steps 1900-1999 | p 5-20c":{"retail":0.2318,"arb":-0.4874,"net":-0.2556,"net_se":0.2254},"steps 1900-1999 | p 20-80c":{"retail":0.0008,"arb":-0.0075,"net":-0.0067,"net_se":0.0015},"steps 1900-1999 | p 80-95c":{"retail":0.0007,"arb":-0.0047,"net":-0.004,"net_se":0.0021},"steps 1900-1999 | p >95c":{"retail":0.2669,"arb":-0.01,"net":0.2569,"net_se":0.0417}}},"3":{"runs":130,"incumbent_mean":115.7553,"retail_mean":140.0142,"arb_mean":-24.2589,"table":{"steps 0-199 | p <5c":{"retail":0.0,"arb":0.0,"net":0.0,"net_se":0.0},"steps 0-199 | p 5-20c":{"retail":0.3762,"arb":-0.0412,"net":0.335,"net_se":0.1569},"steps 0-199 | p 20-80c":{"retail":4.7182,"arb":-1.1374,"net":3.5808,"net_se":0.3107},"steps 0-199 | p 80-95c":{"retail":0.0644,"arb":-0.0256,"net":0.0388,"net_se":0.0222},"steps 0-199 | p >95c":{"retail":0.0,"arb":0.0,"net":0.0,"net_se":0.0},"steps 200-999 | p <5c":{"retail":7.1168,"arb":-1.7038,"net":5.413,"net_se":2.1547},"steps 200-999 | p 5-20c":{"retail":7.3856,"arb":-1.1714,"net":6.2142,"net_se":1.3731},"steps 200-999 | p 20-80c":{"retail":13.8824,"arb":-3.4987,"net":10.3837,"net_se":0.7713},"steps 200-999 | p 80-95c":{"retail":1.0563,"arb":-0.3057,"net":0.7506,"net_se":0.2075},"steps 200-999 | p >95c":{"retail":0.2522,"arb":-0.014,"net":0.2382,"net_se":0.1189},"steps 1000-1599 | p <5c":{"retail":30.6569,"arb":-2.6543,"net":28.0026,"net_se":6.9155},"steps 1000-1599 | p 5-20c":{"retail":6.7633,"arb":-1.563,"net":5.2003,"net_se":1.0647},"steps 1000-1599 | p 20-80c":{"retail":5.631,"arb":-3.6851,"net":1.9459,"net_se":1.5412},"steps 1000-1599 | p 80-95c":{"retail":1.359,"arb":-0.3108,"net":1.0481,"net_se":0.2032},"steps 1000-1599 | p >95c":{"retail":1.0147,"arb":-0.0501,"net":0.9646,"net_se":0.1993},"steps 1600-1899 | p <5c":{"retail":35.8828,"arb":-2.1503,"net":33.7325,"net_se":5.9049},"steps 1600-1899 | p 5-20c":{"retail":3.321,"arb":-0.7041,"net":2.6169,"net_se":0.5736},"steps 1600-1899 | p 20-80c":{"retail":0.9696,"arb":-3.3031,"net":-2.3335,"net_se":1.9371},"steps 1600-1899 | p 80-95c":{"retail":0.3337,"arb":-0.098,"net":0.2357,"net_se":0.0614},"steps 1600-1899 | p >95c":{"retail":1.1905,"arb":-0.0429,"net":1.1476,"net_se":0.1605},"steps 1900-1999 | p <5c":{"retail":17.1927,"arb":-1.2089,"net":15.9838,"net_se":2.0772},"steps 1900-1999 | p 5-20c":{"retail":0.2864,"arb":-0.5217,"net":-0.2353,"net_se":0.361},"steps 1900-1999 | p 20-80c":{"retail":0.0245,"arb":-0.0407,"net":-0.0162,"net_se":0.0105},"steps 1900-1999 | p 80-95c":{"retail":0.0129,"arb":-0.0164,"net":-0.0034,"net_se":0.0063},"steps 1900-1999 | p >95c":{"retail":0.5231,"arb":-0.0118,"net":0.5113,"net_se":0.0636}}},"4":{"runs":131,"incumbent_mean":144.688,"retail_mean":168.9869,"arb_mean":-24.2989,"table":{"steps 0-199 | p <5c":{"retail":0.0,"arb":0.0,"net":0.0,"net_se":0.0},"steps 0-199 | p 5-20c":{"retail":0.2904,"arb":-0.1871,"net":0.1033,"net_se":0.1641},"steps 0-199 | p 20-80c":{"retail":7.412,"arb":-1.2963,"net":6.1156,"net_se":0.4304},"steps 0-199 | p 80-95c":{"retail":0.178,"arb":-0.0707,"net":0.1073,"net_se":0.0866},"steps 0-199 | p >95c":{"retail":0.014,"arb":-0.0002,"net":0.0138,"net_se":0.0138},"steps 200-999 | p <5c":{"retail":6.3219,"arb":-1.0115,"net":5.3105,"net_se":2.5418},"steps 200-999 | p 5-20c":{"retail":8.9642,"arb":-0.8366,"net":8.1275,"net_se":1.6714},"steps 200-999 | p 20-80c":{"retail":21.3809,"arb":-3.3989,"net":17.982,"net_se":1.0767},"steps 200-999 | p 80-95c":{"retail":2.0301,"arb":-0.3589,"net":1.6712,"net_se":0.3844},"steps 200-999 | p >95c":{"retail":0.5588,"arb":-0.0469,"net":0.5118,"net_se":0.2231},"steps 1000-1599 | p <5c":{"retail":31.5466,"arb":-2.3674,"net":29.1792,"net_se":5.7282},"steps 1000-1599 | p 5-20c":{"retail":13.7864,"arb":-1.8341,"net":11.9523,"net_se":2.0636},"steps 1000-1599 | p 20-80c":{"retail":8.8985,"arb":-2.5274,"net":6.3711,"net_se":0.8079},"steps 1000-1599 | p 80-95c":{"retail":1.5258,"arb":-0.3199,"net":1.2059,"net_se":0.2532},"steps 1000-1599 | p >95c":{"retail":1.6497,"arb":-0.0619,"net":1.5878,"net_se":0.4153},"steps 1600-1899 | p <5c":{"retail":34.8293,"arb":-1.7157,"net":33.1137,"net_se":4.583},"steps 1600-1899 | p 5-20c":{"retail":4.2872,"arb":-1.5768,"net":2.7104,"net_se":1.1126},"steps 1600-1899 | p 20-80c":{"retail":1.7796,"arb":-4.4759,"net":-2.6963,"net_se":3.1046},"steps 1600-1899 | p 80-95c":{"retail":0.5375,"arb":-0.1973,"net":0.3402,"net_se":0.1408},"steps 1600-1899 | p >95c":{"retail":1.5062,"arb":-0.1918,"net":1.3144,"net_se":0.2218},"steps 1900-1999 | p <5c":{"retail":20.3451,"arb":-0.5275,"net":19.8176,"net_se":2.555},"steps 1900-1999 | p 5-20c":{"retail":0.4021,"arb":-0.596,"net":-0.1939,"net_se":0.4157},"steps 1900-1999 | p 20-80c":{"retail":0.066,"arb":-0.653,"net":-0.587,"net_se":0.4833},"steps 1900-1999 | p 80-95c":{"retail":0.0366,"arb":-0.0146,"net":0.022,"net_se":0.01},"steps 1900-1999 | p >95c":{"retail":0.6398,"arb":-0.0323,"net":0.6075,"net_se":0.0805}}}},"negative_net_buckets":{"1":["steps 0-199 | p 20-80c: net -0.017 (se 0.0034)","steps 200-999 | p <5c: net -1.5596 (se 2.4715)","steps 200-999 | p 20-80c: net -0.0503 (se 0.0065)","steps 1000-1599 | p 5-20c: net -0.9113 (se 0.6934)","steps 1000-1599 | p 20-80c: net -0.1027 (se 0.0634)","steps 1000-1599 | p 80-95c: net -0.0062 (se 0.0093)","steps 1600-1899 | p 5-20c: net -0.1388 (se 0.1114)","steps 1600-1899 | p 20-80c: net -0.0087 (se 0.0013)","steps 1600-1899 | p 80-95c: net -0.0027 (se 0.0012)","steps 1900-1999 | p 5-20c: net -0.0573 (se 0.0318)","steps 1900-1999 | p 20-80c: net -0.0032 (se 0.0007)","steps 1900-1999 | p 80-95c: net -0.0009 (se 0.0002)"],"2":["steps 200-999 | p <5c: net -2.4022 (se 3.3401)","steps 1000-1599 | p 20-80c: net -0.8935 (se 1.5538)","steps 1600-1899 | p 5-20c: net -2.2965 (se 1.9252)","steps 1600-1899 | p 20-80c: net -0.0303 (se 0.0367)","steps 1900-1999 | p 5-20c: net -0.2556 (se 0.2254)","steps 1900-1999 | p 20-80c: net -0.0067 (se 0.0015)","steps 1900-1999 | p 80-95c: net -0.004 (se 0.0021)"],"3":["steps 1600-1899 | p 20-80c: net -2.3335 (se 1.9371)","steps 1900-1999 | p 5-20c: net -0.2353 (se 0.361)","steps 1900-1999 | p 20-80c: net -0.0162 (se 0.0105)","steps 1900-1999 | p 80-95c: net -0.0034 (se 0.0063)"],"4":["steps 1600-1899 | p 20-80c: net -2.6963 (se 3.1046)","steps 1900-1999 | p 5-20c: net -0.1939 (se 0.4157)","steps 1900-1999 | p 20-80c: net -0.587 (se 0.4833)"]},"negative_note":"Every cell with mean net below 0 is listed per spread. Most are within noise (se larger than |mean|). Beyond 2 se: spread 1 steps 0-199 p20-80c, 200-999 p20-80c, 1600-1899 p20-80c and p80-95c, 1900-1999 p20-80c and p80-95c; spread 2 steps 1900-1999 p20-80c; none for spreads 3 and 4. Spread 2 steps 1900-1999 p80-95c is -0.004 (se 0.0021), just under 2 se.","finding":"Spread 2 (105 runs, net 80.91 = retail 112.20 + arb -31.30): arbitrage loss is largest at p<5c (steps 200-999 -4.85, 1000-1599 -7.31, 1600-1899 -4.13) and -3.66 at steps 1600-1899 p5-20c, but only 200-999 p<5c (net -2.40, se 3.34) and 1600-1899 p5-20c (net -2.30, se 1.93) are net negative, both within noise, so the point is to quote less or wider at low p in those windows. Spread 3 (130 runs, net 115.76 = retail 140.01 + arb -24.26): arb loss is spread over p20-80c (about -3.3 to -3.7 in each of steps 200-1899), and the one material net-negative cell is steps 1600-1899 p20-80c (-2.33, se 1.94, not significant), pointing at a mid-price late-game size cut or widening. Retail edge at p<5c (about 30 per run in steps 1000-1899 for spreads 2 and 3) more than covers the arb loss there, so no whole bucket should be dropped. Net-negative cells are small next to their standard errors. The data do not show that most of the 24.3 arb loss can be removed by one time-price bucket change.","next":"Test a paired candidate for spread 2 (wider or smaller quotes at p5-20c, steps 1600-1899) and spread 3 (mid-price late-game) against N, and split arb loss by fill size and time since last jump.","seconds_per_simulation":5.7}